<tr><td></td><td>AD</td><td>PD</td><td>ALS</td></tr><tr><td colspan=\\\"4\\\">General Characteristics</td></tr><tr><td>Number of cases</td><td>44,078</td><td>33,168</td><td>1316</td></tr><tr><td>Age (SD)</td><td>82.0 (8.0)</td><td>77.2 (9.3)</td><td>65.2 (14.1)</td></tr><tr><td>Male (%)</td><td>32.9</td><td>52.4</td><td>56.5</td></tr><tr><td colspan=\\\"4\\\">Five-year aggregated rates of GT placement per 1000 cases</td></tr><tr><td>1990–1994</td><td>32.2</td><td>19.7</td><td>114</td></tr><tr><td>1995–1999</td><td>31.2</td><td>24.6</td><td>124</td></tr><tr><td>2000–2004</td><td>17.5</td><td>18.5</td><td>128.3</td></tr><tr><td>2005–2009</td><td>13.7</td><td>13.8</td><td>111.7</td></tr><tr><td colspan=\\\"4\\\">Length of Hospital Stay, Median number of days (IQR)</td></tr><tr><td>without GT</td><td>4 (3.6)</td><td>4 (3.8)</td><td>4.6 (3.8)</td></tr><tr><td>with GT</td><td>7.4 (7.0)</td><td>9.5 (12.6)</td><td>7.8 (19.7)</td></tr><tr><td colspan=\\\"4\\\">Discharge destination (%)</td></tr><tr><td colspan=\\\"4\\\">Without GT</td></tr><tr><td>Home</td><td>39.0</td><td>44.4</td><td>61.4</td></tr><tr><td>Short-term facility</td><td>6.2</td><td>6.7</td><td>0.9</td></tr><tr><td>Long-term facility</td><td>42.2</td><td>34.4</td><td>13.8</td></tr><tr><td>Other</td><td>12.2</td><td>13.7</td><td>23.6</td></tr><tr><td colspan=\\\"4\\\">With GT</td></tr><tr><td>Home</td><td>14.1</td><td>16</td><td>63.7</td></tr><tr><td>Short-term facility</td><td>12.3</td><td>11.1</td><td>0</td></tr><tr><td>Long-term facility</td><td>55</td><td>73.9</td><td>27.7</td></tr><tr><td>Other</td><td>11.8</td><td>5.2</td><td>9.6</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1 Patient characteristics, rates, and outcomes of GT placement. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[57,394,485,500]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This was also demonstrated with 5-year aggregate data (Table 1). In AD, the rate dropped from 32.2 to 13.7 per thousand cases when comparing 1990-1994 aggregate to 2005-2009 aggregate $(\\\\mathrm{p} < 0.001)$ . Similarly, in PD, the rate dropped from 19.2 to 13.8 per thousand cases when comparing 1990-1994 aggregate to 2005-2009 aggregate $(\\\\mathrm{p} < 0.001)$ . In contrast, for ALS, the rate dropped only nonsignificantly from 114.0 to 111.7 per thousand cases when comparing the same 5-year aggregate data $(\\\\mathrm{p} = 0.49)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,511,171,525]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.3. Length of stay \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,539,485,605]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Median LOS was higher in all groups with GT placement (Table 1). The median LOS for patients without versus with GT placement, respectively, was 4 versus 7.4 days in AD (Wilcoxon rank-sum test, $p < 0.001$ ), 4 versus 9.5 days in PD ( $p < 0.001$ ), and 4.6 versus 7.8 days in ALS ( $p = 0.01$ ) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,619,211,631]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.4. Discharge destination \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,644,485,750]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Without GT placement, $39.0\\\\%$ of AD patients, $44.4\\\\%$ of PD patients, and $61.4\\\\%$ of ALS patients were discharged home (Table 1). Among AD and PD patients, the odds of being discharged to home were three to four times lower with GT placement (OR 0.28, $95\\\\%$ CI 0.14-0.55 in AD, and OR 0.22, CI 0.11-0.42 in PD, all p values $< 0.001$ ). In contrast, in ALS patients, the odds of being discharged to home remained largely unchanged regardless of GT placement (OR 1.1, $95\\\\%$ CI 0.6-1.9). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,766,149,778]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. Discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,791,485,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We found a decreasing rate of GT placement in AD and PD patients and a relatively unchanged rate in ALS patients over two-decades. Despite the downward trend in the rate of GT placement in AD and PD population, it is noteworthy that even in the later years of the study period, thousands of patients were still undergoing GT placement annually, despite lack of evidence for any benefit of GT in these populations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,883,485,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The level of evidence and guidelines differ regarding GT placement for these conditions. Most well-studied is the dementia population, in which published reports demonstrate no improvement in risk of aspiration, survival, or nutritional status with GT placement [4-6]. There \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,66,937,158]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"fore, the American Geriatric Society (AGS) has recommended against GT placement in advanced dementia [17]. In contrast, in ALS, GT placement has been shown to prolong life, [8,9] guiding current practice. While there are no controlled trials, observational data in PD suggest no survival benefit [18,19]. As the vast majority of advanced PD patients develop dementia, they may be treated under this general guideline (i.e. against GT placement). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,160,937,331]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The analyses also showed that GT placement was associated with a longer hospital stay in all disease groups, and the longest in the PD group. A potential explanation is that PD patients are prone to rapid deconditioning due to decreased ambulation and overall immobility while in the hospital. Furthermore, peri-procedural 'nothing by mouth' (NPO) state may lead to missed doses of PD medications, which have a visible effect on the patient's clinical condition. Increased LOS among AD and ALS patients can be partially explained by the common practice of $48 - 72\\\\mathrm{h}$ of inpatient observation after GT placement, although this can vary depending on institutional policy, physician practices, or both. The longer hospital stay after GT placement may also be due to diligent monitoring of post-procedural complications, which can include gastric perforation, perontinitis, and death [4]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,331,937,634]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Another factor in healthcare utilization is the increased use of long-term facilities after being discharged with GT. Since dysphagia is generally a sign of advanced disease, once discharged to these facilities, patients will likely remain there. The short- and long-term financial ramifications of GT placement in AD and PD are unknown, but expectedly, extend beyond the hospitalization, particularly when accounting for long term nursing care. Our data showed that AD and PD patients were three to four times less likely to be discharged home with GT placement than without. This is different from the ALS patients, in whom the odds of being discharged to home did not change regardless of GT placement. This might be due to ALS patients having a much lower incidence of dementia, potentially making the careless challenging at home. Since the results were adjusted for age and sex, these factors did not account for this difference. However, it is worth mentioning that AD and PD patients were significantly older than ALS patients, making ALS patients easier to care for at home. In addition, ALS patients who undergo invasive procedures were previously shown to have more financial support than those who do not, allowing them to set up care at home [20]. This difference in outcome can also be due to the long-established, widely available multidisciplinary ALS clinics, which provide education to patients and caregivers about management options and prognosis, perhaps including early and effective goals of care planning. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,634,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"There are limitations in our study worth mentioning. We conducted a retrospective, secondary analysis of an administrative database, which does not provide clinical details required to verify the certainty of diagnosis. Specifically, ICD9-CM code for PD may not be specific to idiopathic PD and sometimes may include other parkinsonian syndromes. However, we tried to account for this by excluding codes for atypical parkinsonian disorders, including dementia with Lewy Body (331.82) and other diseases of basal ganglia (progressive supranuclear palsy, corticobasal syndrome) (333.0). Also, previous studies have successfully used this database to study populations with similar neurological disorders [13,21,22], and the predictive value is acceptable. Furthermore, the database lacked details about the severity of PD motor symptoms, dementia, dysphagia, and other clinical factors. We were also unable to determine whether patients were on dopaminergic therapy and if GT was placed for medication administration. This, in our experience, is a rare occurrence. Given the retrospective nature of this study, causality cannot be established. Our study examined 'all-comers' with a given disorder, irrespective of disease severity. The AD and PD populations were older than the ALS patients, but the sex- and age-adjusted analyses did not show that age affected the outcome. Compared to AD and PD, the number of ALS cases were expectedly significantly fewer, so the data should be interpreted with caution. For ALS cases, we also could not identify subtypes of ALS, so it \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,42,129,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"D.S. Kim et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[653,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Clinical Parkinsonism & Related Disorders 4 (2021) 100088 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[492,953,502,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,66,485,160]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"is unclear how patients with bulbar onset ALS differed from the collective ALS cohort. The major strength of the study is that we used a large database with millions of patients to examine yearly trends without the bias of socioeconomic or demographic factors. It is possible that patients in these disease groups could have had GT placement for another indication, but this was addressed by the exclusion of common indications for GT – such as stroke – in this age population. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,161,485,369]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We believe that appropriate expectation and discussion between physicians, patients/caregivers addressing the goals of care may help inform the post-GT trajectory, and potentially decrease the likelihood of unnecessary or undesired nursing home placement. Studies in oncologic populations have shown that earlier goals of care discussion and palliative care consultation were associated with improved quality of life, symptom management, and reduced health care utilization cost [23,24]. However, such discussions often do not occur because of physicians' reluctance to address this issue [25]. Misconceptions about the perceived benefits of GT placement are common and may contribute to the continued use of GT in advanced neurodegenerative diseases. For example, a survey examining GT-related perceptions of 173 physicians found that the most common physician expectations from GT placement were nutritional benefit $(93\\\\%)$ , medication administration $(58\\\\%)$ , prolonging life $(49\\\\%)$ , and preventing aspiration pneumonia $(44\\\\%)$ [26]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,370,485,462]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In 2014, AGS made the recommendation against GT placement in patients with advanced dementia [17]. Therefore, physicians, patients, and caregivers should consider early discussions regarding goals of care, and mutually make informed decisions that impact them directly, and the society indirectly. Further studies should explore patient and caregiver awareness about risks of GT placement, and physicians' knowledge and practices. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,481,117,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Funding \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,506,484,533]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,551,216,563]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Declarations of interest \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,578,117,588]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"None. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,609,339,622]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CRediT authorship contribution statement \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,635,485,713]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Duk soo Kim: Conceptualization, Methodology, Writing - original draft. Richard N. Jones: Formal analysis. Theresa I. Shireman: Supervision, Writing - review & editing. Benzi M. Kluger: Supervision, Writing - review & editing. Joseph H. Friedman: Supervision, Writing - review & editing. Umer Akbar: Conceptualization, Methodology, Supervision, Writing - review & editing. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,730,132,742]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,754,485,876]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[1] Y. 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Center For Health Statistics, National Hospital Discharge Survey 2009 Public Use Data File Documentation, (2009). http://www.cdc.gov/nchs/nhds.htm. \\\",\\\"[12] C.W. Olanow, K. Kieburtz, P. Odin, A.J. Espay, D.G. Standaert, H.H. Fernandez, A. Vanagunas, A.A. Othman, K.L. Widnell, W.Z. Robieson, Y. Pritchett, K. Chatamra, J. Benesh, R.A. Lenz, A. Antonini, Continuous intrajejunal infusion of levodopa-carbidopa intestinal gel for patients with advanced Parkinson's disease: a randomised, controlled, double-blind, double-dummy study, Lancet Neurol. 13 (2014) 141-149, https://doi.org/10.1016/S1474-4422(13)70293-X. \\\",\\\"[13] U. Akbar, B. Dham, Y. He, N. Hack, S. Wu, M. Troche, P. Tighe, E. Nelson, J.H. Friedman, M.S. Okun, Incidence and mortality trends of aspiration pneumonia in Parkinson's disease in the United States, 1979-2010, Park. Relat. Disord. 21 (2015) 1082-1086, https://doi.org/10.1016/j.parkreldis.2015.06.020. \\\",\\\"[14] L.B. Goldstein, Accuracy of ICD-9-CM coding for the identification of patients with acute ischemic stroke: effect of modifier codes, Stroke 29 (1998) 1602-1604. \\\",\\\"[15] N. McCormick, V. Bhole, D. Lacaille, J.A. Avina-Zubieta, Validity of diagnostic codes for acute stroke in administrative databases: a systematic review, PLoS One 10 (2015), https://doi.org/10.1371/journal.pone.0135834. \\\",\\\"[16] J.M. Teno, S.L. Mitchell, P.L. Gozalo, D. Dosa, A. Hsu, O. Intrator, V. Mor, Hospital characteristics associated with feeding tube placement in nursing home residents with advanced cognitive impairment, JAMA 303 (2010) 544-550, https://doi.org/10.1001/jama.2010.79. \\\",\\\"[17] American Geriatrics Society feeding tubes in advanced dementia position statement, J. Am. Geriatr. Soc. 62 (2014) 1590–1593. https://doi.org/10.1111/jgs.12924. \\\",\\\"[18] Y. Yamazaki, K. Kobatake, M. Hara, M. Katagiri, M. Matsumoto, Nutritional support by \\\\\\\"conventional\\\\\\\" percutaneous endoscopic gastrostomy feeding may not result in weight gain in Parkinson's disease, J. Neurol. 258 (2011) 1561-1563, https://doi.org/10.1007/s00415-011-5971-7. \\\",\\\"[19] C. Marois, M.D.M. Amador, C. Payan, L. Lacomblez, A.-M. Bonnet, B. Degos, J.-C. Corvol, M. Vidalhret, N. Le Forestier, V. Mesnage, D. Grabli, Outcome of gastrostomy in parkinsonism: a retrospective study, Parkinsonism Relat. Disord. 43 (2017) 110-113, https://doi.org/10.1016/j.parkreldis.2017.06.012. \\\",\\\"[20] P.M. Andersen, M. Kuzma, J. Keller, H.E.A. Aho, K. Ciewcierska, N. Szejko, C. Vázquez, S. Böhm, G. Badura, L. Thomas, S. Petri, K. Linse, A. Hermann, O. Semb, E. Stenberg, S. Lackberg, J. Dorst, I. Uttner, A. Cristin, H. Albert, C.L. Dorothée, Therapeutic decisions in ALS patients: cross - cultural differences and clinical implications, J. Neurol. 265 (2018) 1600-1606. \\\",\\\"[21] K.W. Altman, G.-P. Yu, S.D. Schaefer, Consequence of dysphagia in the hospitalized patient: impact on prognosis and hospital resources, Arch. Otolaryngol. Head Neck Surg. 136 (2010) 784, https://doi.org/10.1001/archoto.2010.129. \\\",\\\"[22] P.W. Greenwald, M.E. Stern, T. Rosen, S. Clark, N. Flomenbaum, Trends in short-stay hospitalizations for older adults from 1990 to 2010: implications for geriatric emergency care, Am. J. Emerg. Med. 32 (2014) 311-314, https://doi.org/10.1016/j.ajem.2013.12.011. \\\",\\\"[23] J.S. Temel, J.A. Greer, A. Muzikansky, E.R. Gallagher, S. Admane, V.A. Jackson, C. M. Dahlin, C.D. Blinderman, J. Jacobsen, W.F. Pirl, J.A. Billings, T.J. Lynch, Early palliative care for patients with metastatic non-small-cell lung cancer, N. Engl. J. Med. 363 (2010) 733-742, https://doi.org/10.1056/NEJMoa1000678. \\\",\\\"[24] C. Scibetta, K. Kerr, J. Mcguire, M.W. Rabow, The costs of waiting: implications of the timing of palliative care consultation among a cohort of decedents at a Comprehensive Cancer Center, J. Palliat. Med. 19 (1) (2016) 69-75, https://doi.org/10.1089/jpm.2015.0119. \\\",\\\"[25] L. Jones, J. Harrington, C.A. Barlow, A. Tookman, R. Drake, K. Barnes, M. King, Advance care planning in advanced cancer: Can it be achieved? An exploratory randomized patient preference trial of a care planning discussion, Pall. Supp. Care 9 (2011) 3-13, https://doi.org/10.1017/S1478951510000490. \\\",\\\"[26] L.C. Hanson, J.M. Garrett, C. Lewis, N. Phifer, A. Jackman, T.S. Carey, Physicians' expectations of benefit from tube feeding, J. Palliat. Med. 11 (8) (2008) 1130-1134, https://doi.org/10.1089/jpm.2008.0033. \\\"]\",\n \"page_idx\": \"3\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[58,42,129,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"D.S. Kim et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[653,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Clinical Parkinsonism & Related Disorders 4 (2021) 100088 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[494,953,502,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1016/j.prdoa.2020.100088"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Medicine and Health Sciences"},"sha256":{"kind":"string","value":"f25e9da29bfdc7a9fedaefeb6dd14975f2648fa5c8071d69619af3ddfb59f9f9"},"title":{"kind":"string","value":"Trends and outcomes associated with gastrostomy tube placement in common neurodegenerative disorders"}}},{"rowIdx":237,"cells":{"abstract":{"kind":"string","value":""},"author":{"kind":"string","value":"Andrei Tănăse|Somaiah Aroori|Ashwin Dhanda|Adam Streeter|Matthew Cramp"},"content_list":{"kind":"list like","value":[{"bbox":"[112,41,480,288]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Method: Therapeutic milk-derived nanovesicles, tMNVs, were developed, containing an epithelial cellular adhesion molecule (EpCAM) aptamer and small interfering RNA (siRNA) molecule pools targeting YAP, TAZ and LCK. Immunoblot, RT-PCR, and immunofluorescence microscopy were used to confirm siRNA target knockdown in human and murine CCA cell lines. Colony formation, propidium iodide staining, and caspase 3/7 activity assays were performed on tMNV-treated CCA cells in vitro. Flow cytometry was used to validate the aptamer design and selectivity for CCA cells. Syngeneic murine and patient-derived xenograft (PDX) CCA models were employed for tMNV biodistribution and therapeutic efficacy studies of tMNVs alone and in combination with gemcitabine-cisplatin (GC). Flow cytometry was utilized to identify post-therapeutic changes in the CCA tumor microenvironment (TME). Animal work was approved by the institutional ethics committee. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,290,480,564]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results: siYAP/TAZ/LCK tMNVs resulted in simultaneous YAP/TAZ/LCK protein knockdown and decreased downstream target gene levels in vitro. siYAP/TAZ/LCK tMNVs induced apoptotic cell death in human and murine CCA cell lines; siYAP/TAZ/LCK tMNVs with GC significantly increased apoptotic cell death compared to siYAP/TAZ/LCK tMNVs (p-value $< 0.05$ ) or GC treatment (p-value $< 0.05$ ) alone. tMNV uptake was in enhanced in CCA tumors compared to normal adjacent liver and other solid organs demonstrating target specificity. In murine CCA models, siYAP/TAZ/LCK tMNVs reduced tumor size compared to control tMNVs (p-values $< 0.01$ ) and GC (p-values not significant). siYAP/TAZ/LCK tMNV therapy with GC significantly decreased tumor weights compared to GC alone (p-values $< 0.01$ ) in both syngeneic murine and PDX CCA models. Flow cytometry analysis of siYAP/TAZ/LCK tMNV-treated tumors revealed increased accumulation of reactive cytotoxic T lymphocytes (p-value $< 0.05$ ) and natural killer cells (p-value $< 0.05$ ) compared control tMNVs. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[131,576,463,686]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0737/4b842dc0c32606b633b38b75432c8d0e8ee3de5c3a533ed4612f4bee7782fafc.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[109,696,482,752]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conclusion: Inhibition of YAP/TAZ/LCK via tMNVs reduces tumor burden, potentiates cytotoxic chemotherapy, and induces immunomodulatory effects that may augment immunotherapeutic response in preclinical models of CCA. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,781,480,863]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"FP04-08 OUTCOMES OF LAPAROSCOPIC COMMON BILE DUCT EXPLORATION: RESULTS FROM A MULTI-CENTRE UK-WIDE STUDY (R-ALICE) ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,865,435,894]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A. Tanase<sup>1</sup>, A. Dhanda<sup>2</sup>, M. Cramp<sup>2</sup>, A. Streeter<sup>3</sup>, S. Aroori<sup>1</sup> and R-ALiCE Study Group ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,894,478,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{1}$ Derriford Hospital, University Hospitals Plymouth NHS Trust, HPB Surgery, Plymouth, United Kingdom, $^{2}$ Derriford Hospital, University Hospitals Plymouth NHS Trust, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,41,877,81]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"South West Liver Unit, Plymouth, United Kingdom, and University of Plymouth, Medical Statistics, Faculty of Health, Plymouth, United Kingdom ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,85,885,209]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Purpose: Laparoscopic common bile duct exploration with cholecystectomy (LCBDE) is associated with reduced costs, hospital stay, and fewer procedures over an endoscopic approach and cholecystectomy in treating common bile duct stones (BDS). Despite this, the endoscopic method is used more commonly than the LCBDE approach, and this could be due to a lack of LCBDE outcome data from large studies and perceived high risks. This study aims to evaluate the outcomes of the LCBDE approach. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,209,885,277]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methods: Eighteen centres across the UK took part in the multi-centre study called Retrospective Audit of Laparoscopic Common Bile Duct Exploration (R-ALiCE). The study included patients that underwent LCBDEs between 2015 and 2019. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,278,885,485]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results: 1689 patients (68.2% females, median age: 59 years) were included in the study. The conversion rate was $5\\%$ . Trans-cystic exploration (TC-LCBDE) was first attempted in $71.6\\%$ of patients with a success rate of $77.6\\%$ . Trans-ductal exploration (TD-LCBDE) had a success rate of $93.4\\%$ of cases. The 30-day readmission rate was $7.5\\%$ . The median length of stay was three days (range 2-7). The 30-day complication rate was $18.9\\%$ (Clavien-Dindo $>3$ : $8.8\\%$ ). The 30-day mortality was $0.4\\%$ . The bile leak rate was $4.4\\%$ (1.4% for TC-LCBDE vs $8.8\\%$ TD-LCBDE, a Risk ratio of 6.26, (3.53-11.09, $\\mathsf{p} < 0.001$ ). The retained stone rate was $4.4\\%$ (4.1% for TC-LCBDE vs $4.8\\%$ for TD-LCBDE, $\\mathsf{p} = 0.527$ ). The post-op pancreatitis rate was $0.9\\%$ (0.8% for TC-LCBDE vs $1\\%$ for TD-LCBDE, $\\mathsf{p} = 0.65$ ). The delayed CBD stricture rate was $0\\%$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,485,885,525]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conclusions: LCBDE is safe with low overall complication rates, including bile leak, post-op pancreatitis, and retained stone rate. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,557,875,686]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"FP04-09 UTILITY OF MODIFIED PANCREATICODUODENECTOMY FOR MIDDLE-THIRD CHOLANGIOCARCINOMA:AN ALTERNATIVE TO HEPATOPANCREATI-CODUODENECTOMY ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[515,691,880,731]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Onoe, T. Mizuno, N. Watanabe, Y. Yokoyama, T. Igami, J. Yamaguchi, M. Sunagawa, S. Kawakatsu and T. Ebata ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,732,842,760]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nagoya University, Division of Surgical Oncology, Department of Surgery, Nagoya, Japan ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,762,885,843]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Purpose: The standard procedure for middle-third cholangiocarcinoma (MCC) is pancreaticoduodenectomy (PD); hepatopancreaticoduodenectomy (HPD) is often performed despite its high risk. There is no clear selection guidance for these procedures. The aim of this study is to validate an alternative procedure to HPD for MCC. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,844,885,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methods: Patients with MCC who underwent HPD or PD between 2006 and 2020 were retrospectively evaluated. MCC was radiologically defined as cholangiocarcinoma, the center of which was located in the middle-third duct, that was not invading the hepatic confluence. The conventional PD was modified to transect the bile duct beyond ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[398,18,598,32]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Free Paper Orals (FP01 - FP24) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[850,18,884,30]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S211 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[109,958,282,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HPB 2023, 25 (S2), S192-S287 ","text_format":null,"text_level":null,"type":"footer"}],"string":"[\n {\n \"bbox\": \"[112,41,480,288]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Method: Therapeutic milk-derived nanovesicles, tMNVs, were developed, containing an epithelial cellular adhesion molecule (EpCAM) aptamer and small interfering RNA (siRNA) molecule pools targeting YAP, TAZ and LCK. Immunoblot, RT-PCR, and immunofluorescence microscopy were used to confirm siRNA target knockdown in human and murine CCA cell lines. Colony formation, propidium iodide staining, and caspase 3/7 activity assays were performed on tMNV-treated CCA cells in vitro. Flow cytometry was used to validate the aptamer design and selectivity for CCA cells. Syngeneic murine and patient-derived xenograft (PDX) CCA models were employed for tMNV biodistribution and therapeutic efficacy studies of tMNVs alone and in combination with gemcitabine-cisplatin (GC). Flow cytometry was utilized to identify post-therapeutic changes in the CCA tumor microenvironment (TME). Animal work was approved by the institutional ethics committee. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,290,480,564]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results: siYAP/TAZ/LCK tMNVs resulted in simultaneous YAP/TAZ/LCK protein knockdown and decreased downstream target gene levels in vitro. siYAP/TAZ/LCK tMNVs induced apoptotic cell death in human and murine CCA cell lines; siYAP/TAZ/LCK tMNVs with GC significantly increased apoptotic cell death compared to siYAP/TAZ/LCK tMNVs (p-value $< 0.05$ ) or GC treatment (p-value $< 0.05$ ) alone. tMNV uptake was in enhanced in CCA tumors compared to normal adjacent liver and other solid organs demonstrating target specificity. In murine CCA models, siYAP/TAZ/LCK tMNVs reduced tumor size compared to control tMNVs (p-values $< 0.01$ ) and GC (p-values not significant). siYAP/TAZ/LCK tMNV therapy with GC significantly decreased tumor weights compared to GC alone (p-values $< 0.01$ ) in both syngeneic murine and PDX CCA models. Flow cytometry analysis of siYAP/TAZ/LCK tMNV-treated tumors revealed increased accumulation of reactive cytotoxic T lymphocytes (p-value $< 0.05$ ) and natural killer cells (p-value $< 0.05$ ) compared control tMNVs. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[131,576,463,686]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0737/4b842dc0c32606b633b38b75432c8d0e8ee3de5c3a533ed4612f4bee7782fafc.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[109,696,482,752]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conclusion: Inhibition of YAP/TAZ/LCK via tMNVs reduces tumor burden, potentiates cytotoxic chemotherapy, and induces immunomodulatory effects that may augment immunotherapeutic response in preclinical models of CCA. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,781,480,863]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"FP04-08 OUTCOMES OF LAPAROSCOPIC COMMON BILE DUCT EXPLORATION: RESULTS FROM A MULTI-CENTRE UK-WIDE STUDY (R-ALICE) \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,865,435,894]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A. Tanase<sup>1</sup>, A. Dhanda<sup>2</sup>, M. Cramp<sup>2</sup>, A. Streeter<sup>3</sup>, S. Aroori<sup>1</sup> and R-ALiCE Study Group \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,894,478,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{1}$ Derriford Hospital, University Hospitals Plymouth NHS Trust, HPB Surgery, Plymouth, United Kingdom, $^{2}$ Derriford Hospital, University Hospitals Plymouth NHS Trust, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,41,877,81]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"South West Liver Unit, Plymouth, United Kingdom, and University of Plymouth, Medical Statistics, Faculty of Health, Plymouth, United Kingdom \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,85,885,209]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Purpose: Laparoscopic common bile duct exploration with cholecystectomy (LCBDE) is associated with reduced costs, hospital stay, and fewer procedures over an endoscopic approach and cholecystectomy in treating common bile duct stones (BDS). Despite this, the endoscopic method is used more commonly than the LCBDE approach, and this could be due to a lack of LCBDE outcome data from large studies and perceived high risks. This study aims to evaluate the outcomes of the LCBDE approach. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,209,885,277]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methods: Eighteen centres across the UK took part in the multi-centre study called Retrospective Audit of Laparoscopic Common Bile Duct Exploration (R-ALiCE). The study included patients that underwent LCBDEs between 2015 and 2019. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,278,885,485]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results: 1689 patients (68.2% females, median age: 59 years) were included in the study. The conversion rate was $5\\\\%$ . Trans-cystic exploration (TC-LCBDE) was first attempted in $71.6\\\\%$ of patients with a success rate of $77.6\\\\%$ . Trans-ductal exploration (TD-LCBDE) had a success rate of $93.4\\\\%$ of cases. The 30-day readmission rate was $7.5\\\\%$ . The median length of stay was three days (range 2-7). The 30-day complication rate was $18.9\\\\%$ (Clavien-Dindo $>3$ : $8.8\\\\%$ ). The 30-day mortality was $0.4\\\\%$ . The bile leak rate was $4.4\\\\%$ (1.4% for TC-LCBDE vs $8.8\\\\%$ TD-LCBDE, a Risk ratio of 6.26, (3.53-11.09, $\\\\mathsf{p} < 0.001$ ). The retained stone rate was $4.4\\\\%$ (4.1% for TC-LCBDE vs $4.8\\\\%$ for TD-LCBDE, $\\\\mathsf{p} = 0.527$ ). The post-op pancreatitis rate was $0.9\\\\%$ (0.8% for TC-LCBDE vs $1\\\\%$ for TD-LCBDE, $\\\\mathsf{p} = 0.65$ ). The delayed CBD stricture rate was $0\\\\%$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,485,885,525]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conclusions: LCBDE is safe with low overall complication rates, including bile leak, post-op pancreatitis, and retained stone rate. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,557,875,686]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"FP04-09 UTILITY OF MODIFIED PANCREATICODUODENECTOMY FOR MIDDLE-THIRD CHOLANGIOCARCINOMA:AN ALTERNATIVE TO HEPATOPANCREATI-CODUODENECTOMY \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,691,880,731]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Onoe, T. Mizuno, N. Watanabe, Y. Yokoyama, T. Igami, J. Yamaguchi, M. Sunagawa, S. Kawakatsu and T. Ebata \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,732,842,760]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nagoya University, Division of Surgical Oncology, Department of Surgery, Nagoya, Japan \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,762,885,843]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Purpose: The standard procedure for middle-third cholangiocarcinoma (MCC) is pancreaticoduodenectomy (PD); hepatopancreaticoduodenectomy (HPD) is often performed despite its high risk. There is no clear selection guidance for these procedures. The aim of this study is to validate an alternative procedure to HPD for MCC. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,844,885,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methods: Patients with MCC who underwent HPD or PD between 2006 and 2020 were retrospectively evaluated. MCC was radiologically defined as cholangiocarcinoma, the center of which was located in the middle-third duct, that was not invading the hepatic confluence. The conventional PD was modified to transect the bile duct beyond \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[398,18,598,32]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Free Paper Orals (FP01 - FP24) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[850,18,884,30]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S211 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[109,958,282,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HPB 2023, 25 (S2), S192-S287 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1016/j.hpb.2023.07.043"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Medicine and Health Sciences"},"sha256":{"kind":"string","value":"a3284097c7833c9c9c5b5dd5cbcb4f8fd966acb8ad83f535458e19a82190b307"},"title":{"kind":"string","value":"Outcomes of Laparoscopic Common Bile Duct Exploration: Results from a Multi-centre UK-wide Study (R-ALiCE)"}}},{"rowIdx":238,"cells":{"abstract":{"kind":"string","value":"The identification of VHL-binding proteolysis targeting chimeras (PROTACs) that potently degrade the BRM protein (also known as SMARCA2) in SW1573 cell-based experiments is described. These molecules exhibit between 10- and 100-fold degradation selectivity for BRM over the closely related paralog protein BRG1 (SMARCA4). They also selectively impair the proliferation of the H1944 BRG1-mutant NSCLC cell line, which lacks functional BRG1 protein and is thus highly dependent on BRM for growth, relative to the wild-type Calu6 line. In vivo experiments performed with a subset of compounds identified PROTACs that potently and selectively degraded BRM in the Calu6 and/or the HCC2302 BRG1 mutant NSCLC xenograft models and also afforded antitumor efficacy in the latter system. Subsequent PK/PD analysis established a need to achieve strong BRM degradation (>95%) in order to trigger meaningful antitumor activity in vivo. Intratumor quantitation of mRNA associated with two genes whose transcription was controlled by BRM (PLAU and KRT80) also supported this conclusion."},"author":{"kind":"string","value":"Michael Berlin|Jennifer Cantley|Mark Bookbinder|Elizabeth Bortolon|Fabio Broccatelli|Greg Cadelina|Emily W. Chan|Huifen Chen|Xin Chen|Yunxing Cheng|Tommy K. Cheung|Kim Davenport|Dean DiNicola|Debbie Gordon|Brian D. Hamman|Alicia Harbin|Roy Haskell|Mingtao He|Alison J. Hole|Thomas Januario|Philip S. Kerry|Stefan G. Koenig|Limei Li|Mark Merchant|Inmaculada Pérez-Dorado|Jennifer Pizzano|Connor Quinn|Christopher M. Rose|Emma Rousseau|Leofal Soto|Leanna R. Staben|Hongming Sun|Qingping Tian|Jing Wang|Weifeng Wang|Crystal S. Ye|Xiaofen Ye|Penghong Zhang|Yuhui Zhou|Robert Yauch|Peter S. Dragovich"},"content_list":{"kind":"list like","value":[{"bbox":"[79,135,915,203]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PROTACs Targeting BRM (SMARCA2) Afford Selective In Vivo Degradation over BRG1 (SMARCA4) and Are Active in BRG1 Mutant Xenograft Tumor Models ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[77,210,889,351]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Michael Berlin,\\* Jennifer Cantley, Mark Bookbinder, Elizabeth Bortolon, Fabio Broccatelli, Greg Cadelina, Emily W. Chan, Huifen Chen, Xin Chen, Yunxing Cheng, Tommy K. Cheung, Kim Davenport, Dean DiNicola, Debbie Gordon, Brian D. Hamman, Alicia Harbin, Roy Haskell, Mingtao He, Alison J. Hole, Thomas Januario, Philip S. Kerry, Stefan G. Koenig, Limei Li, Mark Merchant, Inmaculada Perez-Dorado, Jennifer Pizzano, Connor Quinn, Christopher M. Rose, Emma Rousseau, Leofal Soto, Leanna R. Staben, Hongming Sun, Qingping Tian, Jing Wang, Weifeng Wang, Crystal S. Ye, Xiaofen Ye, Penghong Zhang, Yuhui Zhou, Robert Yauch, and Peter S. Dragovich\\* ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,358,116,386]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/1023/495c0ee0ad5421084bfb3978d11d23294d8be1088b909fc24b192d01c5085d7a.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[120,365,380,380]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Cite This: J. Med. Chem. 2024, 67, 1262-1313 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,358,550,386]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0937/8e773d004368857f6e11eca166d679db032d9f05ec733678769f802cc6f411c7.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[551,366,635,380]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Read Online ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,405,172,425]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ACCESS ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[232,410,255,423]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0654/41cff44fe515bdbe63919f705755e9760955289c74a02dd0dd26bfe602de1af5.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[257,410,354,422]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Metrics & More ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[449,410,472,425]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0377/425e61feb79f70715f889c8ee9e4b46152affba233455218f44ac44d0cac9766.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[474,410,632,422]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article Recommendations ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[706,410,726,425]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0249/9d858f9edd9dae3a410e72e24499f2ab5155633aaa27a7672c647bc1beb21689.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[731,410,871,425]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Supporting Information ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[205,440,790,555]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/1015/c51e2c04935c0a2df39009ecc4523a27d18033f4de276e17d41f4166ca42b6fc.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,560,915,686]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABSTRACT: The identification of VHL-binding proteolysis targeting chimeras (PROTACs) that potently degrade the BRM protein (also known as SMARCA2) in SW1573 cell-based experiments is described. These molecules exhibit between 10- and 100-fold degradation selectivity for BRM over the closely related paralog protein BRG1 (SMARCA4). They also selectively impair the proliferation of the H1944 \"BRG1-mutant\" NSCLC cell line, which lacks functional BRG1 protein and is thus highly dependent on BRM for growth, relative to the wild-type Calu6 line. In vivo experiments performed with a subset of compounds identified PROTACs that potently and selectively degraded BRM in the Calu6 and/or the HCC2302 BRG1 mutant NSCLC xenograft models and also afforded antitumor efficacy in the latter system. Subsequent PK/PD analysis established a need to achieve strong BRM degradation ( $>95\\%$ ) in order to trigger meaningful antitumor activity in vivo. Intratumor quantitation of mRNA associated with two genes whose transcription was controlled by BRM (PLAU and KRT80) also supported this conclusion. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,713,230,727]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"INTRODUCTION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[77,733,481,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The SWI/SNF chromatin remodeling complexes were originally identified in yeast where they were observed to impact mating-type switch (SWI) and sucrose fermentation $(\\mathrm{SNF} = \\mathrm{succrose}$ nonfermenting) phenotypes. Since these initial discoveries, homologues of these multiprotein entities were characterized in many additional eukaryotic organisms suggesting a strong evolutionary conservation. In mammals, three SWI/SNF complexes have been identified to date: BAF (BRG1/BRM-associated factor; also known as SWI/SNF-A), PBAF (polybromo-associated BAF, also known as SWI/SNF-B), and, more recently, noncanonical BAF (ncBAF or GBAF). These complexes open tightly packed chromatin structures in cell nuclei to enable the binding of transcription factors and associated proteins and thereby initiate gene ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,713,915,830]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"expression. $^{1-4}$ They require the catalytic activity of an ATPase which is provided in a mutually exclusive manner by one of two protein subunits: BRM (Brahma homologue; also known as SWI/SNF-related, matrix-associated, actin-dependent regulator of chromatin subfamily A member 2 or SMARCA2) or BRG1 (Brahma-related gene 1; SMARCA4). $^{5}$ The remaining subunits present in each complex are selected from nearly 30 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,847,706,860]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received: September 25, 2023 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,861,705,873]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Revised: November 25, 2023 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,875,703,887]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Accepted: December 18, 2023 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,888,682,901]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Published: January 5, 2024 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[843,841,914,918]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0467/5996592b412442fc13a7d4d3dfb1192a9826e1a3685890e5992cf9916db15868.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[16,293,32,351]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ished articles. 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Chemical structures of representative known BRM/BRG1 ATPase inhibitors. \"]","image_footnote":"[]","img_path":"images/0333/aae9076928b4eb3db33a336b1c21342d8463f902a75466b27fbc9ecbc991d5c3.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[199,238,388,378]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0362/3e771861e9294e18bf42d2ac3499dd5ddb470960fd4c2626e0827e1fc0c78fa6.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[398,257,594,378]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0844/9d6dc49ea26b5b96fd5f3c6b16de03357bca1e7af1fa0984e3fccfecfb588f7f.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[627,240,795,378]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0574/cf4b857d175daf053ffcd142e6d8ec0fa0f05ccc11f7c511488cf00e1e66152b.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[327,385,680,621]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0873/11cf29a8961db8e213585fa992ac04252c3dfdd23f8b82bcc4151658661936d3.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[220,627,789,760]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 2. Chemical structures of representative known BRM/BRG1 bromodomain binders and PROTACs. \"]","image_footnote":"[]","img_path":"images/0699/865b691555a38a2fd876439ed0d3b0067eaea6ea19f11ae1381b4ff8cda69122.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[79,792,479,822]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"possibilities with the final composition determining the precise biological role of each multicomponent entity. $^{1-4}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,822,482,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Alterations in mammalian SWI/SNF complexes have been characterized in multiple human cancers, and many efforts are currently underway to develop new therapies which exploit these potential vulnerabilities. $^{1-6}$ In particular, cancer cells which harbor homozygous loss-of-function mutations in the BRG1 protein are known to be highly dependent on BRM for their growth and proliferation. $^{7,8}$ These observations have spurred numerous endeavors to develop inhibitors of BRM ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,792,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ATPase activity. Accordingly, an optimized example which exhibited in vivo antitumor efficacy was previously disclosed (1, Figure 1), and another compound was recently advanced to Phase 1 clinical trials (2, Figure 1; for other examples of BRM/BRG1 ATPase inhibitors, see refs 10-13). However, genetic studies indicate that loss of BRG1 (or both BRM and BRG1) may be detrimental to the health of normal cells and tissues.[14-16] Consistent with these findings, preclinical dose-escalation of compound 1 and related molecules which potently inhibit both BRM and BRG1 ATPase activity in ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,313,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1263 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,71,479,98]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"mouse xenograft efficacy studies was limited by tolerability issues. $^{9,17}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,100,481,332]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As an alternate approach to targeting BRM for the treatment of BRG1 mutant cancers, we focused on the bromodomain present in the C-terminal region of the protein. Potent small molecule binders/inhibitors of many bromodomain-containing proteins have been identified in recent years, and some of these compounds have advanced into clinical-stage testing.[18,19] In the case of BRM, several distinct series of potent bromodomain-binding molecules have been reported in the literature by multiple research groups (compounds 3-5, Figure 2).[20-25] However, biological studies employing these compounds demonstrated that simply blocking the bromodomain present in BRM with a potent inhibitor did not afford meaningful antiproliferation effects in cell-based experiments.[26] In contrast, intracellular knock-down of the BRM protein via biological methods potently inhibited the growth and proliferation of BRM-dependent (BRG1 mutant) cancer cells.[26] ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,333,482,610]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Informed by these results, we sought to transform simple BRM bromodomain binders into chimeric entities that could simultaneously recognize an E3 ligase protein and thereby induce BRM degradation via ternary complex formation, BRM ubiquitination, and subsequent destruction via the cellular proteasome. Such heterobifunctional molecules are often termed PROTACs (proteolysis targeting chimeras), and they are becoming an increasingly important component of medicinal and biological chemistry research.[27-29] Several BRM-targeting PROTACs have been disclosed by others in the scientific literature (e.g., compounds 6 and 7, Figure 2),[30-32] and some of these molecules display good degradation selectivity for BRM over BRG1 and/or the potential for oral administration (for other examples of BRM/BRG1 degraders, see refs 33-41). In this report, we describe the initial findings from our own efforts to identify potent and selective chimeric BRM degraders which incorporate BRM bromodomain-binding moieties. These studies significantly expand on our earlier disclosure regarding the detailed biology associated with one of our degrader molecules.[42] ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,620,317,635]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"RESULTS AND DISCUSSION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[77,638,482,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We began our search for BRM-targeting PROTACs by first identifying several potent BRM bromodomain ligands that protruded away from the protein's surface in a variety of distinct conformations. We envisioned employing the solvent-exposed portion of these compounds for subsequent elaboration into the desired heterobifunctional degraders. As shown in Figure 3 and Table 1, the 3-amino-pyridazine-containing compound 8, which was originally discovered as part of a research collaboration between Genentech and Constellation Pharmaceuticals,[23,24] displayed potent binding affinity to both BRM and BRG1 in Alpha-LISA assessments employing the proteins' bromodomain regions and a biotinylated BRM/BRG1-binding probe (see Supporting Information for details). The near-equal affinities exhibited by 8 for both BRM and BRG1 were consistent with the high degree of amino acid conservation among the two proteins in the compound's binding region.[20] At this point in our research endeavors, we did not know whether PROTACs derived from ligands with similar BRM/BRG1 binding affinities could exhibit selective degradation of one protein relative to the other. Encouragingly, however, PROTACs constructed from a relatively promiscuous and nonselective kinase inhibitor ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,71,911,330]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 3. BRM/BRG1 binding ligands employed in this work (9 and 10) and reference ligand 8. \"]","image_footnote":"[]","img_path":"images/0681/70452455be3d2dac8c86e205bc16ab72ab31eeffddb272a28021ebb26dd3c4f4.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[515,410,915,480]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0745/3ec78eed18a83c88d0406874cc82364723a530b87787ec817d471d96d4b03ba1.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":"<table><tr><td>Cmpd</td><td>BRM IC50(nM)a</td><td>BRG1 IC50(nM)b</td><td>H1944 GI50(nM)c</td><td>Calu6 GI50(nM)d</td></tr><tr><td>8</td><td>18</td><td>16</td><td>>300</td><td>>300</td></tr><tr><td>9</td><td>1.2</td><td>3.3</td><td>>300</td><td>>300</td></tr><tr><td>10</td><td>2.7</td><td>2.8</td><td>ND</td><td>ND</td></tr></table>","table_caption":"[\"Table 1. BRM/BRG1 Binding Affinities and Antiproliferation Properties of Compounds 8-10 \"]","table_footnote":"[\"${}^{a}$ BRM binding affinity (bromodomain protein fragment). ${}^{b}$ BRG1 binding affinity (bromodomain protein fragment). ${}^{c}$ H1944 antiproliferation activity (BRM-dependent cell line,time point = 7 days). ${}^{d}$ Calu6 antiproliferation activity (time point = 7 days). ND = not determined. See Supporting Information for additional details and discussion of error associated with each assay. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[510,583,915,665]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"scaffold were previously reported to exhibit selective kinase degradation in cell-based experiments.[43] Similarly, selective degradation of BRD4 over the related BRD2 and BRD3 entities was achieved by a chimeric degrader constructed from a ligand which nonselectively bound to the proteins' respective bromodomains.[44] ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,666,915,898]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Further exploration identified the 3,8-diazabicyclo[3.2.1]-octane-containing molecule 9 and the related analog 10 which both displayed improved BRM/BRG1 binding affinities relative to 8 (Figure 3, Table 1, Figure S1). The ability of 8 and 9 to impact the growth and proliferation of BRMDependent (BRG1 mutant) and non-BRM-dependent (BRG1 \"wild type\") cancers in vitro was respectively assessed using the H1944 and Calu6 cell lines (see Supporting Information for full details). As depicted in Table 1, none of these molecules afforded meaningful antiproliferation effects against either of these lines up to the highest tested concentration $(300\\mathrm{nM})$ These results were consistent with prior literature reports describing the inactivity of other potent BRM-bromodomainbinding compounds in related cell growth experiments (e.g., compound 2).26 They also reinforced our desire to impart BRM degradation properties to the depicted ligands in order to enhance their anticancer characteristics. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,900,914,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To guide transformation of the BRM-binding ligands into the desired heterobifunctional degraders, we obtained high-resolution crystal structures of compound 10 bound to the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1264 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[163,72,833,445]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 4. X-ray crystal structure of compound 10 bound to BRM. Compound 10 (pink): PDB code = 8QJT. Dashed green lines are hydrogen bonds observed between the ligand and the BRM protein. The pink arrow depicts the exit vector from the BRM binding pocket. Resolution = 2.57 Å. \"]","image_footnote":"[]","img_path":"images/0966/c55e2a7c976fbf0013559e37127d7fe0e2d35609891b63f5712d6dbfc0190cf8.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,503,481,658]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"BRM protein. As shown in Figure 4, the ligand formed key hydrogen bonds with the protein that included contacts between the phenol moiety and Tyr1421 as well as H-bonds between the amino-pyridazine fragment and the Asn1464 BRM residue. The 3,8-diazabicyclo[3.2.1]octane group appended to the amino-pyridazine core of the compound afforded a vector that extended away from the BRM protein surface and into solvent (Figure 4). We were therefore curious to learn whether ligand 10 could be elaborated into functionally active BRM degraders with biological potencies similar to those depicted by 6. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,660,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We began our exploration of novel BRM degrader PROTACs by tethering compound 10 via a polyethylene glycol (PEG) linker to a peptidomimetic ligand that was known to efficiently bind to the Von Hippel-Lindau (VHL) E3 ubiquitin ligase.45 As shown in Figure 5 and Table 2, the resulting heterobifunctional molecule (11) displayed potent and extensive $(>85\\%)$ degradation of the targeted BRM protein when assessed in SW1573 cells after a $22\\mathrm{h}$ incubation period (see Supporting Information for full details). Encouragingly, the molecule degraded the BRG1 protein with reduced potency relative to the effect on BRM in the same cell line, although significant protein loss was ultimately achieved at high concentrations (Table 2, cf., Figure S4). Interestingly, compound 11 displayed binding affinities for the BRM and BRG1 proteins that were 20-50-fold weaker than those exhibited by the bromodomain-binding ligands 9 and 10 (61 and $139\\mathrm{nM}$ , respectively; cf., Table 1). These differences may be due to the appended VHL ligand partially interfering with BRM/BRG1 recognition by the PROTAC and/or increased entropic penalties associated with the binding of 11 relative to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,503,915,560]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the simple bromodomain ligands. Similar BRM bromodomain affinity differences between a ligand/inhibitor and the corresponding PROTACs were noted by others during the identification of compound 6.[30] ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,560,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Replacement of the acetylated tert-butyl glycine moiety present in 11 with an isoxazole-containing fragment inspired by previously disclosed VHL-binding ligands significantly improved the BRM degradation activity of the resulting compound (12) relative to its precursor (11) (Figure 5, Table 2).46,47 Unfortunately, this improvement was also accompanied by a strengthening of BRG1 degradation activity which resulted in a poorer BRG1/BRM degradation selectivity ratio for compound 12 as compared to 11 (7.8 and 22, respectively; Table 2). Encouragingly, rigidification of the PEG linker contained in 12 by the introduction of a piperazine moiety afforded a new PROTAC (13) which improved both BRM degradation potency and BRG1 selectivity relative to 12 (Figure 5, Table 2). Compound 13 also potently impeded the growth of the H1944 BRM-dependent (BRG1 mutant) nonsmall cell lung cancer cell line in a 7-day in vitro antiproliferation experiment (Table 2; see Supporting Information for full details). Importantly, and consistent with its weakened degradation activity toward the BRG1 protein relative to BRM, compound 13 was $>10$ -fold less active in suppressing the growth of the non-BRM-dependent (BRG1 wild-type) Calu6 cell line compared to its H1944 potency (Table 2). These observations reassuringly indicated that the BRG1/BRM degradation selectivity measured in SW1573 cells could translate into differentiated antiproliferation effects in cancer cell lines bearing mutant or wild-type forms of the BRG1 protein. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[532,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1265 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[222,70,774,205]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0115/e33a8e37d443f6edd95323639ab0947a35d41ac36d86193124a9df707d6b4220.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[222,236,775,383]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0004/77e7e0828ed51f2c2744988ed0efc4862c23b66a1f904cd8935ffed7e550d099.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[230,410,764,576]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 5. Structures of PROTACs 11-13. \"]","image_footnote":"[]","img_path":"images/0748/4b0cae74c26fc10595391c70a2eda3eed437f3b888c076c5a96e0dacab04075d.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,611,482,811]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Having completed our initial identification of VHL-binding BRM/BRG1-degraders, we next turned to assessing and improving the in vivo pharmacokinetic properties of the PROTACs under study. The initial objective in this portion of our explorations was the identification of at least one in vivo tool compound that could be used to probe BRM-related biologies in PK/PD and/or efficacy experiments. At this juncture, we did not know which route of in vivo administration would be most appropriate for the compounds being evaluated (e.g., oral, intravenous, intraperitoneal, or subcutaneous). Accordingly, we sought to enhance the murine in vivo clearance and half-life properties of the PROTACs with the expectation that such improvements would benefit all of the possible administration routes under consideration. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,811,482,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As shown in Table 2, introduction of a benzylic (S)-methyl group into the PROTAC design significantly improved BRM/BRG1 binding, BRM degradation, and H1944 antiproliferation activity while maintaining degradation selectivity over BRG1 (compare 14 with 13; see also Figure S5). This modification has been successfully incorporated into many other VHL-based PROTAC compounds that are described in the scientific literature.[48,49] Compound 14 was highly labile in an in vitro mouse liver microsome stability assessment, and this ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,611,915,855]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"undesirable characteristic was not improved by simple methyl substitution of the central piperazine contained in the molecule (compounds 15 and 16). However, introduction of a linker derived from a trans-1,3-cyclobutane-diol fragment and simultaneous replacement of the piperazine moiety with a piperidine group afforded a new PROTAC (17) that maintained favorable BRM degradation activity and noticeably improved mouse microsome stability outcomes (Table 2). This compound also exhibited a relatively low (stable) in vivo clearance value and a moderate half-life when administered to mice via IV injection (Table 2). In vitro metabolite identification experiments performed with 17 using mouse hepatocytes determined that piperidine N-dealkylation was a major contributor to the compound's murine metabolism (Figure 6, 17a and 17b). Accordingly, we explored additional linker modifications which altered the piperidine moiety in an effort to further improve in vivo pharmacokinetic properties. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,855,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Incorporation of a piperazine group or a second piperidine moiety adjacent to the VHL-binding portion of 16 improved in vitro and/or in vivo DMPK characteristics (Table 2, 18 and 19). Reversing the orientation of the central piperidine present in the linker relative to its positioning in compound 18 provided a potent PROTAC with acceptable in vitro and/or in ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1266 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[296,91,698,215]","code_body":null,"code_caption":null,"image_caption":"[\"Table 2. Exploration of PROTAC In Vitro and In Vivo DMPK Properties \"]","image_footnote":"[]","img_path":"images/0209/a93c2d174de61ddb8ae52e2e8a57ed5fa36d1f5c4b6c37585c9afa2602f12d8e.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[189,220,805,685]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0011/f176c976a136dd1bd94495bf5e2a3e713bb9d7e58cbd262e999ccf0e5bb234c4.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td>Cmpd</td><td>Linker</td><td>BRM DC50 (nM)a</td><td>BRG1 DC50 (nM)b</td><td>H1944 GI50 (nM)c</td><td>Calu6 GI50 (nM)d</td><td>MLM (ER)e</td><td>Mouse PPB (%)f</td><td>Mouse IV Cl (mL/min/kg)g</td><td>Mouse IV t1/2 (h)h</td></tr><tr><td>6</td><td>Figure 2</td><td>8.2</td><td>32</td><td>17</td><td>41</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td></tr><tr><td>11</td><td>Figure 5</td><td>32</td><td>703i</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td></tr><tr><td>12</td><td>Figure 5</td><td>0.76</td><td>5.9</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td></tr><tr><td>13</td><td>Figure 5</td><td>0.39</td><td>9.5</td><td>3.6</td><td>62</td><td>0.65</td><td>98.5</td><td>ND</td><td>ND</td></tr><tr><td>14</td><td>OCHNCH2O-</td><td>0.068</td><td>1.5</td><td>0.17</td><td>7.0</td><td>0.72</td><td>98.4</td><td>ND</td><td>ND</td></tr><tr><td>15</td><td>OCHNCH2O-</td><td>0.055</td><td>0.71</td><td>0.26</td><td>12</td><td>0.83</td><td>98.5</td><td>ND</td><td>ND</td></tr><tr><td>16</td><td>OCHNCH2O-</td><td>0.11</td><td>2.7</td><td>0.72</td><td>38</td><td>0.83</td><td>ND</td><td>ND</td><td>ND</td></tr><tr><td>17</td><td>OCHNCH2O-</td><td>0.093</td><td>4.9</td><td>0.64</td><td>24</td><td>0.53</td><td>97.3</td><td>22</td><td>2.6</td></tr><tr><td>18</td><td>OCHNCH2O-</td><td>0.085</td><td>3.2</td><td>1.3</td><td>11</td><td>0.40</td><td>96.6</td><td>9.6</td><td>13</td></tr><tr><td>19</td><td>OCHNCH2O-</td><td>0.039</td><td>1.1</td><td>0.58</td><td>6.5</td><td>0.44</td><td>95.2</td><td>9.6</td><td>16</td></tr><tr><td>20</td><td>OCHNCH2O-</td><td>0.062</td><td>1.4</td><td>0.72</td><td>10</td><td>0.15</td><td>96.5</td><td>12</td><td>17</td></tr><tr><td>21</td><td>OCHNCH2O-</td><td>0.14</td><td>1.8</td><td>0.30</td><td>4.4</td><td>0.14</td><td>98.1</td><td>9.2</td><td>1.4</td></tr><tr><td>22</td><td>OCHNCH2O-</td><td>0.09</td><td>1.3</td><td>0.45</td><td>6.8</td><td>0.27</td><td>98.9</td><td>11</td><td>3.7</td></tr><tr><td>23</td><td>OCHNCH2O-</td><td>0.053</td><td>0.99</td><td>0.23</td><td>3.7</td><td>0.41</td><td>99.4</td><td>6.7</td><td>6.7</td></tr><tr><td>24</td><td>OCHNCH2O-</td><td>0.27</td><td>5.1</td><td>0.70</td><td>28</td><td>0.15</td><td>98.4</td><td>22</td><td>1.5</td></tr></table>","table_caption":"[]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[77,690,915,780]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"${}^{a}$ BRM degradation potency (SW1573 cells,time point $= {22}\\mathrm{\\;h}$ ). ${}^{b}$ BRG1 degradation potency (SW1573 cells,time point $= {22}\\mathrm{\\;h}$ ). Extent of BRM and BRG1 degradation $\\left( {D}_{\\max }\\right) > {85}\\%$ unless otherwise indicated; see Table S4 for exact values. ${}^{c}$ H1944 antiproliferation activity (BRM-dependent cell line,time point $= 7$ days). ${}^{d}$ Calu6 antiproliferation activity (time point $= 7$ days). ${}^{e}$ In vitro mouse liver microsome stability [ER = extraction ratio; range $= 0$ (stable) to 1 (labile)]. ${}^{f}$ In vitro binding to mouse plasma proteins (number indicates % bound). ${}^{g}$ In vivo mouse clearance value determined following IV administration at $1\\mathrm{{mg}}/\\mathrm{{kg}}$ . ${}^{h}$ In vivo mouse half-life determined following IV administration at $1\\mathrm{{mg}}/\\mathrm{{kg}}$ . ${}^{i}{D}_{\\max } = {78}\\%$ . ND = not determined. See Supporting Information for discussion of experimental details and error associated with each assay. Literature compound 6 included for comparison purposes. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,795,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"vivo DMPK attributes (Table 2, 20). Combining a central piperazine moiety with other linker fragments identified during exploration of piperidine-containing molecules was also tolerated (22) as was a slight truncation of linker length (Table 2, 21 and 23). In addition, a heteroaromatic moiety could be introduced into the central region of the linker without significantly compromising BRM degradation and/or DMPK properties (compound 24). The propensity for the described PROTACs to bind to mouse plasma proteins was assessed for many of the molecules depicted in Table 2. All ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,795,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tested compounds displayed similar binding characteristics that ranged from 95.2 to $99.4\\%$ bound. In addition, the compounds which exhibited the longest in vivo half-lives typically contained strongly basic amines (calculated $\\mathrm{pK_a} > 8.5$ ; e.g., 18, 19, and 20). These structural attributes afforded relatively large volumes of distribution to these molecules ( $>1~\\mathrm{L / kg}$ ) which, when combined with their low in vivo clearances, resulted in the long half-lives. Additional discussion regarding the BRG1/BRM degradation and Calu6/H1944 antiproliferation selectiv ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1267 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[110,70,884,200]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 6. In vitro MetID assessment of compound 17 using mouse hepatocytes. \"]","image_footnote":"[]","img_path":"images/0696/74cdbcdf321be90eb091caf4e25d454c89712b3c9d50ef75f840344df70d3d47.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[80,252,915,328]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0195/ef1b565e59e1593e287c504eec41652026fa214e50da052106c518e946f95806.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":"<table><tr><td rowspan=\"2\">Cmpd</td><td>Degradation</td><td colspan=\"3\">SPR Bromodomains Only</td><td colspan=\"3\">SPR Full-Length Proteins</td></tr><tr><td>BRG1/BRMa</td><td>BRMT1/2(s)b</td><td>BRGT1(t1/2)(s)c</td><td>BRG1/BRMd</td><td>BRMT1/2(s)e</td><td>BRGT1(t1/2)(s)e</td><td>BRG1/BRMe</td></tr><tr><td>14</td><td>22</td><td>6.0</td><td>2.0</td><td>0.33</td><td>ND</td><td>ND</td><td>ND</td></tr><tr><td>17</td><td>53</td><td>13.3</td><td>9.5</td><td>0.71</td><td>346</td><td>1174</td><td>3.4</td></tr><tr><td>19</td><td>28</td><td>4.0</td><td>9.0</td><td>2.25</td><td>462</td><td>1386</td><td>3</td></tr></table>","table_caption":"[\"Table 3. Half-Lives of Ternary Complexes Formed between Representative PROTACs and the VHL and BRM/BRG1 Proteins \"]","table_footnote":"[\"${}^{a}$ Ratio of BRG1 and BRM degradation ${\\\\mathrm{{DC}}}_{50}$ values (determined in SW1573 cells and depicted in Table 2). ${}^{b}$ SPR half-lives of BRM/PROTAC/ VHL ternary complex determined using bromodomain fragment. ${}^{c}$ SPR half-lives of BRG1/PROTAC/VHL ternary complex determined using bromodomain fragment. ${}^{d}$ Ratio of BRG1/BRM ternary complex half-lives (bromodomain fragments). ${}^{e}$ Ternary complex half-lives and ratios determined using full length BRM or BRG1 proteins. ND = not determined. See Supporting Information for discussion of experimental details and error associated with each assay. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[222,411,775,797]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 7. BRG1/BRM degradation potencies $\\\\left(\\\\mathrm{DC}_{50}\\\\right.$ values) and Calu6/H1944 antiproliferation selectivity ratios of compounds described in Table 2. BRM and BRG1 degradation activity was measured in SW1573 cells (time point $= 22\\\\mathrm{h}$ ). Extent of BRM and BRG1 degradation $\\\\left(D_{\\\\max}\\\\right) > 85\\\\%$ for all compounds (see Table 2 legend for one exception). The Calu6/H1944 $\\\\mathrm{GI}_{50}$ ratio is a unitless parameter. \"]","image_footnote":"[]","img_path":"images/0807/bc967128dad3f3ca2d8a21a2f64632090012f57ee9cce812d8810a4f57690f94.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[79,855,481,882]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ities of the Table 3 compounds is provided below (cf., Figure 7). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,883,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The BRM and BRG1 degradation $\\mathrm{DC}_{50}$ values for the compounds shown in Table 2 are graphically depicted in Figure 7 along with the associated ratios of Calu6 and H1944 antiproliferation potencies. As described in the Table 2 legend, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,855,917,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"nearly all of the molecules afforded extensive BRM and BRG1 degradation outcomes ( $D_{\\mathrm{max}}$ values $>85\\%$ ; see Table S4 for exact values). As can be seen in this illustration, the compounds clustered within a relatively narrow range of BRG1/BRM degradation selectivity (10 to 100-fold) and BRM degradation potency ( $\\mathrm{DC}_{50} = 0.03$ to $0.55 \\mathrm{nM}$ ). Compounds ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,61]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1268 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,72,482,457]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"which resided at the extremes of these ranges were likely differentiated from each other, but those closer to the range medians were not easily distinguished on account of experimental error (even with the multireplicate testing that was typically employed in their characterizations; see Supporting Information for additional discussion). A partial correlation was observed between BRG1/BRM degradation and Calu6/H1944 selectivity ratios (Figure 7, higher on $y$ -axis = more likely to be green versus yellow). However, the relationship was not absolute, and several exceptions were noted in the Figure 7 depiction (e.g., compounds 14, 15, and 18). We do not currently understand the scientific reasons which underlie these selectivity ratio variations. However, they may involve different BRM, BRG1, and/or VHL protein expression levels in the Calu6 and/or H1944 cells employed in the antiproliferation assessments relative to those present in the SW1573 line used for the degradation assay. The time points associated with the two types of biological profilings were also dramatically different: $22\\mathrm{h}$ for the degradation assessments and 7 days for the antiproliferation readouts. In addition, the BRG1/BRM half-lives likely did not influence the described outcomes as they were shown by others to be similar across a range of different cell lines.[50] Given these uncertainties, we advanced compounds which exhibited either promising BRG1/BRM degradation or Calu6/H1944 antiproliferation selectivity (sometimes both) into in vivo PK/PD experiments to better define the in vitro to in vivo translation of these parameters. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,458,482,761]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As is now relatively common in PROTAC-related research, we employed surface plasmon resonance (SPR) biophysical methods to characterize the ternary complexes formed between representative chimeric degraders from Table 2 and the VHL and BRM/BRG1 proteins. Encouragingly, these assessments could readily detect the association of the expected three-component entities when representative examples of the PROTACs under study were tested using the bromodomain fragments of either the BRM or BRG1 proteins (Table 3). However, in contrast to prior literature reports involving BRD4-targeting PROTACs,[51,52] the stabilities of these ternary complexes did not correlate strongly with the corresponding PROTAC degradation activities. As a result, the BRG1/BRM selectivity ratios determined by the ability of the tested PROTACs to form stable (long-lived) ternary complexes with the two proteins did not match well with the BRG1/BRM degradation selectivities measured in the SW1573 cell-based assessments (Table 3). Expanding the SPR-based biophysical half-life characterizations to include full-length BRM and BRG1 proteins did not improve these correlations, although only a relatively small number of PROTACs was assessed via these methods (Table 3, Figures S6 and S7). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,762,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In an alternative approach to characterizing ternary complex formation, we examined the affinities of selected PROTAC molecules for the VHL protein by SPR alone and following precomplexation with BRM or BRG1. Similar to the half-life determinations described above, both BRM/BRG1 bromodomain fragments and full-length proteins were employed in these assessments. In general, these experiments revealed similar or weaker (negative cooperativity) VHL affinities for the bromodomain-PROTAC complexes relative to those determined for the isolated degraders (Table S2). In contrast, stronger (positive cooperativity) VHL binding was generally observed for the same compounds when the assessments were performed using the full-length BRM/BRG1 proteins (Table ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,306]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S2). Similar positive cooperativity behavior was noted by others during the biological profiling of the related BRM/BRG1 degrader 6.30 Unfortunately, the ratios of VHL affinities determined for the BRG1 and BRM PROTAC complexes in these studies did not correlate well with the measured BRG1/BRM degradation selectivities for the isolated compounds determined in SW1573 cells (Table S2). This lack of correlation, as well as the related outcomes in the half-life experiments described above, may be due to an incorrect representation of the BRM/BRG1 proteins in the biophysical assessments relative to the intracellular environment. In particular, it is currently unknown which (if any) BAF complex members are associated with BRM and/or BRG1 when the proteins are engaged intracellularly by the described PROTAC molecules. An alternate possibility involves significantly different ubiquitin transfer rates being associated with the various ternary complexes once they are formed. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,307,915,665]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We also obtained crystal structures of the ternary complexes formed between the chimeric degraders under study and the VHL and BRM or BRG1 proteins. These experiments were conducted using the BRM/BRG1 bromodomain fragments, and both proteins were separately assessed in crystallization studies to increase the likelihood of obtaining crystals and determining structures. These activities successfully afforded multiple structures of various PROTACs bound to both VHL and either BRM or BRG1 from purified ternary complexes. However, few contacts between the proteins were observed in these structures, possibly due to the transient nature of any such interactions that could be disrupted during crystal formation. Figure S8 depicts the solved ternary complex structure formed between VHL, compound 17, and BRG1 and is a good representation of the other examples that were obtained. The described difficulty in obtaining ternary structures which illuminate close contacts between VHL and BRM or BRG1 may be due to the nature of the PROTACs we employed in the experiments (i.e., the compounds contain long and rather rigid linkers). Others have described ternary complexes formed between BRM, VHL, and PROTACs related to compounds 6 and 7 in which the two proteins do closely associate.[30,31] The alternate attachment location of the PROTAC linker to the VHL-binding fragment in compounds 6 and 7 relative to the molecules described in this work may have contributed to the disparate structural outcomes. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,665,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We next progressed promising PROTACs into single-administration in vivo PK/PD experiments in xenograft bearing mice so as to better understand (1) the drivers of in vivo BRM degradation and BRG1 selectivity and (2) the relationships between the various in vitro and in vivo biological parameters under study. We began this phase of our endeavors by employing intraperitoneal (IP) dosing to deliver the assessed compounds. We selected a diverse panel of molecules for such testing that were purposefully chosen to span a range of BRM degradation potencies, BRG1/BRM degradation selectivities, H1944 antiproliferation potencies, Calu6/H1944 antiproliferation selectivities, and stabilities toward mouse liver microsomes. In addition, Calu6 tumors (BRG1 wild-type) were utilized for these initial PK/PD experiments. Although these cancers were not dependent on BRM activity for growth, their use enabled intratumor degradation measurements of both the BRM and BRG1 proteins and thereby facilitated assessment of in vivo BRG1/BRM degradation selectivity outcomes. In contrast, a functional version of the BRG1 protein would presumably be absent in a BRM-dependent xenograft model ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[532,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[484,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1269 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[227,73,769,448]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 8. In vivo BRM and BRG1 degradation observed for selected PROTACs in Calu6 tumors following single IP administration (dose = 10 mg/kg). BRM and BRG1 degradation was measured in Calu6 tumors (time point = 24 h). Compound plasma concentrations were measured at the 24 h time point; [Plasma]/BRM $\\\\mathrm{DC}_{50}$ ratios were subsequently calculated using $\\\\mathrm{DC}_{50}$ data contained in Table 2 (unitless parameter) and are uncorrected for protein binding effects. BRG1 $\\\\mathrm{DC}_{50}$ /BRM $\\\\mathrm{DC}_{50}$ ratios were calculated from the $\\\\mathrm{DC}_{50}$ data contained in Table 2 (unitless parameter). Numbers associated with symbols refer to compounds from Table 2. \"]","image_footnote":"[]","img_path":"images/0479/f519499598e97dfd6ff1a803b98d0dc1128bc17925dab0c446d7844a3e3e8450.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[80,565,914,680]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0054/dc4419c69743bfcc2205e0b8759cc479cdfd0b3cd1528d5625388ab0d181ae86.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":"<table><tr><td>Cmpd</td><td>BRM DC50 (nM)a</td><td>BRG1 DC50/BRM DC50b</td><td>BRM deg. (%)c</td><td>BRG1 deg. (%)d</td><td>[Plasma] (nM)e</td><td>[Plasma]/BRM DC50f</td></tr><tr><td>15</td><td>0.055</td><td>13</td><td>64 ± 14</td><td>14 ± 11</td><td>22 ± 2.1</td><td>400</td></tr><tr><td>16</td><td>0.11</td><td>25</td><td>46 ± 5.5</td><td>0 ± 11</td><td>ND</td><td>NA</td></tr><tr><td>17</td><td>0.093</td><td>53</td><td>83 ± 9.8</td><td>27 ± 23</td><td>26 ± 6.5</td><td>280</td></tr><tr><td>18</td><td>0.085</td><td>38</td><td>81 ± 15</td><td>ND</td><td>108 ± 10</td><td>1270</td></tr><tr><td>19</td><td>0.039</td><td>28</td><td>87 ± 8</td><td>0 ± 17</td><td>71 ± 14</td><td>1820</td></tr><tr><td>21</td><td>0.14</td><td>13</td><td>67 ± 23</td><td>30 ± 28</td><td>112 ± 31</td><td>800</td></tr><tr><td>24</td><td>0.27</td><td>19</td><td>95 ± 2.5</td><td>49 ± 13</td><td>129 ± 65</td><td>478</td></tr></table>","table_caption":"[\"Table 4. In Vivo BRM and BRG1 Degradation Observed for Selected PROTACs in Calu6 Tumors Following Single IP Administration (Dose = 10 mg/kg) \"]","table_footnote":"[\"${}^{a}$ BRM degradation measured in SW1573 cells (Table 2). ${}^{b}$ Ratio of BRG1 and BRM degradation ${\\\\mathrm{{DC}}}_{50}$ values measured in SW1573 cells and calculated from data contained in Table 2. ${}^{c}$ BRM degradation measured in Calu6 tumors (time point $= {24}\\\\mathrm{\\\\;h}$ ). ${}^{d}$ BRG1 degradation measured in Calu6 tumors (time point $= {24}\\\\mathrm{\\\\;h}$ ). ${}^{e}$ Compound plasma concentration measured at the ${24}\\\\mathrm{\\\\;h}$ time point. ${}^{f}$ [Plasma]/BRM ${\\\\mathrm{{DC}}}_{50}$ ratio calculated using BRM ${\\\\mathrm{{DC}}}_{50}$ data (unitless parameter). ND = not determined. NA = not applicable. Reported error = standard deviation. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[79,745,479,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(see below for alternate BRG1 quantitation methods that were employed in such situations). To simplify comparisons among the tested compounds, all PROTACs were administered in solution at a fixed dose of $10\\mathrm{mg / kg}$ using a formulation composed of $10\\%$ EtOH, $10\\%$ DMSO, $20\\%$ Solutol/Kolliphor HS15 in $60\\%$ $10\\mathrm{mM}$ , $\\mathrm{pH}5$ , citrate buffer. BRM and BRG1 protein levels were subsequently quantitated in the tumors 24 h following the administration of each test molecule, and compound plasma concentrations in the mice were also measured at the same time point. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,885,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The collective PK/PD data obtained from the above experiments are depicted in Figure 8 and Table 4. As evident in the tabulated results and somewhat anticipated given the in vivo nature of the studies, considerable variability was observed ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,745,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"in the quantitation of both BRM and BRG1 protein levels during these assessments. Based on these observations, we defined a $>30\\%$ reduction in measured protein levels as significant enough to impact conclusions regarding the performance of a given molecule, and this cutoff is depicted for BRG1 degradation in Figure 8 as a dotted blue line. In addition, we were aware of literature reports suggesting that near-complete BRM degradation might be required to obtain favorable outcomes in our planned antitumor efficacy experiments.[53] We therefore sought to identify compounds which afforded $>80\\%$ BRM degradation in these screening studies (vertical pink line in Figure 8) with the expectation that such protein suppression could be maintained long-term via once-daily administrations if needed. Since we wanted to progress ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[532,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1270 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[140,71,472,265]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0394/45744e5f78e5c79183302badb2910d05be77f40818622784a0d4ec23c3452405.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[518,71,859,266]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 9. In vivo efficacy study employing compound 17 in the HCC2302 BRM-dependent xenograft model. A = tumor volumes; B = body weight changes. Compound 17 was administered once daily via IP injection on days 0 through 11. See Figure S11 for significance analysis. \"]","image_footnote":"[]","img_path":"images/0757/bbe3710ecff19c098ecfe51dc73018f662066575f0827f48b006e05734e38d7d.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[294,335,700,458]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0993/13810b9e96d60dee7a6a3483c5d5edaa4e32e06a7481e0e961704000e32a303b.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[192,462,803,608]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0239/a5e17999b40d602cce296e45b3d2f8fbfe518d5ab6f4f6131e380063918c04c7.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":"<table><tr><td>Cmpd</td><td>Linker</td><td>R1</td><td>R2</td><td>BRM Kd (nM)a</td><td>BRG1 Kd (nM)b</td><td>VHL Kd (nM)c</td><td>BRM DC50 (nM)d</td><td>BRG1 DC50 (nM)e</td><td>H1944 GI50 (nM)f</td></tr><tr><td>17</td><td>O=O, O=OCH2N=O-</td><td>OH</td><td>(R)-OH</td><td>72</td><td>108</td><td>3.4</td><td>0.093</td><td>4.9</td><td>0.64</td></tr><tr><td>25</td><td>same as above</td><td>OH</td><td>(S)-OH</td><td>ND</td><td>ND</td><td>~4700</td><td>>30</td><td>>300</td><td>>300</td></tr><tr><td>26</td><td>same as above</td><td>H</td><td>(R)-OH</td><td>10280</td><td>12620</td><td>ND</td><td>>5000</td><td>>5000</td><td>>5000</td></tr><tr><td>19</td><td>O=O, O=OCH2N=O</td><td>OH</td><td>(R)-OH</td><td>93</td><td>65</td><td>350</td><td>0.039</td><td>1.1</td><td>0.58</td></tr><tr><td>27</td><td>same as above</td><td>OH</td><td>(S)-OH</td><td>ND</td><td>ND</td><td>~4000</td><td>>30</td><td>>300</td><td>>300</td></tr><tr><td>28</td><td>same as above</td><td>H</td><td>(R)-OH</td><td>8540</td><td>5220</td><td>ND</td><td>>5000</td><td>>5000</td><td>>5000</td></tr></table>","table_caption":"[\"Table 5. Inactive Control PROTACs Employed in Mouse Tolerability Assessments \"]","table_footnote":"[\"${}^{a}$ BRM binding affinity (bromodomain protein fragment). ${}^{b}$ BRG1 binding affinity (bromodomain protein fragment). ${}^{c}$ VHL binding affinity. ${}^{d}$ BRM degradation potency (SW1573 cells, time point = 22 h). ${}^{e}$ BRG1 degradation potency (SW1573 cells, time point = 22 h). ${}^{f}$ H1944 antiproliferation activity (BRM-dependent cell line, time point = 7 days). ND = not determined. See Supporting Information for discussion of error associated with each assay. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[77,681,481,797]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"molecules with relatively high in vivo BRG1/BRM degradation selectivities into multiadministration efficacy studies, we targeted a $< 40\\%$ BRG1 degradation outcome in the PK/PD assessment as an additional PROTAC attribute required for such advancement (horizontal pink line in Figure 8). Importantly, all compounds were well-tolerated in these single-administration experiments with minimal impacts observed on animal body-weights and general health. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,797,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As can be seen in the summarized information, several tested PROTACs exhibited meaningful BRM degradation in the Calu6 tumors with several exceeding our $>80\\%$ threshold (17, 18, 19, and 24). The majority of these molecules also afforded the desired $<40\\%$ BRG1 degradation levels (24 was the exception). Somewhat surprisingly, the extent of BRM degradation observed in the tumors did not correlate well with $24\\mathrm{h}$ compound plasma exposures that were normalized using the corresponding in vitro BRM degradation $\\mathrm{DC}_{50}$ values (Table 4; Figure 8, two yellow symbols afforded $>80\\%$ BRM ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,681,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"degradation). The [plasma]/BRM $\\mathrm{DC}_{50}$ ratios were not adjusted for compound interactions with mouse plasma proteins, but the similar binding behavior for all tested PROTACs suggested that such inclusion would not significantly alter the lack of correlation (cf., Table 2). We do not currently understand why stronger relationships were not observed between the normalized plasma exposures of the tested molecules and their in vivo BRM degradation outcomes. It was possible that the BRM degradation potencies varied somewhat between the SW1573 cell lines used for the in vitro assessments and the in vivo Calu6 tumor models and thereby skewed the analyses. Alternatively, measuring compound levels in the tumors as opposed to plasma might have afforded stronger correlations (see discussion of the IV-based PK/PD studies below for implementation of this approach). Reassuringly, however, the in vitro BRG1/BRM degradation selectivities measured in the SW1573 cells translated relatively well to the in vivo setting. Accordingly, the compounds that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1271 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[181,72,813,388]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 10. In vitro proteomics profiling of compound 17 in SW1573 cells. Each axis depicts the change in expression of a given protein in response to treatment with $100\\\\mathrm{nM}$ compound 17 relative to DMSO control (two independent replicates). Time point $= 8\\\\mathrm{h}$ . Negative values depict protein reductions, and outcomes which exceed $\\\\pm 1$ log2 fold-change are considered outside the error of the experiment. \"]","image_footnote":"[]","img_path":"images/0045/7a781240de51178983d3b3de2790120b05e17b7ce75e09948007328acd8d20ec.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,446,481,658]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"exhibited $>80\\%$ BRM degradation and $<40\\%$ BRG1 reductions in the Calu6 assessments also displayed relatively high in vitro BRG1/BRM ratios ( $>28$ , larger symbols in Figure 8, compounds 17 and 19; BRG1 degradation in Calu6 tumors was not measured for 18). Based on the collective PK/PD data, we selected compounds 17 and 19 to advance into multiadministration antitumor efficacy studies employing IP delivery. Both molecules afforded strong in vivo BRM degradation outcomes, and the former PROTAC exhibited one of the highest in vitro BRG1/BRM degradation ratios of the tested entities. In contrast, compound 19 displayed the highest [plasma]/BRM $\\mathrm{DC}_{50}$ ratio of the molecules depicted in Table 4. We were therefore curious to learn how these compounds with somewhat differing biological profiles would perform in multiadministration efficacy studies. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,660,481,898]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the subsequent experiments, compound 17 was administered via IP injection to mice bearing BRM-dependent (BRG1 mutant) HCC2302 xenografts once-daily at both 10 and $30\\mathrm{mg / kg}$ using a solution-based formulation. As shown in Figure 9A, both administration regimens afforded a minor impact on tumor growth relative to vehicle control over 11 days of continuous dosing (no dose-response was detected). Unfortunately, as shown in Figure 9B, extensive body weight loss was observed in the mice in response to these treatments. Such trends were partially reversed by additional feeding initiated on day 9 of the experiment, but all test animals ultimately died or were euthanized by day 13 due to their poor overall health. In addition, a separate pharmacokinetic assessment performed with compound 17 in nonxenograft-bearing mice afforded a relatively flat plasma exposure profile following IP dosing at $10\\mathrm{mg / kg}$ with minimal animal-to-animal variability (Figure S10). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,898,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In an effort to better understand the poor tolerability displayed by the relatively selective compound 17, we prepared the control molecules 25 and 26 (Table 5). The former entity ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,446,915,728]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"inverted the stereochemistry of the hydroxyl group present in the VHL-binding portion of 17 and thereby lost significant affinity for the VHL protein and corresponding BRM degradation properties (compare 25 with 17, Table 5). Compound 26 lacked the phenol moiety present in the BRM-binding portion of 17 and thus exhibited dramatically worsened BRM-binding and degradation characteristics relative to the latter molecule (compare 26 with 17, Table 5). Both 25 and 26 were well tolerated in mice bearing HCC2302 xenografts when administered once-daily via IP injections at $10\\mathrm{mg / kg}$ using the same solution-based formulation previously employed for 17. In each of these experiments, only $1 / 6$ mice exhibited $>10\\%$ body-weight loss during 15 days of continuous dosing, and all animals survived to day 15 (results similar to vehicle control; data not shown). Compound 17 was included in this follow-on experiment for side-by-side comparison purposes and again exhibited poor tolerability when administered IP once-daily at $10\\mathrm{mg / kg}$ (6/6 mice euthanized by day 15 due to poor condition; data not shown). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,730,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Collectively, these results indicated that the poor tolerability exhibited by compound 17 did not result from the molecule's physicochemical properties or from nondegradation-related off-target biological activities. To probe the degradation selectivity of the PROTAC, we performed in vitro proteomics experiments in SW1573 cells using a fixed compound concentration of $100\\mathrm{nM}$ and an $8\\mathrm{h}$ time point. As shown in Figure 10, these studies determined that 17 was a relatively selective degrader across the broad cellular proteome but that the molecule significantly impacted a few proteins in addition to BRM and BRG1 [e.g., PALS1, B4E2N5, PATJ, and smaller effects on MAPKAPK3, PLAU, and PBRM1; PLAU is known to be modulated by BRM (see below), and PBRM1 contains a bromodomain with high homology to that present in BRM/BRG1]. It was not obvious that reductions in these proteins ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[532,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1272 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,105,915,235]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0044/6641f4d4c6cbb6859a190ab6697bdaf247bf4ea37796250e0ab9658b2f4d9f61.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":"<table><tr><td>Cmpd</td><td>BRM DC50 (nM)a</td><td>BRG1 DC50/BRM DC50b</td><td>BRM deg. (%)c</td><td>BRG1 deg. (%)d</td><td>[Tumor] (ng/g)e</td><td>[Tumor]/BRM DC50f</td></tr><tr><td>15</td><td>0.055</td><td>13</td><td>0 ± 8</td><td>0 ± 16</td><td>76 ± 23</td><td>1380</td></tr><tr><td>17g</td><td>0.093</td><td>53</td><td>64 ± 10</td><td>4 ± 12</td><td>158 ± 33</td><td>1700</td></tr><tr><td>18</td><td>0.085</td><td>38</td><td>56 ± 23</td><td>28 ± 16</td><td>840 ± 1250</td><td>9880</td></tr><tr><td>19h</td><td>0.039</td><td>28</td><td>82 ± 3</td><td>22 ± 5</td><td>483 ± 175</td><td>12,380</td></tr><tr><td>20</td><td>0.062</td><td>23</td><td>95 ± 1.5</td><td>83 ± 12</td><td>ND</td><td>NA</td></tr><tr><td>21</td><td>0.14</td><td>13</td><td>70 ± 33</td><td>22 ± 28</td><td>175 ± 167</td><td>1250</td></tr><tr><td>22</td><td>0.09</td><td>14</td><td>87 ± 13</td><td>53 ± 14</td><td>75 ± 47</td><td>833</td></tr><tr><td>23</td><td>0.053</td><td>19</td><td>83 ± 5</td><td>59 ± 5</td><td>774 ± 400</td><td>14,600</td></tr></table>","table_caption":"[\"Table 6. In Vivo BRM and BRG1 Degradation Observed for Selected PROTACs in HCC2302 Tumors Following Single IV Administration (Dose = 20 mg/kg) \"]","table_footnote":"[\"${}^{a}$ BRM degradation measured in SW1573 cells (Table 2). ${}^{b}$ Ratio of BRG1 and BRM degradation ${\\\\mathrm{{DC}}}_{50}$ values measured in SW1573 cells and calculated from data contained in Table 2. ${}^{c}$ BRM degradation measured in HCC2302 tumors (time point = 96 h). ${}^{d}$ BRG1 degradation measured in mouse stroma cells (time point = 96 h). ${}^{e}$ Compound tumor concentration measured at the ${96}\\\\mathrm{\\\\;h}$ time point. ${}^{f}$ [Tumor]/BRM ${\\\\mathrm{{DC}}}_{50}$ ratio calculated using BRM ${\\\\mathrm{{DC}}}_{50}$ data (units $= \\\\mathrm{{ng}}/\\\\mathrm{g}/\\\\mathrm{{nM}}$ ). ${}^{g}$ Dose $= {40}\\\\mathrm{{mg}}/\\\\mathrm{{kg}}$ . ${}^{h}$ Dose $= {10}\\\\mathrm{{mg}}/\\\\mathrm{{kg}}$ . ND $=$ not determined. NA $=$ not applicable. Reported error $=$ standard deviation. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[212,312,779,698]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 11. In vivo BRM degradation observed in HCC2302 tumors for selected PROTACs following single IV administration (dose = 20 mg/kg). BRM degradation was measured in HCC2302 tumors (time point = 96 h). BRG1 degradation was measured in mouse stromal cells (time point = 96 h). Compound tumor concentrations were measured at the 96 h time point; [Tumor]/BRM $\\\\mathrm{DC}_{50}$ ratios were subsequently calculated using $\\\\mathrm{DC}_{50}$ data contained in Table 2 (units = ng/g/nM) and are uncorrected for protein binding effects. BRG1 $\\\\mathrm{DC}_{50}$ /BRM $\\\\mathrm{DC}_{50}$ ratios were calculated from the $\\\\mathrm{DC}_{50}$ data contained in Table 2 (unitless parameter). Numbers associated with symbols refer to compounds from Table 2. \"]","image_footnote":"[]","img_path":"images/0024/5a1a815f6c0592d5dbd95005195dbc236ef109cd20477831522e167195717f50.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,785,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"would result in the poor short-term mouse tolerability outcomes, but we also cannot exclude such possibilities. Based on these observations, the most plausible explanation for the undesired compound 17 tolerability profile was that the IP administration route afforded high concentrations of the molecule in the intraperitoneal cavities and/or gastrointestinal tracts of the animals that produced robust degradation of both the BRM and BRG1 proteins. This hypothesis was consistent with literature reports indicating that BRG1 is required to maintain the intestinal epithelium in mice.[15,16] Our data also aligned with disclosures by others involving nonselective ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,785,915,827]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"BRM/BRG1 ATPase inhibitors which were similarly associated with mouse tolerability issues during oral dose-escalation in vivo studies (cf., compound 1, Figure 1).<sup>9,17</sup> ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,827,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To bolster our understanding, we also performed HCC2302 xenograft efficacy experiments with compound 19 employing once-daily IP administrations of $10\\mathrm{mg / kg}$ and a solution formulation ( $10\\%$ EtOH, $10\\%$ DMSO, $20\\%$ Solutol/Kolliphor HS15 in $60\\%$ $10~\\mathrm{mM}$ $\\mathsf{pH}5,$ citrate buffer). Once again, significant mouse body weight losses were noted in these studies along with deteriorations in the overall health of the animals. As a result, all animals (6/6 mice) either died or were ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[532,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1273 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,71,481,223]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"euthanized by day 7 of the experiment with minimal impact observed on the rate of HCC2302 tumor growth (data not shown). At this juncture, we did not believe that other apparently selective degraders from Table 4 and/or Figure 8 were likely to afford improved outcomes in IP-based, multiadministration xenograft efficacy. We therefore shifted our focus to delivering promising PROTACs via IV administration, which would avoid high compound concentrations in the intraperitoneal cavity, in an effort to achieve in vivo exposures sufficient to drive antitumor activity without triggering unwanted tolerability issues. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,225,479,610]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As was done for the IP-administered studies described above, we again selected a diverse panel of BRM degrader PROTACs for testing in IV-based PK/PD experiments. Since our animal welfare protocols dictated that a maximum of two IV injections could be administered to a given mouse during a one-week period, we primarily chose compounds that exhibited low in vivo mouse clearance values and/or long half-lives in earlier in vivo DMPK profiling (cf., Table 2). In addition, we conducted the IV-administered PK/PD assessments in BRM-dependent HCC2302 xenografted tumors to better align with subsequent efficacy experiments anticipated for the most promising compounds in that model. Since a functional version of the BRG1 protein was not present in the HCC2302 xenografts, we quantitated this entity in the murine stroma cells that were harvested alongside the tumors in this phase of our studies. Given the maximal twice-weekly IV-dosing frequency that could be employed in multiadministration efficacy studies, we measured BRM and BRG1 protein levels $96\\mathrm{h}$ after each compound was dosed in the PK/PD experiments. To facilitate comparisons among the different tested PROTACs, all molecules were administered using a solution formulation (10% 2-hydroxypropyl-beta-cyclodextrin, $40~\\mathrm{mM}$ sodium acetate, $40~\\mathrm{mMNaCl}$ in $\\mathsf{pH}4.5$ water) with the majority dosed at $20\\mathrm{mg / kg}$ (a few exceptions are noted below). As the $96\\mathrm{h}$ mouse plasma concentrations of the assessed molecules were anticipated to be very low, we instead quantitated the amounts of each compound present in the HCC2302 tumors at this time point. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,610,479,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The collective data from this round of PK/PD studies are depicted in Table 6 and Figure 11. As can be seen in the plotted results, several tested PROTACs afforded strong $(>80\\%)$ BRM degradation in the HCC2302 tumors $96\\mathrm{h}$ after their initial IV administrations. The extent of BRM degradation observed in these studies correlated reasonably well with the amount of test compound detected in the tumors at the $96\\mathrm{h}$ time point normalized by in vitro BRM degradation potency (color coding in Figure 11, green symbols afford stronger in vivo BRM degradation relative to other colors; compound 22 was an exception). In addition, the BRG1/BRM degradation selectivity measured in the SW1573 cell based assessments also correlated relatively well with in vivo selectivity (larger symbols typically lower on y-axis in Figure 11). As was the case with the single-administration IP-based PK/PD experiments described above, all compounds tested in this phase of our research were well-tolerated with minimal impacts observed on animal body-weights and general health. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,860,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Since compound 19 was the only example among the molecules depicted in Figure 11 that met our desired in vivo BRM and BRG1 degradation criteria, it was selected for profiling in multiadministration efficacy studies. Accordingly, the degrader was administered twice-per-week (on days 4 and 7) to mice bearing HCC2302 BRM-dependent xenografts via ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,142]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IV injection at $20\\mathrm{mg / kg}$ using the same solution formulation employed for the IV-based PK/PD studies described above. During the majority of the assessment period, this regimen afforded significant tumor growth inhibition with generally acceptable mouse body weight loss (Figures 12 and S13). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[520,155,911,400]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 12. In vivo efficacy study employing compound 19 in the HCC2302 BRM-dependent xenograft model. Compound 19 was administered twice-per-week via IV injection on days 0 through 21. See Figure S12 for significance analysis. \"]","image_footnote":"[]","img_path":"images/0839/eaddf29feadd7850059a8e79ef659fbe803f552d96712c87a15838f46a64514b.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[512,473,915,857]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, weight loss reached concerning levels on day 18, and nutritional supplementation was therefore initiated. In spite of these interventions, $2/10$ mice involved in the study were found dead on day 21, and the experiment was concluded on day 22 due to the deteriorating condition of the remaining animals. The control compounds 27 and 28 (Table 5) which respectively attenuated VHL and BRM binding affinity relative to 19 and thereby lost significant BRM degradation potency were also examined in mice bearing HCC2302 xenografts (the origin of the relatively weak VHL affinity displayed by 19 compared to PROTAC 17 is not currently understood). Twice-weekly IV administration of both compounds at $20\\mathrm{mg}/$ kg over a 21 day period using the same formulation employed for 19 was well-tolerated with $0/6$ mice associated with each molecule exhibiting $>10\\%$ body weight loss (results similar to vehicle; data not shown). These outcomes collectively suggested that, despite the favorable in vivo BRG1/BRM selectivity displayed by 19 in the IV-based single-administration PK/PD studies above, concentrations of the compound likely reached sufficient levels in certain (sensitive) mouse tissues which degraded both proteins during the latter phase of the repeat-administration efficacy experiments. Importantly, broad-spectrum proteomics studies performed with 19 in SW1573 cells indicated that the compound was a highly selective degrader which only impacted BRM, BRG1, and PBRM1.42 These data supported our hypothesis that loss of both BRM and BRG1 contributed to the mouse tolerability issues observed with the molecule. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,858,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The preceding data highlighted a key challenge associated with the compounds described in this work which exhibited relatively high but finite in vitro BRG1/BRM degradation selectivity ratios. Such molecules needed to achieve in vivo exposures in multiadministration antitumor studies sufficient to produce strong BRM degradation outcomes and the desired ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[532,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1274 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[174,72,823,330]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 13. In vivo CD1 mouse PK profiles for compound 19 following IV administration at 10 and $30\\\\mathrm{mg / kg}$ $(n = 3)$ . \"]","image_footnote":"[]","img_path":"images/0844/333ac16a92a62306938b2359fda13223d0f8225bb169c48960e4551bd96bd157.jpg","list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[80,398,915,445]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0898/d37c4303bd17586ad4dc938ec026c12bdecc35fa2e97344666fbdc240ae799f5.jpg","list_items":null,"page_idx":"13","sub_type":null,"table_body":"<table><tr><td>Dose (mg/kg)</td><td>Cl (mL/min/kg)a</td><td>Vss (L/kg)b</td><td>t1/2 (h)c</td><td>C0 (ng/mL)d</td><td>AUClast (h ng/mL)e</td></tr><tr><td>10</td><td>16 ± 4.0</td><td>6.3 ± 0.39</td><td>6.6 ± 1.1</td><td>12,630 ± 1700</td><td>10,160 ± 2600</td></tr><tr><td>30</td><td>15 ± 3.1</td><td>8.7 ± 2.0</td><td>8.9 ± 1.2</td><td>58,000 ± 28,400</td><td>30,850 ± 8650</td></tr></table>","table_caption":"[\"Table 7. In Vivo PK Parameters Obtained for Compound 19 Following IV Administration to CD1 Mice at 10 and ${30}\\\\mathrm{{mg}}/\\\\mathrm{{kg}}\\\\left( {n = 3}\\\\right)$ \"]","table_footnote":"[\"${}^{a}$ In vivo clearance value. ${}^{b}$ In vivo volume of distribution. ${}^{c}$ In vivo half-life. ${}^{d}$ Initial in vivo plasma concentration. ${}^{e}$ In vivo exposure measured over ${24}\\\\mathrm{\\\\;h}$ time period. Formulation $= {10}\\\\%$ HP-beta-CD, ${40}\\\\mathrm{{mM}}\\\\mathrm{{NaOAc}}$ ,and ${40}\\\\mathrm{{mM}}\\\\mathrm{{NaCl}}$ in water pH 4.0. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[80,520,914,578]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0653/4d2abd1bbaf92ee4007b11f32136d44c0a2b9b59ae095187e64e6b88596cad6b.jpg","list_items":null,"page_idx":"13","sub_type":null,"table_body":"<table><tr><td>Dose (mg/kg)a</td><td>#admin.b</td><td>Time point (h)c</td><td>BRM deg. (%)d</td><td>BRG1 deg. (%)e</td><td>PLAU supp. (%)f</td><td>KTR80 supp. (%)g</td><td>Approx. TGI (%)h</td></tr><tr><td>10</td><td>7</td><td>24</td><td>81 ± 8</td><td>30 ± 20</td><td>91 ± 22</td><td>25 ± 27</td><td>1</td></tr><tr><td>20</td><td>7</td><td>24</td><td>99 ± 2</td><td>47 ± 16</td><td>98 ± 19</td><td>71 ± 27</td><td>62</td></tr><tr><td>30</td><td>3</td><td>96</td><td>97 ± 2</td><td>84 ± 6</td><td>97 ± 22</td><td>72 ± 25</td><td>(strong)i</td></tr></table>","table_caption":"[\"Table 8. Pharmacodynamic Effects Observed in HCC2302 Xenografts at the Conclusion of Efficacy Experiments Involving Compound 19 \"]","table_footnote":"[\"${}^{a}$ Dose of 19 administered twice-weekly via IV injection. ${}^{b}$ Number of administrations prior to obtaining PD readouts. ${}^{c}$ Time after last compound administration before obtaining PD readouts. ${}^{d}$ BRM degradation measured in HCC2302 tumors. ${}^{e}$ BRG1 degradation measured in mouse stroma cells. ${}^{f}$ Suppression of PLAU mRNA transcript in HCC2302 tumors. ${}^{g}$ Suppression of KRT80 mRNA transcript in HCC2302 tumors. ${}^{h}$ Approximate tumor growth inhibition (TGI) observed at end of each study. ${}^{i}$ Tumor growth inhibition was strong (>65%) but was not quantitated due to poor tolerability. Reported error = standard deviation. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[77,656,482,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"anticancer efficacy without exceeding levels which simultaneously degraded BRG1 in sensitive animal tissues (see below for discussion regarding the amount of BRM degradation required to afford meaningful antitumor effects). Several additional efficacy studies conducted with 19 in mice bearing HCC2302 xenografts exemplified these challenges. Administering the compound twice-weekly IV at $10\\mathrm{mg / kg}$ was well-tolerated over 21 days but had no impact on tumor growth (tumors in the treatment group grew similar to vehicle control; data not shown). Similarly, increasing the IV dose of 19 to 30 $\\mathrm{mg / kg}$ twice-weekly afforded strong antitumor efficacy, but the regimen could not be sustained for more than 11 days due to poor tolerability (note: these studies were both performed before the $20\\mathrm{mg / kg}$ BIW IV experiment described above was conducted). Strikingly, the in vivo mouse PK profiles for compound 19 obtained following IV administration at 10 and $30\\mathrm{mg / kg}$ to nontumor-bearing mice illustrated that relatively small (within 3-fold) differences in $C_{\\mathrm{max}}$ and AUC values resulted in the disparate efficacy and tolerability outcomes (Figure 13, Table 7). Continued experimentation with 19 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,656,915,798]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(A947) ultimately determined that IV administration of the molecule at $40\\mathrm{mg / kg}$ once every other week provided the optimal balance between strong antitumor efficacy and acceptable tolerability (data not shown). The molecule was subsequently profiled in multiple additional in vivo biological studies employing that regimen, and these data, along with extensive in vitro characterizations of the compound (e.g., degradation potency via Western blot, degradation kinetics, and degradation mechanism of action), were recently communicated in a separate disclosure.[42] ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,800,915,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As part of the above efficacy experiments, we measured the degree of BRM and BRG1 degradation in the tumors at the end of each study period. Such assessments were typically performed $24\\mathrm{h}$ after the final dosing of the compound under study (i.e., measured on day 22 of a 21-day experiment following 7 IV administrations). An alternate time point was employed for degrader 19 dosed at $30~\\mathrm{mg / kg}$ on account of the poor tolerability that led to early study termination after only 3 injections. As shown in Table 8, strong $(>80\\%)$ BRM degradation was observed in all of these assessments. However, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1275 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,561,87]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 1. Preparation of Various Isoxazole-Containing Intermediates ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,91,774,283]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0272/83fbeb646b739d7b7dd376ebfad2f18b86aacd2ad2de2ba66c3a4cf65bac26d5.jpg","list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[314,321,719,540]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[\"${}^{a}$ Reagents and conditions $\\\\left( {\\\\mathrm{{Bn}} = {\\\\mathrm{{CH}}}_{2}\\\\mathrm{{Ph}}}\\\\right)$ : (a) ${\\\\mathrm{{KHCO}}}_{3},{10} : 1\\\\mathrm{{EtOAc}} : {\\\\mathrm{H}}_{2}\\\\mathrm{O},\\\\mathrm{{rt}},{16}\\\\mathrm{\\\\;h},{98}\\\\% ;\\\\left( \\\\mathrm{b}\\\\right) {\\\\mathrm{{CrO}}}_{3},{6.0}\\\\mathrm{M}{\\\\mathrm{H}}_{2}{\\\\mathrm{{SO}}}_{4}$ ,acetone,0to ${25}^{ \\\\circ }\\\\mathrm{C},{12}\\\\mathrm{\\\\;h},{90}\\\\%$ ; (c) con. ${\\\\mathrm{H}}_{2}{\\\\mathrm{{SO}}}_{4}$ ,MeOH, ${70}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h},{65}\\\\%$ ; (d) t-BuOK, 2-Iodopropane,THF,0to ${25}^{ \\\\circ }\\\\mathrm{C},{16}\\\\mathrm{\\\\;h},{56}\\\\%$ ; (e) KOH,MeOH,reflux,4 h,66%; (f) ${\\\\mathrm{K}}_{2}{\\\\mathrm{{CO}}}_{3}$ , Benzyl bromide,NMP, ${60}^{ \\\\circ }\\\\mathrm{C},{4.5}\\\\mathrm{\\\\;h},{46}\\\\%$ ; (g) LDA, Dimethyl carbonate, $- {78}^{ \\\\circ }\\\\mathrm{C},3\\\\mathrm{\\\\;h},{33}\\\\%$ ; (h) t-BuOK, 2-Iodopropane, 2:1 DMF:THF, ${20}^{ \\\\circ }\\\\mathrm{C}$ , ${12}\\\\mathrm{\\\\;h},{82}\\\\%$ ; (i) ${\\\\mathrm{{TiCl}}}_{4}$ ,DCM, ${25}^{ \\\\circ }\\\\mathrm{C},{13}\\\\mathrm{\\\\;h},{94}\\\\%$ ; (j) 2-Bromo-1,1-diethoxyethane, ${\\\\mathrm{K}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,DMF, ${70}^{ \\\\circ }\\\\mathrm{C},8\\\\mathrm{\\\\;h},{49}\\\\%$ ; (k) LiOH, MeOH, ${40}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h}$ . \"]","img_path":"images/0006/ff8c50cc0dbf2b23fd046c50c54597c61f5fa1c47c5a5f6b7f7762bfcdcdd8ac.jpg","list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,611,482,898]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"only experiments in which such BRM alterations exceeded $95\\%$ degradation were associated with tumor growth inhibition outcomes that meaningfully differentiated from vehicle control groups. These results were consistent with reports from others which suggested that near-complete loss of the BRM protein was required to impact the proliferation of BRM-dependent cell lines and tumors.[53] They also paralleled our own observations during the detailed in vitro and in vivo characterizations of compound 19 (A947) that were disclosed in a separate publication.[42] In addition, BRG1 protein levels in mouse stroma cells were monitored as part of the above experiments. The compound 19 dose which afforded the strongest BRG1 reductions was associated with the poorest tolerability results (Table 8, $30~\\mathrm{mg / kg}$ ). These data supported our desire to avoid strong degradation of both the BRM and BRG1 proteins so as to minimize unwanted impacts on noncancerous cells and tissues.[14-17] Given the small number of experiments, additional studies are required to fully define the relationships between BRM/BRG1 degradation and both efficacy and tolerability outcomes. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,898,482,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In addition to measuring the BRM and BRG1 protein levels, we also profiled PLAU and KRT80 mRNA transcripts in the end-of-study HCC2302 tumors to understand the impact of ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,611,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the tested compounds on BRM-related gene expression. We selected PLAU and KRT80 transcripts for this purpose as production of both entities was previously associated with BRM activity via our own research and by disclosures from others.[9,42] As shown in Table 8, both transcripts were significantly suppressed by treatment with degrader 19 with KRT80 mRNA levels providing the better means to differentiate the tested doses. Accordingly, $>70\\%$ suppression of the KRT80 transcript was required to obtain antitumor efficacy outcomes that meaningfully differed from vehicle control. Importantly, the association between alteration of a particular gene transcript and tumor growth inhibition is likely to be dependent on the specific tumor being studied, and these relationships need to be independently assessed and characterized for each individual situation. In addition, although the preceding experiments established a need to achieve strong BRM degradation $(>95\\%)$ to drive meaningful antitumor efficacy, they did not address the duration for which such alterations needed to be maintained. Additional experiments are therefore needed to better define the temporal relationships between BRM degradation and antitumor efficacy. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1276 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,72,561,87]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 2. Preparation of Various Isoazole-Containing Intermediates ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[187,90,817,276]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0459/d40c4c15558f84975c5ab0f1dd79cfba6beac1287941e3be949a94123dbba3ea.jpg","list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[177,305,799,468]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[\"${}^{a}$ Reagents and conditions ${\\\\left( \\\\mathrm{{Boc}} = \\\\mathrm{C}\\\\left( \\\\mathrm{O}\\\\right) \\\\mathrm{{OC}}{\\\\left( {\\\\mathrm{{CH}}}_{3}\\\\right) }_{3},\\\\mathrm{{Cbz}} = \\\\mathrm{C}\\\\left( \\\\mathrm{O}\\\\right) {\\\\mathrm{{OCH}}}_{2}\\\\mathrm{{Ph}}\\\\right) }$ : (a) Perfluorobutyl sulfonyl chloride, ${\\\\mathrm{K}}_{2}{\\\\mathrm{{CO}}}_{3},{\\\\mathrm{{CH}}}_{3}\\\\mathrm{{CN}},2{5}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h},{90}\\\\%$ ; (b) tert-Butyl piperazine-1-carboxylate (44),DMF, ${130}^{ \\\\circ }\\\\mathrm{C},4\\\\mathrm{\\\\;h},{35}\\\\%$ ; (c) LiOH,1:1 THF: ${\\\\mathrm{H}}_{2}\\\\mathrm{O},\\\\mathrm{{rt}},1 - 2\\\\mathrm{\\\\;h},{70} - {99}\\\\%$ ; (d) ${4.0}\\\\mathrm{M}\\\\mathrm{{HCl}},1,4$ -dioxane, ${25}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h},{84}\\\\%$ ; (e) benzyl chloroformate, TEA, DCM, ${25}^{ \\\\circ }\\\\mathrm{C},{15}\\\\mathrm{\\\\;h},{44}\\\\%$ ; (f) Trimethoxymethane, $p$ -TsOH, ${25}^{ \\\\circ }\\\\mathrm{C},{2.0}\\\\mathrm{\\\\;h},{63}\\\\%$ ; (g) Pd/C, ${\\\\mathrm{H}}_{2}$ , THF, ${25}^{ \\\\circ }\\\\mathrm{C},{12}\\\\mathrm{\\\\;h},{85}\\\\%$ ; (h) Intermediate 43, DIEA, DMF, ${80}^{ \\\\circ }\\\\mathrm{C},{12}\\\\mathrm{\\\\;h},{26}\\\\%$ . \"]","img_path":"images/0057/23fd6a075d14d7be2927dbd55db102ff53c0de8ceaac0c55afb0b790318c3041.jpg","list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,537,482,745]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The compounds described in this work were prepared by a variety of related synthetic methods. The generation of several key intermediates is detailed below, and these descriptions also highlight numerous important commercially available building blocks that are widely utilized in subsequent syntheses. These preparations are then followed by the syntheses of the specific final compounds that were profiled in the biological assays described above. Salts of amine-containing products (including final PROTAC molecules) are typically not shown in the various synthetic schemes even though they may have been generated by the synthesis and/or purification conditions employed. All reagents and starting materials were derived from commercial sources unless otherwise indicated. The BRM-binding molecules 8-10 were synthesized using preparations derived from the literature.[23] ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,746,482,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 1 depicts the preparation of several isoxazole-containing intermediates in racemic form. Hydroxycarbonimidic dibromide (29) was condensed with but-3-yn-1-ol (30) at room temperature to give isoxazole 31. Jones oxidation and subsequent esterification under acidic conditions then afforded intermediate 33 (via carboxylic acid 32). Alkylation of this compound with 2-iodopropane provided racemic ester 34, and this entity was then transformed into carboxylic acid 35 via exposure to basic methanol at elevated temperature. Separately, 5-methylisoxazol-3-ol (36) was protected as the corresponding benzyl ether (37). This material was deprotonated with lithium diisopropylamide, and the resulting anion was condensed with dimethyl carbonate to give ester 38. Alkylation of this entity with 2- ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,537,915,635]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"iodopropane then afforded racemic intermediate 39, and the benzyl moiety present in this material was subsequently removed via treatment with titanium tetrachloride to give ester 40. Alkylation of this intermediate with 2-bromo-1,1-diethoxyethane generated acetal 41, and the ester contained in this entity was subsequently hydrolyzed under basic conditions to give carboxylic acid 42. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,635,915,871]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The preparation of several additional racemic isoxazole-containing intermediates is shown in Scheme 2. Ester 40 (Scheme 1) was condensed with perfluorobutyl sulfonyl chloride to give compound 43. This entity was coupled with tert-butyl piperazine-1-carboxylate (44) to provide ester 45, and this material was subsequently hydrolyzed under basic conditions to give carboxylic acid 46. Separately, commercially available tert-butyl 4-formylpiperidine-1-carboxylate (47) was converted to the corresponding Cbz-protected analog 49 by acidic deprotection (to give intermediate 48) and subsequent condensation with benzyl chloroformate. The aldehyde moiety present in 49 was then transformed into the related dimethyl acetal 50, and the Cbz protecting group was removed via hydrogenation to provide intermediate 51. This entity was coupled with compound 43, and the ester contained in the resulting product (52) was hydrolyzed under basic conditions to give carboxylic acid 53. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,872,914,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Several VHL-binding fragments required for the preparation of final PROTAC compounds were synthesized as illustrated in Scheme 3. Commercially available (2S,4R)-4-hydroxy- $N\\cdot$ (4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide $(54)^{46,54}$ was coupled with intermediate 35 (Scheme 1), and the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1277 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,72,464,86]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 3. Preparation of Intermediates 56, 59, and $61^{a}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[151,92,848,291]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0112/0a4dd1e4bc9b5ceb0ac11da8751345f89c1dde0f582e4ea26ccaa4788956577d.jpg","list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[153,332,830,506]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[\"${}^{a}$ Reagents and conditions: (a) Intermediate 35, HATU, DIEA, DMF, rt, $1 - 2\\\\mathrm{\\\\;h},{47} - {75}\\\\%$ ; (b) ${40}\\\\%$ aq. HBr, ${60}^{ \\\\circ }\\\\mathrm{C},4 - {4.5}\\\\mathrm{\\\\;h},{55} - {98}\\\\%$ ; (c) 1,2- dibromoethane, ${\\\\mathrm{{Cs}}}_{2}{\\\\mathrm{{CO}}}_{3},{\\\\mathrm{{CH}}}_{3}\\\\mathrm{{CN}},{70}^{ \\\\circ }\\\\mathrm{C},2 - 3\\\\mathrm{\\\\;h},{38} - {58}\\\\%$ ; (d) Intermediate 42, Intermediate 57, HATU, DIEA, DMF, rt, ${0.5}\\\\mathrm{\\\\;h}$ ; (e) chiral SFC separation, ${31}\\\\%$ (over two steps); (f) 1:1 THF: ${\\\\mathrm{H}}_{2}{\\\\mathrm{{SO}}}_{4}\\\\left( {{1.0}\\\\mathrm{M}}\\\\right) ,{50}^{ \\\\circ }\\\\mathrm{C},5\\\\mathrm{\\\\;h}$ ,used crude. \"]","img_path":"images/0134/6c4abbc9f6a68ceada40e8cd9882b47fb1a56cba1a27ba6a129cb54be06ed0ed.jpg","list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,563,482,828]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"methoxy group present in the resulting product (not shown) was subsequently cleaved by exposure to aqueous HBr to give compound 55. This material was then alkylated with 1,2-dibromoethane to afford intermediate 56. A similar sequence of reactions was applied to $(2S,4R)$ -4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (57) that was prepared by acidic deprotection of the corresponding $N$ -Boc derivative (not shown)[48,55] to provide compound 59 (via intermediate 58). Separately, intermediates 42 (Scheme 1, racemic) and 57 were coupled to give the corresponding product as a $\\sim 1:1$ mixture of diastereomers. This mixture was separated using chiral SFC methods to afford acetal 60 and the related isopropyl epimer (60e, structure not shown). The separated acetals were then deprotected under acidic conditions to provide the corresponding aldehydes (61, shown in Scheme 3, and 61e). The absolute configuration of the isopropyl stereocenter contained in aldehyde 61 (and in acetal 60 by inference) was established as described below in Scheme 9. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,830,482,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The preparation of PROTAC 11 is depicted in Scheme 4. The fluorine group present in 4-bromo-2-fluoropyridine (62) was displaced with 3,6,9-trioxaundecane-1,11-diol (63) under basic conditions to give the ether coupling product (64). The alcohol contained in this intermediate was oxidized to a carboxylic acid moiety (65) by exposure to TEMPO/ $\\mathrm{PhI(OAc)}_2$ ,[56] and this entity was converted to the corresponding methyl ester (66) by treatment with thionyl chloride in ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,563,915,828]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MeOH. Xantphos-mediated coupling of 66 with tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, Scheme 1) provided the corresponding Boc-protected coupling product (68).57 Boc-deprotection was then effected under acidic conditions and the resulting amine (69) was condensed with 4-bromo-6-chloropyridazin-3-amine (70) to afford aminochloro-pyridazine 71 as the major product. This intermediate was subsequently coupled with 2-hydroxyphenylboronic acid (72) to provide 73, and the methyl ester present in this entity was then hydrolyzed under basic conditions to give carboxylic acid 74. HATU-mediated amide formation using the known VHL-binding fragment $75^{48}$ then provided PROTAC 11. Importantly, attempts to improve the convergence of the depicted route via the coupling of preassembled intermediates related to 76 with pyridyl-halides (77) resulted in the unwanted and near-exclusive derivatization of the pyridazine $\\mathrm{NH}_2$ moiety (Scheme 5, product 78) instead of the desired 3,8-diazabicyclo[3.2.1]octane amino group (Scheme 5, product 79). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,830,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 6 describes the synthesis of PROTAC 12. 4-Bromo-2-fluoropyridine (62, Scheme 4) was coupled with 3,6-dioxaoctane-1,8-diol (80) and the resulting bromine-containing intermediate (81) was transformed into alcohol 86 using a sequence of reactions that were analogous to those shown in Scheme 4 to convert ester 66 into phenol 73. In this instance, coupling of 81 with tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, Scheme 4) followed by acidic deprotection of ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1278 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,355,86]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 4. Preparation of PROTAC $11^{a}$ ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[108,92,884,335]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0931/648bfa80357e9da2bd22763d12cdb33989ef18afca246693f376d2743f7c5bf7.jpg","list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[140,368,336,421]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0694/486e44de7d664b85d5f462f06abe6a4b36a363173faf31b105a43b06db1ea759.jpg","list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[347,367,423,420]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0802/149db31eb96e4c573a15da6bbf60aac30958f1df5149ceec5d205b8fe2e2accd.jpg","list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[444,367,525,420]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0136/b3bede3ad03fcdf8ec5fe09179306c456d9e69bb16599e6c2a45a23f853b2f31.jpg","list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[548,363,619,421]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0032/6e940a11b34491bbd9273b6f08e7751e84215289d9d30277153dc3ebdfe9145b.jpg","list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[637,358,833,437]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[\"${}^{a}$ Reagents and conditions ${\\\\left( \\\\mathrm{{Boc}} = \\\\mathrm{C}\\\\left( \\\\mathrm{O}\\\\right) \\\\mathrm{{OC}}{\\\\left( {\\\\mathrm{{CH}}}_{3}\\\\right) }_{3}\\\\right) }$ : (a) 3,6,9-Trioxaundecane-1,11-diol (63),NaH,DMF,75 °C,2 h,70%; (b) TEMPO, $\\\\mathrm{{PhI}}{\\\\left( \\\\mathrm{{OAc}}\\\\right) }_{2}$ ,DCM, ${\\\\mathrm{H}}_{2}\\\\mathrm{O}$ ,rt, $2\\\\mathrm{\\\\;h},{46}\\\\% ;\\\\left( \\\\mathrm{c}\\\\right) {\\\\mathrm{{SOCl}}}_{2}$ ,MeOH,rt, $4\\\\mathrm{\\\\;h},{73}\\\\% ;\\\\left( \\\\mathrm{d}\\\\right)$ tert-Butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67),RuphosPd G2, ${\\\\mathrm{{Cs}}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,toluene, ${90}^{ \\\\circ }\\\\mathrm{C},4\\\\mathrm{\\\\;h},{85}\\\\% ;\\\\left( \\\\mathrm{e}\\\\right) 1 : 5$ TFA:DCM,rt, $2\\\\mathrm{\\\\;h},{85}\\\\% ;\\\\left( \\\\mathrm{f}\\\\right) 4$ -Bromo-6-chloropyridazin-3-amine (70),NMP,DIEA, ${120}^{ \\\\circ }\\\\mathrm{C},3\\\\mathrm{\\\\;h}$ , 50%; (g) 2-Hydroxyphenylboronic acid (72), $\\\\mathrm{{Pd}}{\\\\left( {\\\\mathrm{{PPh}}}_{3}\\\\right) }_{4},{\\\\mathrm{\\\\;K}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${90}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h},{37}\\\\% ;\\\\left( \\\\mathrm{h}\\\\right)$ LiOH,1:1 THF: ${\\\\mathrm{H}}_{2}\\\\mathrm{O}$ ,rt,1 h,94%; (i) Intermediate 75,HATU,DIEA,DMF,rt,2 h,26%. \"]","img_path":"images/0493/7ced20e36c26c3cd4f0149c638c3713120dd65b42b03022665829edd65a85684.jpg","list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[80,527,434,542]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 5. Unwanted Coupling of Pyridazine Amine ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[98,550,897,715]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0703/3e3e57acf92dfd10e2daab1935a153f6d7c5b9df95cdb41fcfe632093692cc75.jpg","list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,727,482,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the resulting product (82) and subsequent condensation of the amine thus obtained (83) with 4-bromo-6-chloropyridazin-3-amine (70, Scheme 4) afforded intermediate 84. This entity was then coupled with (2-(methoxymethoxy)phenyl)boronic acid (85) to provide alcohol 86. Conversion of this alcohol to the corresponding tosylate (87) followed by subsequent alkylation with intermediate 55 (Scheme 2) afforded the coupled product as a mixture of diastereomers (epimeric at the isopropyl center). Removal of the methoxymethoxy protecting groups under acidic conditions and separation of the resulting phenol-containing compounds by chiral HPLC then gave PROTAC 12 along with the corresponding isopropyl epimer (12e, structure not shown). The BRM-degradation activities of both molecules were subsequently assessed, and the molecule with the more potent activity (ca. 100-fold more potent than ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,727,915,770]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the other isopropyl epimer, Table S4) was assigned the absolute configuration depicted for PROTAC 12 in Figure 5 and Table 2. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,770,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The described approach of synthesizing closely related diastereomeric compound pairs, separating the two molecules using chromatographic methods (typically chiral), and testing the purified entities for biological activity was employed in the preparation of the majority of isoxazole-containing PROTACs described in this work. As illustrated in the example of compound 12, the most potent member of each PROTAC pair so evaluated was assigned the absolute isopropyl group configuration shown in Table 2 (as well as Figure 5). In most cases, the alternate diastereomer was at least 100-fold less potent than the more active member of a given compound pair (Table S4). Interestingly, it was not always possible to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1279 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[108,92,887,583]","code_body":null,"code_caption":null,"image_caption":"[\"Scheme 6. Preparation of PROTAC $12^{a}$ \"]","image_footnote":"[\"${}^{a}$ Reagents and conditions $\\\\left( {\\\\mathrm{{Ts}} = {\\\\mathrm{{SO}}}_{2}\\\\mathrm{{Ph}}\\\\left( {4 - \\\\mathrm{{Me}}}\\\\right) ,\\\\mathrm{{Boc}} = \\\\mathrm{C}\\\\left( \\\\mathrm{O}\\\\right) \\\\mathrm{{OC}}{\\\\left( {\\\\mathrm{{CH}}}_{3}\\\\right) }_{3}}\\\\right)$ : (a) 3,6-Dioxoctane-1,8-diol (80),NaH,DMF,rt,1h,69%; (b) tert- Butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67),RuphosPd G3, ${\\\\mathrm{{Cs}}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${90}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h},{97}\\\\% ;\\\\left( \\\\mathrm{c}\\\\right) {4.0}\\\\mathrm{M}\\\\mathrm{{HCl}},\\\\mathrm{{MeOH}},\\\\mathrm{{rt}},4\\\\mathrm{\\\\;h}$ ; (d) 4-Bromo-6-chloropyridazin-3-amine (70),NMP,DIEA, ${120}^{ \\\\circ }\\\\mathrm{C},8\\\\mathrm{\\\\;h},{44}\\\\%$ over 2 steps;(e)(2-(Methoxymethoxy)phenyl)boronic acid (85), Pd ${\\\\left( {\\\\mathrm{{PPh}}}_{3}\\\\right) }_{4},{\\\\mathrm{K}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${\\\\mathrm{H}}_{2}\\\\mathrm{O},{100}^{ \\\\circ }\\\\mathrm{C},4\\\\mathrm{\\\\;h},{73}\\\\% ;\\\\left( \\\\mathrm{f}\\\\right)$ TsCl,TEA,DMAP,DCM,rt,10 h,85%; (g) Intermediate 55, ${\\\\mathrm{K}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,DMF, ${60}^{ \\\\circ }\\\\mathrm{C}$ ,4 h,31%; (h)) ${4.0}\\\\mathrm{M}\\\\mathrm{{HCl}}$ ,MeOH,rt,8 h,(i) chiral HPLC separation, 26% over 2 steps. \"]","img_path":"images/0083/637d82e07a32e795eb23ca57b95846c99ba96d4c4c757fd833e894e25a14e969.jpg","list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,667,484,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"correctly assign the stereocenters using separation retention times and/or ${}^{1}\\mathrm{H}$ NMR spectra comparisons. The accuracy of such structural assignments was supported by the solved crystal structure of the ternary complex formed between PROTAC 17, BRG1, and VHL which verified the configuration of the isopropyl group (see above discussion as well as Figures S8, S9, and S14). The assignments were also consistent with the solved crystal structure of a potent VHL-binding isoxazole-containing moiety in which the isopropyl group stereochemistry corresponded to that shown in Table 2 and Figure 5 (Figures S14-S16). Importantly, the isopropyl stereocenters present in the separated single diastereomers were configurationally stable when subjected to physiological assay conditions and routine solid-state storage and handling procedures. However, they could be racemized by exposure to strongly basic conditions $(\\mathrm{pH} > 9)$ , and their configurational stability during long-term solution-based storage (e.g., DMSO) remains to be determined. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,667,917,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The preparation of PROTACs 13 and 14 is shown in Scheme 7. Commercially available benzyl 4-(2-hydroxyethyl)-piperazine-1-carboxylate (90) was coupled with 5-bromo-2-fluoropyridine (62, Scheme 4) via nucleophilic fluoride displacement to give intermediate 91. This entity was then coupled with Boc-protected 3,8-diazabicyclo[3.2.1]octane 67 (Scheme 4),[57] and the resulting product (not shown) was deprotected under acidic conditions to afford 92. This intermediate was condensed with 4-bromo-6-chloropyridazin-3-amine (70, Scheme 4) to provide 93. Subsequent coupling of 93 with (2-(methoxymethoxy)phenyl)boronic acid (85, Scheme 6) via Pd-mediated catalysis[58] followed by removal of the Cbz moiety present in the resulting product (not shown) then afforded key intermediate 94. This entity was coupled with bromide 56 (Scheme 3; ca. 1:1 mixture of diastereomers) via transient formation of the corresponding iodide. The MOM protecting groups present in coupled diastereomeric products (95) were then removed under acidic conditions, and the compounds thus obtained were separated ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1280 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[108,91,887,553]","code_body":null,"code_caption":null,"image_caption":"[\"Scheme 7. Preparation of PROTACs 13 and $14^{a}$ \"]","image_footnote":"[\"${}^{a}$ Reagents and conditions ${\\\\left( \\\\mathrm{{Boc}} = \\\\mathrm{C}\\\\left( \\\\mathrm{O}\\\\right) \\\\mathrm{{OC}}{\\\\left( {\\\\mathrm{{CH}}}_{3}\\\\right) }_{3};\\\\mathrm{{Cbz}} = \\\\mathrm{C}\\\\left( \\\\mathrm{O}\\\\right) {\\\\mathrm{{OCH}}}_{2}\\\\mathrm{{Ph}}\\\\right) :$ (a) 4-Bromo-2-fluoropyridine (62),NaH,DMF,rt,0.5 h,83%; (b) tert-Butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67),RuPhosPd G2, ${\\\\mathrm{{Cs}}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,toluene, ${90}^{ \\\\circ }\\\\mathrm{C},5\\\\mathrm{\\\\;h},{56}\\\\% ;\\\\left( \\\\mathrm{c}\\\\right)$ TFA,DCM,rt,1 h,93%; (d) 4- Bromo-6-chloropyridazin-3-amine (70),DMP,DIEA,130 °C,3 h,84%; (e) (2-(Methoxymethoxy)phenyl)boronic acid (85),Pd(dppf)- ${\\\\mathrm{{Cl}}}_{2} \\\\bullet {\\\\mathrm{{CH}}}_{2}{\\\\mathrm{{Cl}}}_{2},{\\\\mathrm{\\\\;K}}_{2}{\\\\mathrm{{CO}}}_{3},1,4$ -dioxane, ${\\\\mathrm{H}}_{2}\\\\mathrm{O},{90}^{ \\\\circ }\\\\mathrm{C},{1.5}\\\\mathrm{\\\\;h},{72}\\\\% ;\\\\left( \\\\mathrm{f}\\\\right) \\\\mathrm{{Pd}}$ on $\\\\mathrm{C},{\\\\mathrm{H}}_{2}$ ,MeOH,rt,5 h,59%; (g) Intermediate 56, ${\\\\mathrm{K}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,KI, ${\\\\mathrm{{CH}}}_{3}\\\\mathrm{{CN}},{70}^{ \\\\circ }\\\\mathrm{C}$ , ${12}\\\\mathrm{\\\\;h},{49}\\\\% ;\\\\left( \\\\mathrm{h}\\\\right)$ Intermediate 59, ${\\\\mathrm{K}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,NaI, ${\\\\mathrm{{CH}}}_{3}\\\\mathrm{{CN}},{70}^{ \\\\circ }\\\\mathrm{C},{12}\\\\mathrm{\\\\;h},{68}\\\\% ;\\\\left( \\\\mathrm{i}\\\\right) {4.0}\\\\mathrm{M}\\\\mathrm{{HCl}},\\\\mathrm{{MeOH}},\\\\mathrm{{rt}},3 - {12}\\\\mathrm{\\\\;h};\\\\left( \\\\mathrm{j}\\\\right)$ Chiral HPLC separation, ${15} - {27}\\\\%$ over 2 steps. \"]","img_path":"images/0113/645fe20ae1f8dab53d4766b43944507dfd3652253c64fdf3a8fdd2b41b9f7a7b.jpg","list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,648,481,733]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"by chiral HPLC methods and tested for biological activity. As described above, the more potent diastereomer was assigned the absolute stereochemistry shown for PROTAC 13 in Table 2 (cf., Table S4). Similar derivatization of 94 with bromide 59 (Scheme 3; ca. 1:1 mixture of diastereomers) and subsequent processing of the coupled products afforded PROTAC 14. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,732,482,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The syntheses of several additional PROTAC compounds are illustrated in Scheme 8. 4-Bromo-2-fluoropyridine (62, Scheme 4) was coupled with 2,2-diethoxyethan-1-ol under mildly basic conditions to afford intermediate 97. This entity was condensed with benzyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (98) to give compound 99, and the Cbz protecting group present in this material was subsequently removed via hydrogenation. Elaboration of the resulting amine (100) to intermediate 101 was then accomplished using sequential coupling reactions that were analogous to those employed above to convert 69 to 73 (Scheme 4). Acidic deprotection of the acetal present in 101 gave the corresponding aldehyde (102), and this intermediate was reductively coupled with commercially available tert-butyl-(R)-3-methylpiperazine-1-carboxylate (103) to provide compound 104. Related ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,650,915,746]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"transformation of 102 involving commercially available tert-butyl-(S)-2-methylpiperazine-1-carboxylate (105) afforded compound 106. Independent removal of the Boc protecting groups present in 104 and 106 under acidic conditions followed by reductive amination of the resulting amine products (not shown) using chiral-pure aldehyde 61 (Scheme 3) then respectively provided PROTACs 15 and 16. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,746,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 9 depicts the synthesis of PROTAC 17. Commercially available 3-(benzyloxy)cyclobutan-1-one (107) was reduced to give benzyl-protected-cis-1,3-cyclobutanediol (108).59 This entity was coupled with pyridin-4-ol (4-hydroxypyridine) using Mitsunobu conditions,60 and the resulting trans-cyclobutane product (109) was alkylated with benzyl bromide to give pyridinium salt 110. This material was subsequently reduced to the corresponding 1,2,3,6-tetrahydropyridine (111) by treatment with sodium borohydride. The benzyl alcohol protecting group present in 111 was removed via hydrogenation over a palladium catalyst, and this process also reduced the 1,2,3,6-tetrahydropyridine moiety to a piperidine group (112). This deprotected material was subjected to a second hydrogenation employing a palladium ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1281 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,395,86]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 8. Synthesis of PROTACs 15 and $16^{a}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[181,92,810,561]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0217/befffb78a8c023c74f52b4f146c9868d14b547e994968a8ec6c0aae5a4fb5edc.jpg","list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[286,570,698,667]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[\"${}^{a}$ Reagents and conditions ${\\\\left( \\\\mathrm{{Boc}} = \\\\mathrm{C}\\\\left( \\\\mathrm{O}\\\\right) \\\\mathrm{{OC}}{\\\\left( {\\\\mathrm{{CH}}}_{3}\\\\right) }_{3},\\\\mathrm{{Cbz}} = \\\\mathrm{C}\\\\left( \\\\mathrm{O}\\\\right) {\\\\mathrm{{OCH}}}_{2}\\\\mathrm{{Ph}}\\\\right) :$ (a) 2,2-Diethoxyethan-1-ol,NaH,DMF,rt,2h,59%; (b) Intermediate 98,RuPhosPd G2,Cs ${}_{2}{\\\\mathrm{{CO}}}_{3}$ ,toluene, ${90}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h},{94}\\\\% ;\\\\left( \\\\mathrm{c}\\\\right)$ Pd on $\\\\mathrm{C},{\\\\mathrm{H}}_{2}$ ,EtOAc,rt,12 h,92%; (d) 4-Bromo-6-chloropyridazin-3-amine (70), DIEA, NMP, ${120}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h},{74}\\\\% ;\\\\left( \\\\mathrm{e}\\\\right) 2 -$ Hydroxyphenylboronic acid (72),Pd(PPh ${}_{3}{)}_{4},{\\\\mathrm{\\\\;K}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${\\\\mathrm{H}}_{2}\\\\mathrm{O},{90}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h}{70}\\\\% ;\\\\left( \\\\mathrm{f}\\\\right) {1.0}\\\\mathrm{M}{\\\\mathrm{H}}_{2}{\\\\mathrm{{SO}}}_{4}$ ,THF, ${60}^{ \\\\circ }\\\\mathrm{C},4\\\\mathrm{\\\\;h},{24}\\\\% ;\\\\left( \\\\mathrm{g}\\\\right)$ Intermediate 103,NaBH(OAc) ${}_{3}$ , ${\\\\mathrm{{CH}}}_{3}\\\\mathrm{{CN}}$ ,rt, $2\\\\mathrm{\\\\;h},{91}\\\\% ;\\\\left( \\\\mathrm{h}\\\\right)$ Intermediate 105,NaBH(OAc) ${}_{3}$ , ${\\\\mathrm{{CH}}}_{3}\\\\mathrm{{CN}}$ ,rt, $8\\\\mathrm{\\\\;h},{37}\\\\% ;\\\\left( \\\\mathrm{i}\\\\right) {4.0}\\\\mathrm{M}$ HCl, MeOH, rt, $2 - 8\\\\mathrm{\\\\;h},{90} - {91}\\\\% ;\\\\left( \\\\mathrm{j}\\\\right)$ Intermediate 61,NaBH(OAc) ${}_{3}$ , ${\\\\mathrm{{CH}}}_{3}\\\\mathrm{{CN}}$ ,rt, ${10} - {12}\\\\mathrm{\\\\;h},3 - {8}\\\\%$ . \"]","img_path":"images/0762/7125fbb4a3c1e8373c42af6298549436b982980d4c16390adb95be6551095174.jpg","list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,751,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"hydroxide catalyst in the presence of di-tert-butyl dicarbonate to give Boc-protected piperidine 113. Coupling of this intermediate with 4-bromo-2-fluoro-pyridine (62, Scheme 4) then provided 114, and material was converted to intermediate 115 via condensation with benzyl 3,8-diazabicyclo[3.2.1]-octane-3-carboxylate (97, Scheme 8). Removal of the Cbz protecting group from 115 was accomplished via hydrogenation, and the resulting amine (116) was coupled with 4-bromo-6-chloropyridazin-3-amine (70, Scheme 4) to give intermediate 117. Reaction of 117 with (2-hydroxyphenyl)-boronic acid (72, Scheme 4) then provided compound 118, and the Boc protecting group contained in this material was subsequently removed under acidic conditions to afford amine ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,751,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"119. Coupling of 119 with the chiral-pure VHL-binding fragment 61 (Scheme 3) then provided PROTAC 17. As was described above, the alternate chiral-pure isopropyl epimer corresponding to 61 that was obtained via chiral separation in Scheme 3 (61e, structure not shown) was also converted to the corresponding PROTAC compound (17e, the isopropyl epimer corresponding to 17, not shown). Subsequent biological testing of the two diastereomeric PROTAC molecules was employed to assign the absolute stereochemistries of the isopropyl centers in 17 and, by inference, intermediate 61 (cf., Table S4; more potent diastereomers = isopropyl stereochemistries shown in Table 2 and Schemes 3 and 9). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1282 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,337,86]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 9. Synthesis of PROTAC $17^{a}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[108,90,887,652]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[\"${}^{a}$ Reagents and conditions $\\\\left( {\\\\mathrm{{Bn}} = {\\\\mathrm{{CH}}}_{2}\\\\mathrm{{Ph}},\\\\mathrm{{Boc}} = \\\\mathrm{C}\\\\left( \\\\mathrm{O}\\\\right) \\\\mathrm{{OC}}{\\\\left( {\\\\mathrm{{CH}}}_{3}\\\\right) }_{3},\\\\mathrm{{Cbz}} = \\\\mathrm{C}\\\\left( \\\\mathrm{O}\\\\right) {\\\\mathrm{{OCH}}}_{2}\\\\mathrm{{Ph}}}\\\\right)$ : (a) ${\\\\mathrm{{NaBH}}}_{4}$ ,MeOH, $0{}^{ \\\\circ }\\\\mathrm{C},1\\\\mathrm{\\\\;h},{97}\\\\%$ ; (b) Pyridin-4-ol, DIAD, PPh ${}_{3}$ ,THF, ${50}^{ \\\\circ }\\\\mathrm{C},{12}\\\\mathrm{\\\\;h},{55}\\\\%$ ; (c) BnBr,toluene, ${80}^{ \\\\circ }\\\\mathrm{C},{12}\\\\mathrm{\\\\;h},{92}\\\\%$ ; (d) ${\\\\mathrm{{NaBH}}}_{4}$ ,EtOH, ${15}^{ \\\\circ }\\\\mathrm{C},4\\\\mathrm{\\\\;h},{84}\\\\%$ ; (e) ${\\\\mathrm{H}}_{2}$ (50 psi),Pd/C,THF, EtOH, ${35}^{ \\\\circ }\\\\mathrm{C},{12}\\\\mathrm{\\\\;h};{83}\\\\%$ ; (f) ${\\\\mathrm{H}}_{2}$ (50 psi), $\\\\mathrm{{Pd}}{\\\\left( \\\\mathrm{{OH}}\\\\right) }_{2}/\\\\mathrm{C}$ ,MeOH, ${\\\\left( \\\\text{Boc}\\\\right) }_{2}\\\\mathrm{O}$ ,rt, ${12}\\\\mathrm{\\\\;h},{71}\\\\%$ ; (g) 4-Bromo-2-fluoro-pyridine (62), ${\\\\mathrm{{Cs}}}_{2}{\\\\mathrm{{CO}}}_{3}$ , ${\\\\mathrm{{CH}}}_{3}\\\\mathrm{{CN}}$ ,90 ${}^{ \\\\circ }\\\\mathrm{C},{12}\\\\mathrm{\\\\;h},{86}\\\\%$ ; (h) Benzyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (98), RuphosPd-G2, ${\\\\mathrm{{Cs}}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,toluene, ${110}^{ \\\\circ }\\\\mathrm{C},{12}\\\\mathrm{\\\\;h},{71}\\\\%$ ; (i) $\\\\mathrm{{Pd}}{\\\\left( \\\\mathrm{{OH}}\\\\right) }_{2}/\\\\mathrm{C}$ , ${\\\\mathrm{H}}_{2}$ (50 psi),THF, EtOH, ${60}^{ \\\\circ }\\\\mathrm{C},{12}\\\\mathrm{\\\\;h},{89}\\\\%$ ; (j) 4-Bromo-6-chloropyridazin-3-amine (70), DIEA, DMSO, ${130}^{ \\\\circ }\\\\mathrm{C},3\\\\mathrm{\\\\;h},{64}\\\\%$ ; (k) 2-Hydroxyphenyl boronic acid (72), $\\\\mathrm{{Pd}}{\\\\left( {\\\\mathrm{{PPh}}}_{3}\\\\right) }_{4},{\\\\mathrm{\\\\;K}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${\\\\mathrm{H}}_{2}\\\\mathrm{O},{90}^{ \\\\circ }\\\\mathrm{C},{10}\\\\mathrm{\\\\;h},{54}\\\\%$ ; (l) ${4.0}\\\\mathrm{M}\\\\mathrm{{HCl}},1,4$ -dioxane,DCM,rt, $2\\\\mathrm{\\\\;h}$ ; (m) Intermediate 61, ${\\\\mathrm{{NaBH}}}_{3}\\\\mathrm{{CN}},\\\\mathrm{{NaOAc}},\\\\mathrm{{MeOH}},\\\\mathrm{{DCM}},\\\\mathrm{{rt}},{10}\\\\mathrm{\\\\;h};{45}\\\\%$ over two steps. \"]","img_path":"images/0838/cafd3c7085ff98f1c319211e4577384d495fe748d7ccedf0b37a69d30ff27bf7.jpg","list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,760,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The preparation of PROTACs 18-20 is illustrated in Scheme 10. Intermediate 119 (Scheme 9) was alkylated with 2-bromo-1,1-diethoxyethane and the resulting acetal (120) was deprotected under acidic conditions to give aldehyde 121. Separately, racemic isoxazole-containing carboxylic acid 46 (Scheme 2) was coupled with chiral-pure amine 57 (Scheme 3), and subsequent separation of the diastereomeric products via chiral HPLC provided intermediate 122 and the corresponding isopropyl epimer (122e, structure not shown). Intermediate 122 was deprotected under acidic conditions to give amine 123, and this entity was coupled with aldehyde 121 via reductive amination to afford PROTAC 18. The isopropyl epimer corresponding to intermediate 122 obtained via the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,760,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"chiral separation (122e) was similarly transformed into a closely related diastereomeric PROTAC (18e, the isopropyl epimer corresponding to 18, structure not shown) via the same sequence of reactions. Biological testing of both compounds subsequently established the absolute configuration for PROTAC 18 as that shown in Table 2 and, by inference, the configuration of intermediates 122 and 123 depicted in Scheme 10 (cf., Table S4). In an independent synthesis, enantiomerically pure intermediate 123 was condensed with tert-butyl-4-formylpiperidine-1-carboxylate (124) via a reductive amination process, and the Boc group contained in the resulting product (125) was removed via exposure to acidic ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1283 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,380,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 10. Synthesis of PROTACs $18 - 20^{a}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[222,90,742,610]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0837/4dd35af820bcb1b3a2e768d27a778f5aed1f60ad784ab0bce7a2f8f8bc89b971.jpg","list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[233,668,733,818]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[\"${}^{a}$ Reagents and conditions $\\\\left( {\\\\mathrm{{Boc}} = \\\\mathrm{C}\\\\left( \\\\mathrm{O}\\\\right) \\\\mathrm{{OC}}{\\\\left( {\\\\mathrm{{CH}}}_{3}\\\\right) }_{3}}\\\\right)$ : (a) 2-Bromo-1,1-diethoxyethane,NaI, DIEA, DMF, ${70}^{ \\\\circ }\\\\mathrm{C},{12}\\\\mathrm{\\\\;h},{35}\\\\%$ ; (b) ${1.0}\\\\mathrm{M}{\\\\mathrm{H}}_{2}{\\\\mathrm{{SO}}}_{4}$ , THF, ${60}^{ \\\\circ }\\\\mathrm{C},{12}\\\\mathrm{\\\\;h}$ ; (c) Intermediate 57,HATU,DIEA,DMF,rt,1 h;(d) Chiral HPLC; 24-28% over 2 steps; (e) TFA, DCM, rt, 1 h; (f) Intermediate 121, ${\\\\mathrm{{NaBH}}}_{3}\\\\mathrm{{CN}},2 : 1\\\\mathrm{{MeOH}} : \\\\mathrm{{DCM}},\\\\mathrm{{rt}},{24}\\\\mathrm{\\\\;h},{13}\\\\%$ over 2 steps;(g) Intermediate 124, NaOAc, ${\\\\mathrm{{NaBH}}}_{3}\\\\mathrm{{CN}},3 : 1\\\\mathrm{{MeOH}} : \\\\mathrm{{DCM}},\\\\mathrm{{rt}},1\\\\mathrm{\\\\;h},3\\\\%$ ; (i) Intermediate 57,HATU,DIEA,DMF,rt,2 h; (j) Chiral HPLC; 11-13% over 2 steps; (k) HCOOH, ${\\\\mathrm{H}}_{2}\\\\mathrm{O},{60}^{ \\\\circ }\\\\mathrm{C},1\\\\mathrm{\\\\;h}$ ; (l) Intermediate 119,NaOAc, ${\\\\mathrm{{NaBH}}}_{3}\\\\mathrm{{CN}},1 : 1\\\\mathrm{{MeOH}} : \\\\mathrm{{DCM}},\\\\mathrm{{rt}},1\\\\mathrm{\\\\;h},{34}\\\\%$ over 2 steps. \"]","img_path":"images/0099/0614435a61cc7921f9d3b6a516589ddacae2c61ae695dc49e45c3b7bae230813.jpg","list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[79,913,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"conditions to give 126. This entity was subsequently coupled with aldehyde 138 (Scheme 12) to give PROTAC 20. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,913,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Separately, racemic isoxazole-containing carboxylic acid 53 (Scheme 2) was coupled with enantiomerically pure amine 57 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1284 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,345,86]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 11. Synthesis of PROTAC $21^{a}$ ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[138,92,859,356]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[\"${}^{a}$ Reagents and conditions: (a) TFA,DCM,rt,1 h,80-90%; (b) Intermediate 43, DIEA, DMF, ${130}{}^{ \\\\circ }\\\\mathrm{C},1\\\\mathrm{\\\\;h},{71}\\\\%$ ; (c) tert-Butyl 3,8- diazabicyclo[3.2.1]octane-3-carboxylate (67),RuPhosPd G3, ${\\\\mathrm{{Cs}}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${90}^{ \\\\circ }\\\\mathrm{C},1\\\\mathrm{\\\\;h},{42}\\\\%$ ; (d) 4-Bromo-6-chloropyridazin-3-amine (70), DMSO, DIEA, ${130}{}^{ \\\\circ }\\\\mathrm{C},5\\\\mathrm{\\\\;h},{52}\\\\%$ ; (e) (2-Hydroxyphenyl)boronic acid (72), $\\\\mathrm{{Pd}}{\\\\left( {\\\\mathrm{{PPh}}}_{3}\\\\right) }_{4},{\\\\mathrm{\\\\;K}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${\\\\mathrm{H}}_{2}\\\\mathrm{O},{90}^{ \\\\circ }\\\\mathrm{C},1\\\\mathrm{\\\\;h},{68}\\\\%$ ; (f) LiOH, THF, ${\\\\mathrm{H}}_{2}\\\\mathrm{O}$ ,rt, $1\\\\mathrm{\\\\;h},{95}\\\\%$ ; (g) Intermediate 57,HATU,DIEA,DMF,rt,1 h;(h) Chiral HPLC; 4% over 2 steps. \"]","img_path":"images/0626/b0acba7708620e1369dc5191dd643a1ff29a11bb6216d48d8511a149f7d5af79.jpg","list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,425,481,635]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(Scheme 3), and the diastereomeric products thus obtained were separated by chiral HPLC methods to give intermediate 127 and the corresponding isopropyl epimer (127e, structure not shown). Deprotection of the acetal present in 127 under acidic conditions and reductive coupling of the aldehyde thus obtained (128) with intermediate 119 (Scheme 9) afforded PROTAC 19. Similar to the example of PROTAC 18 above, the isopropyl epimer corresponding to intermediate 127 (i.e., 127e) was converted into a diastereomer of PROTAC 19 (19e, the isopropyl epimer corresponding to 19, structure not shown) via the same two-step sequence. Biological testing of both PROTAC molecules subsequently established the absolute configurations shown for PROTAC 19 and (by inference) intermediates 127 and 128, respectively, shown in Table 2 and Scheme 10 (cf., Table S4). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,635,481,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 11 depicts the synthesis of PROTAC 21. Intermediate 114 (Scheme 9) was deprotected under acidic conditions to provide amine 129. This entity was coupled with racemic intermediate 43 (Scheme 2) to give compound 130. Multistep elaboration of the bromide present in 130 using chemistries analogous to those employed in Scheme 4 above to transform intermediate 69 into compound 73 then provided ester 131 (several synthetic intermediates are not shown in Scheme 11 but are described in the Experimental Section). Hydrolysis of 131 under basic conditions afforded carboxylic acid 132, and this entity was subsequently coupled with enantiomerically pure intermediate 57 (Scheme 3). Separation of the resulting diastereomeric products by chiral HPLC methods then gave PROTAC 21 and the corresponding isopropyl epimer (21e, not shown). As was performed elsewhere in this work, biological testing of the separated diastereomers was employed to assign the absolute configurations of these compounds (cf., Table S4). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,885,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PROTAC 22 was prepared using the method shown in Scheme 12. Commercially available alcohol 133 was coupled with 4-bromopyridin-2-ol to afford intermediate 134 This entity was transformed into compound 135 using a sequence ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,445,917,752]","code_body":null,"code_caption":null,"image_caption":"[\"Scheme 12. Synthesis of PROTAC $22^{a}$ \"]","image_footnote":"[\"${}^{a}$ Reagents and conditions: (a) 4-Bromopyridin-2-ol, ${\\\\mathrm{{PPh}}}_{3}$ ,DIAD, THF,rt,1 h,68%; (b) tert-Butyl 3,8-diazabicyclo[3.2.1]octane-3- carboxylate (67), RuPhosPd G3, ${\\\\mathrm{{Cs}}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${90}^{ \\\\circ }\\\\mathrm{C},1\\\\mathrm{\\\\;h}$ , 80%; (c) TFA,DCM,rt,1 h,79%; (d) 4-Bromo-6-chloropyridazin-3- amine (70),DMSO,DIEA, ${130}{}^{ \\\\circ }\\\\mathrm{C},1\\\\mathrm{\\\\;h},{65}\\\\% ;\\\\;\\\\left( \\\\mathrm{e}\\\\right) \\\\;\\\\left( {2 - }\\\\right.$ Hydroxyphenyl)boronic acid (72), $\\\\mathrm{{Pd}}{\\\\left( {\\\\mathrm{{PPh}}}_{3}\\\\right) }_{4},{\\\\mathrm{\\\\;K}}_{2}{\\\\mathrm{{CO}}}_{3},1,4$ -dioxane, ${90}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h},{56}\\\\% ;\\\\left( \\\\mathrm{f}\\\\right)$ LiOH,THF, ${\\\\mathrm{H}}_{2}\\\\mathrm{O},\\\\mathrm{{rt}},1\\\\mathrm{\\\\;h};\\\\left( \\\\mathrm{g}\\\\right) {\\\\mathrm{{CH}}}_{3}{\\\\mathrm{{ONHCH}}}_{3}$ . HCl,HATU,DIEA,DMF,rt,1 h,33%; (h) ${\\\\mathrm{{LiAlH}}}_{4}$ ,THF,0 to ${25}^{ \\\\circ }\\\\mathrm{C}$ , 1 h,41%; (i) Intermediate 123, ${\\\\mathrm{{NaBH}}}_{3}\\\\mathrm{{CN}}$ ,NaOAc,3:1 MeOH:DCM,rt,1 h,6%. \"]","img_path":"images/0873/09067e4f9f7a1cf6c57bb3e954a954fe6c795d4217e50e43a5a3405b1558bd84.jpg","list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[512,900,915,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"of reactions that was similar to those employed in Scheme 4 above to transform intermediate 69 into compound 73 (several synthetic intermediates are not shown in Scheme 12 but are ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1285 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,345,86]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 13. Synthesis of PROTAC $23^{a}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[187,90,807,468]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[\"${}^{a}$ Reagents and conditions $\\\\left( {\\\\mathrm{{Boc}} = \\\\mathrm{C}\\\\left( \\\\mathrm{O}\\\\right) \\\\mathrm{{OC}}{\\\\left( {\\\\mathrm{{CH}}}_{3}\\\\right) }_{3}}\\\\right)$ : (a) Intermediate 57,HATU,DIEA,DMF,rt,1 h,33%; (b) ${1.0}\\\\mathrm{M}{\\\\mathrm{H}}_{2}{\\\\mathrm{{SO}}}_{4}$ ,THF,60°C,2 h, 74%; (c) tert-Butyl 4-hydroxypiperidine-1-carboxylate (141),NaH,DMF,0 to ${25}^{ \\\\circ }\\\\mathrm{C},1\\\\mathrm{\\\\;h},{76}\\\\%$ ; (d) Benzyl 3,8-diazabicyclo[3.2.1]octane-3- carboxylate (98), RuPhosPd G2, ${\\\\mathrm{{Cs}}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,toluene, ${90}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h},{50}\\\\%$ ; (e) Pd/C, ${\\\\mathrm{H}}_{2}$ ,EtOAc,rt,4 h,64%; (f) 4-Bromo-6-chloropyridazin-3-amine (70),NMP,DIEA, ${120}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h},{91}\\\\%$ ; (g) (2-Hydroxyphenyl)boronic acid (72),Pd(PPh ${}_{3}$ ), ${\\\\mathrm{K}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${90}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h},{54}\\\\%$ ; (h) TFA,DCM, rt,4 h,73%; (i) Intermediate 140, NaBH(OAc), ${\\\\mathrm{{CH}}}_{3}\\\\mathrm{{CN}}$ ,rt,4 h; (j) chiral HPLC,2% over 2 steps. \"]","img_path":"images/0098/bcaaf2cdb07a3905608518a119f2598a5142023e55ed7ae8e408a9bc241f8d08.jpg","list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,552,481,636]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"described in full in the Experimental Section). Hydrolysis of the ester present in 135 was effected under basic conditions, and the resulting acid (136) was converted to aldehyde 138 by reduction of the corresponding Weinreb amide (137). Reductive coupling of 138 with chiral-pure intermediate 123 (Scheme 10) then provided PROTAC 22. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,636,482,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The synthesis of PROTAC 23 is illustrated in Scheme 13. Intermediate 53 (Scheme 2) was coupled with intermediate 57 (Scheme 3) to give compound 139 as a $\\sim 1:1$ mixture of diastereomers (epimeric at the isopropyl group). The acetal present in 139 was then converted to the corresponding aldehyde (140, $\\sim 1:1$ mixture of diastereomers) under acidic conditions. Separately, 4-bromo-2-fluoro-pyridine (62, Scheme 4) was coupled with tert-butyl 4-hydroxypiperidine-1-carboxylate (141) to provide intermediate 142. This entity was subsequently transformed into compound 143 using a sequence of reactions that was analogous to that employed in Scheme 8 above to convert intermediate 97 into compound 101 (several synthetic intermediates are not shown in Scheme 13 but are fully described and characterized in the Experimental Section). Removal of the Boc group present in 143 under acidic conditions followed by reductive coupling of the resulting amine (144) with aldehyde 140 afforded the desired product as a $\\sim 1:1$ mixture of diastereomers (epimeric at the isopropyl group, structure not shown). These molecules were separated by preparative chiral HPLC to afford PROTAC 23 and the corresponding isopropyl epimer (23e, structure not shown). As described elsewhere in this work, the biological ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,552,914,595]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"activities of the separated compounds were assessed, and the more potent entity was assigned the chemical structure depicted for 23 (cf., Table S4). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,595,915,912]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PROTAC 24 was prepared using the methods shown in Scheme 14. Intermediate 58 (Scheme 3) was alkylated with 3-bromoprop-1-yne under mildly basic conditions to give compound 145 ( $\\sim$ 1:1 mixture of diastereomers). Separately, intermediate 108 (Scheme 9) was coupled with 4-bromo-2-fluoropyridine (62, Scheme 4) to afford 146, and this entity was transformed into intermediate 147 via coupling with tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, Scheme 4) and debenzylation. Intermediate 147 was deprotected under acidic conditions, and the resulting amine (not shown) was converted to compound 148 via sequential coupling with 4-bromo-6-chloropyridazin-3-amine (70) and (2-(methoxymethoxy)phenyl)boronic acid (85). Intermediate 148 was condensed with 6-iodopyridin-3-ol under Mitsunobu conditions to afford the trans-cyclobutane product (149).[60] This compound was subsequently coupled with the alkyne-containing intermediate 145 and the resulting products were deprotected under acidic conditions to afford PROTAC 24 and the corresponding isopropyl epimer (24e, not shown). Separation of these two PROTACs via preparative chiral HPLC and biological testing of the individual diastereomers enabled assignment of the absolute configuration of 24 as that shown in Table 3 (cf., Table S4). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,913,914,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The syntheses of control PROTACs 25-28 are described in Scheme 15 below. Inversion of the secondary alcohol present ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1286 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[329,92,650,225]","code_body":null,"code_caption":null,"image_caption":"[\"Scheme 14. Synthesis of PROTAC $24^{a}$ \"]","image_footnote":"[]","img_path":"images/0377/df00c42ef99d011c519b3e616ca2dae683c67addbbc9e032ae0948dd42b21763.jpg","list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[151,268,848,533]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[\"${}^{a}$ Reagents and conditions $\\\\left( {\\\\mathrm{{Bn}} = {\\\\mathrm{{CH}}}_{2}\\\\mathrm{{Ph}},\\\\mathrm{{Boc}} = \\\\mathrm{C}\\\\left( \\\\mathrm{O}\\\\right) \\\\mathrm{{OC}}{\\\\left( {\\\\mathrm{{CH}}}_{3}\\\\right) }_{3}}\\\\right)$ : (a) Propargyl bromide, ${\\\\mathrm{K}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,DMF,rt, $2\\\\mathrm{\\\\;h},{44}\\\\%$ ; (b) 4-Bromo-2-fluoropyridine (62),NaH,DMF,0 to ${25}^{ \\\\circ }\\\\mathrm{C},1\\\\mathrm{\\\\;h},{72}\\\\%$ ; (c) tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67),RuPhosPd G2, ${\\\\mathrm{{Cs}}}_{2}{\\\\mathrm{{CO}}}_{3},{90}{}^{ \\\\circ }\\\\mathrm{C},2$ h, 79%; (d) Pd/C, ${\\\\mathrm{H}}_{2}$ ,MeOH,rt,12 h,56%; (e) TFA,DCM,,rt,4 h,62%; (f) 4-Bromo-6-chloro-pyridazin-3-amine (70), DIEA,NMP, ${1200}^{ \\\\circ }\\\\mathrm{C},2$ h, 65%; (g) (2-(Methoxymethoxy)-phenyl)boronic acid (85),Pd(PPh ${}_{3}{)}_{4},{\\\\mathrm{\\\\;K}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,10:1 1,4-dioxane: ${\\\\mathrm{H}}_{2}\\\\mathrm{O},{90}^{ \\\\circ }\\\\mathrm{C},2\\\\mathrm{\\\\;h},{60}\\\\%$ ; (h) 6-Iodopyridin-3-ol, PPh ${}_{3}$ ,DIAD,0 to ${25}^{ \\\\circ }\\\\mathrm{C},{12}\\\\mathrm{\\\\;h},{58}\\\\%$ ; (i) Intermediate 145,TEA,Pd(PPh ${}_{3}{)}_{2}{\\\\mathrm{{Cl}}}_{2}$ ,CuI,DMF, ${65}^{ \\\\circ }\\\\mathrm{C},3\\\\mathrm{\\\\;h},{76}\\\\%$ ; (j) ${4.0}\\\\mathrm{M}\\\\mathrm{{HCl}}$ in $\\\\mathrm{{MeOH}},\\\\mathrm{{rt}},4\\\\mathrm{\\\\;h};\\\\left( \\\\mathrm{k}\\\\right)$ chiral HPLC, $3\\\\%$ over 2 steps. \"]","img_path":"images/0371/b8002d9d770f581c009fba241aef8042c6ad270648804eed092883a61f55cae9.jpg","list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,630,482,870]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"in enantiopure intermediate 60 (Scheme 3) via a Mitsunobu process provided intermediate 150. This entity was then deprotected by exposure to aqueous acid, and the resulting aldehyde (151) was reductively coupled with intermediate 119 (Scheme 9) to afford PROTAC 25. Alternatively, intermediate 117 (Scheme 9) was coupled with phenylboronic acid, and the resulting product (not shown) was deprotected under acidic conditions to give amine 152. This entity was then reductively coupled with enantiopure aldehyde 61 (Scheme 3) to afford PROTAC 26. Similarly, inversion of the secondary hydroxyl group present in enantiopure intermediate 127 (Scheme 10) provided intermediate 153. Conversion of this material to the corresponding aldehyde (154) and subsequent reductive coupling with intermediate 119 (Scheme 9) then gave PROTAC 27. To complete these syntheses, enantiopure aldehyde 128 (Scheme 10) was reductively coupled with intermediate 152 to afford control compound 28. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,870,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, the preparation of VHL binding fragments 155 and 156 that were employed to confirm the stereochemistries of the majority of the degrader compounds described in this work is shown in Scheme 16. Racemic intermediate 40 (Scheme 1) was condensed with 1-bromo-2-(2-methoxyethoxy)ethane ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,630,917,770]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"under mildly basic conditions to give ester 157. This material was subsequently hydrolyzed, and the resulting carboxylic acid (158) was coupled with enantiomerically pure intermediate 57 (Scheme 3) to afford a mixture of compounds 155 and 156 ( $\\sim$ 1:1). These molecules were then separated using preparative chiral HPLC to afford the individual compounds. VHL binding assessments and crystal structure determination of the complex formed between 155 and VHL (Figures S14-S16) then enabled assignment of the isopropyl group stereocenters contained in the two compounds. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,783,658,797]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CONCLUSIONS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,803,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This work describes the identification and subsequent exploration of novel PROTAC molecules which utilize the VHL E3 ubiquitin ligase to potently and extensively degrade the BRM (SMARCA2) protein. These compounds were derived from a 3,8-diazabicyclo[3.2.1]octane BRM-binding fragment that extended from the protein into solvent. The majority of the PROTACs depicted in these studies exhibited some degree of degradation selectivity for BRM over the closely related BRG1 paralog in in vitro assessments. Enhancement of in vivo DMPK properties, in particular ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1287 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,380,86]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 15. Synthesis of PROTACs $25 - 28^{a}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[153,90,835,250]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0656/238964dc05d54e4e9edc8150e83cd2607a44f3217d250548c395cb83f2bc288a.jpg","list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[153,282,739,396]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0066/f4ce988e67f856b26c18b49894fa99c4ddb4180918bbcd222d3c71b1a0393a75.jpg","list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[153,418,840,578]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0867/3dabbf883541335d3e799756473334629932b4ca4046a560e943cd3703753bf6.jpg","list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[362,623,515,646]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[\"${}^{a}$ Reagents and conditions: (a) ${\\\\mathrm{{PPh}}}_{3}$ ,DIAD,AcOH,THF,0 to ${25}^{ \\\\circ }\\\\mathrm{C},1 - 3\\\\mathrm{\\\\;h},{32} - {94}\\\\% ;\\\\left( \\\\mathrm{b}\\\\right) {\\\\mathrm{{NH}}}_{3}$ ,MeOH,rt,2 h,69-80%; (c) ${\\\\mathrm{{HCO}}}_{2}\\\\mathrm{H},{\\\\mathrm{H}}_{2}\\\\mathrm{O},{60}$ ${}^{ \\\\circ }\\\\mathrm{C},1 - 2\\\\mathrm{\\\\;h}$ ; (d) Intermediate 119, NaOAc, ${\\\\mathrm{{NaBH}}}_{3}\\\\mathrm{{CN}},3 : 1\\\\mathrm{{MeOH}} : \\\\mathrm{{DCM}},\\\\mathrm{{rt}},{12}\\\\mathrm{\\\\;h},{33} - {43}\\\\%$ over 2 steps; (e) Phenylboronic acid, $\\\\mathrm{{Pd}}{\\\\left( {\\\\mathrm{{PPh}}}_{3}\\\\right) }_{4}$ , ${\\\\mathrm{K}}_{2}{\\\\mathrm{{CO}}}_{3},{90}^{ \\\\circ }\\\\mathrm{C},3\\\\mathrm{\\\\;h},{61}\\\\% ;\\\\left( \\\\mathrm{f}\\\\right) {4.0}\\\\mathrm{M}\\\\mathrm{{HCl}}$ in $\\\\mathrm{{MeOH}},\\\\mathrm{{rt}},2\\\\mathrm{\\\\;h},{94}\\\\% ;\\\\left( \\\\mathrm{g}\\\\right)$ Intermediate 61, NaOAc, ${\\\\mathrm{{NaBH}}}_{3}\\\\mathrm{{CN}},\\\\mathrm{{MeOH}},\\\\mathrm{{rt}},3\\\\mathrm{\\\\;h},{11}\\\\% ;\\\\left( \\\\mathrm{h}\\\\right)$ Intermediate 152, NaOAc, ${\\\\mathrm{{NaBH}}}_{3}\\\\mathrm{{CN}},3 : 1\\\\mathrm{{MeOH}} : \\\\mathrm{{DCM}},\\\\mathrm{{rt}},1\\\\mathrm{\\\\;h},6\\\\%$ . \"]","img_path":"images/0499/ed6df892aea495b8f3b857874c6fe2f5e45ca6e273515e9da935ebb74f2fafff.jpg","list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[80,718,515,735]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scheme 16. Synthesis of VHL Binding Fragments 155 and $156^{a}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[144,738,851,880]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[\"${}^{a}$ Reagents and conditions: (a) 1-Bromo-2-(2-methoxyethoxy)ethane, ${\\\\mathrm{K}}_{2}{\\\\mathrm{{CO}}}_{3}$ ,DMF, ${60}^{ \\\\circ }\\\\mathrm{C},1\\\\mathrm{\\\\;h},{81}\\\\%$ ; (b) LiOH, 1:1 THF: ${\\\\mathrm{H}}_{2}\\\\mathrm{O}$ ,rt, $2\\\\mathrm{\\\\;h},{88}\\\\%$ ; (c) Intermediate 57,HATU,DIEA, ${25}^{ \\\\circ }\\\\mathrm{C},1\\\\mathrm{\\\\;h}$ ; (d) Chiral HPLC, ${20}\\\\%$ over 2 steps. \"]","img_path":"images/0754/3ffc1f9e5e026fe81f1e68abb060b25b9bd94be8edcb6f0ed17677876cfb1266.jpg","list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1288 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,481,250]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"mouse IV clearance and half-life parameters, afforded multiple compounds which displayed selective in vivo BRM degradation activity in single-administration PK/PD experiments (both IP and IV dosing; for other recent examples of in vivo exploration of a BRM-targeting PROTAC, see refs31, 32). Quantitation of mRNA associated with two genes whose transcription was controlled by BRM (PLAU and KRT80) provided additional differentiation of tested compounds beyond the protein degradation results. These studies, coupled with the associated in vitro characterization data, enabled the successful identification of an in vivo tool compound that was progressed into multiadministration efficacy experiments (compound 19; A947). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,250,479,692]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"These endeavors demonstrated the ability of compound 19 to afford meaningful in vivo antitumor activity against the HCC2302 BRM-dependent xenograft model. They also illustrated a need for near-complete BRM degradation in order to achieve the desired efficacy results, although the time course associated with such suppression was not explored. In addition, the multiadministration in vivo studies revealed that, in spite of the selective BRM degradation activity mentioned above, long-term dosing of the compound was often associated with suboptimal mouse tolerability outcomes. Several in vivo control experiments demonstrated that the poor tolerability results were not due to the physicochemical properties of the tested molecules and were also likely not related to degradation and/or inhibition of proteins other than BRM and/or BRG1. We currently suspect that the finite BRG1/BRM degradation selectivities exhibited by the identified PROTACs were eroded by high local concentrations of the compounds in sensitive tissues during the multiadministration efficacy experiments. Accordingly, it was important to independently customize the doses and administration frequencies so as to maximize antitumor effects while retaining acceptable tolerability results (see ref 42 for additional descriptions of such explorations for PROTAC 19). For the degraders described in this work, IV administration afforded improved in vivo efficacy performance relative to IP dosing, and the former dosing route was employed to achieve the antitumor effects associated with compound 19. Collectively, the results described in this work suggest that the identification of BRM-degrader PROTACs with further improved BRG1/BRM degradation selectivity properties and/or the use of alternate in vivo delivery strategies may be required to afford robust development candidates. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,710,296,722]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"EXPERIMENTAL SECTION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[80,730,481,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"General Chemistry Methods. All chemicals, reagents, and solvents were at least reagent grade and were obtained from various commercial sources. The general removal of solvents was conducted by using a rotary evaporator. Residual solvents were then removed from the compounds using a vacuum manifold with $< 10 \\mathrm{mmHg}$ pressure and/or via compound lyophilization. ${}^{1}\\mathrm{H}$ NMR spectra were recorded on spectrometers operating at 500, 400, or $300\\mathrm{MHz}$ and are reported in parts per million (ppm) using signals from nondeuterated solvent components as references. LC-MS spectral data were obtained using standard electrospray ionization mass spectrometry. Normal phase silica gel chromatography, both flash column and preparatory thin-layer, was conducted using Merck silica gel 60 as specifically indicated. Reverse phase and chiral chromatographic separations were conducted using columns and conditions specifically indicated in the experimental procedures below. All reagents and starting materials were derived from commercial sources unless otherwise indicated. All reactions were conducted under a nitrogen ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,71,915,158]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"atmosphere unless otherwise indicated. Salts of amine-containing products (including final PROTAC molecules) are typically not mentioned in the various experimental descriptions even though they may have been generated by the synthesis and/or purification conditions employed. Chemical purities were $\\geq 95\\%$ for all Table 2 compounds as assessed by LC-MS analysis at UV $254~\\mathrm{nm}$ (exception $= 22$ ; $93\\%$ pure). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,158,915,343]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(3-Bromoisoxazol-5-yl)ethan-1-ol (31). A solution of hydroxycarbonimidic dibromide (29, 20.0 g, 98.6 mmol, 1.0 equiv) in EtOAc (50 mL) was added dropwise at room temperature to a solution of but-3-yn-1-ol (30, 28.0 g, 399 mmol, 4.0 equiv) and potassium bicarbonate (30.0 g, 300 mmol, 3.0 equiv) in EtOAc:water (200:20 mL). The resulting mixture was stirred at room temperature for 16 h then was diluted with water (100 mL). The organic layer was separated, and the aqueous layer was extracted with EtOAc (100 mL × 2). The combined organic layers were washed with brine (150 mL), dried over anhydrous sodium sulfate, and were concentrated under reduced pressure. The residue was purified by silica gel chromatography eluting with EtOAc:petroleum ether (0:100 to 25:75) to give the title compound 31 (18.5 g, 98%) as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(\\mathrm{CD}_3\\mathrm{OD}, 400\\mathrm{MHz})$ $\\delta$ 6.23 (s, 1H), 3.96 (t, $J = 6.1\\mathrm{Hz}$ , 2H), 3.03 (t, $J = 6.1\\mathrm{Hz}$ , 2H). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,345,914,480]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(3-Bromoisoxazol-5-yl)-3-methylbutanoic acid (32). 2-(3-Bromoisoxazol-5-yl)ethan-1-ol (31, $18.5\\mathrm{g}$ , $96.3\\mathrm{mmol}$ ) was dissolved in acetone $(220~\\mathrm{mL})$ at $0^{\\circ}\\mathrm{C}$ , and Jones reagent $(19.2\\mathrm{g}$ $\\mathrm{CrO}_3$ dissolved in $90~\\mathrm{mL}$ of $6.0\\mathrm{M}$ $\\mathrm{H}_2\\mathrm{SO}_4$ at $0^{\\circ}\\mathrm{C}$ ) was added dropwise. The resulting solution was stirred at $25^{\\circ}\\mathrm{C}$ for $12\\mathrm{h}$ then was diluted with water $(100~\\mathrm{mL})$ and extracted with EtOAc $(200~\\mathrm{mL} \\times 3)$ . The combined organic layers were washed with brine, dried over anhydrous sodium sulfate, and were concentrated under reduced pressure to afford the crude title compound 32 $(17.9\\mathrm{g}, 90\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ , $\\mathrm{CDCl}_3$ $\\delta 6.43$ (s, 1H), 3.81-3.74 (m, 2H). LC-MS $(\\mathrm{ES+}): m/z 205.9$ $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,481,914,641]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methyl 2-(3-bromoisoxazol-5-yl)-3-methylbutanoate (33). A solution of 2-(3-bromoisoxazol-5-yl)-3-methylbutanoic acid (32, 17.9 g, 86.9 mmol) and concentrated $\\mathrm{H}_2\\mathrm{SO}_4$ (1.5 mL, 28.1 mmol) in MeOH (150 mL) was stirred at $70^{\\circ}\\mathrm{C}$ for 2 h. The resulting mixture was cooled to room temperature and was concentrated under reduced pressure. The residue was diluted with water (100 mL) and then extracted with EtOAc (200 mL × 3). The combined organic layers were washed with brine (100 mL), dried over anhydrous sodium sulfate, and were concentrated under reduced pressure. The residue was purified by silica gel chromatography eluting with EtOAc:petroleum ether (0:100 to 25:75) to give the title compound 33 (12.4 g, 65%) as a yellow oil. ${}^{1}\\mathrm{H}$ NMR (400 MHz, CDCl₃) δ 6.39 (s, 1H), 3.84 (s, 2H), 3.76 (s, 3H). LC-MS (ES+): m/z 221.9 $[\\mathrm{M} + \\mathrm{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,641,914,840]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methyl 2-(3-bromoisoxazol-5-yl)-3-methylbutanoate (34). Methyl 2-(3-bromoisoxazol-5-yl)-3-methylbutanoate (33, $12.4\\mathrm{g}$ 56.3 mmol, 1.0 equiv) was dissolved in THF $(120~\\mathrm{mL})$ at $0^{\\circ}\\mathrm{C}$ and t-BuOK $(9.17\\mathrm{g},81.7\\mathrm{mmol},1.45\\mathrm{equiv})$ was added. After stirring for $10\\mathrm{min}$ at $0^{\\circ}\\mathrm{C}$ , a solution of 2-iodopropane $(12.2\\mathrm{g},71.7\\mathrm{mmol},$ 1.27 equiv) in THF was added dropwise. The reaction mixture was stirred at room temperature for $16\\mathrm{h}$ then was quenched with ice water $(200~\\mathrm{mL})$ . The resulting mixture was extracted with EtOAc $(200~\\mathrm{mL}\\times 3)$ , and the combined organic layers were washed with brine $(100~\\mathrm{mL})$ , dried over anhydrous sodium sulfate, and were concentrated under reduced pressure. The residue was purified by silica gel chromatography eluting with EtOAc:petroleum ether (0:100 to 20:80) to afford the title compound 34 $(8.2\\mathrm{g},56\\%)$ as a yellow oil. ${}^{1}\\mathbf{H}$ NMR $\\mathrm{(CD_3OD}$ $400\\mathrm{MHz}$ $\\delta 6.38$ s,1H)3.74s3H)3.65d $J$ $= 8.4\\mathrm{Hz}$ 1H)2.44-2.31 m,1H)1.01 d $J = 2.4\\mathrm{Hz}$ 3H)0.92 d $J = 6.8\\mathrm{Hz}$ 3H). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,841,914,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(3-Methoxyisoxazol-5-yl)-3-methylbutanoic acid (35). To a room temperature solution of a portion of methyl 2-(3-bromoisoxazol-5-yl)-3-methylbutanoate prepared above (34, $3.0\\mathrm{g}$ , $11.4\\mathrm{mmol}$ , $1.0\\mathrm{equiv}$ ) in $\\mathrm{MeOH}$ ( $22\\mathrm{mL}$ ) was added KOH ( $6.6\\mathrm{g}$ , $115\\mathrm{mmol}$ , $10\\mathrm{equiv}$ ). The reaction mixture was refluxed for $4\\mathrm{h}$ then was cooled to room temperature. The resulting solution was acidified to $\\mathrm{pH} \\approx 5$ with HCl ( $1.0\\mathrm{M}$ aqueous solution) and then was concentrated under reduced pressure. The residue was purified by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[532,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[485,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1289 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,953,912,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[764,962,912,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,71,481,135]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"reverse phase chromatography (gradient: $5\\% -40\\%$ $\\mathrm{CH}_3\\mathrm{CN}$ in water $(0.1\\%$ formic acid)) to yield the title compound 35 $(1.51\\mathrm{g},66\\%)$ as a colorless thick oil. ${}^{1}\\mathrm{H}$ NMR $(\\mathrm{CD}_3\\mathrm{OD},400\\mathrm{MHz})$ $\\delta$ 5.93s,1H),3.97 s,3H),3.53d $J = 8.4 \\mathrm{Hz}$ 1H2.44-2.35m1H)1.06d $J = 6.8$ Hz,3H),0.96d $J = 6.4 \\mathrm{Hz}$ 3H). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,133,481,308]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3-(Benzyloxy)-5-methylisoxazole (37). To a stirred mixture of 5-methylisoxazol-3-ol $(36,50\\mathrm{g},505\\mathrm{mmol},1.0$ equiv) and potassium carbonate $(105\\mathrm{g},757\\mathrm{mmol})$ in 1-methyl-2-pyrrolidinone $(400~\\mathrm{mL})$ was added benzyl bromide $(72~\\mathrm{mL}$ $605~\\mathrm{mmol}$ 1.2 equiv) in 1- methyl-2-pyrrolidinone $(100~\\mathrm{mL})$ dropwise at $60^{\\circ}\\mathrm{C}$ over $4\\mathrm{h}$ The mixture was stirred at $60^{\\circ}\\mathrm{C}$ for an additional $0.5\\mathrm{h}$ then was cooled to room temperature and was diluted with EtOAc $(500~\\mathrm{mL})$ .The diluted mixture was washed with water $(200~\\mathrm{mL}\\times 2)$ and brine (300 $\\mathrm{mL}\\times 3)$ , and the organic layer was dried over sodium sulfate and concentrated under reduced pressure. The residue was purified by chromatography on silica gel (solvent gradient: $0 - 5\\%$ EtOAc in petroleum ether) to afford the title compound 37 $(44\\mathrm{g},46\\%)$ as colorless oil. ${}^{1}\\mathrm{H}$ NMR $(\\mathrm{CDCl}_3,400\\mathrm{MHz})$ $\\delta 7.29 - 7.53$ m5H),5.66 $(d,J = 0.8\\mathrm{Hz},1\\mathrm{H})$ 5.25s2H2.34d $J = 0.8 \\mathrm{Hz}$ 3H). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,308,481,507]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methyl 2-(3-(benzyloxy)isoxazol-5-yl)acetate (38). To a mixture of 3-(benzyloxy)-5-methylisoxazole (37, 44 g, 233 mmol, 1.0 equiv) in THF (770 mL) was added lithium diisopropylamide (2.0 M in THF, 128 mL, 256 mmol, 1.1 equiv) dropwise at $-78^{\\circ}\\mathrm{C}$ . The mixture was stirred at $-78^{\\circ}\\mathrm{C}$ for $0.5\\mathrm{h}$ then dimethyl carbonate (23.5 mL, 279 mmol, 1.2 equiv) in THF (66 mL) was added dropwise, and stirring was continued at $-78^{\\circ}\\mathrm{C}$ for an additional $3\\mathrm{h}$ . The mixture was quenched at $-78^{\\circ}\\mathrm{C}$ with saturated aqueous $\\mathrm{NH}_4\\mathrm{Cl}$ (100 mL), diluted with EtOAc (300 mL), and was washed sequentially with water (300 mL × 2) and brine (200 mL). The organic layer was dried over sodium sulfate and was concentrated under reduced pressure. The residue was purified by chromatography on silica gel (solvent gradient: $0 - 20\\%$ EtOAc in petroleum ether) to afford the title compound 38 (19 g, 33%). ${}^{1}\\mathrm{H}$ NMR $(\\mathrm{CDCl}_3, 400\\mathrm{MHz})$ $\\delta$ 7.31–7.50 (m, 5H), 5.95 (s, 1H), 5.27 (s, 2H), 3.76 (s, 3H), 3.74 (s, 2H). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,507,481,706]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methyl 2-(3-(benzyloxy)isoxazol-5-yl)-3-methylbutanoate (39). To a $20^{\\circ}\\mathrm{C}$ mixture of methyl 2-(3-(benzyloxy)isoxazol-5-yl)acetate (38, 19.0 g, 76.9 mmol, 1.0 equiv) and 2-iodopropane (14.4 g, 84.5 mmol, 1.1 equiv) in DMF (190 mL) was added 1.0 M KOtBu in THF (99.9 mL, 99.9 mmol, 1.3 equiv). The mixture was stirred at $20^{\\circ}\\mathrm{C}$ for $12\\mathrm{h}$ then was diluted with EtOAc $(300\\times 2\\mathrm{mL})$ .The diluted mixture was quenched with water $(300~\\mathrm{mL})$ and was subsequently washed with water $(200~\\mathrm{mL}\\times 2)$ and brine $(300~\\mathrm{mL})$ The organic layer was dried over sodium sulfate and was concentrated under reduced pressure. The residue was purified by chromatography on silica gel (solvent gradient: $0 - 5\\%$ EtOAc in petroleum ether) to afford the title compound 39 $(18.3\\mathrm{g},82\\%)$ as yellow oil. ${}^{1}\\mathrm{H}$ NMR $\\mathrm{(CDCl_3}$ $400\\mathrm{MHz})$ $\\delta$ 7.49-7.33 m5H5.94s1H5.26s2H), 3.77-3.68 m3H),3.51d $J = 8.8\\mathrm{Hz}$ 1H2.49-2.25m1H), 1.01 d $J = 6.4\\mathrm{Hz}$ 3H),0.94d $J = 6.8\\mathrm{Hz}$ 3H.LC-MS $(\\mathrm{ES + })$ .. $m/$ $z290.0[\\mathrm{M} + \\mathrm{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,706,481,855]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methyl 2-(3-hydroxy-1,2-oxazol-5-yl)-3-methylbutanoate (40). A mixture of methyl 2-(3-(benzyloxy)isoxazol-5-yl)-3-methylbutanoate (39, 2.0 g, 6.91 mmol, 1.0 equiv) and titanium tetrachloride (0.99 mL, 8.99 mmol, 1.3 equiv) in DCM (20 mL) was stirred at 25 °C for 13 h then was quenched with water (10 mL). The resulting solution was extracted with EtOAc (30 mL × 3) and the combined organic layers were dried over sodium sulfate and concentrated under reduced pressure. The residue was purified by silica gel chromatography (0–15% EtOAc in petroleum ether) to afford the title compound 40 (1.30 g, 94%) as yellow oil. $^1\\mathrm{H}$ NMR (400 MHz, CDCl₃) δ 5.94 (s, 1H), 3.73 (s, 3H), 3.47 (d, J = 9.2 Hz, 1H), 2.43–2.30 (m, 1H), 1.00 (d, J = 6.8 Hz, 3H), 0.92 (d, J = 6.8 Hz, 3H). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,855,481,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methyl 2-(3-(2,2-diethoxyethoxy)isoxazol-5-yl)-3-methylbutanoate (41). A solution of methyl 2-(3-hydroxyisoxazol-5-yl)-3-methylbutanoate (40, 500 mg, 2.51 mmol, 1.0 equiv), 2-bromo-1,1-diethoxyethane (743 mg, 3.77 mmol, 1.5 equiv) and $\\mathrm{K}_2\\mathrm{CO}_3$ (693 mg, 5.02 mmol, 2.0 equiv) in DMF (7 mL) was stirred at $70^{\\circ}\\mathrm{C}$ for $8\\mathrm{h}$ . The mixture was allowed to cool to room temperature, and the reaction was quenched by the addition of saturated aqueous $\\mathrm{NH}_4\\mathrm{Cl}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,275]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The aqueous layer was extracted with EtOAc $(100\\mathrm{mL}\\times 3)$ , and the combined organic layers were dried over anhydrous sodium sulfate and concentrated under reduced pressure. The residue was purified by prepacked C18 column (CH $_3$ CN in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3, 0$ to $80\\%)$ to afford the title compound 41 $(0.39\\mathrm{g}, 49\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\delta$ 6.26 (s, 1H), 4.81 (t, $J = 5.2\\mathrm{Hz}$ , 1H), 4.11 (d, $J = 5.2\\mathrm{Hz}$ , 2H), 3.73-3.60 (m, 6H), 3.60-3.48 (m, 2H), 2.37-2.24 (m, 1H), 1.13 (t, $J = 7.0\\mathrm{Hz}$ , 6H), 0.94 (d, $J = 6.7\\mathrm{Hz}$ , 3H), 0.85 (d, $J = 6.7\\mathrm{Hz}$ , 3H). LC-MS (ESI): $m/z$ 316 $[\\mathbf{M} + \\mathbf{H}]^+$ . A small amount of the corresponding isoxazole $N$ -alkylation product (structure not shown) eluted ahead of compound 41 and was isolated as a yellow oil $(0.077\\mathrm{g}, 7\\%)$ . ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\delta$ 5.87 (s, 1H), 4.70 (t, $J = 5.5\\mathrm{Hz}$ , 1H), 3.88 (d, $J = 5.5\\mathrm{Hz}$ , 2H), 3.66 (s, 3H), 3.62-3.51 (m, 3H), 3.41-3.39 (m, 2H), 2.34-2.21 (m, 1H), 1.12-1.04 (m, 6H), 0.95 (d, $J = 6.7\\mathrm{Hz}$ , 3H), 0.91 (d, $J = 6.7\\mathrm{Hz}$ , 3H). LC-MS $(\\mathrm{ES}+): m/z$ 316 $[\\mathbf{M} + \\mathbf{H}]^+$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,275,915,462]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(3-(2,2-Diethoxyethoxy)isoxazol-5-yl)-3-methylbutanoic acid (42). To a room temperature solution of methyl 2-(3-(2,2-diethoxyethoxy)isoxazol-5-yl)-3-methylbutanoate (41, 4.38 g, 12.5 mmol, 1.0 equiv) in MeOH (30 mL) and water (15 mL) was added lithium hydroxide (2.10 g, 50 mmol, 4.0 equiv). The reaction mixture was stirred at $40^{\\circ}\\mathrm{C}$ for 2 h then was cooled to room temperature. The pH was adjusted to $\\sim 5$ with $1.0\\mathrm{M}$ HCl, and the mixture was extracted with EtOAc (50 mL × 2). The combined organic layers were dried over anhydrous sodium sulfate, filtered and the filtrate was concentrated to produce the title compound 42 (4.0 g, crude) as a colorless oil. ${}^{1}\\mathrm{H}$ NMR (400 MHz, CDCl₃) δ 5.96 (s, 1H), 4.85 (t, J = 5.2 Hz, 1H), 4.25 (d, J = 5.2 Hz, 2H), 3.81–3.70 (m, 2H), 3.66–3.57 (m, 2H), 3.53 (d, J = 8.4 Hz, 1H), 2.48–2.28 (m, 1H), 1.24 (t, J = 6.8 Hz, 6H), 1.05 (d, J = 6.4 Hz, 3H), 0.95 (d, J = 6.8 Hz, 3H). LC-MS (ES+): m/z 302.1 [M + H]+. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,462,915,663]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methyl 3-methyl-2-[3-(1,1,2,2,3,3,4,4,4-nonafluorobutylsulfonyloxy)isoxazol-5-yl]butanoate (43). 1,1,2,2,3,3,4,4,4-Nonafluorobutane-1-sulfonyl chloride (2.81 g, 8.84 mmol, 1.1 equiv) was added dropwise to a $0^{\\circ}\\mathrm{C}$ solution of methyl 2-(3-hydroxyisoxazol-5-yl)-3-methylbutanoate (40, 1.60 g, 8.03 mmol, 1.0 equiv) and $\\mathrm{K}_2\\mathrm{CO}_3$ (2.22 g, 16.0 mmol, 2.0 equiv) in $\\mathrm{CH}_3\\mathrm{CN}$ (20 mL). The resulting mixture was stirred at room temperature for $2\\mathrm{h}$ then was quenched with saturated aqueous $\\mathrm{NH}_4\\mathrm{Cl}$ and extracted with EtOAc $(100\\mathrm{mL} \\times 3)$ . The combined organic layers were dried over sodium sulfate and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (DCM: petroleum ether, 0:100 to 2:3) to afford the title compound (3.48 g, 90%) as a colorless oil. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\delta$ 7.03 (s, 1H), 4.03 (d, $J = 7.9~\\mathrm{Hz}$ , 1H), 3.70 (s, 3H), 2.45–2.30 (m, 1H), 0.94 (d, $J = 6.7~\\mathrm{Hz}$ , 3H), 0.86 (d, $J = 6.7~\\mathrm{Hz}$ , 3H). LC-MS (ES+): $m/z$ 482 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,663,915,815]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tert-Butyl 4-(5-(1-methoxy-3-methyl-1-oxobutan-2-yl)-isoxazol-3-yl)piperazine-1-carboxylate (45). A solution of intermediate 43 $(3.20\\mathrm{g},6.65\\mathrm{mmol}$ 1.0 equiv and tert-butyl piperazine-1-carboxylate (44, $1.24\\mathrm{g},6.65\\mathrm{mmol}$ 1.0 equiv) in DMF $(32~\\mathrm{mL})$ was stirred at $130^{\\circ}\\mathrm{C}$ for $4\\mathrm{h}$ After cooling to room temperature, the reaction mixture was directly purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ - 0 to $60\\%$ ) to afford the title compound $(860\\mathrm{mg},35\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 6.28 $\\left(\\mathrm{d},J = 1.1\\mathrm{Hz},1\\mathrm{H}\\right)$ 3.69- 3.58 m4H3.48-3.36m4H3.22-3.11m4H2.36-2.21 m1H),1.42 $\\left(\\mathrm{d},J = 1.2\\mathrm{Hz},9\\mathrm{H}\\right)$ 0.98-0.88m3H0.88-0.81m 3H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 368 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,815,915,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(3-(4-(tert-Butoxycarbonyl)piperazin-1-yl)isoxazol-5-yl)-3-methylbutanoic acid (46). To a room temperature solution of intermediate 45 $(860\\mathrm{mg},2.34\\mathrm{mmol},1.0$ equiv) in THF $(5\\mathrm{mL})$ was added a solution of LiOH $(112\\mathrm{mg},4.68\\mathrm{mmol})$ in $\\mathrm{H}_2\\mathrm{O}$ $(5\\mathrm{mL})$ . The resulting mixture was stirred at room temperature for $1\\textrm{h}$ then was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\%)$ $\\mathrm{NH_4HCO_3)}$ 0 to $50\\%$ ) to afford the title compound $(820\\mathrm{mg},99\\%)$ as a white solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 6.01s,1H), 3.45-3.35 m,3H),3.22-2.99 m,6H),2.27-2.08 m,1H),1.41 s, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1290 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,70,481,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"9H), 0.92 (d, $J = 6.6\\\\mathrm{Hz}$ 3H), 0.76 (d, $J = 6.7\\\\mathrm{Hz}$ 3H). LC-MS (ES +): $m / z$ 354 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\"Piperidine-4-carbaldehyde (48). A solution of tert-butyl 4-formylpiperidine-1-carboxylate (47, 500 mg, 2.34 mmol) was stirred at room temperature for $2\\\\mathrm{h}$ in a solution of HCl in 1,4-dioxane (4.0 M, 5.0 mL). The mixture was then poured into MTBE (60 mL) and the solids were collected by filtration. The filter cake was dried under reduced pressure to give the title compound (294 mg, 84%) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (400 MHz, DMSO- $\\\\tilde{d}_6$ ) $\\\\delta$ 9.59 (s, 1H), 9.09 (s, 1H), 8.86 (s, 1H), 3.29–3.13 (m, 2H), 3.00–2.79 (m, 2H), 2.69–2.58 (m, 1H), 2.09–1.95 (m, 2H), 1.72–1.60 (m, 2H). LC-MS (ES+): $m/z$ 114 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\"Benzyl 4-formylpiperidine-1-carboxylate (49). To a $25^{\\\\circ}\\\\mathrm{C}$ solution of piperidine-4-carbaldehyde (48, 250 g, 1.34 mol, 1.0 equiv) in DCM (1.75 L) was added TEA (411 mL, 2.96 mol) and benzyl chloroformate (210 mL, 1.48 mol, 1.1 equiv). The mixture was stirred at $25^{\\\\circ}\\\\mathrm{C}$ for $15\\\\mathrm{h}$ whereupon TLC analysis (petroleum ether:EtOAc = 3:1) showed that the starting material $(\\\\mathbb{R}_{\\\\mathrm{f}} = 0.0)$ was completely consumed. The reaction mixture was quenched by addition water (2 L) and was subsequently extracted with DCM $(600~\\\\mathrm{mL} \\\\times 3)$ . The combined organic layers were washed with brine $(600~\\\\mathrm{mL})$ , dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (petroleum ether:EtOAc = 50:1 to 0:1) to give the title compound 49 (440 g, 44%) as a green oil. ${}^{1}\\\\mathrm{H}$ NMR (400 MHz, $\\\\mathrm{CDCl}_3$ ) $\\\\delta$ 9.66 (s, 1H), 7.37-7.33 (m, 3H), 7.33-7.30 (m, 2H), 5.13 (s, 2H), 4.11-4.05 (m, 2H), 3.05-3.00 (m, 2H), 2.46-2.40 (m, 1H), 1.91 (br s, 2H), 1.63-1.54 (m, 2H). \",\"Benzyl 4-(dimethoxymethyl)piperidine-1-carboxylate (50). To a $25^{\\\\circ}\\\\mathrm{C}$ solution of benzyl 4-formylpiperidine-1-carboxylate (49, $450\\\\mathrm{g},$ $1.82\\\\mathrm{mol}$ 1.0 equiv) in trimethoxymethane $(997~\\\\mathrm{mL},$ $9.10\\\\mathrm{mol})$ was added p-TsOH $(15.7\\\\mathrm{g},$ 91 mmol, 0.50 equiv). The mixture was stirred at $25^{\\\\circ}\\\\mathrm{C}$ for $2\\\\textrm{h}$ after which TLC analysis (petroleum ether:EtOAc $= 2:1$ ) showed that the starting material $\\\\left(\\\\mathbb{R}_{\\\\mathrm{f}} = 0.40\\\\right)$ was completely consumed. The pH of the reaction mixture was adjusted to 8.0 with saturated aqueous sodium bicarbonate, and the mixture was extracted with EtOAc $(1\\\\mathrm{L}\\\\times 3)$ .The combined organic layers were washed with brine $(300~\\\\mathrm{mL})$ , dried over anhydrous sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (petroleum ether:EtOAc $= 80:1$ to 0:1) to give the title compound 50 $(330\\\\mathrm{g},63\\\\%)$ as a light yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ $\\\\mathrm{CDCl}_3$ ) $\\\\delta$ 7.36-7.26 (m, 5H), 5.12 (s, 1H), 4.12-4.11 (m, 2H), 4.02-4.01 (m, 1H), 3.34 (s, 6H), 2.75 (s, 2H), 1.77-1.76 (m, 1H), 1.75-1.71 (m, 2H), 1.27-1.23 (m, 2H). \",\"4-(Dimethoxymethyl)piperidine (51). To a mixture of $\\\\mathrm{Pd / C}$ $(10\\\\mathrm{g},5\\\\%)$ in THF $(500~\\\\mathrm{mL})$ was added a solution of benzyl 4- dimethoxymethyl)piperidine-1-carboxylate (50, $95\\\\mathrm{g}$ $324\\\\mathrm{mmol}$ ) in THF $(500~\\\\mathrm{mL})$ at $25^{\\\\circ}C.$ The reaction mixture was purged with $\\\\mathrm{H}_{2}$ three times and was then stirred at $25^{\\\\circ}C$ under an $\\\\mathrm{H}_{2}$ atmosphere (45 psi) for $12\\\\mathrm{h}$ TLC analysis (petroleum ether:EtOAc $= 2:1$ showed that the starting material $(R_{\\\\mathrm{f}} = 0.50)$ was completely consumed. The reaction mixture was filtered, and the filter cake was washed with THF $(1.5\\\\mathrm{L}\\\\times 5)$ .The combined filtrate and washings were concentrated under reduced pressure to provide the title compound 51 as a brown oil. The products obtained from three additional preparations of 51 using the above method and scale were combined to give a single lot of the material $(175\\\\mathrm{g},85\\\\%)$ . ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ $\\\\mathrm{CDCl}_3$ 84.00-3.99 m1H3.31s6H3.07-3.04 m2H2.57-2.51m2H1.73-1.70m1H1.69-1.64m 2H),1.18-1.15m2H). \",\"Methyl 2-(3-(4-(dimethoxymethyl)piperidin-1-yl)isoxazol-5- yl)-3-methylbutanoate (52). To a $25^{\\\\circ}\\\\mathrm{C}$ mixture of intermediate 43 $(160\\\\mathrm{g},332\\\\mathrm{mmol},1.0$ equiv) and 4-(dimethoxymethyl)piperidine (51, $79\\\\mathrm{g},499\\\\mathrm{mmol},1.5$ equiv) in DMF $(1.6~\\\\mathrm{L})$ was added DIEA $(173~\\\\mathrm{mL},997~\\\\mathrm{mmol},3.0$ equiv) in one portion. The mixture was stirred at $80^{\\\\circ}\\\\mathrm{C}$ for $12\\\\mathrm{h}$ then was cooled to $25^{\\\\circ}\\\\mathrm{C}$ and poured into ice-water $(10\\\\mathrm{L})$ . After stirring for $15\\\\mathrm{min}$ the mixture was extracted with EtOAc $(3\\\\mathrm{L}\\\\times 5)$ . The combined organic phases were washed with brine $(1\\\\mathrm{L}\\\\times 3)$ ,dried over sodium sulfate, filtered, and were \"]","page_idx":"29","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[512,71,915,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"concentrated in vacuum. The above procedure was repeated two additional times, and the combined crude products were dissolved in EtOAc $(200\\\\mathrm{mL})$ and filtered to remove insoluble materials. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (petroleum ether:EtOAc, 80:1 to 0:1) to give the title compound 52 $(102\\\\mathrm{g}, 26\\\\%$ yield) as a orange syrup. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}, \\\\mathrm{CDCl}_3)$ $\\\\delta$ 5.90 (s, 1H), 4.06-4.04 (m, 1H), 3.72-3.69 (m, 5H), 3.47-3.45 (m, 1H), 3.36 (s, 6H), 2.82-2.76 (m, 2H), 2.33-2.32 (m, 1H), 1.18-1.18 (m, 1H), 1.77-1.78 (m, 2H), 1.39-1.35 (m, 2H), 0.99-0.98 (m, 3H), 0.92-0.90 (m, 3H). \",\"2-(3-(4-(Dimethoxymethyl)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoic acid (53). A solution of intermediate 52 $(480\\\\mathrm{mg},$ $1.41\\\\mathrm{mmol}$ 1.0 equiv) and LiOH $(102\\\\mathrm{mg}$ $4.23\\\\mathrm{mmol}$ 3.0 equiv) in tetrahydrofuran $(2\\\\mathrm{mL})$ and water $(2\\\\mathrm{mL})$ was stirred at room temperature for $2\\\\mathrm{h}$ The crude reaction mixture was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ ,0 to $100\\\\%$ ) to afford the title compound $(320\\\\mathrm{mg},70\\\\%)$ as a yellow oil. ${}^{1}\\\\mathbf{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 6.13s,1H4.05 $\\\\left(\\\\mathrm{d},J = 6.7\\\\mathrm{Hz},1\\\\mathrm{H}\\\\right)$ 3.63 $\\\\left(\\\\mathrm{d},J = 12.4\\\\mathrm{Hz},2\\\\mathrm{H}\\\\right)$ 3.34 $\\\\left(\\\\mathrm{d},J = 9.0\\\\mathrm{Hz},\\\\right.$ 1H),3.25s,6H),2.76-2.62 m,2H),2.30-2.12 m,1H),1.80- 1.56 m,3H),1.32-1.14 m,2H),0.93 $\\\\left(\\\\mathrm{d},J = 6.6\\\\mathrm{Hz},3\\\\mathrm{H}\\\\right)$ 0.80 d $J$ $= 6.7~\\\\mathrm{Hz}$ 3H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 327 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\"(2S,4R)-4-Hydroxy-1-(2-(3-hydroxyisoxazol-5-yl)-3-methylbutanoyl)-N-(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (55). A solution of intermediate 35 (248 mg, 1.24 mmol, 1.0 equiv), (2S,4R)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (54,46,54 HCl salt, 790 mg, 2.23 mmol, 1.8 equiv), HATU (710 mg, 1.87 mmol, 1.5 equiv) and DIEA (642 mg, 4.98 mmol, 4.0 equiv) in DMF (8 mL) was stirred at room temperature for 2 h. The resulting mixture was diluted with EtOAc (100 mL) and washed with water (100 mL). The organic layer was dried over sodium sulfate and was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CN_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ to afford (2S,4R)-4-hydroxy-1-(2-(3-methoxyisoxazol-5-yl)-3-methylbutanoyl)-N-(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (290 mg, $48\\\\%$ ) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 8.99 (s, 1H), 8.64–8.31 (m, 1H), 7.45–7.29 (m, 4H), 6.16–5.97 (m, 1H), 5.12 (t, $J = 4.1~\\\\mathrm{Hz}$ , 1H), 4.57–4.19 (m, 4H), 3.90–3.64 (m, 4H), 3.57 (s, 1H), 3.45 (d, $J = 10.3~\\\\mathrm{Hz}$ , 1H), 2.45 (d, $J = 4.4~\\\\mathrm{Hz}$ , 3H), 2.30–2.16 (m, 1H), 2.12–1.98 (m, 1H), 1.98–1.81 (m, 1H), 1.00–0.55 (m, 6H). LC-MS $(\\\\mathrm{ES}+)$ : $m/z$ 499 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . A solution of this material (380 mg, 0.762 mmol) and aqueous HBr (40%, 5 mL) was stirred at $60^{\\\\circ}\\\\mathrm{C}$ for $4\\\\mathrm{h}$ . The mixture was cooled to room temperature and was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ to afford the title compound (210 mg, $55\\\\%$ ) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 8.99 (s, 1H), 8.55–8.40 (m, 1H), 7.54–7.27 (m, 4H), 5.95–5.60 (m, 1H), 5.21–4.92 (m, 1H), 4.54–4.19 (m, 4H), 3.81–3.61 (m, 1H), 3.60–3.49 (m, 1H), 3.48–3.36 (m, 1H), 2.45 (d, $J = 4.4~\\\\mathrm{Hz}$ , 3H), 2.32–2.11 (m, 1H), 2.09–1.82 (m, 2H), 1.01–0.55 (m, 6H). LC-MS $(\\\\mathrm{ES}+)$ : $m/z$ 485 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\"(2S,4R)-1-(2-(3-(2-Bromoethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)benzyl)-pyrrolidine-2-carboxamide (56). A mixture of intermediate 55 $(175\\\\mathrm{mg},0.361\\\\mathrm{mmol},1.0$ equiv), 1,2-dibromoethane $(67.8\\\\mathrm{mg},0.361$ mmol, 1.0 equiv) and $\\\\mathrm{Cs_2CO_3}$ $353~\\\\mathrm{mg}$ 1.08 mmol, 3.0 equiv) in $\\\\mathrm{CH}_3\\\\mathrm{CN}$ $(2\\\\mathrm{mL})$ was stirred at $70^{\\\\circ}\\\\mathrm{C}$ for $3\\\\mathrm{h}$ The resulting mixture was cooled to room temperature and was filtered. The filter cake was washed with $\\\\mathrm{CH}_3\\\\mathrm{CN}$ $(10~\\\\mathrm{mL})$ , and the combined filtrate and washings were concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH_4HCO_3}$ 0 to $100\\\\%$ ) to afford the title compound $(123\\\\mathrm{mg},58\\\\%)$ as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8.98s,1H)8.49dt $J = 11.8$ $5.8~\\\\mathrm{Hz}$ 1H7.51-7.29 m4H) 6.19-6.07 m1H5.12 t $J = 3.8~\\\\mathrm{Hz}$ 1H4.71-4.19 m6H) 3.92-3.37 m5H2.44 d $J = 5.1~\\\\mathrm{Hz}$ 3H2.30-2.24 m1H) 2.07-2.01 m1H)1.98-1.83 m1H)1.05-0.50 m6H.LCMS $(\\\\mathrm{ES + })$ .. $m / z~591 / 593[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ \"]","page_idx":"29","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1291 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,70,481,245]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-4-Hydroxy- $N\\cdot$ ((S)-1-(4-(4-methylthiazol-5-yl)- phenyl)ethyl)pyrrolidine-2-carboxamide (57). A solution of tert-butyl (2S,4R)-4-hydroxy-2-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)- ethyl)carbamoyl)pyrrolidine-1-carboxylate[48,55] $(2.56~\\mathrm{g}, 5.93~\\mathrm{mmol})$ and TFA $(5\\mathrm{mL})$ in DCM $(25~\\mathrm{mL})$ was stirred at room temperature overnight. The mixture was then concentrated under reduced pressure, and the residue was purified by silica gel column chromatography (MeOH:DCM, 0:100 to 1:5) to afford the title compound (TFA salt, $2.39\\mathrm{g}$ , $91\\%$ ) as a white solid. ${}^{1}\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) $\\delta$ 9.80 (br, 1H), 9.42–8.95 (m, 2H), 8.64 (s, 1H), 7.55–7.35 (m, 4H), 5.53 (s, 1H), 5.10–4.95 (m, 1H), 4.55–4.28 (m, 2H), 3.35–3.05 (m, 2H), 2.46 (s, 3H), 2.40–2.30 (m, 1H), 1.92–1.74 (m, 1H), 1.43 (d, $J = 7.0~\\mathrm{Hz}$ , 3H). LC-MS $(\\mathrm{ES+})$ : $m/z$ 332 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,245,481,607]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-4-Hydroxy-1-(2-(3-hydroxyisoxazol-5-yl)-3-methylbutanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)-pyrrolidine-2-carboxamide (58). To a room temperature solution of intermediate 57 (TFA salt, $912\\mathrm{mg}$ , $2.05\\mathrm{mmol}$ , 1.0 equiv) in DMF $(7.5\\mathrm{mL})$ were added intermediate 35 $(449\\mathrm{mg},2.25\\mathrm{mmol},1.1\\mathrm{equiv})$ and DIEA $(874\\mathrm{mg},6.77\\mathrm{mmol},3.3\\mathrm{equiv})$ , and HATU $(1.29\\mathrm{g},3.39\\mathrm{mmol},1.65\\mathrm{equiv})$ . The reaction was stirred at room temperature for $1\\mathrm{h}$ , then was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\left(\\mathrm{CH}_3\\mathrm{CN}\\right.$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ , 0 to $100\\%$ to afford $(2S,4R)$ -4-hydroxy-1-(2-(3-methoxyisoxazol-5-yl)-3-methylbutanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide $(865\\mathrm{mg},75\\%)$ as a white solid. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\delta$ 8.98 (s, 1H), 8.48–8.27 (m, 1H), 7.51–7.30 (m, 4H), 6.08 (d, $J = 1.0~\\mathrm{Hz}$ , 1H), 5.10 (t, $J = 3.9~\\mathrm{Hz}$ , 1H), 5.07–4.83 (m, 1H), 4.53–4.32 (m, 1H), 4.27 (s, 1H), 3.90–3.81 (m, 3H), 3.80–3.60 (m, 1H), 3.60–3.44 (m, 2H), 2.49–2.42 (m, 3H), 2.34–2.19 (m, 1H), 2.19–1.98 (m, 1H), 1.98–1.72 (m, 1H), 1.49–1.33 (m, 3H), 1.05–0.71 (m, 6H). LC-MS $(\\mathrm{ES}+)$ : $m/z$ 513 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . A solution of this material $(400\\mathrm{mg},0.78\\mathrm{mmol})$ in aqueous HBr $(40\\%,10\\mathrm{mL})$ was stirred at $60^{\\circ}\\mathrm{C}$ for $4.5\\mathrm{h}$ then was cooled to room temperature and directly purified by prepacked C18 column chromatography $\\left(\\mathrm{CH}_3\\mathrm{CN}\\right.$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ , 0 to $100\\%$ to afford the title compound $(380\\mathrm{mg},98\\%)$ as a white solid. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\delta$ 9.01–8.89 (m, 1H), 8.47–9.25 (m, 1H), 7.51–7.30 (m, 4H), 5.88–5.78 (m, 1H), 5.09 (s, 1H), 5.03–4.85 (m, 1H), 4.56–4.34 (m, 1H), 4.27 (s, 1H), 3.74–3.64 (m, 1H), 3.60–3.02 (m, 2H), 2.49–2.43 (m, 3H), 2.30–2.16 (m, 1H), 2.09–1.97 (m, 1H), 1.84–1.73 (m, 1H), 1.48–1.33 (m, 3H), 1.00–0.72 (m, 6H). LC-MS $(\\mathrm{ES}+)$ : $m/z$ 499 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,607,481,830]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-(2-(3-(2-Bromoethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)-ethyl)pyrrolidine-2-carboxamide (59). A mixture of intermediate 58 $(350\\mathrm{mg},0.702\\mathrm{mmol},1.0\\mathrm{equiv})$ , 1,2-dibromoethane $(263\\mathrm{mg}$ $1.40\\mathrm{mmol},2.0\\mathrm{equiv})$ and $\\mathrm{Cs_2CO_3}$ $(457\\mathrm{mg},1.41\\mathrm{mmol},2.0\\mathrm{equiv})$ in $\\mathrm{CH}_3\\mathrm{CN}$ $(3.5\\mathrm{mL})$ was stirred at $70^{\\circ}\\mathrm{C}$ for $2\\textrm{h}$ then was cooled to room temperature. The mixture was then filtered, and the filter cake was washed with $\\mathrm{CH}_3\\mathrm{CN}$ $(10~\\mathrm{mL})$ . The combined filtrate and washings were concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\%)$ $\\mathrm{NH_4HCO_3}$ 0 to $100\\%$ ) to afford the title compound $(160\\mathrm{mg},38\\%)$ as a light yellow solid. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ DMSO $d_{6})$ $\\delta$ 9.02-8.88 (m, 1H), 8.47-8.25 (m, 1H), 7.52-7.28 (m, 4H), 6.19-6.08 (m, 1H), 5.09 (t, $J = 3.5~\\mathrm{Hz}$ 1H), 4.98-4.85 (m, 1H), 4.56-4.33 (m, 3H), 4.27 (s, 1H), 3.85-3.63 (m, 3H), 3.59-3.38 (m, 2H), 2.47-2.42 (m, 3H), 2.35-2.20 (m, 1H), 2.19-1.98 (m, 1H), 1.97-1.70 (m, 1H), 1.50-1.31 (m, 3H), 1.02-0.73 (m, 6H). LCMS $(\\mathrm{ES + })$ .. $m / z$ 605/607 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,830,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-(2-(3-(2,2-Diethoxyethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (60). A solution of intermediate 42 (4.80 g, 15.9 mmol, 1.01 equiv), (2S,4R)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (57, 5.78 g, 15.7 mmol, 1.0 equiv), HATU (7.29 g, 19.2 mmol, 1.2 equiv) and DIEA (6.19 g, 48.0 mmol, 3.06 equiv) in DMF (60 mL) was stirred at room temperature for 30 min. The reaction mixture was then directly purified by prepacked C18 column ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,383]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ 0 to $100\\%$ to afford $7.8\\mathrm{g}$ of a $\\sim 1:1$ mixture of 60 and the corresponding isopropyl epimer (structure not shown) as a yellow solid. This mixture was separated by preparative chiral SFC [column: CHIRAL ART Amylose-SA, $5\\times 25~\\mathrm{cm}^2$ $5\\mu \\mathrm{m}$ mobile phase A: $\\mathrm{CO}_{2}$ mobile phase B: MeOH; flow rate: $200~\\mathrm{mL / min}$ ; gradient: isocratic $40\\%$ B; column temperature $35^{\\circ}\\mathrm{C}$ back pressure: 100 bar; wavelength: 220 nm; RT1:2.61 min; RT2:3.63 min; sample solvent: MeOH $(0.1\\% 2\\mathrm{M}$ $\\mathrm{NH}_3$ -MeOH)] to yield $2.57\\mathrm{g}$ faster peak (60e, isopropyl isomer corresponding to 60, structure not shown) and $3.00\\mathrm{g}$ slower peak (desired isopropyl isomer, 60, $31\\%$ ) as yellow solids. Faster peak (undesired isomer, 60e): ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz},$ DMSO- $d_{6})$ 9.02 s, 1H),8.31 d, $J = 7.8\\mathrm{Hz}$ 1H),7.58-7.29 m4H),6.16s1H),5.09 $\\left(\\mathrm{d},J = 3.6\\mathrm{Hz},1\\mathrm{H}\\right)$ 5.05-4.71 m,2H),4.52-4.38 m,1H),4.25 s, 1H),4.19-4.04 m,2H),3.83-3.39 m,7H),2.44 d, $J = 3.4\\mathrm{Hz}$ 3H),2.32-1.74 m,3H),1.54-1.30 m,3H),1.23-1.09 m,6H), 1.08-0.73 m,6H).LC-MS $(\\mathrm{ES + })$ ..m/z 615 $[\\mathbf{M} + \\mathbf{H}]^{+}$ .Slower peak (desired isomer, 60): ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz},$ DMSO- $d_{6})$ 8.97 d, $J =$ $2.6\\mathrm{Hz},1\\mathrm{H})$ 8.40d $J = 7.7\\mathrm{Hz},1\\mathrm{H})$ 7.50-7.26 m,4H),6.12 s, 1H),5.08 d, $J = 3.3\\mathrm{Hz},1\\mathrm{H})$ ,4.95-4.80 m,1H),4.79 t $J = 5.2\\mathrm{Hz}$ 1H),4.36 t, $J = 7.8\\mathrm{Hz},1\\mathrm{H})$ ,4.26 s, 1H),4.08 d, $J = 5.2\\mathrm{Hz},2\\mathrm{H})$ 3.73-3.36 m,7H),2.44 d, $J = 1.5\\mathrm{Hz},3\\mathrm{H})$ ,2.29-1.96 m,2H), 1.80-1.65 m,1H),1.50-1.30 m,3H),1.20-1.05 m,6H),1.05- 0.90 m,3H),0.85-0.70 m,3H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 615 $[\\mathbf{M}+$ $\\mathrm{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,383,915,568]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-4-Hydroxy-1-((R)-3-methyl-2-(3-(2-oxoethoxy)-isoxazol-5-yl)butanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (61). A solution of intermediate 60 $(200\\mathrm{mg},0.325\\mathrm{mmol})$ in $1\\mathrm{M}\\mathrm{H}_2\\mathrm{SO}_4$ $(3\\mathrm{mL})$ and THF $(3\\mathrm{mL})$ was stirred at $50^{\\circ}\\mathrm{C}$ for $5\\mathrm{h}$ then was concentrated under reduced pressure. The $\\mathsf{pH}$ of the residue was adjusted to 7.0 with saturated aqueous $\\mathrm{NaHCO_3}$ solution, and the resulting mixture was extracted with EtOAc $(100~\\mathrm{mL}\\times 3)$ . The combined organic layers were washed with brine $(50~\\mathrm{mL})$ , dried over sodium sulfate, and were concentrated under reduced pressure to afford the crude title compound $(220\\mathrm{mg})$ as a yellow solid. The crude product was used in subsequent steps without further purification. LC-MS $(\\mathrm{ES}+)$ : $m/z$ 541 $[\\mathrm{M} + \\mathrm{H}]^{+}$ . Similar transformation of intermediate 60e afforded compound 61e (isopropyl isomer corresponding to 61, structure not shown). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,568,915,792]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(2-(2-(2-((4-Bromopyridin-2-yl)oxy)ethoxy)ethoxy)-ethoxy)ethan-1-ol (64). To a $0^{\\circ}\\mathrm{C}$ solution of 3,6,9-trioxaundecane-1,11-diol $(63,4.78\\mathrm{g},24.6\\mathrm{mmol},2.0$ equiv) in DMF $(25~\\mathrm{mL})$ was added NaH $(60\\%)$ in mineral oil, $540\\mathrm{mg}$ $13.5\\mathrm{mmol}$ 1.1 equiv). The reaction was warmed to room temperature and was stirred for 30 min whereupon 4-bromo-2-fluoropyridine $(62,2.17\\mathrm{g},12.3\\mathrm{mmol},1.0$ equiv) was added. The resulting mixture was stirred for additional $2\\textrm{h}$ at $75^{\\circ}\\mathrm{C}$ then was cooled to $0^{\\circ}\\mathrm{C}$ and was quenched with water (100 mL). The resulting mixture was extracted with EtOAc $(150~\\mathrm{mL}\\times 3)$ , and the combined organic layers were dried over sodium sulfate and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 100:0) to afford the title compound $(3.0\\mathrm{g},70\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 8.07 d $J = 5.5\\mathrm{Hz}$ 1H7.23dd $J = 5.5$ $1.7\\mathrm{Hz}$ 1H 7.15d $J = 1.6\\mathrm{Hz}$ 1H4.58t $J = 5.4\\mathrm{Hz}$ 1H4.43-4.34m2H 3.78-3.68m2H3.62-3.45m10H3.45-3.36m2H.LCMS $(\\mathrm{ES + })$ .. $m / z$ 350 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,791,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(2-(2-(2-((4-Bromopyridin-2-yl)oxy)ethoxy)ethoxy)-ethoxy)acetic acid (65). A solution of intermediate 64 $(1.68\\mathrm{g},4.81$ mmol, 1.0 equiv), TEMPO $(149~\\mathrm{mg}$ $0.96\\mathrm{mmol}$ $0.20$ equiv and $\\mathrm{PhI(OAc)_2}$ $(4.63\\mathrm{g},14.4\\mathrm{mmol},3.0$ equiv) in DCM $(15~\\mathrm{mL})$ and water $(7.5~\\mathrm{mL})$ was stirred at room temperature for $2\\textrm{h}$ The resulting mixture was extracted with EtOAc $(100~\\mathrm{mL}\\times 3)$ ,and the combined organic layers were washed with water $(100~\\mathrm{mL})$ , dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (MeOH:DCM, 0:100 to 7:93) to afford the title compound $(810\\mathrm{mg},$ $46\\%)$ as a yellow oil. ${}^{1}\\mathbf{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 8 12.56s, 1H),8.07d $J = 5.5\\mathrm{Hz}$ 1H),7.23dd $J = 5.5$ $1.7\\mathrm{Hz}$ 1H),7.15d, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1292 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,71,481,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"$J = 1.6\\\\mathrm{Hz}$ 1H),4.43-4.34 (m,2H),4.02 (s,2H),3.78-3.69 (m, 2H),3.63-3.48 (m,8H). LC-MS $(\\\\mathrm{ES} + )$ .. $m / z$ 364 $[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ \",\"Methyl 2-(2-(2-(4-bromopyridin-2-yl)oxy)ethoxy)-ethoxy)ethoxy)acetate (66). To a $0^{\\\\circ}\\\\mathrm{C}$ solution of intermediate 65 $(790\\\\mathrm{mg},$ 2.17 mmol, 1.0 equiv) in MeOH $(8\\\\mathrm{mL})$ was added $\\\\mathrm{SOCl}_2$ $(1.02\\\\mathrm{g},$ 8.68 mmol, 4.0 equiv). The reaction was warmed to room temperature and was stirred for $4\\\\mathrm{h}$ After quenching the reaction with aqueous $\\\\mathrm{NaHCO_3}$ solution (to adjust the $\\\\mathsf{pH}$ to $\\\\sim 8)$ the resulting mixture was extracted with DCM $(100~\\\\mathrm{mL}\\\\times 3)$ .The combined organic layers were washed with water $(100~\\\\mathrm{mL})$ ,dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure to afford the title compound $(600\\\\mathrm{mg},73\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ ,DMSO- $d_{6})$ $\\\\delta 8.07$ d $J = 5.5\\\\mathrm{Hz}$ 1H),7.23dd $J = 5.5$ 1.7 Hz1H),7.18-7.12 m1H),4.43-4.34 m,2H),4.13s,2H),3.78-3.68m2H),3.65s,3H),3.62-3.49 m,8H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z378[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ \",\"tert-Butyl 8-(2-((3-oxo-2,5,8,11-tetraoxatridecan-13-yl)oxy)-pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate (68). A solution of intermediate 66 $(580\\\\mathrm{mg},1.53\\\\mathrm{mmol},1.0$ equiv), tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, $651~\\\\mathrm{mg}$ 3.07 mmol, 2.0 equiv), RuphosPd G2 (119 mg, 0.15 mmol, 0.10 equiv) and $\\\\mathrm{Cs}_2\\\\mathrm{CO}_3$ $(1.50\\\\mathrm{g},4.60\\\\mathrm{mmol},3.0$ equiv) in toluene (10 mL) was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for $^{\\\\textrm{\\\\scriptsize 4h}}$ . After cooling to room temperature, the mixture was diluted with EtOAc $(100~\\\\mathrm{mL})$ and was washed with water $(100~\\\\mathrm{mL})$ . The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 90:10) to afford the title compound $(670~\\\\mathrm{mg},85\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 7.78 d $J = 6.0~\\\\mathrm{Hz}$ 1H)6.49dd $J = 6.0$ $2.1\\\\mathrm{Hz}$ 1H) 6.15d $J = 2.0\\\\mathrm{Hz}$ 1H4.36s2H4.29t $J = 4.8~\\\\mathrm{Hz}$ 2H4.14 s,2H)3.74-3.66 m2H)3.64 s,3H)3.62-2.50(m,10H)3.07 d $J = 12.9\\\\mathrm{Hz}$ 1H)2.93d $J = 13.0\\\\mathrm{Hz}$ 1H)1.96-1.86m2H) 1.74-1.61 m,2H),1.39 s,9H.LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 510 $[\\\\mathbf{M}+$ $\\\\mathrm{H}]^{+}$ \",\"Methyl 2-(2-(2-(2-((4-(3,8-diazabicyclo[3.2.1]octan-8-yl)-pyridin-2-yl)oxy)ethoxy)ethoxy)ethoxy)ethoxy)acetate (69). A solution of intermediate 68 $(555\\\\mathrm{mg},1.09\\\\mathrm{mmol})$ in TFA $(1\\\\mathrm{mL})$ and DCM $(5\\\\mathrm{mL})$ was stirred at room temperature for $2\\\\textrm{h}$ The volatiles were removed under vacuum, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ 0 to $100\\\\%$ ) to afford the title compound $(380\\\\mathrm{mg},85\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ ,DMSO- $d_{6})$ 7.72d $J = 6.0~\\\\mathrm{Hz}$ 1H),6.40 (dd, $J = 6.0$ $2.1\\\\mathrm{Hz}$ 1H),6.01d $J = 2.1\\\\mathrm{Hz}$ 1H),4.28t $J = 4.8\\\\mathrm{Hz}$ 2H),4.16s,2H),4.14s,2H),3.73-3.66m2H),3.65s,3H), 3.62-3.51 m8H),2.84 d $J = 12.2\\\\mathrm{Hz}$ 2H),2.43d $J = 12.2\\\\mathrm{Hz}$ 2H),1.99-1.80 m,4H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 410 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\"Methyl 2-(2-(2-(4-(3-(3-amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)ethoxy)acetate (71). A solution of intermediate 69 (460 mg, 1.12 mmol, 1.0 equiv), 4-bromo-6-chloro-pyridazin-3-amine (70, 351 mg, 1.69 mmol, 1.5 equiv) and DIEA (434 mg, 3.37 mmol, 3.0 equiv) in NMP (8 mL) was stirred at $120^{\\\\circ}\\\\mathrm{C}$ for 3 h. After cooling to room temperature, the crude mixture was purified by prepacked C18 column chromatography $\\\\left(\\\\mathrm{CH}_3\\\\mathrm{CN}\\\\right.$ in water $(0.05\\\\%)$ $\\\\mathrm{NH_4HCO_3)}$ , 0 to $100\\\\%$ ) to afford the title compound $(300~\\\\mathrm{mg},~50\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 7.78 d $J = 6.0\\\\mathrm{Hz}$ 1H6.90s1H) 6.52dd $J = 6.1$ $2.1\\\\mathrm{Hz}$ 1H6.17d $J = 2.0\\\\mathrm{Hz}$ 1H5.84s2H) 4.47s2H4.34-4.26m2H4.13s2H3.73-3.66m2H) 3.64s3H)3.62-3.50m8H)3.18d $J = 11.6\\\\mathrm{Hz}$ 2H2.87d $J$ $= 11.6\\\\mathrm{Hz}$ 2H)2.20-2.10m2H)1.98-1.89m2H.LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 537 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\"Methyl 2-(2-(2-(2-((4-(3-(3-amino-6-(2-hydroxyphenyl)- pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)- oxy)ethoxy)ethoxy)ethoxy)acetate (73). A solution of intermediate 71 $(290\\\\mathrm{mg},0.54\\\\mathrm{mmol},1.0$ equiv), 2-hydroxyphenylboronic acid $(72,223\\\\mathrm{mg},1.62\\\\mathrm{mmol},3.0$ equiv), $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ $(223\\\\mathrm{mg},1.62\\\\mathrm{mmol},$ 3.0 equiv) and $\\\\mathrm{Pd(PPh_3)_4}$ $(62.3\\\\mathrm{mg},0.0538\\\\mathrm{mmol},0.10$ equiv) in 1,4- dioxane $(3\\\\mathrm{mL})$ was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for $2\\\\textrm{h}$ then was cooled to room temperature. The resulting mixture was diluted with EtOAc $(100~\\\\mathrm{mL})$ and was washed with water $(100~\\\\mathrm{mL})$ .The organic layer was dried \"]","page_idx":"31","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[512,71,915,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ to afford the title compound $(120~\\\\mathrm{mg},37\\\\%)$ as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.15 (s, 1H), 7.93 (dd, $J = 8.1$ $1.6\\\\mathrm{Hz}$ 1H), 7.80 (d, $J = 6.0\\\\mathrm{Hz}$ 1H), 7.51 (s, 1H), 7.27-7.18 (m, 1H), 6.91-6.81 (m, 2H), 6.55 (dd, $J = 6.1$ $2.1\\\\mathrm{Hz}$ 1H), 6.20 (d, $J = 2.1\\\\mathrm{Hz}$ 1H), 5.98 (s, 2H), 4.51 (d, $J = 4.4\\\\mathrm{Hz}$ 2H), 4.33-4.26 (m, 2H), 4.13 (s, 2H), 3.73-3.66 (m, 2H), 3.64 (s, 3H), 3.62-3.50 (m, 8H), 3.25 (d, $J = 11.3\\\\mathrm{Hz}$ ,2H), 3.03 (d, $J = 11.6\\\\mathrm{Hz}$ ,2H), 2.23-2.15 (m, 2H), 2.01-1.94 (m, 2H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 595 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\"2-(2-(2-(4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4- yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)- ethoxy)ethoxy)acetic acid (74). A solution of intermediate 73 $(120\\\\mathrm{mg},0.20\\\\mathrm{mmol},1.0$ equiv) and LiOH $(9.7\\\\mathrm{mg},0.40\\\\mathrm{mmol},2.0$ equiv) in THF $(2\\\\mathrm{mL})$ and water $(2\\\\mathrm{mL})$ was stirred at room temperature for $^{\\\\textrm{\\\\scriptsize 1h}}$ . The crude mixture was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.1\\\\%)$ TFA), 0 to $100\\\\%$ ) to afford the title compound $(110\\\\mathrm{mg},94\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 7.93 d $J = 7.0~\\\\mathrm{Hz}$ 1H),7.63d $J = 7.4\\\\mathrm{Hz}$ 1H),7.52s,1H),7.42-7.31m1H) 7.05-6.91 m,2H),6.89-6.72 m,3H),6.55 s,1H),4.84 s,2H) 4.48-4.41 m,2H),4.01 s,2H),3.84-3.75 m,2H),3.64-3.50 m, 10H),3.23-3.12 m,2H),2.29-2.19 m,2H),2.08-1.95 m,2H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 581 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\"(2S,4R)-1-((2S)-14-((4-(3-(3-Amino-6-(2-hydroxyphenyl)-pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)-2-(tert-butyl)-4-oxo-6,9,12-trioxa-3-azatetradecanoyl)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (11). A room temperature solution of intermediate 74 $(110\\\\mathrm{mg},0.19\\\\mathrm{mmol},1.1$ equiv), intermediate $75^{48}$ (HCl salt, 81.5 mg, 0.174 mmol, 1.0 equiv), HATU $(108\\\\mathrm{mg},0.284\\\\mathrm{mmol},1.6$ equiv) and DIEA $(164\\\\mathrm{mg},1.27\\\\mathrm{mmol},7.3$ equiv) in DMF $(3\\\\mathrm{mL})$ was stirred for $2\\\\mathrm{h}$ . The resulting mixture was diluted with EtOAc $(100\\\\mathrm{mL})$ and was washed with water $(100\\\\mathrm{mL})$ . The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by preparative HPLC [column: XBridge Prep OBD C18 column, 30 $\\\\times 150\\\\mathrm{mm}^2$ , $5\\\\mu \\\\mathrm{m}$ ; mobile phase A: water $(10\\\\mathrm{mmol / L}$ $\\\\mathrm{NH_4HCO_3})$ , mobile phase B: $\\\\mathrm{CH}_3\\\\mathrm{CN}$ ; flow rate: $60~\\\\mathrm{mL / min}$ ; gradient: $39\\\\%$ B to $56\\\\%$ B over $9\\\\mathrm{min}$ ; RT: $8.1\\\\mathrm{min}$ ] to afford the title compound $(49\\\\mathrm{mg},26\\\\%)$ as a white solid. ${}^{1}\\\\mathbf{H}$ NMR $(300\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 14.14 (s, 1H), 8.97 (s, 1H), 8.60 (t, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 7.96-7.87 (m, 1H), 7.78 (d, $J = 5.9~\\\\mathrm{Hz}$ , 1H), 7.49 (s, 1H), 7.45-7.35 (m, 5H), 7.22 (t, $J = 7.8~\\\\mathrm{Hz}$ , 1H), 6.91-6.79 (m, 2H), 6.57-6.51 (m, 1H), 6.18 (s, 1H), 5.97 (s, 2H), 5.14 (d, $J = 3.5~\\\\mathrm{Hz}$ , 1H), 4.56 (d, $J = 9.7~\\\\mathrm{Hz}$ , 1H), 4.52-4.48 (m, 2H), 4.47-4.39 (m, 1H), 4.39-4.33 (m, 2H), 4.31-4.25 (m, 3H), 3.97 (s, 2H), 3.72-3.52 (m, 12H), 3.25 (d, $J = 11.4~\\\\mathrm{Hz}$ , 2H), 3.02 (d, $J = 11.6~\\\\mathrm{Hz}$ , 2H), 2.44 (s, 3H), 2.23-2.14 (m, 2H), 2.12-2.00 (m, 1H), 2.00-1.87 (m, 3H), 0.94 (s, 9H). LC-MS $(ES+)$ : $m/z$ 993 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\"2-(2-(2-((4-Bromopyridin-2-yl)oxy)ethoxy)ethoxy)ethoxy)ethan-1-ol (81). A solution of 3,6-dioxoacetane-1,8-diol (80, 853 mg, 5.68 mmol, 2.0 equiv) and NaH (60% in mineral oil, 114 mg, 2.85 mmol, 1.05 equiv) in DMF (10 mL) was stirred at $0^{\\\\circ}\\\\mathrm{C}$ for 30 min. 4-Bromo-2-fluoro-pyridine (62, 500 mg, 2.84 mmol, 1.0 equiv) was then added and the resulting mixture was stirred at room temperature for 1 h. The reaction was quenched with saturated aqueous $\\\\mathrm{NH}_4\\\\mathrm{Cl}$ (100 mL) and was extracted with EtOAc (100 mL × 3). The combined organic layers were dried over sodium sulfate and were concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3$ ), 0 to 100%) to afford the title compound (600 mg, 69%) as a colorless oil. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 8.07 (d, J = 5.5 Hz, 1H), 7.23 (dd, J = 5.5, 1.6 Hz, 1H), 7.15 (d, J = 1.6 Hz, 1H), 4.58 (t, J = 5.4 Hz, 1H), 4.43–4.33 (m, 2H), 3.78–3.68 (m, 2H), 3.62–3.36 (m, 8H). LC-MS (ES+): m/z 306 [M + H]+. \",\"tert-Butyl 8-(2-(2-(2-(2-hydroxyethoxy)ethoxy)ethoxy)-pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate (82). A solution of tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, $3.22\\\\mathrm{g}$ , 15.1 mmol, 1.5 equiv), intermediate 81 (3.10 g, 10.1 \"]","page_idx":"31","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,951,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1293 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,71,481,260]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"mmol, 1.0 equiv), RuPhosPd G3 (785 mg, 0.937 mmol, 0.10 equiv) and $\\mathrm{Cs_2CO_3}$ (9.90 g, 30.4 mmol, 3.0 equiv) in 1,4-dioxane (30 mL) was stirred at $90^{\\circ}\\mathrm{C}$ for 2 h. The reaction was cooled to room temperature and was quenched by the addition of saturated aqueous $\\mathrm{NH}_4\\mathrm{Cl}$ (100 mL). The resulting mixture was extracted with EtOAc (100 mL × 3), and the combined organic layers were dried over sodium sulfate, filtered, and concentrated under vacuum. The residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% $\\mathrm{NH}_4\\mathrm{HCO}_3$ ), 0 to 100%) to afford the title compound (4.3 g, 97%) as a colorless oil. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_{6}$ ) δ 7.78 (d, $J = 5.9~\\mathrm{Hz}$ , 1H), 6.50 (dd, $J = 6.1$ , 2.1 Hz, 1H), 6.15 (d, $J = 2.0~\\mathrm{Hz}$ , 1H), 4.59 (t, $J = 5.4~\\mathrm{Hz}$ , 1H), 4.36 (s, 2H), 4.29 (t, $J = 4.8~\\mathrm{Hz}$ , 2H), 3.69 (t, $J = 4.8~\\mathrm{Hz}$ , 2H), 3.65–3.37 (m, 10H), 3.07 (d, $J = 12.9~\\mathrm{Hz}$ , 1H), 2.93 (d, $J = 13.0~\\mathrm{Hz}$ , 1H), 1.96–1.86 (m, 2H), 1.74–1.56 (m, 2H), 1.40 (s, 9H). LC-MS (ES+): m/z 438 [M + H]+. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,260,481,410]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(2-(2-((4-(3,8-Diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)ethoxy)ethoxy)ethan-1-ol (83). Intermediate 82 $(4.30\\mathrm{g},9.83$ mmol) was stirred at room temperature for $^{\\textrm{\\scriptsize 4h}}$ in a solution of HCl $(4.0\\mathrm{M})$ in MeOH $(50~\\mathrm{mL})$ . The resulting mixture was concentrated under vacuum to afford the crude title compound (HCl salt, $2.8\\mathrm{g}$ ) as a white solid. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ DMSO- $d_{6}$ 8 10.26s1H9.73 s,1H),7.98d $J = 7.2\\mathrm{Hz}$ 1H),6.88dd $J = 7.3$ $2.1\\mathrm{Hz}$ 1H),6.63 d $J = 2.2\\mathrm{Hz}$ 1H),4.88s,2H),4.50t $J = 4.1\\mathrm{Hz}$ 2H),4.13s, 1H),3.81t $J = 4.3\\mathrm{Hz}$ 2H),3.56-3.53m3H),3.50-3.47 m, 2H),3.45-3.37m2H),3.25d $J = 13.4\\mathrm{Hz}$ 1H),3.17d $J = 12.1$ Hz,2H),3.11-2.99m2H),2.30-2.20m2H),2.15-2.04m, 2H).LC-MS $(\\mathrm{ES + })$ .. $m / z$ 338 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,410,481,607]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(2-(2-((4-(3-(3-Amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)ethan-1-ol (84). A solution of intermediate 83 (HCl salt, $1.00\\mathrm{g}$ , $2.67\\mathrm{mmol}$ , $1.0$ equiv), 4-bromo-6-chloro-pyridazin-3-amine $(70,617\\mathrm{mg},2.96\\mathrm{mmol},1.1$ equiv) and DIEA $(1.15\\mathrm{g},8.89\\mathrm{mmol},3.3$ equiv) in NMP $(10\\mathrm{mL})$ was stirred at $120^{\\circ}\\mathrm{C}$ for $8\\mathrm{h}$ . After cooling to room temperature, the crude reaction mixture was directly purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\%)$ $\\mathrm{NH}_4\\mathrm{HCO}_3)$ , 0 to $100\\%$ to afford the title compound $(600\\mathrm{mg},44\\%$ over 2 steps) as a colorless oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\delta$ 7.78 (d, $J = 6.0~\\mathrm{Hz}$ , 1H), 6.90 (s, 1H), 6.52 (dd, $J = 6.1$ , $2.1~\\mathrm{Hz}$ , 1H), 6.17 (d, $J = 2.0~\\mathrm{Hz}$ , 1H), 5.84 (s, 2H), 4.58 (t, $J = 5.4~\\mathrm{Hz}$ , 1H), 4.46 (d, $J = 4.5~\\mathrm{Hz}$ , 2H), 4.29 (dd, $J = 5.8$ , $3.7~\\mathrm{Hz}$ , 2H), 3.69 (dd, $J = 5.8$ , $3.7~\\mathrm{Hz}$ , 2H), 3.60–3.51 (m, 4H), 3.48 (t, $J = 5.0~\\mathrm{Hz}$ , 2H), 3.45–3.39 (m, 2H), 3.23–3.13 (m, 2H), 2.87 (d, $J = 11.6~\\mathrm{Hz}$ , 2H), 2.19–2.08 (m, 2H), 1.98–1.88 (m, 2H). LC-MS $(ES+)$ : $m/z$ 465 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,607,481,867]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(2-(2-((4-(3-(3-Amino-6-(2-(methoxymethoxy)phenyl)- pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)ethan-1-ol (86). A solution of intermediate 84 $(493\\mathrm{mg},1.06\\mathrm{mmol},1.0$ equiv), (2-(methoxymethoxy)phenyl)- boronic acid $(85,289\\mathrm{mg},1.59\\mathrm{mmol},1.5$ equiv), $\\mathrm{Pd(PPh_3)_4}$ 122 mg, 0.11 mmol. 0.10 equiv) and $\\mathrm{K}_2\\mathrm{CO}_3$ 438 mg, 3.18 mmol, 3.0 equiv) in 1,4-dioxane $(5\\mathrm{mL})$ and water $(0.5\\mathrm{mL})$ was stirred at $100^{\\circ}C$ for $4\\mathrm{h}$ . After cooling to room temperature, the reaction was diluted with water $(100~\\mathrm{mL})$ and extracted with EtOAc $(100~\\mathrm{mL}\\times$ 3). The combined organic layers were dried over sodium sulfate, filtered, and were concentrated under vacuum. The residue was purified by silica gel chromatography (MeOH:DCM, 0:100 to 13:87) to afford the title compound $(540\\mathrm{mg},73\\%)$ as a brown solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 7.77 d $J = 6.0~\\mathrm{Hz}$ 1H),7.58dd $J =$ 7.6,1.8 Hz,1H),7.40-7.28 m,1H),7.18-7.11 m,2H),7.11-7.03 m,1H),6.52 dd $J = 6.1$ 2.1 Hz,1H),6.18 d $J = 2.0~\\mathrm{Hz}$ 1H),5.73 s,2H),5.14 s,2H),4.58 t $J = 5.3~\\mathrm{Hz}$ 1H),4.48 s,2H),4.28 dd $J = 5.9$ 3.7 Hz,2H),3.68dd $J = 5.8$ 3.7 Hz2H),3.60-3.46 m, 6H),3.44-3.37 m,2H),3.23 s,3H),3.14 d $J = 11.3~\\mathrm{Hz}$ ,2H), 2.85 d $J = 11.3~\\mathrm{Hz}$ ,2H),2.24-2.13 m,2H),2.01-1.91 m,2H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 567 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,867,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(2-(2-((4-(3-(3-Amino-6-(2-(methoxymethoxy)phenyl)- pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)ethyl 4-methylbenzenesulfonate (87). A solution of intermediate 86 $(371\\mathrm{mg},0.655\\mathrm{mmol},1.0$ equiv), 4- methylbenzenesulfonyl chloride $(124\\mathrm{mg},0.651\\mathrm{mmol},1.0$ equiv), DMAP $(7.9\\mathrm{mg},0.065\\mathrm{mmol},0.10$ equiv) and TEA $(198\\mathrm{mg},1.96$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,235]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"mmol, 3.0 equiv) in DCM (3 mL) was stirred at room temperature for 10 h. The resulting mixture was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (MeOH/DCM, 0:100 to 13:87) to afford the title compound (400 mg, 85%) as a white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_{6}$ ) $\\delta$ 7.81-7.73 (m, 3H), 7.58 (dd, $J = 7.6$ , 1.8 Hz, 1H), 7.45 (d, $J = 8.1\\mathrm{Hz}$ , 2H), 7.41-7.28 (m, 1H), 7.14 (t, $J = 4.1\\mathrm{Hz}$ , 2H), 7.07 (t, $J = 7.6\\mathrm{Hz}$ , 1H), 6.56-6.48 (m, 1H), 6.17 (d, $J = 2.0\\mathrm{Hz}$ , 1H), 5.74 (s, 2H), 5.14 (s, 2H), 4.48 (s, 2H), 4.27 (t, $J = 4.8\\mathrm{Hz}$ , 2H), 4.15-4.06 (m, 2H), 3.65 (t, $J = 4.9\\mathrm{Hz}$ , 2H), 3.61-3.52 (m, 2H), 3.51-3.40 (m, 4H), 3.22 (s, 3H), 3.14 (d, $J = 11.4\\mathrm{Hz}$ , 2H), 2.85 (d, $J = 11.4\\mathrm{Hz}$ , 2H), 2.39 (s, 3H), 2.24-2.10 (m, 2H), 2.03-1.87 (m, 2H). LC-MS (ES+): $m/z$ 721 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,235,915,695]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-(2-(3-(2-(2-((4-(3-(3-Amino-6-(2- (methoxymethoxy)phenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (88). A solution of intermediate 87 $(400\\mathrm{mg},0.55\\mathrm{mmol},1.0$ equiv), $(2S,4R)\\cdot +$ hydroxy-1-(2-(3-hydroxyisoxazol-5-yl)-3-methylbutanoyl)- $N$ -(4-(4- methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (55, 268 mg, 0.55 mmol, 1.0 equiv) and $\\mathrm{K}_2\\mathrm{CO}_3$ $(229\\mathrm{mg},1.66\\mathrm{mmol},3.0$ equiv) in DMF $(5\\mathrm{mL})$ was stirred at $60^{\\circ}\\mathrm{C}$ for $4\\mathrm{h}$ . The mixture was allowed to cool to room temperature then was quenched with saturated aqueous $\\mathrm{NH_4Cl}$ $(100~\\mathrm{mL})$ and was extracted with EtOAc $(100~\\mathrm{mL}\\times$ 3). The combined organic layers were dried over sodium sulfate, filtered, and the filtrate was concentrated under vacuum. The residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH_4HCO_3})$ , 0 to $100\\%$ ) to afford the title compound ( $\\sim 1:1$ mixture of isopropyl group isomers, $180\\mathrm{mg}$ $31\\%$ yield) as a white solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6}$ ) $\\delta$ 8.98 (d, $J = 4.1~\\mathrm{Hz}$ 1H), 8.58-8.42 (m, 1H), 7.76 (dd, $J = 6.0$ $2.1\\mathrm{Hz}$ 1H), 7.58 (dd, $J =$ 7.3, 1.6 Hz, 1H), 7.48-7.27 (m, 5H), 7.18-7.10 (m, 2H), 7.06 (t, $J =$ 7.5 Hz, 1H), 6.56-6.48 (m, 1H), 6.18 (d, $J = 2.1~\\mathrm{Hz}$ 1H), 6.09 (d, $J$ $= 8.9~\\mathrm{Hz}$ , 1H), 5.73 (s, 2H), 5.28-4.95 (m, 3H), 4.48 (s, 2H), 4.43- 4.15 (m, 8H), 3.82-3.36 (m, 11H), 3.22 (d, $J = 1.5~\\mathrm{Hz}$ , 3H), 3.14 (d, $J =$ $11.4~\\mathrm{Hz}$ , 2H), 2.85 (d, $J = 11.4~\\mathrm{Hz}$ , 2H), 2.44 (dd, $J = 4.7$ $2.8~\\mathrm{Hz}$ - 3H), 2.32-2.11 (m, 3H), 2.11-1.82 (m, 4H), $0.98 - 0.55$ (m, 6H). LC-MS $(\\mathrm{ES}+)$ : $m / z$ 1033 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . A small amount of the corresponding isoxazole $N$ -alkylation product (structure not shown) eluted ahead of compound 88 and was isolated as a white solid (20 mg, $4\\%$ ). ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6}$ ) $\\delta$ 8.98 (d, $J = 3.9~\\mathrm{Hz}$ , 1H), 8.60-8.43 (m, 1H), 7.76 (d, $J = 5.9~\\mathrm{Hz}$ , 1H), 7.58 (dd, $J = 7.7$ , 1.8 Hz, 1H), 7.46-7.38 (m, 3H), 7.37-7.29 (m, 2H), 7.18-7.11 (m, 2H), 7.06 (td, $J = 7.5$ , 1.1 Hz, 1H), 6.52 (dd, $J = 6.1$ , 2.1 Hz, 1H), 6.17 (t, $J = 2.2~\\mathrm{Hz}$ , 1H), 5.78-5.67 (m, 3H), 5.20-5.00 (m, 3H), 4.47 (d, $J = 4.4~\\mathrm{Hz}$ , 2H), 4.45-4.19 (m, 6H), 3.97-3.86 (m, 2H), 3.75-3.41 (m, 11H), 3.22 (s, 3H), 3.14 (d, $J = 11.4~\\mathrm{Hz}$ , 2H), 2.85 (d, $J =$ $11.4~\\mathrm{Hz}$ , 2H), 2.47-2.42 (m, 3H), 2.31-2.13 (m, 3H), 2.11-1.84 (m, 4H), $1.00 - 0.60$ (m, 6H). LC-MS $(\\mathrm{ES}+)$ : $m / z$ $1033[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,695,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-(2-(3-(2-(2-(4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)-benzyl)pyrrolidine-2-carboxamide (89). A solution of intermediate 88 (180 mg, 0.174 mmol) in HCl (4.0 M in MeOH, 5 mL) was stirred at room temperature for 8 h. The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 100%) to afford the title compound (~1:1 mixture of isopropyl group isomers, 146 mg) as an off-white solid.¹H NMR (300 MHz, DMSO- $d_{6}$ ) δ 14.15 (s, 1H), 8.98 (d, J = 2.6 Hz, 1H), 8.48 (t, J = 6.0 Hz, 1H), 7.96–7.87 (m, 1H), 7.79 (d, J = 6.0 Hz, 1H), 7.54–7.29 (m, 5H), 7.28–7.16 (m, 1H), 6.91–6.78 (m, 2H), 6.54 (dd, J = 6.1, 2.2 Hz, 1H), 6.19 (d, J = 2.0 Hz, 1H), 6.08 (s, 1H), 5.98 (s, 2H), 5.13 (d, J = 3.6 Hz, 1H), 4.50 (s, 2H), 4.43 (t, J = 7.7 Hz, 1H), 4.37–4.16 (m, 7H), 3.80–3.63 (m, 5H), 3.62–3.43 (m, 6H), 3.24 (d, J = 11.6 Hz, 2H), 3.02 (d, J = 11.7 Hz, 2H), 2.44 (d, J = 2.2 Hz, 3H), 2.32–2.13 (m, 3H), 2.12–1.83 (m, 4H), 1.00–0.53 (m, 6H). LC-MS (ES+): m/z 989.6 [M + H]+. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[532,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1294 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,479,480]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-((2R)-2-(3-(2-(2-(4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)-benzyl)pyrrolidine-2-carboxamide (12). The mixture of isomers isolated in the previous step was separated by preparative chiral HPLC [CHIRALPAK IE, $2\\times 25\\mathrm{cm}^2$ $5\\mu \\mathrm{m}$ ; mobile phase A: 1:1 hexane:DCM (0.5% 2 M NH $_3$ -MeOH), mobile phase B: EtOH; flow rate: $20~\\mathrm{mL / min}$ ; gradient: isocratic 20% B; wavelength: 220/254 nm; RT1:19.7 min; RT2:34.0 min; sample solvent: EtOH; injection volume: 1 mL; number of runs: 4] to afford the title compound (slower peak, 45 mg, 26%) as a white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\delta$ 14.15 (s, 1H), 8.98 (d, $J = 3.3\\mathrm{Hz}$ , 1H), 8.53 (t, $J = 6.0\\mathrm{Hz}$ , 1H), 7.92 (dd, $J = 8.1$ , 1.6 Hz, 1H), 7.79 (dd, $J = 5.9$ , 1.9 Hz, 1H), 7.50 (s, 1H), 7.48-7.30 (m, 4H), 7.28-7.17 (m, 1H), 6.91-6.79 (m, 2H), 6.54 (dd, $J = 6.1$ , 2.1 Hz, 1H), 6.20 (d, $J = 2.0\\mathrm{Hz}$ , 1H), 6.11 (s, 1H), 5.98 (s, 2H), 5.12 (d, $J = 3.7\\mathrm{Hz}$ , 1H), 4.51 (s, 2H), 4.43-4.15 (m, 8H), 3.83-3.63 (m, 6H), 3.62-3.51 (m, 4H), 3.45 (d, $J = 10.5\\mathrm{Hz}$ , 1H), 3.25 (d, $J = 11.5\\mathrm{Hz}$ , 2H), 3.02 (d, $J = 11.6\\mathrm{Hz}$ , 2H), 2.44 (d, $J = 7.4\\mathrm{Hz}$ , 3H), 2.32-2.13 (m, 3H), 2.11-1.86 (m, 4H), 0.99-0.75 (m, 6H). LC-MS $(\\mathrm{ES}+)$ : m/z 989.6 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . The isomer bearing the undesired isopropyl stereocenter (12e, isopropyl isomer corresponding to 12, structure not shown) was also isolated (faster peak, $30\\mathrm{mg},$ $17\\%$ ) as a white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\delta$ 14.15 (s, 1H), 8.98 (d, $J = 2.6\\mathrm{Hz}$ , 1H), 8.48 (t, $J = 6.0\\mathrm{Hz}$ , 1H), 7.96-7.87 (m, 1H), 7.79 (d, $J = 6.0\\mathrm{Hz}$ , 1H), 7.54-7.29 (m, 5H), 7.28-7.16 (m, 1H), 6.91-6.78 (m, 2H), 6.54 (dd, $J = 6.1$ , 2.2 Hz, 1H), 6.19 (d, $J = 2.0\\mathrm{Hz}$ , 1H), 6.08 (s, 1H), 5.98 (s, 2H), 5.13 (d, $J = 3.6\\mathrm{Hz}$ , 1H), 4.50 (s, 2H), 4.43 (t, $J = 7.7\\mathrm{Hz}$ , 1H), 4.37-4.16 (m, 7H), 3.80-3.63 (m, 5H), 3.62-3.43 (m, 6H), 3.24 (d, $J = 11.6\\mathrm{Hz}$ , 2H), 3.02 (d, $J = 11.7\\mathrm{Hz}$ , 2H), 2.44 (d, $J = 2.2\\mathrm{Hz}$ , 3H), 2.32-2.13 (m, 3H), 2.12-1.83 (m, 4H), $1.00 - 0.53$ (m, 6H). LC-MS $(\\mathrm{ES}+)$ : m/z $989.6[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,480,479,728]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Benzyl 4-(2-((4-bromopyridin-2-yl)oxy)ethyl)piperazine-1-carboxylate (91). To a $0^{\\circ}\\mathrm{C}$ solution of benzyl 4-(2-hydroxyethyl)-piperazine-1-carboxylate (90, $3.00\\mathrm{g},$ 11.3 mmol, 1.0 equiv) in DMF $(30~\\mathrm{mL})$ was added NaH $(60\\%)$ in mineral oil, $910\\mathrm{mg},$ 22.7 mmol, 2.0 equiv) in portions. After stirring $10\\mathrm{min}$ at $0^{\\circ}\\mathrm{C},$ 4-bromo-2-fluoropyridine (62, $2.00\\mathrm{g},$ 11.3 mmol, 1.0 equiv) was added over 10 min at the same temperature. The resulting mixture was warmed to room temperature and was stirred for an additional $0.5\\mathrm{h}$ The reaction was then cooled to $0^{\\circ}\\mathrm{C}$ and was quenched with saturated aqueous $\\mathrm{NH_4Cl}$ $(100~\\mathrm{mL})$ . The resulting mixture was extracted with EtOAc $(100~\\mathrm{mL}\\times 3)$ , and the combined organic layers were washed with brine $(100~\\mathrm{mL})$ , dried over sodium sulfate, and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 55:45) to afford the title compound $(3.95\\mathrm{g},83\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz},$ DMSO- $d_{6})$ $\\delta$ 8.06 d $J = 5.5\\mathrm{Hz}$ 1H7.45- 7.26 m5H7.22dd $J = 5.5$ $1.7\\mathrm{Hz}$ 1H7.13d $J = 1.6\\mathrm{Hz}$ 1H), 5.07s2H)4.38t $J = 5.7\\mathrm{Hz},$ 2H)3.4-3.33m4H2.70t $J =$ $5.9\\mathrm{Hz},$ 2H)2.44t $J = 5.0\\mathrm{Hz},$ 4H.LC-MS $(\\mathrm{ES + })$ .. $m / z$ 420/422 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,730,479,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Benzyl 4-(2-((4-(3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2- yl)oxy)ethyl)piperazine-1-carboxylate (92). A solution of benzyl 4-(2-((4-bromopyridin-2-yl)oxy)ethyl)piperazine-1-carboxylate (91, $1.50\\mathrm{g},$ 3.57 mmol, 1.0 equiv), tert-butyl 3,8-diazabicyclo[3.2.1]- octane-3-carboxylate (67, $760~\\mathrm{mg}$ 3.57 mmol, 1.0 equiv), RuPhosPd G2 $(280~\\mathrm{mg},$ 0.36 mmol, 0.10 equiv), and $\\mathrm{Cs_2CO_3}$ 2.33 g, 7.14 mmol, 2.0 equiv) in toluene $(15~\\mathrm{mL})$ was stirred at $90^{\\circ}\\mathrm{C}$ for $5\\mathrm{h}$ The resulting mixture was cooled to room temperature, diluted with EtOAc $(50~\\mathrm{mL})$ , and was quenched with saturated aqueous $\\mathrm{NH}_4\\mathrm{Cl}$ $(100~\\mathrm{mL})$ . The aqueous layer was extracted with EtOAc $(100~\\mathrm{mL}\\times$ 3), and the combined organic layers were dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH_4HCO_3})$ 0 to $75\\%$ to afford tertbutyl 8-(2-(2-(4-((benzyloxy)carbonyl)piperazin-1-yl)ethoxy)pyridin4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate $(1.1~\\mathrm{g},$ $56\\%$ as a light yellow solid. ${}^{1}\\mathbf{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 8 7.77 d $J = 6.0$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,283]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\mathrm{Hz}$ 1H),7.45-7.20 (m, 5H),6.48dd $J = 6.1$ $2.1\\mathrm{Hz}$ 1H),6.11d $J$ $= 2.0~\\mathrm{Hz}$ 1H),5.07s2H),4.35s2H),4.28t $J = 5.8\\mathrm{Hz}$ 2H), 3.57t $J = 16.3\\mathrm{Hz}$ 2H),3.45-3.34(m,4H),3.06d $J = 12.6\\mathrm{Hz}$ 1H),2.92d $J = 12.8\\mathrm{Hz}$ 1H),2.65t $J = 5.8\\mathrm{Hz}$ 2H),2.43t $J =$ $5.1\\mathrm{Hz}$ 4H),1.94-1.85m2H),1.73-1.62m2H),1.39s9H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 552 $[\\mathbf{M} + \\mathbf{H}]^{+}$ .A solution of this material (750 mg, 1.36 mmol) in TFA $(1.5\\mathrm{mL})$ and DCM $(7.5\\mathrm{mL})$ was stirred at room temperature for $^{\\textrm{\\scriptsize 1h}}$ The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ 0 to $100\\%$ ) to afford the title compound $(570\\mathrm{mg},93\\%)$ as a light yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ ,DMSO- $d_{6})$ 7.72d $J = 6.0~\\mathrm{Hz}$ 1H),7.44-7.26 m5H),6.39dd $J = 6.1$ $2.1\\mathrm{Hz}$ 1H),5.98d $J =$ $2.0\\mathrm{Hz}$ 1H),5.08s2H),4.28t $J = 5.8\\mathrm{Hz}$ 2H),4.15s2H),3.39 s,4H),3.17d $J = 3.2\\mathrm{Hz}$ 1H),2.89-2.78m2H),2.66t $J = 5.8$ Hz,2H),2.47-2.38m6H),1.98-1.80m4H).LC-MS $(\\mathrm{ES + })$ .. $m / z$ 452 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,283,915,470]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Benzyl 4-(2-((4-(3-(3-amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)-piperazine-1-carboxylate (93). A solution of intermediate 92 (530 mg, 1.17 mmol, 1.0 equiv), 4-bromo-6-chloropyridazin-3-amine (70, 366 mg, 1.76 mmol, 1.5 equiv), and DIEA (758 mg, 5.87 mmol, 5.0 equiv) in NMP (6 mL) was stirred at $130^{\\circ}\\mathrm{C}$ for 3 h. After cooling to room temperature, the crude mixture was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ , 0 to $100\\%$ to afford the title compound $(570\\mathrm{mg},84\\%)$ as a light yellow solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\delta$ 7.77 (d, $J = 5.9\\mathrm{Hz}$ , 1H), 7.43-7.25 (m, 5H), 6.89 (s, 1H), 6.50 (dd, $J = 6.1$ , 2.0 Hz, 1H), 6.13 (d, $J = 2.0\\mathrm{Hz}$ , 1H), 5.84 (s, 2H), 5.07 (s, 2H), 4.45 (s, 2H), 4.28 (t, $J = 5.8\\mathrm{Hz}$ , 2H), 3.39 (s, 4H), 3.22-3.12 (m, 2H), 2.86 (d, $J = 11.6\\mathrm{Hz}$ , 2H), 2.65 (t, $J = 5.8\\mathrm{Hz}$ , 2H), 2.43 (t, $J = 5.0\\mathrm{Hz}$ , 4H), 2.17-2.06 (m, 2H), 1.97-1.87 (m, 2H). LC-MS $(\\mathrm{ES}+)$ : $m/z$ 579 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,470,915,905]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6-(2-(Methoxymethoxy)phenyl)-4-(8-(2-(piperazin-1-yl)-ethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)-pyridazin-3-amine (94). A solution of intermediate 93 (560 mg, 0.967 mmol, 1.0 equiv), 2-(methoxymethoxy)phenylboronic acid (85, 263 mg, 1.45 mmol, 1.5 equiv), $\\mathrm{Pd}(\\mathrm{dppf})\\mathrm{Cl}_2\\bullet \\mathrm{CH}_2\\mathrm{Cl}_2$ (78.7 mg, 0.0963 mmol, 0.10 equiv) and $\\mathrm{K}_2\\mathrm{CO}_3$ (400 mg, 2.90 mmol, 3.0 equiv) in 1,4-dioxane (6 mL) and water (1.2 mL) was stirred at $90^{\\circ}\\mathrm{C}$ for 1.5 h. After cooling to room temperature, the crude mixture was purified by prepacked C18 column chromatography $(\\mathrm{CH}_3\\mathrm{CN}$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ , 0 to $100\\%$ ) to afford benzyl 4-(2-((4-(3-(3-amino-6-(2-(methoxymethoxy)phenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)piperazine-1-carboxylate (475 mg, 72%) as a light brown solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\delta$ 7.75 (d, $J = 6.0~\\mathrm{Hz}$ , 1H), 7.56 (dd, $J = 7.6$ , 1.8 Hz, 1H), 7.41-7.23 (m, 6H), 7.16-6.99 (m, 3H), 6.55-6.45 (m, 1H), 6.13 (d, $J = 2.0~\\mathrm{Hz}$ , 1H), 5.72 (s, 2H), 5.12 (s, 2H), 5.05 (s, 2H), 4.45 (d, $J = 4.2~\\mathrm{Hz}$ , 2H), 4.26 (t, $J = 5.7~\\mathrm{Hz}$ , 2H), 3.37 (s, 4H), 3.20 (s, 3H), 3.12 (d, $J = 11.3~\\mathrm{Hz}$ , 2H), 2.83 (d, $J = 11.3~\\mathrm{Hz}$ , 2H), 2.64 (t, $J = 5.8~\\mathrm{Hz}$ , 2H), 2.41 (t, $J = 5.0~\\mathrm{Hz}$ , 4H), 2.23-2.11 (m, 2H), 2.03-1.85 (m, 2H). LC-MS $(\\mathrm{ES}+)$ : $m/z$ 681 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . A suspension of this material (465 mg, 0.68 mmol) and $10\\%$ Pd/C (25 mg, dry) in MeOH (20 mL) was stirred under a hydrogen atmosphere (3 atm), at room temperature for 5 h. The resulting mixture was filtered, and the filter cake was washed with MeOH (25 mL × 3). The combined filtrate and washings were concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $(\\mathrm{CH}_3\\mathrm{CN}$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ , 0 to $100\\%$ ) to afford the title compound (220 mg, 59%) as a light yellow solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\delta$ 7.75 (d, $J = 5.9~\\mathrm{Hz}$ , 1H), 7.57 (dd, $J = 7.6$ , 1.8 Hz, 1H), 7.37-7.27 (m, 1H), 7.16-7.09 (m, 2H), 7.05 (td, $J = 7.5$ , 1.1 Hz, 1H), 6.49 (dd, $J = 6.1$ , 2.1 Hz, 1H), 6.12 (d, $J = 2.0~\\mathrm{Hz}$ , 1H), 5.71 (s, 2H), 5.12 (s, 2H), 4.46 (s, 2H), 4.24 (t, $J = 5.9~\\mathrm{Hz}$ , 2H), 3.20 (s, 3H), 3.12 (d, $J = 11.3~\\mathrm{Hz}$ , 2H), 2.83 (d, $J = 11.3~\\mathrm{Hz}$ , 2H), 2.70-2.51 (m, 6H), 2.34 (s, 4H), 2.22-2.11 (m, 2H), 2.01-1.87 (m, 2H). LC-MS $(\\mathrm{ES}+)$ : $m/z$ 547 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,905,915,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-(2-(3-(2-(4-(4-(3-(3-Amino-6-(2-(methoxymethoxy)phenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)piperazin-1-yl)- ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[484,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1295 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,71,482,305]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (95). A mixture of intermediate 94 $(100\\mathrm{mg},0.183\\mathrm{mmol},1.0$ equiv) and intermediate 56 $(108\\mathrm{mg},0.183\\mathrm{mmol},1.0$ equiv), $\\mathrm{Cs_2CO_3}$ $(178\\mathrm{mg},$ $0.551\\mathrm{mmol},3.0$ equiv) and KI $(45.5\\mathrm{mg},0.274\\mathrm{mmol},1.5$ equiv) in $\\mathrm{CH}_3\\mathrm{CN}$ $(2\\mathrm{mL})$ was stirred at $70^{\\circ}\\mathrm{C}$ overnight. The reaction was cooled to room temperature, and the solids were filtered off. The filtrate was directly purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH_4HCO_3})$ 0 to $100\\%$ ) to afford the title compound ( $\\sim 1:1$ mixture of isopropyl group isomers, $95\\mathrm{mg},$ $49\\%$ as a light yellow solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6}$ 8 8.98 $(\\mathrm{d},J = 4.1~\\mathrm{Hz},1\\mathrm{H})$ $8.58 - 8.41$ m1H7.76d $J = 5.9 \\mathrm{Hz}$ 1H) 7.58dd $J = 7.6$ $1.8~\\mathrm{Hz}$ 1H7.50-7.27m5H7.17-7.02m 3H6.50dd $J = 6.3$ $2.0~\\mathrm{Hz}$ 1H6.17-6.03m2H5.72s2H) 5.13d $J = 1.3~\\mathrm{Hz}$ 3H4.45d $J = 11.6~\\mathrm{Hz}$ 2H4.40-4.10m 7H3.76dd $J = 9.8$ $4.9~\\mathrm{Hz}$ 1H3.71-3.36m2H3.25-3.08 m6H2.85d $J = 11.3~\\mathrm{Hz}$ 2H2.68-2.54m4H2.47-2.34 m, $10\\mathrm{H})$ 2.30-2.09 m4H)2.07-1.84 m4H)1.01-0.54 m, 6H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 1057 $[\\mathbf{M} + \\mathbf{H}]^+$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,305,481,585]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-(2-(3-(2-(4-(3-(3-(3-Amino-6-(2- (methoxymethoxy)phenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)piperazin-1-yl)-ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (96). A mixture of intermediate 94 (100 mg, 0.183 mmol, 1.0 equiv), intermediate 59 (149 mg, 0.246 mmol, 1.3 equiv), $\\mathrm{K}_2\\mathrm{CO}_3$ (75.8 mg, 0.549 mmol, 3.0 equiv), and KI (45.5 mg, 0.274 mmol, 1.5 equiv) in $\\mathrm{CH}_3\\mathrm{CN}$ (2 mL) was stirred at $70^{\\circ}\\mathrm{C}$ overnight. The reaction was cooled to room temperature, and the solids were filtered off. The filtrate was directly purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ , 0 to $100\\%$ to afford the title compound ( $\\sim$ 1:1 mixture of isopropyl group isomers, $134\\mathrm{mg}, 68\\%$ ) as a white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\delta$ 9.03–8.88 (m, 1H), 8.47–8.25 (m, 1H), 7.76 (dd, $J = 5.9$ , 1.2 Hz, 1H), 7.62–7.55 (m, 1H), 7.53–7.27 (m, 5H), 7.17–7.00 (m, 3H), 6.57–6.46 (m, 1H), 6.14 (t, $J = 2.2\\mathrm{Hz}$ , 1H), 6.08 (d, $J = 2.7\\mathrm{Hz}$ , 1H), 5.72 (s, 2H), 5.17–5.06 (m, 3H), 5.04–4.83 (m, 1H), 4.55–4.32 (m, 3H), 4.32–4.04 (m, 5H), 3.79–3.55 (m, 1H), 3.55–3.39 (m, 2H), 3.22 (d, $J = 1.2\\mathrm{Hz}$ , 3H), 3.19–3.08 (m, 3H), 2.84 (d, $J = 11.3\\mathrm{Hz}$ , 2H), 2.69–2.55 (m, 4H), 2.50–2.32 (m, 10H), 2.32–2.08 (m, 3H), 2.08–1.91 (m, 3H), 1.84–1.70 (m, 1H), 1.49–1.30 (m, 3H), 1.00–0.70 (m, 6H). LC–MS $(ES+): m/z$ 1071 $[M + H]^+$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,585,482,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-((2R)-2-(3-(2-(4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)piperazin-1-yl)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (13). A solution of intermediate 95 (95.0 mg, 0.0898 mmol) was stirred in HCl (4.0 M in MeOH, 2 mL) at room temperature overnight. The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacted C18 column chromatography (CH $_3$ CN in water (0.05% $\\mathrm{NH}_4\\mathrm{HCO}_3$ ), 0 to 100%) to afford 60 mg of the MOM-deprotected product (~1:1 mixture of isopropyl group isomers). These compounds were separated by preparative chiral HPLC [column: CHIRALPAK ID, $2\\times 25~\\mathrm{cm}^2$ , 5 μm; mobile phase A: 1:1 hexane: DCM (0.5% 2 M $\\mathrm{NH}_3/\\mathrm{MeOH}$ ), mobile phase B: EtOH; flow rate: 20 mL/min; gradient: isocratic 30% B; wavelength: 220/254 nm; RT1:7.08 min; RT2:14.99 min; sample solvent: EtOH; injection volume: 1 mL; number of runs: 5] to afford the title compound (faster peak, 24.5 mg, 27%) as an off-white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 14.14 (s, 1H), 8.98 (s, 1H), 8.50 (t, $J = 6.1~\\mathrm{Hz}$ , 1H), 7.91 (d, $J = 7.9~\\mathrm{Hz}$ , 1H), 7.78 (d, $J = 5.9~\\mathrm{Hz}$ , 1H), 7.49 (s, 1H), 7.47–7.33 (m, 4H), 7.22 (t, $J = 7.6~\\mathrm{Hz}$ , 1H), 6.91–6.77 (m, 2H), 6.53 (d, $J = 6.4~\\mathrm{Hz}$ , 1H), 6.19–6.07 (m, 2H), 5.97 (s, 2H), 5.14–4.97 (m, 1H), 4.50 (s, 2H), 4.42–4.30 (m, 3H), 4.30–4.14 (m, 4H), 3.80–3.72 (m, 1H), 3.66 (d, $J = 9.6~\\mathrm{Hz}$ , 1H), 3.61–3.37 (m, 2H), 3.25 (d, $J = 12.1~\\mathrm{Hz}$ , 2H), 3.01 (d, $J = 11.7~\\mathrm{Hz}$ , 2H), 2.68–2.57 (m, 4H), 2.48–2.39 (m, 10H), 2.32–1.83 (m, 8H), 0.94 (d, $J = 6.5~\\mathrm{Hz}$ , 3H), 0.80 (d, $J = 6.7~\\mathrm{Hz}$ , 3H). LC-MS $(\\mathrm{ES}+)$ : m/z 1013 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . The isomer bearing the undesired isopropyl stereocenter (13e, isopropyl isomer corresponding to 13, structure not shown) was also isolated (slower ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,198]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"peak, $19\\mathrm{mg}$ $20\\%$ ) as an off-white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO $d_{6}$ ) $\\delta$ 14.14 (s, 1H), 8.98 (d, $J = 2.7\\mathrm{Hz}$ 1H), 8.46 (t, $J = 6.0\\mathrm{Hz}$ 1H), 7.91 (dd, $J = 8.0$ $1.6\\mathrm{Hz}$ 1H), 7.78 (d, $J = 5.9\\mathrm{Hz}$ 1H), 7.52-7.36 (m, 3H), 7.32 (d, $J = 8.1\\mathrm{Hz}$ 2H), 7.26-7.15 (m, 1H), 6.91-6.78 (m, 2H), 6.53 (dd, $J = 6.3$ $2.0\\mathrm{Hz}$ 1H), 6.15 (d, $J = 2.0\\mathrm{Hz}$ 1H), 6.06 (d, $J = 4.7\\mathrm{Hz}$ 1H), 5.97 (s, 2H), 5.12 (d, $J = 3.6\\mathrm{Hz}$ 1H), 4.52-4.38 (m, 3H), 4.37-4.20 (m, 5H), 4.20-4.11 (m, 1H), 3.76 (d, $J = 8.5\\mathrm{Hz}$ 1H), 3.59-3.40 (m, 2H), 3.29-3.09 (m, 3H), 3.01 (d, $J = 11.6\\mathrm{Hz}$ 2H), 2.69-2.53 (m, 4H), 2.47-2.33 (m, 11H), 2.31-1.83 (m, 7H), 1.00-0.53 (m, 6H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 1013 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,198,915,725]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-((2R)-2-(3-(2-(4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)piperazin-1-yl)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (14). A solution of intermediate 96 (135 mg, 0.126 mmol) in HCl (4.0 M in MeOH, 2 mL) was stirred at room temperature for 3 h. The solvent was evaporated, and the residue was purified by prepacked C18 column chromatography (MeOH in water (0.05% $\\mathrm{NH_4HCO_3}$ ), 0 to 100%) to afford 85 mg of the MOM-deprotected product (~1:1 mixture of isopropyl group isomers). These compounds were separated by preparative chiral HPLC [column: CHIRALPAK IK, $4.6\\times 150~\\mathrm{mm}^2$ , $5\\mu \\mathrm{m}$ ; mobile phase A: 1:1 hexane: DCM (0.5% 2 M $\\mathrm{NH}_3 / \\mathrm{MeOH}$ ), mobile phase B: EtOH; flow rate: 20 mL/min; gradient: isocratic 30% B; wavelength: 220/254 nm; RT1:10.8 min; RT2:20.4 min; sample solvent: EtOH; injection volume: 1 mL; number of runs: 5] to afford the title compound (slower peak, 19.6 mg, 15%) as an off-white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 14.14 (s, 1H), 8.98 (s, 1H), 8.41 (d, $J = 7.6~\\mathrm{Hz}$ , 1H), 7.96–7.87 (m, 1H), 7.79 (d, $J = 6.0~\\mathrm{Hz}$ , 1H), 7.49 (s, 1H), 7.47–7.40 (m, 2H), 7.36 (d, $J = 8.1~\\mathrm{Hz}$ , 2H), 7.25–7.16 (m, 1H), 6.91–6.79 (m, 2H), 6.53 (dd, $J = 6.2$ , 2.0 Hz, 1H), 6.15 (d, $J = 2.0~\\mathrm{Hz}$ , 1H), 6.09 (s, 1H), 5.97 (s, 2H), 5.09 (d, $J = 3.7~\\mathrm{Hz}$ , 1H), 5.04–4.83 (m, 1H), 4.50 (s, 2H), 4.37 (t, $J = 7.9~\\mathrm{Hz}$ , 1H), 4.31–4.16 (m, 5H), 3.75–3.60 (m, 2H), 3.55–3.40 (m, 1H), 3.25 (d, $J = 11.5~\\mathrm{Hz}$ , 2H), 3.01 (d, $J = 11.6~\\mathrm{Hz}$ , 2H), 2.70–2.58 (m, 4H), 2.50–2.39 (m, 10H), 2.30–2.15 (m, 4H), 2.10–1.85 (m, 3H), 1.85–1.70 (m, 1H), 1.50–1.35 (m, 3H), 0.95 (d, $J = 6.4~\\mathrm{Hz}$ , 3H), 0.90–0.75 (m, 3H). LC-MS $(\\mathrm{ES}+)$ : m/z 1027 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . The isomer bearing the undesired isopropyl stereocenter (14e, isopropyl isomer corresponding to 14, structure not shown) was also isolated (faster peak, $40~\\mathrm{mg}$ , $31\\%$ ) as an off-white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 14.14 (s, 1H), 9.00–8.88 (m, 1H), 8.29 (d, $J = 7.8~\\mathrm{Hz}$ , 1H), 7.91 (dd, $J = 8.0$ , 1.6 Hz, 1H), 7.78 (d, $J = 6.0~\\mathrm{Hz}$ , 1H), 7.48 (d, $J = 7.6~\\mathrm{Hz}$ , 1H), 7.46–7.36 (m, 2H), 7.31 (d, $J = 8.3~\\mathrm{Hz}$ , 2H), 7.25–7.16 (m, 1H), 6.91–6.78 (m, 2H), 6.53 (dd, $J = 6.1$ , 2.0 Hz, 1H), 6.19–6.11 (m, 1H), 6.08 (s, 1H), 5.97 (s, 2H), 5.10 (d, $J = 3.6~\\mathrm{Hz}$ , 1H), 5.06–4.81 (m, 1H), 4.50 (s, 2H), 4.42 (t, $J = 7.7~\\mathrm{Hz}$ , 1H), 4.33–4.14 (m, 5H), 3.74 (d, $J = 8.5~\\mathrm{Hz}$ , 1H), 3.60–3.38 (m, 2H), 3.33–3.19 (m, 2H), 3.01 (d, $J = 11.6~\\mathrm{Hz}$ , 2H), 2.70–2.58 (m, 4H), 2.49–2.39 (m, 10H), 2.34–2.11 (m, 4H), 2.10–1.91 (m, 3H), 1.84–1.70 (m, 1H), 1.50–1.30 (m, 3H), 1.00–0.71 (m, 6H). LC-MS $(\\mathrm{ES}+)$ : m/z $1027[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,725,915,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4-Bromo-2-(2,2-diethoxyethoxy)pyridine (97). A mixture of 2,2-diethoxyethan-1-ol $(5.71\\mathrm{g},42.6\\mathrm{mmol},1.0$ equiv) and NaH $(60\\%)$ in mineral oil, $1.36\\mathrm{g}$ $56.8~\\mathrm{mmol}$ 1.3 equiv) in DMF $(30~\\mathrm{mL})$ was stirred at $0^{\\circ}\\mathrm{C}$ for $0.5\\mathrm{h}$ 4-Bromo-2-fluoro-pyridine (62, $5.00\\mathrm{g}$ 28.4 mmol) was then added, and the mixture was stirred at room temperature for $2\\textrm{h}$ The reaction was quenched with saturated aqueous $\\mathrm{NH_4Cl}$ $(100~\\mathrm{mL})$ at room temperature, and the resulting mixture was extracted with EtOAc $(100~\\mathrm{mL}\\times 3)$ .The combined organic layers were washed with water $(100~\\mathrm{mL})$ and were dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 1:3) to afford the title compound $(6.4\\mathrm{g},53\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 8.07 d $J = 5.5\\mathrm{Hz}$ 1H),7.24dd $J = 5.5$ $1.7\\mathrm{Hz}$ 1H), 7.15d $J = 1.7\\mathrm{Hz}$ 1H),4.80t $J = 5.3\\mathrm{Hz}$ 1H),4.24d $J = 5.3\\mathrm{Hz}$ 2H),3.75-3.45 m4H),1.12 t $J = 7.1\\mathrm{Hz}$ 6H).LC-MS $(\\mathrm{ES + })$ .. $m / z290[\\mathrm{M} + \\mathrm{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[484,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1296 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,479,370]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Benzyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (98). Benzyl chloroformate $(4.83\\mathrm{g},28.2\\mathrm{mmol},1.2$ equiv) was added to a $0^{\\circ}\\mathrm{C}$ solution of tert-butyl 3,8-diazabicyclo[3.2.1]octane-8-carboxylate $(5.00\\mathrm{g},23.5\\mathrm{mmol},1.0$ equiv) and TEA $(7.14\\mathrm{g},70.6$ mmol, 3.0 equiv) in DCM $(30~\\mathrm{mL})$ . The reaction was stirred at $0^{\\circ}\\mathrm{C}$ for $2\\textrm{h}$ then was diluted with EtOAc $(300~\\mathrm{mL})$ and washed with water $(200~\\mathrm{mL})$ . The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 30:70) to afford 3-benzyl 8-(tert-butyl) 3,8- diazabicyclo[3.2.1]octane-3,8-dicarboxylate $(5.33\\mathrm{g},65\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ ,DMSO- $d_{6})$ $\\delta$ 7.44-7.26 (m, 5H), 5.10 (d, $J$ $= 4.1\\mathrm{Hz},2\\mathrm{H})$ 4.11s2H)3.75d $J = 12.7\\mathrm{Hz}$ 2H)3.05d $J=$ $12.7\\mathrm{Hz},1\\mathrm{H})$ 2.94d $J = 12.7\\mathrm{Hz},1\\mathrm{H})$ 1.87-1.75 (m, 2H), 1.61- 1.48 (m, 2H), 1.41 (s, 9H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 347 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . A solution of this material $(5.23\\mathrm{g},15.1\\mathrm{mmol})$ in TFA $(10~\\mathrm{mL})$ and DCM $(50~\\mathrm{mL})$ was stirred at room temperature for $^{\\textrm{\\scriptsize 4h}}$ . The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.1\\%$ TFA), 0 to $100\\%$ ) to afford the title compound (TFA salt, $3.40\\mathrm{g},62\\%$ ) as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ ,DMSO- $d_{6})$ $\\delta$ 9.20s,2H)7.45-7.27m5H)5.11s,2H)4.03s,2H)3.86d $J = 13.5\\mathrm{Hz},2\\mathrm{H})$ 3.43-3.21 m,2H)1.99-1.88 m,2H)1.78-1.65 m,2H).LC-MS $(\\mathrm{ES + })$ .. $m / z$ 247 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,370,479,606]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Benzyl 8-(2-(2,2-diethoxyethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate (99). A solution of 4-bromo-2-(2,2-diethoxyethoxy)pyridine (97, $2.70\\mathrm{g}$ , $9.31\\mathrm{mmol}$ , 1.0 equiv), benzyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (98, TFA salt, $4.58\\mathrm{g}$ , $12.7\\mathrm{mmol}$ , 1.4 equiv), RuPhosPd G2 $(720\\mathrm{mg}, 0.927\\mathrm{mmol}, 0.10\\mathrm{equiv})$ and $\\mathrm{Cs_2CO_3}$ $(9.10\\mathrm{g}, 27.9\\mathrm{mmol}, 3.0\\mathrm{equiv})$ in toluene $(13\\mathrm{mL})$ was stirred at $90^{\\circ}\\mathrm{C}$ for $4\\mathrm{h}$ . The resulting mixture was cooled to room temperature and was diluted with EtOAc (100 mL) and washed with water $(100\\mathrm{mL})$ . The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 35:65) to afford the title compound $(4.0\\mathrm{g}, 94\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\delta$ 7.78 $(\\mathrm{d}, J = 5.9\\mathrm{Hz}, 1\\mathrm{H})$ , 7.43-7.27 $(\\mathrm{m}, 5\\mathrm{H})$ , 6.51 $(\\mathrm{dd}, J = 6.2, 2.1\\mathrm{Hz}, 1\\mathrm{H})$ , 6.16 $(\\mathrm{d}, J = 2.0\\mathrm{Hz}, 1\\mathrm{H})$ , 5.08 $(\\mathrm{d}, J = 3.9\\mathrm{Hz}, 2\\mathrm{H})$ , 4.77 $(\\mathrm{t}, J = 5.3\\mathrm{Hz}, 1\\mathrm{H})$ , 4.39 $(\\mathrm{d}, J = 10.3\\mathrm{Hz}, 2\\mathrm{H})$ , 4.15 $(\\mathrm{d}, J = 5.3\\mathrm{Hz}, 2\\mathrm{H})$ , 3.73-3.59 $(\\mathrm{m}, 4\\mathrm{H})$ , 3.59-3.45 $(\\mathrm{m}, 2\\mathrm{H})$ , 3.15 $(\\mathrm{d}, J = 12.9\\mathrm{Hz}, 1\\mathrm{H})$ , 3.03 $(\\mathrm{d}, J = 12.9\\mathrm{Hz}, 1\\mathrm{H})$ , 1.96-1.86 $(\\mathrm{m}, 2\\mathrm{H})$ , 1.73-1.63 $(\\mathrm{m}, 2\\mathrm{H})$ , 1.13 $(\\mathrm{t}, J = 7.0\\mathrm{Hz}, 6\\mathrm{H})$ . LC-MS $(ES+)$ : $m/z$ 456 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,606,479,766]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8-(2-(2,2-Diethoxyethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane (100). A solution of intermediate 99 $(4.15\\mathrm{g},9.11$ mmol) and $10\\%$ Pd/C $(484\\mathrm{mg})$ in EtOAc $(25~\\mathrm{mL})$ was stirred under a hydrogen atmosphere (3 atm) at room temperature for $12\\mathrm{h}$ The resulting mixture was filtered, and the filter cake was washed with EtOAc $(30~\\mathrm{mL}\\times 3)$ .The combined filtrate and washings were concentrated under reduced pressure to afford the title compound $(2.68\\mathrm{g},92\\%)$ as a black oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 7.73 $\\left(\\mathrm{d},J = 6.0\\mathrm{Hz},1\\mathrm{H}\\right)$ 6.41dd $J = 6.1$ 2.1 Hz1H),6.02 $\\left(\\mathrm{d},J = 2.1\\mathrm{Hz}\\right.$ 1H),4.76t $J = 5.3\\mathrm{Hz}$ 1H),4.20-4.11m4H),3.72-3.45m 4H),2.84d $J = 12.2\\mathrm{Hz}$ 2H),2.44d $J = 12.2\\mathrm{Hz}$ 2H),2.01-1.80 m,4H),1.13t $J = 7.1\\mathrm{Hz}$ 6H).LC-MS $(\\mathrm{ES + })$ .. $m / z$ 322 $[\\mathbf{M}+$ $\\mathrm{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,767,479,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(6-Amino-5-(8-(2-(2,2-diethoxyethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)pyridazin-3-yl)phenol (101). A solution of intermediate 100 $(2.60\\mathrm{g},8.09\\mathrm{mmol},1.0$ equiv), 4-bromo-6-chloro-pyridazin-3-amine (70, $2.53\\mathrm{g}$ 12.1 mmol, 1.5 equiv) and DIEA $(3.13\\mathrm{g},24.2\\mathrm{mmol},3.0$ equiv) in NMP $(20~\\mathrm{mL})$ was stirred at $120^{\\circ}\\mathrm{C}$ for $2\\textrm{h}$ . After cooling to room temperature, the crude was directly purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\%)$ $\\mathrm{NH_4HCO_3)}$ , 0 to $100\\%$ ) to afford 6-chloro4-(8-(2-(2,2-diethoxyethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]-octan-3-yl)pyridazin-3-amine $(2.67\\mathrm{g},74\\%)$ as a yellow solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 8 7.79 d $J = 6.0 \\mathrm{Hz}$ 1H6.89s1H) 6.53dd $J = 6.1$ $2.0\\mathrm{Hz}$ 1H6.17d $J = 2.0\\mathrm{Hz}$ 1H5.85s2H) 4.77t $J = 5.3\\mathrm{Hz}$ 1H4.47s2H4.15d $J = 5.2\\mathrm{Hz}$ 2H3.72- 3.45m4H)3.18d $J = 11.6\\mathrm{Hz}$ 2H)2.86d $J = 11.6\\mathrm{Hz}$ 2H ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,306]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.19-2.09 (m, 2H), 1.98-1.88 (m, 2H), 1.13 (t, $J = 7.0\\mathrm{Hz}$ 6H). LC-MS $(\\mathrm{ES + })$ .. $m / z449[\\mathrm{M} + \\mathrm{H}]^{+}$ . A solution of this material (2.66 g, 5.92 mmol, 1.0 equiv), 2-hydroxyphenylboronic acid (72, 1.23 g, 8.91 mmol, 1.5 equiv), $\\mathrm{Pd(PPh_3)_4}$ (0.680 g, 0.589 mmol, 0.10 equiv), and $\\mathrm{K}_2\\mathrm{CO}_3$ (2.45 g, 17.7 mmol, 3.0 equiv) in 1,4-dioxane (20 mL) and water (2 mL) was stirred at $90^{\\circ}\\mathrm{C}$ for $2\\mathrm{h}$ The resulting mixture was cooled to room temperature, and was diluted with EtOAc (100 mL) and washed with water (100 mL). The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (0-100% CH3CN in water (0.05% $\\mathrm{NH_4HCO_3})$ , 0 to $100\\%$ ) to afford the title compound (2.1 g, $70\\%$ ) as a yellow solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_{6})$ 8 14.14 s, 1H),7.92 $(\\mathrm{d},J = 7.8~\\mathrm{Hz}$ 1H),7.80 $(\\mathrm{d},J = 6.0~\\mathrm{Hz}$ 1H),7.50s1H)7.25-7.19 m, 1H),6.92-6.80 (m, 2H),6.61-6.51 (m, 1H),6.20s,1H),5.98 s,2H),4.77 t $J = 5.3\\mathrm{Hz}$ 1H),4.52 s,2H),4.16 d $J = 5.2\\mathrm{Hz}$ 2H),3.71-3.47 (m, 4H),3.26 d $J = 11.6\\mathrm{Hz}$ 2H),3.02 d $J = 11.5$ Hz,2H),2.25-2.15 (m, 2H), 2.03-1.90 (m, 2H), 1.13 (t, $J = 7.0\\mathrm{Hz}$ 6H). LC-MS $(\\mathrm{ES + })$ .. $m / z507[\\mathrm{M} + \\mathrm{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,307,915,527]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)acetaldehyde (102). A solution of intermediate 101 $(2.00\\mathrm{g}, 3.95\\mathrm{mmol})$ in $1\\mathrm{M}$ $\\mathrm{H}_2\\mathrm{SO}_4$ $(10\\mathrm{mL})$ and THF $(10\\mathrm{mL})$ was stirred at $60^{\\circ}\\mathrm{C}$ for $4\\mathrm{h}$ . The mixture was cooled to room temperature and was basified to $\\mathrm{pH}9$ with $1\\mathrm{M}$ NaOH solution. The resulting mixture was extracted with EtOAc $(100\\mathrm{mL}\\times 3)$ , and the combined organic layers were washed with water $(100\\mathrm{mL})$ , dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\left(\\mathrm{CH}_3\\mathrm{CN}\\right.$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ , 0 to $100\\%$ to afford the title compound $(410\\mathrm{mg}, 24\\%)$ as a yellow solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\delta$ 8.24–8.15 (m, 1H), 8.10 (s, 1H), 7.78 (d, $J = 7.8~\\mathrm{Hz}$ , 1H), 7.55 (d, $J = 5.8~\\mathrm{Hz}$ , 1H), 7.35–7.25 (m, 1H), 7.08 (dd, $J = 7.6$ , 2.2 Hz, 1H), 6.94–6.86 (m, 1H), 6.76 (s, 1H), 6.44 (s, 2H), 6.32 (s, 1H), 5.03–4.79 (m, 3H), 4.68–4.55 (m, 1H), 3.63–3.42 (m, 2H), 3.21–2.96 (m, 2H), 2.33–2.24 (m, 2H), 2.09–1.95 (m, 2H). LC–MS $(ES+)$ : $m/z$ 433 $[\\mathbf{M} + \\mathbf{H}]^+$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,528,915,760]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tert-Butyl (3R)-4-(2-((4-(3-(3-amino-6-(2-hydroxyphenyl)-pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)ethyl)-3-methylpiperazine-1-carboxylate (104). A solution of intermediate 102 $(200\\mathrm{mg},0.462\\mathrm{mmol},1.0$ equiv), tert-butyl (3R)-3-methyl-1-piperazinecarboxylate (103, $92.6\\mathrm{mg}$ $0.463\\mathrm{mmol}$ 1.0 equiv), and $\\mathrm{NaBH(OAc)_3}$ $(636\\mathrm{mg},3.00\\mathrm{mmol},6.5$ equiv) in $\\mathrm{CH}_3\\mathrm{CN}$ $(3\\mathrm{mL})$ was stirred at room temperature for $2\\mathrm{h}$ The resulting mixture was diluted with EtOAc $(100~\\mathrm{mL})$ washed with water $(100~\\mathrm{mL})$ ,and the organic layer was dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.1\\%$ TFA), 0 to $100\\%$ ) to afford the title compound $(260\\mathrm{mg}$ $91\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 7.93 d $J =$ $6.4\\mathrm{Hz}$ 1H7.61d $J = 7.4\\mathrm{Hz}$ 1H7.49s1H7.42-7.31 m 1H7.06-6.99m1H6.99-6.89m1H6.84s2H6.79- 6.74m1H6.40s1H4.69s2H4.60s2H3.87-3.71m 2H3.69-3.55m3H3.53-3.41m4H3.29-3.11m4H 2.24-2.12m2H)2.05-1.90m2H)1.42s9H)1.29d $J = 6.3$ Hz, 3H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 617 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,760,915,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-((2R)-2-(3-(2-(3R)-4-(2-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)-3-methylpiperazin-1-yl)ethoxy)-isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (15). A solution of intermediate 104 $(250\\mathrm{mg},0.406\\mathrm{mmol})$ in HCl $(4.0\\mathrm{M}$ in MeOH, $5\\mathrm{mL})$ was stirred at room temperature for $2\\mathrm{h}$ The volatiles were then removed under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ 0 to $100\\%$ to afford 2-(6-amino-5-(8-(2-((R)-2-methylpiperazin-1-yl)ethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)pyridazin-3-yl)phenol $(190~\\mathrm{mg},91\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(500\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.15s1H7.92dd $J =$ 8.0, $1.6\\mathrm{Hz}$ 1H),7.79d $J = 5.9\\mathrm{Hz}$ 1H7.50s1H7.26-7.20 m,1H),6.90-6.81m2H),6.53dd $J = 6.0$ $2.1\\mathrm{Hz}$ 1H),6.14d ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[532,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[484,951,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1297 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,70,481,385]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$J = 2.1\\mathrm{Hz},1\\mathrm{H})$ 5.99s,2H)4.50s,2H)4.25 $\\mathrm{(t,J = 6.3~Hz,2H)}$ $3.25$ d $J = 11.6\\mathrm{Hz}$ 2H),3.01d $J = 11.6\\mathrm{Hz}$ 2H)2.98-2.90m 1H),2.77-2.66 m,3H),2.64-2.53 m,2H),2.33-2.22 m,3H), 2.21-2.15 m,2H),2.01-1.92 m,2H),0.95 d $J = 5.6\\mathrm{Hz}$ 3H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 517 $[\\mathrm{M} + \\mathrm{H}]^{+}$ .A solution of this material (180 mg, 0.349 mmol, 1.0 equiv), intermediate 61 (188 mg, 0.348 mmol, 1.0 equiv) and $\\mathrm{NaBH(OAc)_3}$ 221 mg, 1.04 mmol, 3.0 equiv) in $\\mathrm{CH}_3\\mathrm{CN}$ - $4\\mathrm{mL}$ ) was stirred at room temperature for $12\\mathrm{h}$ The resulting mixture was concentrated under reduced pressure, and the residue was purified by preparative HPLC [column: XBridge Prep OBD C18 Column $19\\times 250\\mathrm{mm}^2$ $5\\mu \\mathrm{m}$ mobile phase A: water (10 mmol/L $\\mathrm{NH_4HCO_3}$ ), mobile phase B: $\\mathrm{CH}_3\\mathrm{CN}$ ; flow rate: $25~\\mathrm{mL}/$ min; gradient: $35\\%$ B to $55\\%$ B over $10\\mathrm{min}$ wavelength: 254/220 nmRT: $10\\mathrm{min}]$ to afford the title compound ( $29\\mathrm{mg}$ $7.9\\%$ yield as a white solid. ${}^{1}\\mathbf{H}$ NMR (300 MHz,DMSO- $d_{6}$ ) $\\delta$ 14.13 s,1H),8.99 s,1H),8.40d $J = 7.7\\mathrm{Hz}$ 1H7.92d $J = 8.0~\\mathrm{Hz}$ 1H7.80d $J=$ $5.9\\mathrm{Hz}$ 1H),7.53-7.33 m,5H),7.23 t $J = 7.8~\\mathrm{Hz}$ 1H),6.91-6.79 m,2H),6.53d $J = 5.9~\\mathrm{Hz}$ 1H),6.14s,1H),6.09s,1H),5.97s, 2H),5.09d $J = 3.7~\\mathrm{Hz}$ 1H),4.97-4.86 m,1H),4.50s,2H),4.38 t $J = 7.8~\\mathrm{Hz}$ ,1H),4.32-4.17 m,5H),3.76-3.68 m,1H),3.65 d $J = 9.8~\\mathrm{Hz}$ ,1H),3.51-3.41 m,1H),3.26d $J = 11.6~\\mathrm{Hz}$ ,2H),3.07- 2.92m3H)2.87-2.77m1H)2.75-2.59m4H)2.46s,3H), 2.43-2.33m2H)2.30-2.11m5H)2.08-1.93m3H)1.91- 1.74m2H)1.49-1.34m3H)1.02-0.91m6H)0.88-0.76 m,3H).LC-MS $(\\mathrm{ES + })$ .. $m / z$ 1042 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,385,481,620]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tert-Butyl (2S)-4-(2-((4-(3-(3-amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)-2-methylpiperazine-1-carboxylate (106). A solution of intermediate 102 $(300\\mathrm{mg},0.694\\mathrm{mmol},1.0$ equiv), tert-butyl (S)-2-methylpiperazine-1-carboxylate (105, $139~\\mathrm{mg}$ $0.695\\mathrm{mmol}$ 1.0 equiv), and $\\mathrm{NaBH(OAc)_3}$ $(1.47\\mathrm{g},6.94\\mathrm{mmol},10$ equiv) in $\\mathrm{CH}_3\\mathrm{CN}$ $(5\\mathrm{mL})$ was stirred at room temperature for $8\\mathrm{h}$ . The reaction was quenched with MeOH $(5\\mathrm{mL})$ , and the volatiles were removed under vacuum. The residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\%)$ $\\mathrm{NH_4HCO_3)}$ 0 to $100\\%$ ) to afford the title compound $(160~\\mathrm{mg},37\\%)$ as a white solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6}$ 8 14.15s1H7.92dd $J =$ 8.0, $1.6~\\mathrm{Hz}$ 1H7.80d $J = 5.9~\\mathrm{Hz}$ 1H7.49s1H7.29-7.17 m, 1H),6.92-6.79m2H6.54dd $J = 6.1$ $2.0~\\mathrm{Hz}$ 1H6.16d $J = 2.0~\\mathrm{Hz}$ 1H),5.98s2H),4.51s2H),4.30t $J = 5.9~\\mathrm{Hz}$ 2H), 4.05s1H),3.65d $J = 12.8~\\mathrm{Hz}$ 1H),3.26d $J = 11.6~\\mathrm{Hz}$ 2H), 3.01-2.80m4H),2.78-2.53m3H),2.23-2.05m3H),2.01- 1.86m3H),1.38s9H),1.10d $J = 6.7~\\mathrm{Hz}$ 3H).LC-MS $(\\mathrm{ES + })$ .. $m / z$ 617 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,620,479,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-((2R)-2-(3-(2-(2S)-4-(2-(4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)-2-methylpiperazin-1-yl)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (16). A solution of intermediate 106 $(160\\mathrm{mg},0.259\\mathrm{mmol})$ in HCl $(4.0\\mathrm{M}$ in MeOH, $5\\mathrm{mL})$ was stirred at room temperature for $8\\mathrm{h}$ The volatiles were then removed under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ 0 to $100\\%$ to afford 2-(6-amino-5-(8-(2-(2-((S)-3-methylpiperazin-1-yl)ethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)pyridazin-3-yl)phenol $(120~\\mathrm{mg},90\\%)$ as a white solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.13s1H7.92d $J =$ $8.0\\mathrm{Hz}$ 1H7.79d $J = 5.9\\mathrm{Hz}$ 1H7.50s1H7.23t $J = 7.7$ Hz1H6.92-6.80m2H6.54dd $J = 6.1$ $2.1\\mathrm{Hz}$ 1H6.16d $J$ $= 2.0\\mathrm{Hz}$ 1H),5.97s2H4.51s2H4.27t $J = 6.0~\\mathrm{Hz}$ 2H), 3.26d $J = 11.4~\\mathrm{Hz}$ 2H),3.02d $J = 11.6~\\mathrm{Hz}$ 2H),2.82-2.70m, 3H),2.70-2.54m4H),2.25-2.12m2H),2.02-1.86m3H), 1.60t $J = 10.1~\\mathrm{Hz}$ 1H),0.90d $J = 6.3~\\mathrm{Hz}$ 3H.LC-MS $(ES+)$ : $m / z517[\\mathbf{M} + \\mathbf{H}]^{+}$ .A solution of this material $(88.9\\mathrm{mg},0.172\\mathrm{mmol},$ 1.1 equiv), intermediate 61 $(85.0\\mathrm{mg},0.157\\mathrm{mmol},$ 1.0 equiv and $\\mathrm{NaBH(OAc)_3}$ 175 mg, 0.825 mmol, 5.3 equiv in $\\mathrm{CH}_3\\mathrm{CN}$ $5\\mathrm{mL})$ was stirred at room temperature for $10\\mathrm{h}$ The reaction was quenched with MeOH $(10~\\mathrm{mL})$ and the solvents were evaporated under vacuum.The residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH_4HCO_3})$ ,0 to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,298]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"100%) to afford $67~\\mathrm{mg}$ of impure product as a white solid. This material was further purified by preparative HPLC [column: XSelect CSH Fluoro Phenyl $30\\times 150\\mathrm{mm}^2$ $5\\mu \\mathrm{m}$ ; mobile phase A: water (10 mmol/L $\\mathrm{NH_4HCO_3}$ ), mobile phase B: $\\mathrm{CH}_3\\mathrm{CN}$ ; flow rate: $60~\\mathrm{mL}/$ min; gradient: $27\\%$ B to $50\\%$ B over $10\\mathrm{min}$ ; wavelength: 254/220 nm; RT: $8.1\\mathrm{min}$ ] to afford the title compound $(4.2\\mathrm{mg},2.5\\%)$ as a light yellow solid. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ , DMSO- $d_{6})$ $\\delta$ 14.16 (s, 1H), 8.99 (s, 1H), 8.43 (d, $J = 7.6~\\mathrm{Hz}$ , 1H), 7.92 (dd, $J = 8.1$ , $1.6~\\mathrm{Hz}$ , 1H), 7.79 (dd, $J = 6.0$ , $1.8~\\mathrm{Hz}$ , 1H), 7.50 (s, 1H), 7.47-7.40 (m, 2H), 7.40-7.33 (m, 2H), 7.27-7.17 (m, 1H), 6.92-6.77 (m, 2H), 6.54 (dd, $J = 6.1$ , $2.1~\\mathrm{Hz}$ , 1H), 6.16 (d, $J = 2.0~\\mathrm{Hz}$ , 1H), 6.08 (s, 1H), 5.99 (s, 2H), 5.10 (d, $J = 3.7~\\mathrm{Hz}$ , 1H), 4.97-4.85 (m, 1H), 4.50 (s, 2H), 4.37 (t, $J = 7.8~\\mathrm{Hz}$ , 1H), 4.33-4.25 (m, 3H), 4.22-4.12 (m, 2H), 3.74-3.55 (m, 2H), 3.45 (dd, $J = 10.0$ , $4.9~\\mathrm{Hz}$ , 1H), 3.33-3.30 (m, 1H), 3.25 (d, $J = 11.5~\\mathrm{Hz}$ , 2H), 3.08-2.95 (m, 3H), 2.87-2.63 (m, 2H), 2.63-2.55 (m, 3H), 2.46 (s, 3H), 2.45-2.33 (m, 2H), 2.30-2.12 (m, 4H), 2.07-1.74 (m, 5H), 1.50-1.34 (m, 3H), 0.98-0.95 (m, 6H), 0.87-0.75 (m,3H). LC-MS $(ES+)$ : $m / z$ 1041.7 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,298,915,425]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"cis-3-(Benzyloxy)cyclobutan-1-ol (108). To a $0^{\\circ}\\mathrm{C}$ solution of 3-(benzyloxy)cyclobutan-1-one (107, $10.0\\mathrm{g}$ , 56.8 mmol, 1.0 equiv) in MeOH $(100~\\mathrm{mL})$ was added $\\mathrm{NaBH}_4$ $(2.15\\mathrm{g},56.9\\mathrm{mmol},1.0$ equiv). The resulting solution was stirred at $0^{\\circ}\\mathrm{C}$ for $1\\textrm{h}$ then was quenched with water $(200~\\mathrm{mL})$ and extracted with EtOAc $(200~\\mathrm{mL}\\times 3)$ . The organic layers were combined, dried over sodium sulfate, and were concentrated under vacuum. The residue was purified by flash chromatography on silica gel (petroleum ether:EtOAc, 80:1 to 1:1) to give the title compound $(9.85\\mathrm{g},97\\%)$ as a colorless oil. LC-MS (ES +): $m / z$ 200.9 $[\\mathbf{M} + \\mathbf{N}\\mathbf{a}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,425,915,665]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"trans-4-(3-(Benzyloxy)cyclobutoxy)pyridine (109). To a solution of pyridin-4-ol $(3.20\\mathrm{g}, 33.7\\mathrm{mmol}, 1.5\\mathrm{equiv})$ and cis-3-(benzyloxy)cyclobutan-1-ol $(108, 4.0\\mathrm{g}, 22.4\\mathrm{mmol}, 1.0\\mathrm{equiv})$ in THF $(200\\mathrm{mL})$ was added triphenylphosphine $(7.06\\mathrm{g}, 26.9\\mathrm{mmol}, 1.2\\mathrm{equiv})$ and DIAD $(5.45\\mathrm{g}, 26.9\\mathrm{mmol}, 1.2\\mathrm{equiv})$ in one portion at $10^{\\circ}\\mathrm{C}$ . The mixture was stirred at $50^{\\circ}\\mathrm{C}$ for $12\\mathrm{h}$ , then was cooled to room temperature and was concentrated under reduced pressure. Water $(50\\mathrm{mL})$ was added, and the mixture was stirred for $1\\mathrm{min}$ . The aqueous phase was extracted with DCM $(50\\mathrm{mL} \\times 3)$ , and the combined organic phases were washed with brine $(50\\mathrm{mL} \\times 2)$ , dried with sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (petroleum ether:THF, 20:1 to 5:1). Additional purification by reverse phase C18 column chromatography [5 to $50\\%$ $\\mathrm{CH}_3\\mathrm{CN}$ in water (with $0.5\\%$ $\\mathrm{NH}_4\\mathrm{OH}$ ] then provided the title compound $(3.2\\mathrm{g}, 55\\%)$ as a white solid. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}, \\mathrm{CDCl}_3)$ $\\delta$ 8.32–8.34 (m, 2H), 7.22–7.39 (m, 5H), 6.60–6.62 (m, 2H), 4.80–4.84 (m, 1H), 4.37 (s, 2H), 4.24–4.28 (m, 1H), 2.37–2.46 (m, 4H). LC–MS $(\\mathrm{ES+}): m/z$ 256.0 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,665,915,765]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1-Benzyl-4-(trans-3-(benzyloxy)cyclobutoxy)pyridin-1-ium bromide (110). To a solution of intermediate 109 $(4.2\\mathrm{g},16.5\\mathrm{mmol}$ 1.0 equiv) in toluene $(65~\\mathrm{mL})$ was added benzyl bromide $(2.81\\mathrm{g},$ $16.5\\mathrm{mmol}$ 1.0 equiv). The mixture was stirred at $80^{\\circ}\\mathrm{C}$ for $12\\mathrm{h}$ then was cooled to room temperature and was concentrated under reduced pressure. The crude product was triturated with petroleum ether (80 mL) to give the title compound $(6.5\\mathrm{g},92\\%)$ as a white solid. LC-MS $(\\mathrm{ES + })$ .. $m / z346.0[\\mathrm{M}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,765,915,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"trans-1-Benzyl-4-(3-(benzyloxy)cyclobutoxy)-1,2,3,6-tetrahydropyridine (111). To a $0^{\\circ}\\mathrm{C}$ solution of intermediate 110 $(6.5\\mathrm{g},15.3\\mathrm{mmol},1.0$ equiv) in EtOH $(120~\\mathrm{mL})$ was added $\\mathrm{NaBH}_4$ $(3.46\\mathrm{g},91.5\\mathrm{mmol},6.0$ equiv). The mixture was stirred at $15^{\\circ}\\mathrm{C}$ for 4 h then was concentrated under reduced pressure. The residue was diluted with water $(25~\\mathrm{mL})$ and was extracted with EtOAc $(50~\\mathrm{mL}\\times$ 2). The combined organic phases were washed with brine $(40~\\mathrm{mL}\\times$ 3), dried with sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure to give the title compound (4.5 g, $84\\%$ ) as a colorless oil. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz},\\mathrm{CDCl}_3)$ $\\delta 7.28 - 7.38$ m, 10H), 4.57-4.58 (m, 1H), 4.42 (s, 2H), 4.36-4.38 (m, 1H), 4.13-4.28 (m, 1H), 3.59 (s, 2H), 3.01-3.02 (m, 2H), 2.60-2.62 (m, 2H), 2.36-2.38 (m, 4H), 2.06-2.35 (m, 2H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 350.1 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[484,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1298 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,70,481,195]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"trans-3-((1-Benzylpiperidin-4-yl)oxy)cyclobutan-1-ol (112). To a room temperature solution of intermediate 111 $(4.5\\mathrm{g},12.9$ mmol) in THF $(95~\\mathrm{mL})$ and EtOH $(70~\\mathrm{mL})$ was added $10\\%$ palladium on activated carbon $(0.5\\mathrm{g})$ . The suspension was degassed and purged with hydrogen three times then was stirred under a hydrogen atmosphere $(50~\\mathrm{psi})$ at $35^{\\circ}\\mathrm{C}$ for $12\\mathrm{h}$ . The reaction mixture was filtered, and the filtrate was concentrated. The residue was purified by silica gel chromatography (DCM:MeOH: $\\mathrm{NH_4OH}$ , 20:1:0 to 10:1:0.1) to give the title compound $(2.8\\mathrm{g},83\\%)$ as a colorless oil. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,196,481,370]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tert-Butyl 4-(trans-3-hydroxyclobutoxy)piperidine-1-carboxylate (113). To a room temperature solution of intermediate 112 $(1.1\\mathrm{g},4.21\\mathrm{mmol},1.0$ equiv) in MeOH $(10~\\mathrm{mL})$ was added $10\\%$ $\\mathrm{Pd(OH)_2}$ on activated carbon $(591\\mathrm{mg})$ and di-tert-butyl dicarbonate $(1.84\\mathrm{g},8.42\\mathrm{mmol},2.0$ equiv). The suspension was degassed and purged with hydrogen three times then was stirred under a hydrogen atmosphere (50 psi) at $25^{\\circ}\\mathrm{C}$ for $12\\mathrm{h}$ . The reaction mixture was filtered, and the filtrate was concentrated. The residue was purified by silica gel chromatography (petroleum ether:EtOAc, 20:1 to 2:1) to afford the title compound $(820\\mathrm{mg},71\\%)$ as a colorless oil. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz},\\mathrm{CDCl}_3)$ $\\delta$ 4.51s,1H),4.32-4.37m1H),3.79-3.82 m,2H),3.40-3.44m1H),2.99-3.04m2H),2.20-2.28m 4H),1.76-1.80m3H),1.60-1.62m1H),1.45-1.47m,12H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 172.0 $[\\mathbf{M - B o c + H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,370,481,568]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tert-Butyl 4-(trans-3-((4-bromopyridin-2-yl)oxy)-cyclobutoxy)piperidine-1-carboxylate (114). A room temperature mixture of intermediate 113 $(1.0\\mathrm{g},3.69\\mathrm{mmol},1.0$ equiv), 4-bromo-2-fluoro-pyridine (72, $778~\\mathrm{mg}$ $4.42\\mathrm{mmol}$ 1.2 equiv), and $\\mathrm{Cs_2CO_3}$ $(2.40\\mathrm{g},7.37\\mathrm{mmol},2.0$ equiv) in $\\mathrm{CH}_3\\mathrm{CN}$ $(10~\\mathrm{mL})$ was degassed and purged with nitrogen three times. The mixture was then stirred at $90^{\\circ}\\mathrm{C}$ for $12\\mathrm{h}$ after which it was cooled to room temperature and filtered. The filtrate was concentrated under reduced pressure, and the crude product thus obtained was purified by silica gel chromatography (petroleum ether:EtOAc, 1:0 to 10:1) to give the title compound $(1.36\\mathrm{g},86\\%)$ as colorless oil. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ $\\mathrm{CDCl}_3$ ) $\\delta$ 7.97d $J = 5.6\\mathrm{Hz}$ 1H)7.03-7.01m1H6.91d $J=$ $1.2\\mathrm{Hz}$ 1H),5.30-5.23m1H)4.43-4.31m1H)3.81d $J=$ $12.8\\mathrm{Hz}$ 2H),3.49-3.42m1H)3.07-3.01m2H)2.52-2.36 m,4H),1.80d $J = 8.8\\mathrm{Hz}$ 2H),1.55-1.47m2H)1.46s,9H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 427.1 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,568,481,828]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Benzyl 8-(2-(trans-3-((1-(tert-butoxycarbonyl)piperidin-4- yl)oxy)cyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]-octane-3-carboxylate (115). A room temperature mixture of intermediate 114 $(1.36\\mathrm{g},3.18\\mathrm{mmol}$ 1.0 equiv), benzyl 3,8- diazabicyclo[3.2.1]octane-3-carboxylate (98, $784~\\mathrm{mg}$ 3.18 mmol, 1.0 equiv), RuPhosPd-G2 $(148\\mathrm{mg},0.19\\mathrm{mmol},0.06$ equiv), and $\\mathrm{Cs_2CO_3}$ $(2.07\\mathrm{g},6.37\\mathrm{mmol},2.0$ equiv) in toluene $(27~\\mathrm{mL})$ was degassed and purged with nitrogen three times. The mixture was then stirred at $110^{\\circ}C$ for $12\\mathrm{h}$ after which it was cooled to room temperature. Water (30 mL) was added, and the mixture was extracted with EtOAc $(40~\\mathrm{mL}\\times$ 2). The combined organic layers were washed with brine $(30~\\mathrm{mL}\\times$ 2), dried over sodium sulfate, filtered, and the filtrate was concentrated under reduced pressure. The crude product was purified by silica gel chromatography (petroleum ether:EtOAc, 1:0 to 1:1) to give the title compound $(1.35\\mathrm{g},71\\%)$ as a colorless oil. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz},\\mathrm{CDCl}_3)\\delta 7.86$ d $J = 6.0~\\mathrm{Hz}$ 1H)7.40-7.29 m5H) 6.27dd $J = 6.0$ $2.4~\\mathrm{Hz}$ 1H5.94d $J = 2.0~\\mathrm{Hz}$ 1H5.29-5.24 m, 1H),5.13s,2H),4.38m1H4.22s,2H)3.86-3.68 m, 4H),3.49-3.41 m, 1H),3.33-3.18 m, 2H),3.06-3.00 m, 2H), 2.46-2.36 m, 4H),1.94-1.74 m, 4H),1.63-1.51 m, 4H),1.46 s, 9H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 593.4 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,830,481,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tert-Butyl 4-(trans-3-((4-(3,8-diazabicyclo[3.2.1]octan-8-yl)-pyridin-2-yl)oxy)cyclobutoxy)piperidine-1-carboxylate (116). To a room temperature solution of intermediate 115 $(1.35\\mathrm{g},2.28$ mmol) in a mixture of THF $(27~\\mathrm{mL})$ and EtOH $(27~\\mathrm{mL})$ was added $10\\%$ palladium hydroxide on activated carbon $(320~\\mathrm{mg})$ . The resulting suspension was degassed under vacuum and purged with hydrogen several times then was stirred under a hydrogen atmosphere (50 psi) at $60^{\\circ}\\mathrm{C}$ for $12\\mathrm{h}$ . After cooling to room temperature, the reaction mixture was filtered, and the filtrate was concentrated to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,914,95]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"provide the title compound $(932\\mathrm{mg},89\\%)$ as a brown solid. LC-MS $(\\mathrm{ES + })$ .. $m / z459.3[\\mathrm{M} + \\mathrm{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,96,915,380]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tert-Butyl 4-(trans-3-((4-(3-(3-amino-6-chloropyridazin-4- yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidine-1-carboxylate (117). A room temperature mixture of intermediate 116 $(932\\mathrm{mg},2.03\\mathrm{mmol}$ 1.0 equiv), 4-bromo-6-chloro-pyridazin-3-amine (70, $508~\\mathrm{mg}$ 2.44 mmol, 1.2 equiv), and DIEA $(3.54~\\mathrm{mL}$ 20.3 mmol, 10 equiv) in DMSO (30 mL) was degassed and purged with nitrogen three times. The mixture was stirred at $130^{\\circ}C$ for $3\\textrm{h}$ then was cooled to room temperature. Water $(30~\\mathrm{mL})$ was added, and the mixture was extracted with EtOAc $(30~\\mathrm{mL}\\times 2)$ . The combined organic layers were washed with saturated aqueous sodium chloride $(30~\\mathrm{mL}\\times 2)$ , dried over sodium sulfate, and were concentrated. The residue was purified by semipreparative reverse phase HPLC [column: Phenomenex Gemini C18 $250\\times 50\\mathrm{mm}^2$ $10~\\mu \\mathrm{m}$ ; mobile phase A: water (with $0.05\\%$ $\\mathrm{NH_4OHv / v)}$ mobile phase B: $\\mathrm{CH}_3\\mathrm{CN}$ ; gradient: $45 - 70\\%$ B] to provide the title compound $(772\\mathrm{mg},64\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 7.76 d $J = 6.0~\\mathrm{Hz}$ 1H)6.90s1H6.50 dd $J = 6.1$ 2.1 Hz,1H)6.12d $J = 2.0~\\mathrm{Hz}$ 1H)5.85s2H) 5.26-5.12 m1H4.45 s2H4.31 p $J = 6.0~\\mathrm{Hz}$ 1H)3.66 dt $J$ $= 13.4$ $4.7\\mathrm{Hz}$ 2H)3.50-3.37 m1H)3.18 d $J = 11.5\\mathrm{Hz}$ 2H) 2.92dd $J = 35.6$ $11.5\\mathrm{Hz}$ 4H)2.40-2.21 m4H)2.13 d $J = 7.2$ Hz,2H),1.97-1.88 m2H)1.80-1.70 m2H)1.39 s9H) 1.33-1.20 m2H.LC-MS $(\\mathrm{ES + })$ .. $m / z$ 586.5 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,380,915,563]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tert-Butyl 4-(trans-3-((4-(3-(3-amino-6-(2-hydroxyphenyl)-pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)cyclobutoxy)piperidine-1-carboxylate (118). A room temperature mixture of intermediate 117 $(772\\mathrm{mg},$ $1.32\\mathrm{mmol}$ 1.0 equiv), (2-hydroxyphenyl)boronic acid (72, $218\\mathrm{mg}$ $1.58\\mathrm{mmol}$ 1.2 equiv), $\\mathrm{Pd(PPh_3)_4}$ $(152\\mathrm{mg},$ $0.13\\mathrm{mmol}$ 0.1 equiv), and $\\mathrm{K}_2\\mathrm{CO}_3$ $364\\mathrm{mg}$ $2.63\\mathrm{mmol}$ 2.0 equiv) in a mixture of 1,4-dioxane $(12~\\mathrm{mL})$ and water $(2\\mathrm{mL})$ was degassed and purged with nitrogen three times. The mixture was then stirred at $90^{\\circ}C$ for $10\\mathrm{h}$ After cooling to room temperature, the reaction mixture was concentrated, and the residue was purified by semipreparative reverse phase HPLC [column: Kromasil $250\\times 50\\mathrm{mm}^2$ $10~\\mu \\mathrm{m}$ mobile phase A: water (with $0.1\\%$ TFA), mobile phase B: $\\mathrm{CH}_3\\mathrm{CN};$ gradient: $20 - 50\\%$ B] to give the title compound $(500\\mathrm{mg},54\\%)$ as a yellow solid. LC-MS $(\\mathrm{ES + })$ .. $m / z$ 644.4 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,563,915,710]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(6-Amino-5-(8-(2-((trans)-3-(piperidin-4-yloxy)cyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)-pyridazin-3-yl)phenol (119). To a room temperature solution of intermediate 118 $(500\\mathrm{mg},0.78\\mathrm{mmol})$ in DCM $(5\\mathrm{mL})$ was added HCl $(4.0\\mathrm{M}$ in 1,4-dioxane, $5\\mathrm{mL}$ ). The mixture was stirred at $20^{\\circ}\\mathrm{C}$ for $2\\mathrm{h}$ then was concentrated to give the crude title compound (HCl salt, $500\\mathrm{mg}$ ) as a yellow solid. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz},\\mathrm{D}_2\\mathrm{O})$ $\\delta 7.72$ (d, $J = 7.2\\mathrm{Hz}$ , 1H), 7.40-7.55 (m, 3H), 6.99-7.11 (m, 2H), 6.68-6.76 (m, 1H), 6.02 (d, $J = 2.0\\mathrm{Hz}$ , 1H), 5.10 (dt, $J = 6.4$ , 3.2 Hz, 1H), 4.52 (m, 1H), 3.70-3.84 (m, 3H), 3.30-3.42 (m, 5H), 3.25 (br d, $J = 12.4\\mathrm{Hz}$ , 2H), 3.02-3.14 (m, 2H), 2.46-2.64 (m, 4H), 2.01-2.22 (m, 6H), 1.67-1.83 (m, 2H). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,710,915,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-((2R)-2-(3-(2-(4-((trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)ethoxy)-isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (17). To a solution of intermediate 119 (HCl salt, $70.0\\mathrm{mg}$ , 0.121 mmol, 1.0 equiv) and $\\mathrm{NaOAc}$ $(31.6\\mathrm{mg},0.385\\mathrm{mmol},3.2$ equiv) in MeOH $(2.1~\\mathrm{mL})$ and DCM $(0.7~\\mathrm{mL})$ was added intermediate 61 $(104\\mathrm{mg},0.192\\mathrm{mmol},1.6$ equiv) at room temperature. The reaction was stirred at room temperature for $30\\mathrm{min}$ after which $\\mathrm{NaBH}_3\\mathrm{CN}$ $(12.1\\mathrm{mg},0.192\\mathrm{mmol},1.6$ equiv) was addd in portions at the same temperature. The resulting mixture was stirred at room temperature for another $2\\mathrm{h}$ then was directly purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH_4HCO_3})$ 0 to $100\\%$ to afford the title compound $(34\\mathrm{mg},25\\%)$ as an off-white solid. ${}^{1}\\mathbf{H}$ NMR $(400\\mathrm{MHz}$ DMSO- $d_{6}$ ) $\\delta$ 14.15 (s, 1H), 8.99 (d, $J = 1.6~\\mathrm{Hz}$ , 1H), 8.41 (d, $J = 7.7~\\mathrm{Hz}$ , 1H), 7.96-7.89 (m, 1H), 7.78 (d, $J = 5.9~\\mathrm{Hz}$ , 1H), 7.50 (s, 1H), 7.49-7.41 (m, 2H), 7.41-7.34 (m, 2H), 7.27-7.18 (m, 1H), 6.91-6.81 (m, 2H), 6.56-6.50 (m, 1H), 6.14 (d, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[484,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1299 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,70,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"$J = 2.0\\\\mathrm{Hz},1\\\\mathrm{H})$ 6.10s,1H)5.98s,2H),5.24-5.14m,1H)5.10 $(\\\\mathrm{d},J = 3.7\\\\mathrm{Hz},1\\\\mathrm{H}),$ 4.98-4.86m,1H)4.50d $J = 4.5\\\\mathrm{Hz},2\\\\mathrm{H})$ 4.38t $J = 7.9\\\\mathrm{Hz},1\\\\mathrm{H})$ 4.32-4.25m,2H)4.22t $J = 5.7\\\\mathrm{Hz},2\\\\mathrm{H})$ 3.75-3.61m,2H)3.50-3.41m,1H)3.31-3.22m,3H)3.02d $J = 11.6\\\\mathrm{Hz},2\\\\mathrm{H}),$ 2.80-2.71m,2H)2.69-2.61m,2H)2.46s, 3H)2.39-2.23m,5H)2.23-1.90m,7H)1.84-1.73m,3H) 1.49-1.35m,5H)0.96d $J = 6.4\\\\mathrm{Hz},3\\\\mathrm{H}),$ 0.87-0.77m,3H). LC-MS $\\\\left(\\\\mathrm{ES}+\\\\right)$ .. $m / z$ 1068.7 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\"To confirm the absolute stereochemistry of intermediate 61 employed in the syntheses of 15, 16, and 17, the isopropyl epimer corresponding to 61 (61e, prepared above) was similarly transformed into the isopropyl epimer of PROTAC 17 (17e, structure not shown). To a solution of intermediate 119 (HCl salt, $150\\\\mathrm{mg}$ , $0.259\\\\mathrm{mmol}$ , 1.0 equiv) and $\\\\mathrm{NaOAc}$ (67.9 mg, 0.828 mmol, 3.2 equiv) in MeOH (2.1 mL) and DCM (0.7 mL) was added intermediate 61e (223 mg, 0.41 mmol, 1.6 equiv) at room temperature. The reaction was stirred at room temperature for 30 min after which $\\\\mathrm{NaBH}_3\\\\mathrm{CN}$ (26.0 mg, 0.414 mmol, 1.6 equiv) was added in portions at the same temperature. The resulting mixture was stirred at room temperature for another 2 h then was directly purified by prepacked C18 column chromatography $(\\\\mathrm{CH}_3\\\\mathrm{CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ to afford 17e (67 mg, $23\\\\%$ ) as an off-white solid. ${}^{1}\\\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) $\\\\delta$ 14.15 (s, 1H), 9.05–8.87 (m, 1H), 8.30 (d, $J = 7.9~\\\\mathrm{Hz}$ , 1H), 7.97–7.89 (m, 1H), 7.77 (d, $J = 5.9~\\\\mathrm{Hz}$ , 1H), 7.55–7.28 (m, 5H), 7.28–7.18 (m, 1H), 6.92–6.81 (m, 2H), 6.57–6.49 (m, 1H), 6.18–6.13 (m, 1H), 6.09 (s, 1H), 5.98 (s, 2H), 5.25–5.15 (m, 1H), 5.13–4.86 (m, 2H), 4.50 (s, 2H), 4.42 (t, $J = 7.8~\\\\mathrm{Hz}$ , 1H), 4.33–4.12 (m, 4H), 3.75 (d, $J = 8.6~\\\\mathrm{Hz}$ , 1H), 3.60–3.46 (m, 2H), 3.30–3.18 (m, 3H), 3.02 (d, $J = 11.6~\\\\mathrm{Hz}$ , 2H), 2.83–2.56 (m, 4H), 2.46 (s, 3H), 2.36–2.22 (m, 5H), 2.22–2.16 (m, 2H), 2.16–2.02 (m, 3H), 2.01–1.91 (m, 2H), 1.84–1.69 (m, 3H), 1.50–1.31 (m, 5H), 0.97 (d, $J = 6.6~\\\\mathrm{Hz}$ , 2H), 0.88–0.80 (m, 3H), 0.76 (d, $J = 6.7~\\\\mathrm{Hz}$ , 1H). LC–MS $(\\\\mathrm{ES+})$ .. $m/z$ 1068.7 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\"Both 17 and 17e PROTACs were profiled in biological assessments, and the more potent diastereomer was assigned the absolute stereochemistry shown for 17 in Table 2 (cf., Table S4). This stereochemistry was consistent with that observed in the crystal structure of the BRG1-17-VBC ternary complex (Figure S8 and S9). By inference, the chiral-pure intermediate employed to generate 17 was assigned the absolute stereochemistry shown in Scheme 3 (i.e., intermediate 61). \",\"2-(6-Amino-5-(8-(2-(trans-3-((1-(2,2-diethoxyethyl)-piperidin-4-yl)oxy)cyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)pyridazin-3-yl)phenol (120). A solution of intermediate 119 $(200\\\\mathrm{mg},0.368\\\\mathrm{mmol},1.0$ equiv) and 2-bromo1,1-diethoxyethane $(145\\\\mathrm{mg},0.736\\\\mathrm{mmol},2.0$ equiv), DIEA $(143\\\\mathrm{mg},$ $1.10\\\\mathrm{mmol},3.0$ equiv), and NaI $(110\\\\mathrm{mg},0.736\\\\mathrm{mmol},2.0$ equiv) in DMF $(2\\\\mathrm{mL})$ was stirred at $70^{\\\\circ}\\\\mathrm{C}$ overnight. The mixture was cooled to room temperature and was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH_4HCO_3})$ , 0 to $100\\\\%$ ) to afford the title compound $(85\\\\mathrm{mg},35\\\\%)$ as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.16s,1H)7.92dd $J = 8.0$ $1.6~\\\\mathrm{Hz}$ 1H7.77d $J = 6.0~\\\\mathrm{Hz}$ 1H7.50s,1H)7.28-7.17m, 1H)6.91-6.79m2H)6.52dd $J = 6.1$ 2.0 Hz1H)6.14d $J =$ $2.0~\\\\mathrm{Hz}$ 1H5.98s2H)5.28-5.12m1H4.58-4.45m3H) 4.27p $J = 6.1~\\\\mathrm{Hz}$ 1H)3.65-3.52m2H)3.52-3.46m2H) 3.30-3.14m3H)3.01d $J = 11.6~\\\\mathrm{Hz}$ 2H)2.80-2.65m2H) 2.37d $J = 5.2~\\\\mathrm{Hz}$ 2H)2.33-2.22m4H)2.22-2.03m4H) 2.01-1.91m2H)1.80-1.69m2H)1.46-1.29m2H)1.10t $J = 7.0~\\\\mathrm{Hz}$ 6H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 660 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\"2-(4-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)- pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)cyclobutoxy)piperidin-1-yl)acetaldehyde (121). A solution of intermediate 120 $(100\\\\mathrm{mg},0.152\\\\mathrm{mmol})$ in $1.0\\\\mathrm{M}$ $\\\\mathrm{H}_2\\\\mathrm{SO}_4$ $(1\\\\mathrm{mL})$ and THF $(1\\\\mathrm{mL})$ was stirred at $60^{\\\\circ}\\\\mathrm{C}$ overnight. The mixture was then cooled to room temperature and was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH_4HCO_3)}$ , 0 to $30\\\\%$ ) to afford the title compound $(50\\\\mathrm{mg},66\\\\%$ purity) as an off-white solid. LC-MS $(\\\\mathrm{ES + })$ .. $m / z~586[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ \"]","page_idx":"38","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[512,71,915,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Additional purification attempts did not improve the purity, and the material was therefore used in its impure form in the next step. \",\"tert-Butyl 4-(5-((R)-1-((2S,4R)-4-hydroxy-2-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)carbamoyl)pyrrolidin-1-yl)-3-methyl-1-oxobutan-2-yl)isoxazol-3-yl)piperazine-1-carboxylate (122). To a stirred solution of intermediate 46 $(820\\\\mathrm{mg},2.32$ mmol, 1.0 equiv), (2S,4R)-4-hydroxy- $N - ((S)$ -1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (57, TFA salt, $1.02\\\\mathrm{g},2.32$ mmol, 1.0 equiv) and DIEA $(900\\\\mathrm{mg},6.96\\\\mathrm{mmol},3.0$ equiv) in DMF $(9~\\\\mathrm{mL})$ was added HATU $(1323\\\\mathrm{mg},3.48\\\\mathrm{mmol},1.5$ equiv) in portions at room temperature. The resulting mixture was stirred at room temperature for $^{\\\\textrm{\\\\scriptsize 1h}}$ then was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $40 \\\\%$ to afford the coupled product $\\\\left(\\\\sim 1:1\\\\right.$ mixture of two isopropyl group isomers, $950~\\\\mathrm{mg})$ as a yellow solid. The two isomers were separated by preparative chiral HPLC [column: CHIRALPAK IF, $2\\\\times 25~\\\\mathrm{cm}^2$ $5$ $\\\\mu \\\\mathrm{m}$ ; mobile phase A: 3:1 hexane:DCM $(0.5\\\\% 2\\\\mathrm{M}\\\\mathrm{NH}_{3}\\\\cdot \\\\mathrm{MeOH})$ mobile phase B: MeOH; flow rate: $20~\\\\mathrm{mL / min}$ ; gradient: isocratic $20\\\\%$ B; wavelength: $220 / 254~\\\\mathrm{nm}$ RT1:7.39 minRT2:11.24 min sample solvent: EtOH; injection volume: $3.5~\\\\mathrm{mL}$ ; number of runs: S] to afford the title compound (slower peak, $378~\\\\mathrm{mg}$ $24\\\\%$ ) as a yellow solid. ${}^{1}\\\\mathbf{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 89.02-8.77 (m, 1H), 8.41 (d, $J = 7.7~\\\\mathrm{Hz}$ 1H),7.51-7.40 (m, 2H),7.40-7.32 (m, 2H),6.20-6.03 (m, 1H),5.09 (d, $J = 3.2~\\\\mathrm{Hz}$ 1H),4.97-4.61 (m, 1H),4.36 (t, $J = 7.8$ Hz, 1H),4.28 (s, 1H),3.71 (dd, $J = 10.6$ $4.4~\\\\mathrm{Hz}$ 1H),3.59 (d, $J = 9.8$ Hz, 1H),3.49-3.35 (m, 5H),3.20-3.05 (m, 4H),2.46 (s, 3H), 2.32-2.10 (m, 1H),2.08-1.96 (m, 1H),1.83-1.69 (m, 1H),1.49- 1.33 (m, 12H), 1.01-0.91 (m, 3H), 0.87-0.75 (m, 3H). LC-MS (ES +): m/z 667 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . The isomer bearing the undesired isopropyl stereocenter (122e, isopropyl isomer corresponding to 122, structure not shown) was also isolated (faster peak, $440~\\\\mathrm{mg}$ $28\\\\%$ ) as a yellow solid. ${}^{1}\\\\mathbf{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 89.03-8.86 (m, 1H),8.23 (d, $J = 8.0~\\\\mathrm{Hz}$ , 1H),7.54-7.26 (m, 4H),6.18 (s, 1H),5.10 (d, $J = 3.6~\\\\mathrm{Hz}$ 1H),5.05-4.82 (m, 1H),4.56-4.39 (m, 1H),4.27 (s, 1H),3.71 (d, $J$ $= 8.9~\\\\mathrm{Hz}$ , 1H),3.58-3.50 (m, 2H),3.54-3.25 (m, 4H),3.23-3.00 (m, 4H),2.46 (d, $J = 5.2~\\\\mathrm{Hz}$ , 3H),2.33-2.19 (m, 1H),2.11-1.90 (m, 1H),1.88-1.75 (m, 1H),1.50-1.31 (m, 12H), $1.00 - 0.72$ (m, 6H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z667[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ \",\"(2S,4R)-4-Hydroxy-1-((R)-3-methyl-2-(3-(piperazin-1-yl)-isoxazol-5-yl)butanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (123). A solution of intermediate 122 $(378\\\\mathrm{mg},0.567\\\\mathrm{mmol})$ in DCM $(5\\\\mathrm{mL})$ and TFA $(1\\\\mathrm{mL})$ was stirred at room temperature for $1\\\\textrm{h}$ then was concentrated under reduced pressure. The residue was purified by prepacted C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $35\\\\%$ ) to afford the title compound $(330\\\\mathrm{mg},103\\\\%$ slightly impure) as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 9.02-8.75 m1H),8.39 d $J = 7.7~\\\\mathrm{Hz}$ 1H7.51-7.40 m2H 7.37d $J = 8.5\\\\mathrm{Hz}$ 2H6.22-6.05 m1H),5.14-5.07 m1H) 5.04-4.61 m1H),4.36 t $J = 7.8~\\\\mathrm{Hz}$ 1H4.29s1H3.72dd $J$ $= 10.5$ $4.5\\\\mathrm{Hz}$ 1H),3.64-3.53 m1H),3.50-3.38 m1H),3.38- 3.15 m4H),3.10-2.93 m4H),2.49-2.43 m3H),2.31-2.11 m1H),2.09-1.88 m1H),1.83-1.69 m1H),1.52-1.30 m 3H),1.01-0.92 m3H),0.89-0.70 m3H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 567 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . Similar transformation of intermediate 122e afforded 123e (the isopropyl group imper corresponding to 123, structure not shown, $395\\\\mathrm{mg}$ $105\\\\%$ ,slightly impure) as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 9.01-8.88 m1H),8.29 d $J = 7.7~\\\\mathrm{Hz}$ 1H),7.53-7.28 m4H),6.17 s1H),5.11 d $J = 3.6~\\\\mathrm{Hz}$ 1H) 5.05-4.79 m1H),4.56-4.38 m1H),4.27 s1H),3.70 d $J = 8.9$ Hz, 1H),3.61-3.39 m2H),3.25-3.15 m4H),2.97-2.88 m 4H),2.46 d $J = 4.2~\\\\mathrm{Hz}$ 3H),2.35-2.10 m1H),2.09-1.86 m, 1H),1.85-1.71 m, 1H),1.49-1.30 m, 3H),1.02-0.71 m, 6H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 567 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\"(2S,4R)-1-((2R)-2-(3-(4-(2-(4-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)ethyl)piperazin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (18). A solution of intermediate 121 (25 mg, 0.043 mmol, \"]","page_idx":"38","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"38","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"38","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"38","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"38","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1300 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"38","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"38","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,71,482,332]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.0 equiv) and intermediate 123 (25 mg, 0.044 mmol, 1.0 equiv) in MeOH (0.5 mL) and DCM (0.25 mL) was stirred at room temperature for 30 min. Then $\\mathrm{NaBH}_3\\mathrm{CN}$ (8.0 mg, 0.13 mmol, 3.0 equiv) was added, and the resulting mixture was stirred at room temperature for 24 h. The mixture was then concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 80%) to afford the title compound (4.8 mg, 10%) as a white solid. $^1\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) δ 14.16 (s, 1H), 9.02–8.76 (m, 1H), 8.41 (d, $J = 7.7~\\mathrm{Hz}$ , 1H), 7.92 (dd, $J = 8.1$ , 1.6 Hz, 1H), 7.77 (d, $J = 6.0~\\mathrm{Hz}$ , 1H), 7.48 (d, $J = 9.8~\\mathrm{Hz}$ , 1H), 7.44 (d, $J = 8.4~\\mathrm{Hz}$ , 2H), 7.37 (d, $J = 8.3~\\mathrm{Hz}$ , 2H), 7.28–7.19 (m, 1H), 6.90–6.80 (m, 2H), 6.53 (dd, $J = 6.1$ , 2.1 Hz, 1H), 6.14 (d, $J = 2.1~\\mathrm{Hz}$ , 2H), 5.98 (s, 2H), 5.18 (td, $J = 6.8$ , 3.4 Hz, 1H), 5.11 (d, $J = 3.3~\\mathrm{Hz}$ , 1H), 4.95–4.62 (m, 1H), 4.49 (s, 2H), 4.36 (t, $J = 7.8~\\mathrm{Hz}$ , 1H), 4.28 (t, $J = 5.6~\\mathrm{Hz}$ , 2H), 3.71 (dd, $J = 10.5$ , 4.5 Hz, 1H), 3.57 (d, $J = 9.8~\\mathrm{Hz}$ , 1H), 3.45–3.38 (m, 2H), 3.29–3.20 (m, 3H), 3.14 (s, 4H), 3.01 (d, $J = 11.5~\\mathrm{Hz}$ , 2H), 2.84–2.64 (m, 2H), 2.50–2.40 (m, 11H), 2.34–2.24 (m, 3H), 2.24–2.13 (m, 4H), 2.06–1.93 (m, 4H), 1.83–1.73 (m, 3H), 1.50–1.35 (m, 5H), 0.99–0.92 (m, 3H), 0.89–0.75 (m, 3H). LC–MS (ES+): m/z 1136.6 [M + H]⁺ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,333,479,656]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To confirm the absolute stereochemistry of intermediate 123 employed in the syntheses of 18 and 20, the isopropyl epimer corresponding to 123 (123e, prepared above) was similarly transformed into the isopropyl epimer of PROTAC 18 (18e, structure not shown). A solution of intermediate 121 (25 mg, 0.043 mmol, 1.0 equiv) and intermediate 123e (25 mg, 0.044 mmol, 1.0 equiv) in MeOH (0.5 mL) and DCM (0.25 mL) was stirred at room temperature for 30 min. Then $\\mathrm{NaBH}_3\\mathrm{CN}$ (8.0 mg, 0.13 mmol, 3.0 equiv) was added, and the resulting mixture was stirred at room temperature for 24 h. The mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO), 0 to 80%) to afford 18e (6.3 mg, 13%) as a white solid. $^1\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) $\\delta$ 14.16 (s, 1H), 9.02–8.89 (m, 1H), 8.22 (d, $J = 7.8~\\mathrm{Hz}$ , 1H), 7.92 (dd, $J = 8.0$ , 1.6 Hz, 1H), 7.77 (d, $J = 6.0~\\mathrm{Hz}$ , 1H), 7.52–7.45 (m, 2H), 7.45–7.38 (m, 2H), 7.35–7.28 (m, 1H), 7.26–7.18 (m, 1H), 6.90–6.80 (m, 2H), 6.56–6.49 (m, 1H), 6.17–6.11 (m, 2H), 5.98 (s, 2H), 5.18 (t, $J = 6.4~\\mathrm{Hz}$ , 1H), 5.11 (d, $J = 3.6~\\mathrm{Hz}$ , 1H), 5.05–4.80 (m, 1H), 4.49 (s, 2H), 4.41 (t, $J = 7.7~\\mathrm{Hz}$ , 1H), 4.27 (t, $J = 6.2~\\mathrm{Hz}$ , 2H), 3.69 (d, $J = 8.9~\\mathrm{Hz}$ , 1H), 3.59–3.37 (m, 2H), 3.27 (s, 1H), 3.24 (d, $J = 10.5~\\mathrm{Hz}$ , 3H), 3.14 (s, 1H), 3.08 (d, $J = 5.7~\\mathrm{Hz}$ , 3H), 3.01 (d, $J = 11.7~\\mathrm{Hz}$ , 2H), 2.71 (d, $J = 10.4~\\mathrm{Hz}$ , 2H), 2.47–2.33 (m, 9H), 2.33–2.22 (m, 5H), 2.18 (d, $J = 7.3~\\mathrm{Hz}$ , 2H), 2.08–1.89 (m, 6H), 1.87–1.71 (m, 3H), 1.45 (d, $J = 7.0~\\mathrm{Hz}$ , 1H), 1.41–1.30 (m, 4H), 0.95 (d, $J = 6.6~\\mathrm{Hz}$ , 2H), 0.89–0.72 (m, 4H). LC–MS (ES+): m/z 1136.5 [M + H]⁺ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,657,479,731]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Both 18 and 18e PROTACs were profiled in biological assessments, and the more potent diastereomer was assigned the absolute stereochemistry shown for 18 in Table 2 (cf., Table S4). By inference, the chiral-pure intermediates employed to generate 18 were assigned the absolute stereochemistries shown in Scheme 10 (i.e., intermediates 122 and 123). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,732,479,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tert-Butyl 4-((4-(5-((R)-1-((2S,4R)-4-hydroxy-2-(((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)carbamoyl)pyrrolidin-1-yl)-3-methyl-1-oxobutan-2-yl)isoxazol-3-yl)piperazin-1-yl)methyl)-piperidine-1-carboxylate (125). A solution of chiral-pure intermediate 123 $(100\\mathrm{mg},0.18\\mathrm{mmol},1.0$ equiv), tert-butyl 4-formylpiperidine-1-carboxylate (124, $56.5\\mathrm{mg}$ $0.26\\mathrm{mmol}$ 1.4 equiv), and NaOAc $(72.4\\mathrm{mg},0.88\\mathrm{mmol}$ 4.9 equiv) in MeOH (3 mL) and DCM $(1\\mathrm{mL})$ was stirred at room temperature for $30\\mathrm{min}$ Then $\\mathrm{NaBH}_3\\mathrm{CN}$ $(16.6\\mathrm{mg},0.26\\mathrm{mmol},1.4$ equiv) was added in portions at the same temperature and the resulting mixture was stirred for an additional $1\\textrm{h}$ The mixture was then concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH_4HCO_3})$ 0 to $60\\%$ ) to afford the title compound $(130\\mathrm{mg},96\\%)$ as a yellow solid. ${}^{1}\\mathbf{H}$ NMR $(500\\mathrm{MHz}$ ,DMSO- $d_{6})$ 8.99 $\\left(\\mathrm{d},J = 3.1\\mathrm{Hz},1\\mathrm{H}\\right)$ 8.40 $\\left(\\mathrm{d},J\\right.$ $= 7.7~\\mathrm{Hz}$ 1H),7.49-7.42 m2H7.37 $\\left(\\mathrm{d},J = 8.1\\mathrm{Hz},2\\mathrm{H}\\right)$ 6.14s, 1H),5.10 $\\left(\\mathrm{d},J = 3.6\\mathrm{Hz},1\\mathrm{H}\\right)$ 4.97-4.89 $\\left(\\mathrm{m},1\\mathrm{H}\\right)$ 4.37 $\\left(\\mathrm{t},J = 7.9\\mathrm{Hz},\\right.$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,145]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1H), 4.32-4.25 (m, 1H), 3.92 (d, $J = 12.7\\mathrm{Hz}$ 2H), 3.75-3.69 (m, 1H), 3.58 (d, $J = 9.9\\mathrm{Hz}$ 1H), 3.43 (d, $J = 10.9\\mathrm{Hz}$ 1H), 3.20-3.13 (m, 4H), 2.70 (s, 2H), 2.47-2.31 (m, 7H), 2.28-2.13 (m, 3H), 2.07-1.98 (m, 1H), 1.84-1.75 (m, 1H), 1.68 (d, $J = 12.2\\mathrm{Hz}$ 3H), 1.49-1.30 (m, 12H), 1.00-0.89 (m, 5H), 0.86-0.77 (m, 3H). LC-MS $(\\mathrm{ES}+)$ : $m/z$ 764 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,146,915,341]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$(2S,4R)$ 4-Hydroxy-1-((R)-3-methyl-2-(3-(4-(piperidin-4- ylmethyl)piperazin-1-yl)isoxazol-5-yl)butanoyl)-N-(S)-1-(4-(4- methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (126). A mixture of intermediate 125 $(130\\mathrm{mg},0.17\\mathrm{mmol})$ in DCM $(3\\mathrm{mL})$ and TFA $(1\\mathrm{mL})$ were stirred at room temperature for $^{\\textrm{\\scriptsize 1h}}$ then was concentrated under reduced pressure to afford the title compound (TFA salt, $250~\\mathrm{mg}$ crude) as yellow oil. The crude product was used in the next step directly without further purification. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ ,DMSO- $d_{6}$ ) $\\delta$ 9.78s,1H),9.01d $J = 3.2 \\mathrm{Hz}$ 1H),8.64s,1H),8.39d $J = 7.8 \\mathrm{Hz}$ 2H),7.51-7.42 m2H), 7.42-7.34 m,2H),6.30 s,1H),4.94-4.90 m,2H),4.43-4.25 m, 2H),3.85-3.68 m,3H),3.67-3.52 m,3H),3.51-3.41 m,1H), 3.36-2.99 m,8H),2.95-2.80 m,2H),2.46 s,3H),2.29-2.12 m, 2H),2.09-1.97 m,1H),1.90 d $J = 13.4 \\mathrm{Hz}$ 2H),1.86-1.75 m, 1H),1.50-1.29 m,5H),0.98 d $J = 6.3 \\mathrm{Hz}$ 3H),0.87-0.78 m, 3H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 664 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,342,915,732]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-((2R)-2-(3-(4-((1-((trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutyl)methyl)piperidin-4-yl)methyl)piperazin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)-pyrrolidine-2-carboxamide (20). A solution of intermediate 126 (TFA salt, $175\\mathrm{mg}$ , crude from the previous step), intermediate 138 $(170\\mathrm{mg},0.36\\mathrm{mmol})$ and NaOAc $(49.4\\mathrm{mg},0.60\\mathrm{mmol})$ in MeOH $(2.1\\mathrm{mL})$ and DCM $(0.7\\mathrm{mL})$ was stirred at room temperature for 30 min. Then $\\mathrm{NaBH}_3\\mathrm{CN}$ $(11.9\\mathrm{mg},0.19\\mathrm{mmol})$ was added in portions at the same temperature, and the resulting mixture was stirred at room temperature for an additional $1\\textrm{h}$ . The mixture was then concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH_4HCO_3})$ $0$ to $100\\%$ ) to afford the crude product $(70\\mathrm{mg})$ . This material was further purified by preparative HPLC [column: XBridge Prep OBD C18 Column, $30\\times 150\\mathrm{mm}^2$ $5\\mu \\mathrm{m}$ ; mobile phase A: water $(10\\mathrm{mmol}/$ L $\\mathrm{NH_4HCO_3}$ ), mobile phase B: $\\mathrm{CH}_3\\mathrm{CN}$ ; flow rate: $60~\\mathrm{mL / min}$ ; gradient: $28\\%$ to $47\\%$ B over $10\\mathrm{min}$ ; wavelength: $254 / 220\\mathrm{nm}$ ; RT: $10.0\\mathrm{min}$ ] to afford the title compound $(8.3\\mathrm{mg},6.1\\%)$ as a yellow solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\delta$ 14.13 (s, 1H), 8.97 (d, $J = 1.4~\\mathrm{Hz}$ , 1H), 8.38 (d, $J = 7.4~\\mathrm{Hz}$ , 1H), 7.90 (d, $J = 7.8~\\mathrm{Hz}$ , 1H), 7.75 (d, $J = 6.0~\\mathrm{Hz}$ , 1H), 7.47 (d, $J = 6.2~\\mathrm{Hz}$ , 1H), 7.46-7.31 (m, 4H), 7.25-7.17 (m, 1H), 6.89-6.78 (m, 2H), 6.57-6.44 (m, 1H), 6.11 (d, $J = 5.2~\\mathrm{Hz}$ , 2H), 5.97 (d, $J = 11.4~\\mathrm{Hz}$ , 2H), 5.19-4.88 (m, 3H), 4.47 (s, 2H), 4.35 (t, $J = 7.8~\\mathrm{Hz}$ , 1H), 4.27 (s, 1H), 3.75-3.63 (m, 1H), 3.56 (d, $J = 9.9~\\mathrm{Hz}$ , 1H), 3.40 (d, $J = 10.6~\\mathrm{Hz}$ , 1H), 3.23 (d, $J = 11.6~\\mathrm{Hz}$ , 2H), 3.13 (s, 4H), 3.00 (d, $J = 11.6~\\mathrm{Hz}$ , 2H), 2.85-2.69 (m, 2H), 2.44 (s, 3H), 2.42-2.31 (m, 6H), 2.28-2.06 (m, 8H), 2.06-1.71 (m, 7H), 1.70-1.55 (m, 3H), 1.54-1.30 (m, 4H), 1.16-1.01 (m, 2H), 0.94 (d, $J = 6.4~\\mathrm{Hz}$ , 3H), 0.89-0.72 (m, 3H). LC-MS $(ES+)$ : $m/z$ $1120[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,733,915,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-((R)-2-(3-(4-(Dimethoxymethyl)piperidin-1-yl)- isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N - ((S) - 1 - (4 - (4-$ methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (127). To a room temperature solution of racemic carboxylic acid 53 $(470\\mathrm{mg},1.44\\mathrm{mmol},1.1$ equiv), chiral-pure intermediate 57 (HCl salt, $486~\\mathrm{mg}$ 1.32 mmol, 1.0 equiv) and DIEA $(1.86\\mathrm{g},14.4\\mathrm{mmol},$ 10.9 equiv) in DMF $(4\\mathrm{mL})$ was added HATU $(600\\mathrm{mg},1.58\\mathrm{mmol},$ 1.2 equiv). The reaction was stirred at room temperature for $^{\\textrm{\\scriptsize 2h}}$ then was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water containing $0.05\\%$ $\\mathrm{NH}_4\\mathrm{HCO}_3$ 0 to $100\\%$ ) to afford a mixture of the two diastereomeric coupling products $(450\\mathrm{mg})$ . This mixture was separated by preparative chiral HPLC [column: CHIRALPAK IF, $2\\times$ $25~\\mathrm{cm}^2$ $5\\mu \\mathrm{m}$ ; mobile phase A: MTBE (containing $0.5\\%$ 2.0 M $\\mathrm{NH}_{3}$ in MeOH), mobile phase B: 1:1 MeOH:DCM, flow rate: $17~\\mathrm{mL / min}$ gradient: 0 to $30\\%$ B over $10.5\\mathrm{min}$ wavelength: $220 / 254~\\mathrm{nm}$ peak 1 $\\mathrm{RT} = 5.8\\mathrm{min}$ peak $2\\mathrm{RT} = 8.6\\mathrm{min}$ to afford the title compound 127 as the slower eluting entity (peak 2, $100~\\mathrm{mg}$ $11\\%$ white solid). ${}^{1}\\mathbf{H}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1301 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,481,306]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"NMR (300 MHz, DMSO- $d_{6}$ 89.00 d $J = 2.5\\mathrm{Hz}$ 1H),8.41 d $J =$ $7.7\\mathrm{Hz}$ 1H),7.51-7.42 m,2H),7.41-7.34 m,2H),6.13 s,1H), 5.11 d $J = 3.6\\mathrm{Hz}$ 1H),4.98-4.82 m,1H),4.37 t $J = 7.8\\mathrm{Hz}$ 1H), 4.29 s,1H),4.13-4.02 m,1H),3.77-3.51 m,4H),3.49-3.38 m, 1H),3.27 s,6H),2.79-2.63 m,2H),2.46s,3H),2.31-2.14 m, 1H),2.09-1.96 m,1H),1.86-1.70 m,2H),1.67 d $J = 13.1\\mathrm{Hz}$ 2H),1.50-1.34 m,3H),1.33-1.16 m,2H),1.01-0.91 m,3H), 0.86-0.76 m,3H).LC-MS $(\\mathrm{ES + })$ .. $m / z$ 640 $[\\mathbf{M} + \\mathbf{H}]^{+}$ .The alternate diastereomer (127e, epimeric at the isopropyl stereocenter) was also isolated as the faster eluting entity (peak 1, $120~\\mathrm{mg},$ $13\\%$ white solid): ${}^{1}\\mathrm{H}$ NMR (300 MHz,DMSO- $d_{6}$ )89.00 d $J = 3.9\\mathrm{Hz}$ 1H),8.23 d $J = 7.8\\mathrm{Hz}$ 1H),7.54-7.28 m,4H),6.15 d $J = 3.2$ Hz, 1H),5.11 d $J = 3.6\\mathrm{Hz}$ ,1H),5.08-4.81 m,1H),4.58-4.37 m, 1H),4.32-4.23 m,1H),4.11-3.97 m,1H),3.73-3.41 m,5H), 3.26 d $J = 4.3\\mathrm{Hz}$ 6H),2.79-2.59 m,2H),2.46 d $J = 5.6\\mathrm{Hz}$ 3H),2.33-2.14 m,1H),2.14-1.86 m,1H),1.86-1.58 m,4H), 1.46 d $J = 6.9\\mathrm{Hz}$ ,1H),1.36 d $J = 7.0\\mathrm{Hz},$ 2H),1.30-1.13 m, 2H),0.96 d $J = 6.6\\mathrm{Hz},$ 2H),0.82 d $J = 6.6\\mathrm{Hz},$ 3H),0.75 d $J =$ $6.6\\mathrm{Hz},$ 1H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 640 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,307,481,440]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-((R)-2-(3-(4-Formylpiperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (128). A solution of intermediate 127 $(50\\mathrm{mg},0.0780\\mathrm{mmol})$ in formic acid $(1.0~\\mathrm{mL})$ and water $(1.0~\\mathrm{mL})$ was stirred at $60^{\\circ}\\mathrm{C}$ for $1\\textrm{h}$ The mixture was cooled to room temperature and was concentrated under reduced pressure to afford the crude title compound $(46\\mathrm{mg})$ as an off-white solid. LCMS $(\\mathrm{ES + })$ .. $m / z$ 594 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . Related transformation of the alternate diastereomer (127e, epimeric at the isopropyl center) afforded 128e (the isopropyl isomer corresponding to 128, structure not shown). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,440,481,743]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$(2S,4R)$ 1-((2R)-2-(3-(4-((4-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)methyl)-piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (19). A room temperature solution of intermediate 128 $(46\\mathrm{mg},0.077\\mathrm{mmol},1.0$ equiv), intermediate 119 (Scheme 9, $75~\\mathrm{mg}$ $0.14\\mathrm{mmol}$ 1.7 equiv), and NaOAc ( $19\\mathrm{mg}$ $0.23\\mathrm{mmol}$ 3.0 equiv) in DCM $(1.0~\\mathrm{mL})$ and MeOH $(1.0~\\mathrm{mL})$ was stirred for $^{\\textrm{\\scriptsize 1h}}$ . $\\mathrm{NaBH}_3\\mathrm{CN}$ $(14\\mathrm{mg},0.23\\mathrm{mmol},3.0$ equiv) was then added, and the mixture was stirred at room temperature for an additional $^{\\textrm{\\scriptsize 1h}}$ then was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography (MeOH in water containing $0.05\\%$ $\\mathrm{NH_4HCO_3}$ 0 to $100\\%$ ) to yield the title compound $(30\\mathrm{mg},$ $34 \\%$ as a white solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ ,DMSO- $d_{6})$ 8 14.15 s, 1H),8.99 d, $J = 1.5 \\mathrm{Hz}$ 1H),8.42 d, $J = 7.7 \\mathrm{Hz}$ 1H),7.96-7.88 m,1H),7.78 d, $J = 6.0 \\mathrm{Hz}$ 1H),7.53-7.33 m,5H),7.28-7.17 m, 1H),6.92-6.79 m,2H),6.57-6.49 m,1H),6.18-6.08 m,2H), 5.99 s,2H),5.26-5.08 m,2H),5.05-4.84 m,1H),4.50 s,2H), 4.37 t, $J = 7.8~\\mathrm{Hz}$ 1H),4.33-4.24 m,2H),3.77-3.67 m,1H), 3.66-3.52 m,3H),3.49-3.41 m,1H),3.30-3.21 m,3H),3.02 d, $J = 11.5~\\mathrm{Hz}$ 2H),2.79-2.60 m,4H),2.46 s,3H),2.39-2.14 m, 7H),2.13-1.89 m,7H),1.86-1.55 m,6H),1.50-1.34 m,5H), 1.19-1.02 m,2H),1.00-0.89 m,3H),0.87-0.76 m,3H).LCMS $(\\mathrm{ES + })$ .. $m / z$ 1121.8 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,745,481,866]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To confirm the absolute stereochemistry of intermediate 128 employed in the syntheses of 19, the isopropyl epimer corresponding to 128 (128e, prepared above) was similarly transformed into the isopropyl epimer of PROTAC 19 (19e, structure not shown). Both 19 and 19e PROTACs were profiled in biological assessments, and the more potent diastereomer was assigned the absolute stereochemistry shown for 19 in Table 2 (cf., Table S4). By inference, the chiral-pure intermediates employed to generate 19 was assigned the absolute stereochemistry shown in Scheme 10 (i.e., intermediates 127 and 128). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,867,481,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4-Bromo-2-(trans-3-(piperidin-4-yloxy)cyclobutoxy)-pyridine (129). A solution of intermediate 114 $(3.50\\mathrm{g},8.19\\mathrm{mmol})$ in DCM $(30~\\mathrm{mL})$ and TFA $(10~\\mathrm{mL})$ was stirred at room temperature for $^{1\\textrm{h}}$ . The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\%)$ $\\mathrm{NH_4HCO_3}$ , 0 to $80\\%$ ) to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,145]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"afford the title compound $(2.4\\mathrm{g},90\\%)$ as a white solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6}$ 8.06 d, $J = 5.5~\\mathrm{Hz}$ 1H7.28-7.19 m, 1H),7.11 (d, $J = 1.6\\mathrm{Hz}$ 1H),5.31-5.17 (m, 1H),4.41-4.27 (m, 1H),3.62-3.48 (m, 1H),3.22-3.08 (m, 2H),2.97-2.83 (m, 2H), 2.46-2.26 (m, 4H), 1.99-1.85 (m, 2H), 1.67-1.49 (m, 2H). LCMS $\\mathrm{(ES + )}$ .. $m / z$ 327/329 $[\\mathrm{M} + \\mathrm{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,146,915,330]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methyl 2-(3-(4-(trans-3-((4-bromopyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoate (130). A mixture of intermediate 129 $(2.00\\mathrm{g},6.11\\mathrm{mmol},1.0$ equiv), intermediate 43 $(2.94\\mathrm{g},6.11\\mathrm{mmol},1.0$ equiv) and DIEA $(2.37\\mathrm{g},$ $18.3\\mathrm{mmol},3.0$ equiv) in DMF $(25~\\mathrm{mL})$ was stirred at $130^{\\circ}\\mathrm{C}$ for $1\\textrm{h}$ The mixture was then cooled to room temperature and was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\%)$ $\\mathrm{NH}_4\\mathrm{HCO}_3)$ , 0 to $75\\%$ ) to afford the title compound $(2.2\\mathrm{g},71\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 8 8.10-8.02 m, 1H), 7.27-7.18 (m, 1H), 7.11 (d, $J = 1.6~\\mathrm{Hz}$ 1H), 6.25 (s, 1H), 5.30-5.17 (m, 1H), 4.43-4.29 (m, 1H), 3.66 (s, 3H), 3.63-3.45 (m, 4H), 3.00-2.85 (m, 2H), 2.46-2.18 (m, 5H), 1.90-1.79 (m, 2H), 1.54- 1.36 (m, 2H), 0.93 (d, $J = 6.7~\\mathrm{Hz}$ , 3H), 0.84 (d, $J = 6.7~\\mathrm{Hz}$ , 3H). LCMS $(\\mathrm{ES + })$ .. $m / z~508 / s10[\\mathrm{M} + \\mathrm{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,331,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methyl 2-(3-(4-(trans-3-((4-(3-(3-amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoate (131). A mixture of intermediate 130 (2.20 g, 4.33 mmol, 1.0 equiv), tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, 1.38 g, 6.49 mmol, 1.5 equiv), RuPhosPd G3 (0.36 g, 0.43 mmol, 0.10 equiv) and $\\mathrm{Cs_2CO_3}$ (4.23 g, 12.9 mmol, 3.0 equiv) in 1,4-dioxane (30 mL) was stirred at $90^{\\circ}\\mathrm{C}$ for 1 h. The reaction was cooled to room temperature and was quenched with $\\mathrm{H}_2\\mathrm{O}$ (50 mL). The resulting mixture was extracted with EtOAc (100 mL × 3), and the combined organic layers were washed with brine (100 mL), dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 100%) to afford tert-butyl 8-(2-(trans-3-((1-(5-(1-methoxy-3-methyl-1-oxobutan-2-yl) isoxazol-3-yl) piperidin-4-yl) oxy)cyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate (1.2 g, 43% yield) as a brown solid. ${}^{1}\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) δ 7.76 (d, J = 6.0 Hz, 1H), 6.51–6.45 (m, 1H), 6.25 (s, 1H), 6.10 (d, J = 2.1 Hz, 1H), 5.25–5.15 (m, 1H), 4.39–4.28 (m, 3H), 3.68–3.40 (m, 9H), 3.07 (d, J = 13.0 Hz, 1H), 2.98–2.87 (m, 3H), 2.39–2.21 (m, 5H), 1.95–1.81 (m, 4H), 1.75–1.61 (m, 2H), 1.52–1.42 (m, 2H), 1.40 (s, 9H), 0.93 (d, J = 6.6 Hz, 3H), 0.84 (d, J = 6.7 Hz, 3H). LC−MS (ES+): m/z 640 [M + H]+. A mixture of this material (1.2 g, 1.88 mmol) in TFA (4 mL) and DCM (12 mL) was stirred at room temperature for 1 h. The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepaked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 30%) to afford methyl 2-(3-(4-(trans-3-((4-(3,8-diazabicyclo[3.2.1]-octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy) piperidin-1-yl) isoxazol-5-yl)-3-methylbutanoate (810 mg, 80%) as a white solid. ${}^{1}\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) δ 7.71 (d, J = 6.0 Hz, 1H), 6.42–6.35 (m, 1H), 6.25 (s, 1H), 5.98 (d, J = 2.1 Hz, 1H), 5.24–5.14 (m, 1H), 4.39–4.28 (m, 1H), 4.19–4.13 (m, 2H), 3.66 (s, 3H), 3.59 (d, J = 8.9 Hz, 1H), 3.55–3.42 (m, 3H), 3.02–2.87 (m, 2H), 2.85 (d, J = 1.8 Hz, 1H), 2.82 (d, J = 1.7 Hz, 1H), 2.48–2.40 (m, 2H), 2.39–2.21 (m, 6H), 1.98–1.80 (m, 6H), 1.52–1.38 (m, 2H), 0.93 (d, J = 6.6 Hz, 3H), 0.84 (d, J = 6.7 Hz, 3H). LC−MS (ES+): m/z 540 [M + H]+. A mixture of this intermediate (810 mg, 1.5 mmol, 1.0 equiv), 4-bromo-6-chloropyridazin-3-amine (70, 469 mg, 2.25 mmol, 1.5 equiv), and DIEA (968 mg, 7.5 mmol, 5.0 equiv) in DMSO (10 mL) was stirred at $130^{\\circ}\\mathrm{C}$ for 5 h. The reaction was cooled to room tempetature, and the mixture was directly purified by prepaked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 50%) to afford methyl 2-(3-(4-(trans-3-((4-(3-(3-amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl) oxy)cyclobutoxy) piperidin-1-yl) isoxazol-5-yl)-3-methylbutanoate (520 mg, 52%) as a yellow solid. ${}^{1}\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) δ 7.77 (d, J = 6.0 Hz, 1H), 6.90 (s, 1H), 6.54–6.47 (m, 1H), 6.25 (s ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1302 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"40","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,479,408]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1H), 6.12 (d, $J = 2.1\\mathrm{Hz}$ 1H), 5.85 (s, 2H), 5.25-5.15 (m, 1H), 4.45 (s, 2H), 4.39-4.28 (m, 1H), 3.65 (s, 3H), 3.59 (d, $J = 8.9\\mathrm{Hz}$ 1H), 3.55-3.43 (m, 3H), 3.22-3.14 (m, 2H), 2.98-2.83 (m, 4H), 2.40-2.21 (m, 5H), 2.18-2.09 (m, 2H), 1.96-1.89 (m, 2H), 1.89-1.80 (m, 2H), 1.51-1.38 (m, 2H), 0.93 (d, $J = 6.6\\mathrm{Hz}$ 3H), 0.84 (d, $J = 6.7\\mathrm{Hz}$ 3H). LC-MS $(\\mathrm{ES}+)$ : $m/z$ 667 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . A mixture of this material (510 mg, 0.76 mmol, 1.0 equiv), (2-hydroxyphenyl)boronic acid (72, 158 mg, 1.15 mmol, 1.6 equiv), $\\mathrm{Pd(PPh_3)_4}$ (88.3 mg, 0.08 mmol, 0.10 equiv) and $\\mathrm{K}_2\\mathrm{CO}_3$ (317 mg, 2.29 mmol, 3.0 equiv) in 1,4-dioxane (15 mL) and water (1.5 mL) was stirred at $90^{\\circ}\\mathrm{C}$ for $1\\mathrm{h}$ . The reaction was cooled to room temperature and was diluted with water (50 mL). The mixture was extracted with EtOAc (100 mL × 3) and the combined organic layers were washed with brine (100 mL), dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ - 0 to $70\\%$ ) to afford the title compound (375 mg, $68\\%$ ) as a yellow solid. ${}^{1}\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) $\\delta$ 14.16 (s, 1H), 7.96-7.89 (m, 1H), 7.78 (d, $J = 6.0~\\mathrm{Hz}$ , 1H), 7.51 (s, 1H), 7.27-7.18 (m, 1H), 6.91-6.81 (m, 2H), 6.57-6.50 (m, 1H), 6.25 (s, 1H), 6.15 (d, $J = 2.1$ Hz, 1H), 5.98 (s, 2H), 5.25-5.15 (m, 1H), 4.50 (d, $J = 4.2~\\mathrm{Hz}$ , 2H), 4.39-4.28 (m, 1H), 3.65 (s, 3H), 3.59 (d, $J = 8.9~\\mathrm{Hz}$ , 1H), 3.55-3.42 (m, 3H), 3.25 (d, $J = 11.4~\\mathrm{Hz}$ , 2H), 3.02 (d, $J = 11.6~\\mathrm{Hz}$ , 2H), 2.98-2.87 (m, 2H), 2.40-2.22 (m, 5H), 2.18 (d, $J = 7.2~\\mathrm{Hz}$ , 2H), 2.00-1.93 (m, 2H), 1.89-1.80 (m, 2H), 1.51-1.38 (m, 2H), 0.93 (d, $J =$ $6.6~\\mathrm{Hz}$ ,3H),0.84 $(\\mathrm{d},J = 6.8~\\mathrm{Hz}$ ,3H). LC-MS $(\\mathrm{ES}+)$ : $m/z$ 725 $[\\mathbf{M}+$ $\\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,410,479,620]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(3-(4-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)- pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoic acid (132). A solution of intermediate 131 $(365\\mathrm{mg},0.503$ mmol, 1.0 equiv) and LiOH $(24.2\\mathrm{mg},1.01\\mathrm{mmol},2.0$ equiv) in water $(6\\mathrm{mL})$ and THF $(6\\mathrm{mL})$ was stirred at room temperature for $1\\textrm{h}$ The resulting mixture was concentrated under reduced pressure to afford the crude title compound as a yellow solid. This material was used in the next step without further purification. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\delta$ 7.95-7.86 (m, 1H), 7.76 (d, $J = 5.9~\\mathrm{Hz}$ , 1H), 7.48 (s, 1H), 7.27-7.15 (m, 1H), 6.90-6.78 (m, 2H), 6.55-6.47 (m, 1H), 6.16-6.04 (m, 2H), 5.95 (s, 2H), 5.18 (t, $J = 6.0~\\mathrm{Hz}$ , 1H), 4.48 (s, 2H), 4.36-4.26 (m, 1H), 3.53-3.42 (m, 3H), 3.28-3.18 (m, 3H), 3.00 (d, $J = 11.6~\\mathrm{Hz}$ , 2H), 2.88 (t, $J = 10.7~\\mathrm{Hz}$ , 2H), 2.38-2.25 (m, 4H), 2.25-2.12 (m, 3H), 1.95 (s, 2H), 1.82 (d, $J = 12.4~\\mathrm{Hz}$ , 2H), 1.52-1.33 (m, 2H), 0.92 (d, $J = 6.6~\\mathrm{Hz}$ , 3H), 0.78 (d, $J = 6.7~\\mathrm{Hz}$ , 3H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 711 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,620,479,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(25,4R)-1-((2R)-2-(3-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $(S)$ -1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (21). To a room temperature solution of intermediate 132 (290 mg, 0.41 mmol, 1.0 equiv), intermediate 57 (203 mg, 0.61 mmol, 1.5 equiv) and DIEA (264 mg, 2.04 mmol, 5.0 equiv) in DMF (5 mL) was added HATU (186 mg, 0.489 mmol, 1.2 equiv) in portions. The resulting mixture was stirred at room temperature for 1 h. The reaction mixture was directly purified by prepacked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 55%) to afford 100 mg of the coupled product as a ~1:1 mixture of isopropyl group isomers. This material was further purified by preparative chiral HPLC [column: CHIRALPAK IA, 2 × 25 cm², 5 μm; mobile phase A: 1:1 hexane:DCM (0.5% 2 M NH₃-MeOH), mobile phase B: EtOH; flow rate: 20 mL/min; gradient: isocratic 40% B; wavelength: 220/254 nm; RT1:6.30 min; RT2:9.16 min; sample solvent: EtOH; injection volume: 0.40 mL; number of runs: 12] to afford the title compound (slower peak, 16 mg, 3.9%) as a yellow solid. $^1\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 14.13 (s, 1H), 8.97 (s, 1H), 8.38 (d, J = 7.7 Hz, 1H), 7.96–7.87 (m, 1H), 7.76 (d, J = 5.9 Hz, 1H), 7.52–7.39 (m, 3H), 7.35 (d, J = 8.2 Hz, 2H), 7.27–7.15 (m, 1H), 6.90–6.79 (m, 2H), 6.58–6.46 (m, 1H), 6.16–6.06 (m, 2H), 5.97 (d, J = 6.7 Hz, 2H), 5.25–5.14 (m, 1H), 5.08 (d, J = 3.7 Hz, 1H), 5.00–4.83 (m, 1H), 4.48 (s, 2H), 4.40–4.21 (m, 3H), 3.76–3.64 (m, 1H), 3.55 (d, J ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,308]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$= 9.8\\mathrm{Hz}$ 1H),3.53-3.36 (m,4H),3.24 (d, $J = 11.5\\mathrm{Hz}$ 2H),3.00 (d, $J = 11.6\\mathrm{Hz}$ 2H),2.96-2.80 (m,2H),2.44s,3H),2.39-2.25 (m, 4H),2.25-2.10 (m,3H),2.06-1.90 (m,3H),1.90-1.70 (m,3H), 1.54-1.40 (m,2H),1.36 (d, $J = 7.0~\\mathrm{Hz}$ 3H),0.93 (d, $J = 6.4~\\mathrm{Hz}$ 3H),0.86-0.69 (m,3H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 1024 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . The isomer bearing the undesired isopropyl stereocenter (21e, isopropyl isomer corresponding to 21, structure not shown) was also isolated faster peak, $25.5\\mathrm{mg},6.1\\%$ as a yellow solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.13 s,1H),9.00-8.85 m,1H),8.25-7.86 m,2H), 7.76 d, $J = 6.0\\mathrm{Hz}$ 1H),7.53-7.35 (m,4H),7.30 d, $J = 8.2\\mathrm{Hz}$ 1H),7.26-7.15 (m,1H),6.89-6.78 (m,2H),6.57-6.48 (m,1H), 6.13 d, $J = 2.0\\mathrm{Hz}$ ,2H),5.96s,2H),5.19d $J = 6.1\\mathrm{Hz}$ ,1H),5.13- 4.80 (m,2H),4.48s,2H),4.41t $J = 7.6\\mathrm{Hz}$ ,1H),4.36-4.18 (m, 2H),3.67d $J = 8.9\\mathrm{Hz}$ ,1H),3.60-3.35 (m,5H),3.24d $J = 11.2$ Hz,2H),3.00d $J = 11.7\\mathrm{Hz}$ ,2H),2.94-2.74 (m,2H),2.44d $J =$ $6.6\\mathrm{Hz}$ ,3H),2.29s,5H),2.17d $J = 7.3\\mathrm{Hz}$ ,2H),2.07-1.89 (m, 3H),1.89-1.72 (m,3H),1.53-1.38 (m,3H),1.34d $J = 7.0~\\mathrm{Hz}$ 2H),0.94d $J = 6.6~\\mathrm{Hz}$ ,2H),0.87-0.70 (m,4H).LC-MS $(\\mathrm{ES + })$ .. $m / z$ 1024 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,308,915,518]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methyl trans-3-(4-bromopyridin-2-yl)oxy)cyclobutane-1-carboxylate (134). To a stirred mixture of cis-methyl 3-hydroxycyclobutanecarboxylate (133, $2.00\\mathrm{g}$ , $15.3\\mathrm{mmol}$ , 1.0 equiv), 4-bromopyridin-2-ol $(2.67\\mathrm{g}, 15.3\\mathrm{mmol}, 1.0\\mathrm{equiv})$ , and $\\mathrm{PPh}_3$ (6.04 g, $23.0\\mathrm{mmol}$ , 1.5 equiv) in THF $(25\\mathrm{mL})$ was added DIAD $(4.66\\mathrm{g}, 23.0\\mathrm{mmol}, 1.5\\mathrm{equiv})$ dropwise at $0^{\\circ}\\mathrm{C}$ . The resulting mixture was stirred for $1\\mathrm{h}$ at room temperature then was diluted with water (75 mL) and extracted with EtOAc $(100\\mathrm{mL} \\times 3)$ . The combined organic layers were washed with brine $(100\\mathrm{mL})$ and were dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\left(\\mathrm{CH}_3\\mathrm{CN}\\right.$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ , 0 to $100\\%$ to afford the title compound $(3.0\\mathrm{g}, 68\\%)$ as a yellow solid. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\delta$ 8.06 (d, $J = 5.5\\mathrm{Hz}$ , 1H), 7.26-7.19 (m, 1H), 7.13-7.07 (m, 1H), 5.34-5.22 (m, 1H), 3.66 (s, 3H), 3.22-3.10 (m, 1H), 2.68-2.57 (m, 2H), 2.44-2.31 (m, 2H). LC-MS (ES +): $m/z$ 286/288 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,518,915,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methyl trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)-pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)cyclobutane-1-carboxylate (135). A mixture of intermediate 134 $(3.00\\mathrm{g},10.4\\mathrm{mmol},1.0$ equiv), tert-butyl 3,8-diazabicyclo[3.2.1]-octane-3-carboxylate (67, $3.34\\mathrm{g}$ 15.7 mmol, 1.5 equiv), RuPhosPd G3 $(880\\mathrm{mg},1.05\\mathrm{mmol},0.10$ equiv) and $\\mathrm{Cs_2CO_3}$ $(10.2\\mathrm{g},31.4\\mathrm{mmol},$ 3.0 equiv) in 1,4-dioxane $(30~\\mathrm{mL})$ was stirred at $90^{\\circ}C$ for $1\\textrm{h}$ The resulting mixture was cooled to room temperature and was diluted with water $(75~\\mathrm{mL})$ . The mixture was then extracted with EtOAc $(100~\\mathrm{mL}\\times 3)$ , and the combined organic layers were washed with brine $(100~\\mathrm{mL})$ , dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 30:70) to afford tert-butyl 8-(2-(trans-3-(methoxycarbonyl)cyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate $(3.5\\mathrm{g},80\\%)$ as a yellow solid. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ DMSO- $d_{6})$ 7.76 d, $J = 6.0\\mathrm{Hz}$ 1H),6.52-6.45 m1H6.11d $J = 2.1\\mathrm{Hz}$ 1H) 5.31-5.19 m, 1H),4.35 s,2H),3.65 s,3H),3.62-3.50 m,2H), 3.19-3.03 m,2H),2.92 d $J = 12.9\\mathrm{Hz}$ 1H),2.63-2.53 m,2H), 2.38-2.26 m,2H),1.95-1.87 m,2H),1.75-1.62 m,2H),1.40 s, 9H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 418 $[\\mathbf{M} + \\mathbf{H}]^{+}$ .A solution of this material $(3.50\\mathrm{g},8.38\\mathrm{mmol})$ in DCM $(30~\\mathrm{mL})$ and TFA $(10~\\mathrm{mL})$ was stirred at room temperature for $^{\\textrm{\\scriptsize 1h}}$ . The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ 0 to $100\\%$ ) to afford methyl trans-3-((4-(3,8-diazabicyclo[3.2.1]- octan-8-yl)pyridin-2-yl)oxy)cyclobutane-1-carboxylate $(2.1\\mathrm{g},79\\%)$ as a yellow solid. $^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 7.83 d $J = 6.0\\mathrm{Hz}$ 1H),6.57-6.49 m, 1H),6.18 d $J = 2.0~\\mathrm{Hz}$ 1H),5.35-5.19 m, 1H),4.45 s,2H),3.66 s,3H),3.21-3.07 m, 1H),3.07-2.92 m, 4H),2.66-2.52 m,2H),2.41-2.25 m,2H),2.11-1.96 m,4H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 318 $[\\mathbf{M} + \\mathbf{H}]^{+}$ .A solution of this material (2.10 g, 6.62 mmol, 1.0 equiv), 4-bromo-6-chloro-pyridazin-3-amine (70, $1.38\\mathrm{g},6.62\\mathrm{mmol},1.0$ equiv) and DIEA $(2.57\\mathrm{g},19.8\\mathrm{mmol},3.0$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[484,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1303 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,71,482,421]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"equiv) in DMSO $(20~\\mathrm{mL})$ was stirred at $130^{\\circ}\\mathrm{C}$ for $1\\textrm{h}$ . After cooling to room temperature, the mixture was directly purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\%)$ $\\mathrm{NH_4HCO_3)}$ 0 to $100\\%$ ) to afford methyl trans-3-((4-(3-(3-amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutane-1-carboxylate $(1.9\\mathrm{g},65\\%)$ as a yellow solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ ,DMSO- $d_{6}$ 7.76 (d, $J = 6.0~\\mathrm{Hz}$ 1H),6.90s1H) $6.55 - 6.47$ m1H)6.12d $J = 2.0\\mathrm{Hz}$ 1H)5.84s2H)5.33-5.18 m1H)4.45s2H)3.65s3H)3.23-3.05m3H)2.87d $J =$ $11.6\\mathrm{Hz}$ 2H)2.65-2.51m2H)2.40-2.24m2H)2.20-2.02 m2H)1.97-1.88m2H.LC-MS $(\\mathrm{ES + })$ .. $m / z$ 445 $[\\mathbf{M} + \\mathbf{H}]^{+}$ .A mixture of this material $(1.90\\mathrm{g},$ 4.27 mmol, 1.0 equiv), 2-hydroxyphenylboronic acid (72, 883 mg, 6.41 mmol, 1.5 equiv), $\\mathrm{K}_2\\mathrm{CO}_3$ 1.77 g, 12.8 mmol, 3.0 equiv and $\\mathrm{Pd(PPh_3)_4}$ 493 mg, 0.426 mmol, 0.10 equiv) in 1,4-dioxane $(30~\\mathrm{mL})$ was stirred at $90^{\\circ}\\mathrm{C}$ for 2 h. The resulting mixture was cooled to room temperature then was diluted with EtOAc $(100~\\mathrm{mL})$ . The mixture was washed with brine $(100~\\mathrm{mL})$ , and the organic layer was dried over sodium sulfate and filtered. The filtrate was concentrated under vacuum, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 3:1) to afford the title compound (1.2 g, $56 \\%$ ) as a yellow solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz,DMSO- $d_{6}$ 8 14.15 s, 1H)7.97-7.88 m1H)7.78d $J = 6.0\\mathrm{Hz}$ 1H7.50s1H7.29-7.17m1H) 6.92-6.79m2H6.58-6.50m1H6.15d $J = 2.0~\\mathrm{Hz}$ 1H) 5.98s2H)5.34-5.18m1H)4.50s2H)3.65s3H)3.25d $J =$ $11.5\\mathrm{Hz}$ 2H)3.20-3.05m1H)3.02d $J =$ $11.6\\mathrm{Hz}$ 2H) 2.65-2.51m2H)2.41-2.25m2H)2.23-2.10m2H)2.02- 1.85m2H.LC-MS $(\\mathrm{ES + })$ .. $m / z$ 503 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,421,481,595]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4- yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutane-1-carboxylic acid (136). A mixture of intermediate 135 $(890\\mathrm{mg},$ $1.77\\mathrm{mmol}$ , 1.0 equiv) and LiOH $(85.0\\mathrm{mg},$ $3.54\\mathrm{mmol}$ 2.0 equiv) in THF $(5\\mathrm{mL})$ and water $(5\\mathrm{mL})$ was stirred at room temperature for $1\\textrm{h}$ . The resulting mixture was concentrated under vacuum to afford the crude title compound as a yellow solid. The crude product was used in the next step without further purification. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ DMSO- $d_{6})$ 7.97 $\\left(\\mathrm{d},J = 7.2\\mathrm{Hz},1\\mathrm{H}\\right)$ 7.56dd, $J = 7.9$ $1.7~\\mathrm{Hz}$ 1H),7.52s,1H),7.45-7.37m1H)7.15-6.92m 4H),6.92-6.82 m,1H),6.27 d $J = 2.2\\mathrm{Hz}$ 1H),5.27-5.15 m, 1H),4.88 s,2H),3.66 d $J = 12.2\\mathrm{Hz}$ 2H),3.25-3.09 m,3H), 2.85-2.72 m,2H),2.47-2.35 m,2H),2.29-2.16 m,2H),2.01 d, $J = 9.6\\mathrm{Hz}$ 2H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 489 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,595,482,805]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4- yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)-N-methoxy-N-methylcyclobutane-1-carboxamide (137). A mixture of intermediate 136 $(880\\mathrm{mg},$ $1.80\\mathrm{mmol}$ 1.0 equiv), N,O-dimethylhydroxylamine hydrochloride $(263~\\mathrm{mg},$ $2.68~\\mathrm{mmol}$ 2.0 equiv), DIEA $(1.16\\mathrm{g},$ $9.01\\mathrm{mmol}$ 5.0 equiv), and HATU $(1.02\\mathrm{g},$ $2.68\\mathrm{mmol}$ 2.0 equiv) in DMF $(15~\\mathrm{mL})$ was stirred at room temperature for $1\\textrm{h}$ The reaction mixture was directly purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\%)$ $\\mathrm{NH}_4\\mathrm{HCO}_3)$ , 0 to $100\\%$ to afford the title compound $(320\\mathrm{mg},$ $33\\%$ as a yellow solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.15 s,1H)7.99-7.87 m,1H) 7.77 d, $J = 5.9\\mathrm{Hz}$ 1H7.51s1H7.28-7.15m1H6.94-6.79 m,2H)6.59-6.49 m,1H)6.16d $J = 2.0\\mathrm{Hz}$ 1H5.98s,2H) 5.25-5.13 m,1H)4.50 s,2H)3.62 s,3H)3.45 s,1H)3.25 d, $J = 11.4\\mathrm{Hz}$ 2H)3.12 s,3H)3.02 d, $J = 11.6\\mathrm{Hz}$ 2H)2.62-2.53 s,2H)2.36-2.24 m,2H)2.24-2.10 m,2H)2.05-1.90 m,2H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 532 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,805,482,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4- yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutane-1-carbaldehyde (138). To a $0^{\\circ}\\mathrm{C}$ solution of intermediate 137 $(300\\mathrm{mg},0.564\\mathrm{mmol},1.0$ equiv) in THF (15 mL) was added $\\mathrm{LiAlH_4}$ $(1.0\\mathrm{M}$ in THF, $0.85~\\mathrm{mL}$ $0.85\\mathrm{mmol}$ 1.5 equiv). The resulting mixture was stirred at room temperature for $1\\textrm{h}$ then was cooled to $0^{\\circ}\\mathrm{C}$ and quenched with solid $\\mathrm{Na}_2\\mathrm{SO}_4\\cdot 10\\mathrm{H}_2\\mathrm{O}$ $(200\\mathrm{mg})$ . The resulting mixture was filtered, and the filter cake was washed with MeOH $(30~\\mathrm{mL})$ . The filtrate and washings were concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\%)$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,172]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\mathrm{NH_4HCO_3)}$ 0 to $100\\%$ ) to afford the title compound $(110\\mathrm{mg},41\\%)$ as a yellow solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.16 (s, 1H), $9.86 - 9.61(\\mathrm{m},1\\mathrm{H})$ 7.97-7.88 (m, 1H), 7.82-7.70 (m, 1H), 7.50 (s, 1H), 7.29-7.17 (m, 1H), 6.97-6.77 (m, 2H), 6.60-6.42 (s, 1H), 6.19-6.09 (m, 1H), 5.98 (s, 2H), 5.20-5.04 (m, 1H), 4.50 (s, 2H), 3.55-3.40 (m, 1H),3.25 (d, $J = 11.6~\\mathrm{Hz}$ ,2H),3.02 (d, $J = 11.7~\\mathrm{Hz}$ $2\\mathrm{H})$ ,2.60-2.53 (m, 2H), 2.34-2.06 (m, 4H), 2.03-1.80 (m, 2H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 473 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,172,915,492]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-((2R)-2-(3-(4-((trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutyl)methyl)piperazin-1-yl)-isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (22). A solution of intermediate 138 (50 mg, 0.106 mmol, 1.0 equiv), chiral-pure intermediate 123 (60 mg, 0.106 mmol, 1.0 equiv), and NaOAc (43 mg, 0.529 mmol, 5.0 equiv) in MeOH (2.1 mL) and DCM (0.7 mL) was stirred at room temperature for 30 min. Then $\\mathrm{NaBH}_3\\mathrm{CN}$ (8.6 mg, 0.14 mmol, 1.3 equiv) was added in portions at the same temperature. The resulting mixture was stirred at room temperature for 1 h then was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH_4HCO_3})$ 0 to $100\\%$ ) to afford the title compound (6.6 mg, $6.1\\%$ ) as a white solid. ${}^{1}\\mathrm{H}$ NMR (500 MHz, DMSO- $d_6$ ) $\\delta$ 14.15 (s, 1H), 8.99 (d, $J = 2.4~\\mathrm{Hz}$ , 1H), 8.41 (d, $J = 7.7~\\mathrm{Hz}$ , 1H), 7.92 (d, $J = 7.9~\\mathrm{Hz}$ , 1H), 7.77 (d, $J = 5.9~\\mathrm{Hz}$ , 1H), 7.50 (d, $J = 1.9~\\mathrm{Hz}$ , 1H), 7.49-7.42 (m, 2H), 7.37 (d, $J = 8.0~\\mathrm{Hz}$ , 2H), 7.26-7.19 (m, 1H), 6.90-6.82 (m, 2H), 6.55-6.50 (m, 1H), 6.17-6.10 (m, 2H), 5.99 (s, 2H), 5.24-5.09 (m, 1H), 5.04-4.87 (m, 2H), 4.50 (s, 2H), 4.36 (t, $J = 7.8~\\mathrm{Hz}$ , 1H), 4.29 (t, $J = 4.2~\\mathrm{Hz}$ , 1H), 3.75-3.68 (m, 1H), 3.58 (d, $J = 10.0~\\mathrm{Hz}$ , 1H), 3.43 (d, $J = 10.9~\\mathrm{Hz}$ , 1H), 3.30-3.11 (m, 6H), 3.02 (d, $J = 11.7~\\mathrm{Hz}$ , 2H), 2.54-2.40 (m, 10H), 2.28-2.10 (m, 6H), 2.06-1.90 (m, 3H), 1.83-1.74 (m, 1H), 1.69 (s, 1H), 1.48-1.35 (m, 3H), 0.95 (d, $J = 6.6~\\mathrm{Hz}$ , 3H), $0.85 - 0.77$ (m, 3H). LC-MS $(\\mathrm{ES + })$ : m/z 1024 $[\\mathbf{M} + \\mathbf{H}]^+$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,492,915,755]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-(2-(3-(4-(Dimethoxymethyl)piperidin-1-yl)- isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -((S)-1-(4-(4- methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (139). A solution of intermediate 53 $(280~\\mathrm{mg}$ $0.860~\\mathrm{mmol}$ 1.0 equiv), intermediate 57 (free base, $284~\\mathrm{mg}$ $0.860~\\mathrm{mmol}$ 1.0 equiv), DIEA $(332~\\mathrm{mg}$ $2.57~\\mathrm{mmol}$ 3.0 equiv), and HATU $(489~\\mathrm{mg}$ 1.29 mmol, 1.5 equiv) in DMF $(3\\mathrm{mL})$ was stirred at room temperature for $2\\mathrm{h}$ The resulting mixture was diluted with EtOAc $(100~\\mathrm{mL})$ washed with water $(100~\\mathrm{mL})$ ,and the organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH}_4\\mathrm{HCO}_3)$ 0 to $100\\%$ to afford the title compound ( $\\sim 1:1$ mixture of diastereomers, $220~\\mathrm{mg}$ $40\\%$ ) as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 8 8.99s,1H) 8.41d $J = 7.8 \\mathrm{Hz}$ 1H7.53-7.28m4H6.18-6.09m1H) 5.11d $J = 3.6 \\mathrm{Hz}$ 1H5.05-4.83m1H4.48-4.32m1H) 4.28s1H4.12-3.98m1H3.77-3.48m5H3.26d $J = 4.3$ Hz,6H2.78-2.60m3H2.48-2.44m3H2.31-2.10m 1H2.10-1.87m1H1.85-1.52m3H1.50-1.08m5H) 0.96dd $J = 6.7$ $2.5\\mathrm{Hz}$ 3H0.86-0.71m3H.LC-MS $(ES+)$ .. $m / z640[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,755,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-(2-(3-(4-Formylpiperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $(N$ -(S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (140). A solution of intermediate 139 $(220\\mathrm{mg},0.343\\mathrm{mmol})$ in aqueous $\\mathrm{H}_2\\mathrm{SO}_4$ $(1.0\\mathrm{M},2\\mathrm{mL})$ and THF $(2\\mathrm{mL})$ was stirred at $60^{\\circ}\\mathrm{C}$ for $2\\mathrm{h}$ . The mixture was then cooled to room temperature and was directly purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\%)$ $\\mathrm{NH}_4\\mathrm{HCO}_3)$ , 0 to $100\\%$ ) to afford the title compound $(150\\mathrm{mg},74\\%)$ as a yellow solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\delta$ 9.60 $(d,J = 7.9\\mathrm{Hz},1\\mathrm{H})$ , 9.03-8.88 $(m,1\\mathrm{H})$ , 8.47-8.18 $(m,1\\mathrm{H})$ , 7.53-7.28 $(m,4\\mathrm{H})$ , 6.21-6.13 $(m,1\\mathrm{H})$ , 5.11 $(s,1\\mathrm{H})$ , 5.03-4.82 $(m,1\\mathrm{H})$ , 4.60-4.33 $(m,1\\mathrm{H})$ , 4.28 $(s,1\\mathrm{H})$ , 3.76-3.65 $(m,1\\mathrm{H})$ , 3.65-3.48 $(m,3\\mathrm{H})$ , 3.48-3.35 $(m,1\\mathrm{H})$ , 3.25-3.13 $(m,1\\mathrm{H})$ , 2.95-2.75 $(m,2\\mathrm{H})$ , 2.48-2.41 $(m,3\\mathrm{H})$ , 2.33-2.10 $(m,1\\mathrm{H})$ , 2.10-1.69 $(m,4\\mathrm{H})$ , 1.55-1.31 $(m,5\\mathrm{H})$ , 1.00-0.71 $(m,6\\mathrm{H})$ . LC-MS $(ES+)$ : $m/z$ 594 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1304 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"42","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,71,481,295]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"43","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tert-Butyl 4-((4-bromopyridin-2-yl)oxy)piperidine-1-carboxylate (142). A suspension of tert-butyl 4-hydroxypiperidine-1-carboxylate (141, $2.00\\mathrm{g}$ , $9.94\\mathrm{mmol}$ , 1.0 equiv) and $\\mathrm{NaH}$ ( $60\\%$ in mineral oil, $0.480\\mathrm{g}$ , $12.0\\mathrm{mmol}$ , 1.2 equiv) in DMF ( $20\\mathrm{mL}$ ) was stirred at $0^{\\circ}\\mathrm{C}$ for $1\\mathrm{h}$ . 4-Bromo-2-fluoro-pyridine ( $62$ , $2.62\\mathrm{g}$ , $14.9\\mathrm{mmol}$ , 1.5 equiv) was then added, and the mixture was warmed to room temperature and stirred for $1\\mathrm{h}$ . After quenching at room temperature with saturated aqueous $\\mathrm{NH}_4\\mathrm{Cl}$ , the mixture was extracted with EtOAc ( $100\\mathrm{mL} \\times 3$ ). The combined organic layers were washed with water ( $100\\mathrm{mL}$ ), dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography ((EtOAc: petroleum ether, 0:100 to 66:44) to afford the title compound ( $2.70\\mathrm{g}$ , $76\\%$ ) as a yellow oil. ${}^{1}\\mathrm{H}$ NMR ( $300\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\delta$ 8.07 (d, $J = 5.5\\mathrm{Hz}$ , 1H), 7.22 (dd, $J = 5.5$ , $1.7\\mathrm{Hz}$ , 1H), 7.11 (d, $J = 1.6\\mathrm{Hz}$ , 1H), 5.22–5.10 (m, 1H), 3.75–3.60 (m, 2H), 3.17 (t, $J = 11.2\\mathrm{Hz}$ , 2H), 1.99–1.87 (m, 2H), 1.62–1.46 (m, 2H), 1.41 (s, 9H). LC-MS (ES+): $m/z$ 357 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,295,481,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"43","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tert-Butyl 4-((4-(3-(3-amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)-piperidine-1-carboxylate (143). A solution of intermediate 142 $(2.65\\mathrm{g},7.42\\mathrm{mmol},1.0$ equiv), benzyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (98, TFA salt, $3.65\\mathrm{g}$ $10.1\\mathrm{mmol}$ , 1.4 equiv), $\\mathrm{Cs_2CO_3}$ $(7.25\\mathrm{g},22.3\\mathrm{mmol},3.0$ equiv), and RuPhosPd G2 $(0.580\\mathrm{g},0.746$ mmol, 0.10 equiv) in toluene $(20~\\mathrm{mL})$ was stirred at $90^{\\circ}\\mathrm{C}$ for $2\\textrm{h}$ The reaction mixture was cooled to room temperature and was diluted with EtOAc $(100~\\mathrm{mL})$ . The resulting mixture was washed with water $(100~\\mathrm{mL})$ , and the organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 1:1) to afford benzyl 8-(2-((1- tert-butoxycarbonyl)piperidin-4-yl)oxy)pyridin-4-yl)-3,8- diazabicyclo[3.2.1]octane-3-carboxylate $(1.95\\mathrm{g},50\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ $\\mathrm{DMSO - d_6})$ 7.78 $(d,J = 6.0\\mathrm{Hz}$ 1H),7.52- 7.11 (m, 5H), 6.48 (dd, $J = 6.0$ $2.1\\mathrm{Hz}$ 1H), 6.11 (d, $J = 2.0\\mathrm{Hz}$ 1H), 5.17-5.01 (m, 3H), 4.38 (d, $J = 10.0\\mathrm{Hz}$ 2H), 3.80-3.58 (m, 4H), 3.21-2.95 (m, 4H), 1.95-1.80 (m, 4H), 1.72-1.59 (m, 2H), 1.55- 1.43 (m, 2H), 1.41 (s, 9H). LC-MS $(\\mathrm{ES + })$ .. $m / z523[\\mathrm{M} + \\mathrm{H}]^{+}$ . This material $(1.90\\mathrm{g},3.64\\mathrm{mmol})$ was combined with $10\\%$ Pd/C (300 mg) in EtOAc $(20~\\mathrm{mL})$ , and the resulting suspension was stirred at room temperature for $^{\\textrm{\\scriptsize 4h}}$ under hydrogen (3 atm). The mixture was then filtered, and the filter cake was washed with EtOAc $(20~\\mathrm{mL}\\times 2)$ The combined filtrate and washings were concentrated under reduced pressure, and the residue was purified by prepacted C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH_4HCO_3})$ , 0 to $100 \\%$ ) to afford tert-butyl 4-((4-(3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2- yl)oxy)piperidine-1-carboxylate $(900~\\mathrm{mg}$ $64 \\%$ ) as a white solid. $^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 7.72 (d, $J = 6.0~\\mathrm{Hz}$ , 1H), 6.38 (dd, $J =$ $6.0$ $2.0~\\mathrm{Hz}$ , 1H), 5.97 (d, $J = 2.1~\\mathrm{Hz}$ , 1H), 5.16-5.04 (m, 1H), 4.14 (s, 2H), 3.78-3.60 (m, 2H), 3.12 (t, $J = 11.2~\\mathrm{Hz}$ , 2H), 2.83 (d, $J =$ $12.2~\\mathrm{Hz}$ , 2H), 2.42 (d, $J = 12.2~\\mathrm{Hz}$ , 2H), 1.97-1.80 (m, 6H), 1.56- 1.45 (m, 2H), 1.41 (s, 9H). LC-MS $(\\mathrm{ES + })$ .. $m / z389[\\mathrm{M} + \\mathrm{H}]^{+}$ . A solution of this material $(880~\\mathrm{mg}$ $2.27~\\mathrm{mmol}$ , 1.0 equiv), 4-bromo-6-chloro-pyridazin-3-amine (70, $708~\\mathrm{mg}$ $3.40~\\mathrm{mmol}$ , 1.5 equiv) and DIEA $(877~\\mathrm{mg},6.80~\\mathrm{mmol}$ , 3.0 equiv) in NMP $(10~\\mathrm{mL})$ was stirred at $120^{\\circ}\\mathrm{C}$ for $^{\\textrm{\\scriptsize 2h}}$ After cooling to room temperature, the mixture was directly purified by prepacted C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH_4HCO_3})$ , 0 to $100 \\%$ ) to afford tert-butyl 4-(4-(3-(3-amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)- pyridin-2-yl)oxy)piperidine-1-carboxylate $(1.06~\\mathrm{g},91\\%)$ as a yellow solid. $^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ $7.78$ d, $J = 5.6~\\mathrm{Hz}$ , 1H), 6.91 (d, $J = 1.7~\\mathrm{Hz}$ , 1H), 6.51 (d, $J = 5.9~\\mathrm{Hz}$ , 1H), 6.13 (s, 1H), 5.84 (s, 2H), 5.11 (s, 1H), 4.46 (s, 2H), 3.71 (d, $J = 13.1~\\mathrm{Hz}$ , 2H), 3.25- $3.05(\\mathfrak{m},4\\mathsf{H})$ , 2.87 (d, $J = 11.7~\\mathrm{Hz}$ , 2H), 2.17-2.05 (m, 2H), 1.97- $1.82(\\mathfrak{m},4\\mathsf{H})$ , 1.60-1.45 (m, 2H), 1.41 (d, $J = 1.8~\\mathrm{Hz}$ , 9H). LC-MS $(\\mathrm{ES + })$ .. $m / z516[\\mathrm{M} + \\mathrm{H}]^{+}$ . A solution of this material $(1.00~\\mathrm{g},$ 1.94 mmol, 1.0 equiv), 2-hydroxyphenylboronic acid (72, $401~\\mathrm{mg}$ , 2.91 mmol, 1.5 equiv), $\\mathbb { K } _ { 2 } \\mathbb { C } \\mathbb { O } _ { 3 }$ $(802~\\mathrm{mg},$ $5.81~\\mathrm{mmol}$ .3.O equiv and Pd(PPh<sub>3</sub>)<sub>4</sub> $(224~\\mathrm{mg},$ $0.190~\\mathrm{mmol},$ $0.10~\\mathrm{equiv})$ in I,4-dioxane $(10~\\mathrm{mL})$ and water $(1~\\mathrm{mL})$ was stirred at $90^{\\circ}\\mathrm{C}$ for $^{\\textrm{\\scriptsize}2\\textrm{h}}$ . The reaction was then ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,235]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"43","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"cooled to room temperature and was diluted with EtOAc $(100~\\mathrm{mL})$ The resulting mixture was washed with water $(100~\\mathrm{mL})$ ,and the organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 100:0) to afford the title compound $(600\\mathrm{mg},54\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.15s1H7.93d $J = 7.7\\mathrm{Hz}$ 1H),7.79d $J = 5.9\\mathrm{Hz}$ 1H),7.51s1H),7.24t $J = 7.4\\mathrm{Hz}$ 1H), 6.96-6.80 m2H),6.58-6.49 m1H),6.15 s1H),5.98 s2H), 5.18-5.04 m1H),4.50 s2H),3.78-3.62 m2H),3.26 d $J =$ $11.7\\mathrm{Hz}$ 2H),3.20-3.08 m2H),3.02 d $J = 11.5\\mathrm{Hz}$ 2H),2.18 d $J = 7.3\\mathrm{Hz}$ 2H),2.04-1.85 m4H),1.59-1.45m2H),1.41 s, 9H). LC-MS $\\left(\\mathrm{ES + }\\right)$ .. $m / z$ 574 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,235,915,396]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"43","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(6-Amino-5-(8-(2-(piperidin-4-yloxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)pyridazin-3-yl)phenol (144). A solution of intermediate 143 $(550\\mathrm{mg},0.960\\mathrm{mmol})$ and TFA (1 mL) in dichloromethane $(5\\mathrm{mL})$ was stirred at room temperature for $4\\mathrm{h}$ . The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.1\\%$ TFA), 0 to $100\\%$ ) to afford the title compound (TFA salt, $410\\mathrm{mg},73\\%$ yield) as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6}$ 8.73s2H7.95d $J = 6.7~\\mathrm{Hz}$ 1H7.58 $(\\mathrm{d},J = 7.8\\mathrm{Hz}$ 1H7.50s1H7.39t $J = 7.6\\mathrm{Hz}$ 1H7.08-6.91 m4H6.82d $J = 6.9\\mathrm{Hz}$ 1H6.50s1H5.14s1H4.79 s, 2H),3.62d $J = 12.1\\mathrm{Hz}$ 2H),3.33-3.05m6H2.25-2.06m 4H),2.05-1.81m4H.LC-MS $(\\mathrm{ES + })$ .. $m / z$ 474 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,396,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"43","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-((2R)-2-(3-(4-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)piperidin-1-yl)methyl)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (23). A solution of intermediate 144 (130 mg, 0.275 mmol, 1.0 equiv), intermediate 140 (163 mg, 0.275 mmol, 1.0 equiv), and $\\mathrm{NaBH(OAc)_3}$ (175 mg, 0.825 mmol, 3.0 equiv) in $\\mathrm{CH}_3\\mathrm{CN}$ (4 mL) was stirred at room temperature for 4 h. The resulting mixture was diluted with EtOAc (100 mL) and was washed with water (100 mL). The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by preparative HPLC [column: XBridge Shield RP18 OBD Column, $30\\times 150~\\mathrm{mm}^2$ $5\\mu \\mathrm{m}$ ; mobile phase A: Water (10 mmol/L $\\mathrm{NH_4HCO_3}$ ), mobile phase B: $\\mathrm{CH}_3\\mathrm{CN}$ ; flow rate: 60 mL/min; gradient: 40 to 63% B over 10 min; wavelength: 254/220 nm; RT: 8.83 min] to afford a $\\sim 1:1$ mixture of the title compound and the corresponding isopropyl group epimer (38 mg). This mixture was subsequently separated by preparative chiral HPLC [column: CHIRAL ART Amylose-SA, $5\\times 25~\\mathrm{cm}^2$ $5\\mu \\mathrm{m}$ ; mobile phase A: 3:1 hexane:DCM (0.5% 2 M $\\mathrm{NH}_3$ -MeOH), mobile phase B: EtOH; flow rate: 20 mL/min; gradient: isocratic 50% B; wavelength: 220/254 nm; RT1:13.23 min; RT2:29.80 min; sample solvent: EtOH] to afford the title compound (slower peak, 6.2 mg, 2.1%) as a white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\delta$ 14.14 (s, 1H), 8.99 (s, 1H), 8.40 (d, $J = 7.7~\\mathrm{Hz}$ , 1H), 7.97–7.89 (m, 1H), 7.79 (d, $J = 5.9~\\mathrm{Hz}$ , 1H), 7.49 (d, $J = 8.5~\\mathrm{Hz}$ , 1H), 7.45 (d, $J = 8.0~\\mathrm{Hz}$ , 2H), 7.37 (d, $J = 8.2~\\mathrm{Hz}$ , 2H), 7.29–7.17 (m, 1H), 6.92–6.80 (m, 2H), 6.51 (dd, $J = 6.2$ , 2.0 Hz, 1H), 6.16–6.08 (m, 2H), 5.98 (d, $J = 5.0~\\mathrm{Hz}$ , 2H), 5.10 (d, $J = 3.6~\\mathrm{Hz}$ , 1H), 5.04–4.87 (m, 2H), 4.51 (d, $J = 4.5~\\mathrm{Hz}$ , 2H), 4.37 (t, $J = 7.8~\\mathrm{Hz}$ , 1H), 4.29 (s, 1H), 3.78–3.49 (m, 4H), 3.42 (d, $J = 10.2~\\mathrm{Hz}$ , 1H), 3.31–3.24 (m, 2H), 3.02 (d, $J = 11.5~\\mathrm{Hz}$ , 2H), 2.81–2.66 (m, 4H), 2.50–2.42 (m, 3H), 2.30–1.87 (m, 12H), 1.87–1.51 (m, 6H), 1.50–1.30 (m, 3H), 1.21–1.07 (m, 2H), 0.96 (t, $J = 5.8~\\mathrm{Hz}$ , 3H), 0.89–0.76 (m, 3H). LC-MS $(\\mathrm{ES + })$ : m/z 1051.6 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . The compound bearing the undesired isopropyl stereocenter $(23e,$ isopropyl isomer corresponding to 23, structure not shown) was also isolated (faster peak, $6.2~\\mathrm{mg}$ , $2.1\\%$ ) as a white solid. ${}^{1}\\mathrm{H}$ NMR $(300~\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\delta$ 14.14 (s, 1H), 9.0–8.87 (m, 1H), 8.20 (d, $J = 7.8~\\mathrm{Hz}$ , 1H), 7.97–7.88 (m, 1H), 7.79 (d, $J = 5.9~\\mathrm{Hz}$ , 1H), 7.56–7.28 (m, 5H), 7.23 (t, $J = 7.7~\\mathrm{Hz}$ , 1H), 6.92–6.80 (m, 2H), 6.59–6.47 (m, 1H), 6.13 (d, $J = 2.0~\\mathrm{Hz}$ , 2H), 5.97 (s, 2H), 5.10 (d, $J = 3.6~\\mathrm{Hz}$ , 1H), 5.07–4.84 (m, 2H), 4.50 (s, 2H), 4.43 (t, $J = 7.6~\\mathrm{Hz}$ , 1H), 4.33–4.22 (m, 1H), 3.77–3.40 (m, 5H), 3.26 (d, $J = 11.7~\\mathrm{Hz}$ , 2H), ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"43","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[532,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"43","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"43","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[484,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"43","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1305 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"43","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"43","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,70,482,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"3.02 (d, $J = 11.5\\\\mathrm{Hz}$ 2H), 2.82-2.60 (m, 4H), 2.50-2.42 (m, 3H), 2.32-2.05 (m, 8H), 2.00-1.88 (m, 4H), 1.88-1.50 (m, 6H), 1.47 (d, $J = 6.9\\\\mathrm{Hz}$ 1H), 1.36 (d, $J = 6.9\\\\mathrm{Hz}$ 2H), 1.19-1.00 (m, 2H), 0.98-0.67 (m, 6H). LC-MS $(\\\\mathrm{ES}+)$ : $m / z$ 1051.5 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\"(2S,4R)-4-Hydroxy-1-(3-methyl-2-(3-(prop-2-yn-1-xyloxy)- isoxazol-5-yl)butanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)- phenyl)ethyl)pyrrolidine-2-carboxamide (145). A solution of intermediate 58 $(250\\\\mathrm{mg},0.501\\\\mathrm{mmol},1.0$ equiv), propargyl bromide $(59.5\\\\mathrm{mg},0.500\\\\mathrm{mmol},1.0$ equiv), and $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ $208\\\\mathrm{mg}$ $1.50\\\\mathrm{mmol}$ 3.0 equiv) in DMF $(4\\\\mathrm{mL})$ was stirred at room temperature for $2\\\\mathrm{h}$ The reaction was diluted with EtOAc $(100~\\\\mathrm{mL})$ , and the resulting mixture was washed with water $(100~\\\\mathrm{mL})$ . The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH_4HCO_3)}$ 0 to $100\\\\%$ ) to afford the title compound $(120\\\\mathrm{mg},45\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6}$ 89.01-8.88 m, 1H),8.50-8.32 m, 1H),7.56-7.21 m, 4H),6.22-6.10 m, 1H), 5.10 s, 1H),5.03-4.81 m, 3H),4.57-4.31 m, 1H),4.26 s, 1H), 3.81-3.59 m, 2H),3.57-3.34 m, 2H),2.45 d, $J = 2.6~\\\\mathrm{Hz}$ 3H), 2.35-2.14 m, 1H),2.14-1.86 m, 1H),1.86-1.64 m, 1H),1.49- 1.27 m, 3H),1.01-0.71 m, 6H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 537 $[\\\\mathbf{M}+$ $\\\\mathrm{H}]^{+}$ . A considerable amount of the corresponding isoxazole Nalkylation product eluted from the column ahead of the desired compound and was also isolated $(90\\\\mathrm{mg},33\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6}$ 89.02-8.94 m, 1H),8.50-8.32 m, 1H),7.52-7.29 m, 4H),5.79 s, 1H),5.11 d, $J = 3.7~\\\\mathrm{Hz}$ 1H), 5.08-4.85 m, 1H),4.58 d, $J = 2.6~\\\\mathrm{Hz}$ 2H),4.48-4.35 m, 1H), 4.27 s, 1H),3.72-3.39 m, 4H),2.45 d, $J = 2.8~\\\\mathrm{Hz}$ , 3H),2.35-2.12 m, 1H),2.12-1.98(m, 1H),1.85-1.62 m, 1H),1.48-1.31 m, 3H),1.02-0.66 m, 6H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 537 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\"2-trans-3-(Benzyloxy)cyclobutoxy)-4-bromopyridine (146). A suspension of 3-benzyloxycyclobutanol $(108,2.95\\\\mathrm{g},16.6\\\\mathrm{mmol},$ 1.0 equiv) and NaH $60\\\\%$ in mineral oil, $0.790\\\\mathrm{g}$ 19.7 mmol, 1.2 equiv) in DMF $(20.0~\\\\mathrm{mL})$ was stirred at $0^{\\\\circ}C$ for $0.5\\\\mathrm{h}$ 4-Bromo-2fluoro-pyridine $(4.37\\\\mathrm{g},24.8\\\\mathrm{mmol},1.5$ equiv) was then added, and the reaction was warmed to room temperature and was stirred for $1\\\\textrm{h}$ The mixture was quenched at room temperature with saturated aqueous $\\\\mathrm{NH_4Cl}$ and was subsequently extracted with EtOAc $(100~\\\\mathrm{mL}$ $\\\\times 3)$ .The combined organic layers were washed with water $(100~\\\\mathrm{mL})$ and were dried over magnesium sulfate. After filtration, the filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 65:35) to afford the title compound $(4.00\\\\mathrm{g},72\\\\%)$ as a colorless oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8.02 d $J = 5.5\\\\mathrm{Hz}$ 1H),7.37-7.23 m, 5H),7.19dd $J = 5.5$ $1.7\\\\mathrm{Hz}$ 1H),7.08d $J = 1.6\\\\mathrm{Hz}$ 1H4.77p $J = 7.1\\\\mathrm{Hz}$ 1H),4.37s2H),3.78p $J = 6.9\\\\mathrm{Hz}$ 1H2.86-2.72m, 2H),2.05-1.87m2H.LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 334 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\"tert-Butyl 8-(2-(trans-3-hydroxycyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate (147). A solution of intermediate 146 $(3.90\\\\mathrm{g},11.7\\\\mathrm{mmol},1.0$ equiv), tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, $4.95\\\\mathrm{g}$ 23.3 mmol, 2.0 equiv), $\\\\mathrm{Cs_2CO_3}$ $(11.4\\\\mathrm{g},35.0\\\\mathrm{mmol},3.0$ equiv) and RuPhosPd G2 $(0.910\\\\mathrm{g},1.17\\\\mathrm{mmol},0.10$ equiv) in toluene $(35~\\\\mathrm{mL})$ was stirred at 90 $^\\\\circ \\\\mathrm{C}$ for $^{\\\\textrm{\\\\scriptsize 2h}}$ The reaction was cooled to room temperature and was diluted with EtOAc $(100~\\\\mathrm{mL})$ . The resulting mixture was washed with water $(100~\\\\mathrm{mL})$ , and the organic layer was dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 65:35) to afford tert-butyl 8-(2- (trans-3-(benzyloxy)cyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]-octane-3-carboxylate $(4.27\\\\mathrm{g},79\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6}$ ) $\\\\delta$ 7.81-7.69 m, 1H), 7.47-7.08 m, 5H), 6.45dd $J = 6.1$ $2.1\\\\mathrm{Hz}$ 1H),6.09d $J = 2.0\\\\mathrm{Hz}$ 1H),4.74p $J =$ $7.2\\\\mathrm{Hz}$ 1H),4.37s2H),4.32s2H),3.76p $J = 6.9~\\\\mathrm{Hz}$ 1H), 3.65-3.42 m, 2H),3.12-2.82 m, 2H),2.80-2.66 m, 2H),1.98- 1.80m4H)1.72-1.58m2H)1.37s9H.LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ $466[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ . This material $(4.20\\\\mathrm{g},9.02\\\\mathrm{mmol})$ was dissolved in MeOH $(100~\\\\mathrm{mL})$ and $10\\\\%$ Pd/C $(2.50\\\\mathrm{g})$ was added in portions. The resulting suspension was stirred at room temperature for $^{12\\\\mathrm{h}}$ under a \"]","page_idx":"44","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[512,71,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"hydrogen atmosphere then was filtered. The filter cake was washed with $\\\\mathrm{MeOH}$ $(20\\\\mathrm{mL}\\\\times 3)$ , and the combined filtrate and washings were concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ 0 to $70\\\\%$ ) to afford the title compound $(1.90\\\\mathrm{g},56\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 7.73 (d, $J = 6.0~\\\\mathrm{Hz}$ 1H),6.45dd, $J = 6.0$ 2.1 Hz1H),6.07d $J = 2.0\\\\mathrm{Hz}$ 1H),5.09 d, $J = 6.5\\\\mathrm{Hz}$ 1H),4.62p, $J = 7.2\\\\mathrm{Hz}$ 1H),4.33s,2H),3.88-3.71 m, 1H),3.67-3.45 m,2H),3.04d $J = 13.1\\\\mathrm{Hz}$ 1H),2.90d $J = 13.0$ $\\\\mathrm{Hz}$ 1H),2.77-2.62m2H),1.97-1.75m4H),1.71-1.56m, 2H),1.37s9H.LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 376 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\"trans-3-((4-(3-(3-Amino-6-(2-(methoxymethoxy)phenyl)-pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)cyclobutan-1-ol (148). A solution of intermediate 147 $(1.88\\\\mathrm{g},$ 5.01 mmol) in TFA $(4\\\\mathrm{mL})$ and DCM $(20~\\\\mathrm{mL})$ was stirred at room temperature for $4\\\\mathrm{h}$ The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in Water $(0.1\\\\%$ TFA), 0 to $50\\\\%$ to afford trans-3-((4-(3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)cyclobutan-1-ol (TFA salt, $1.20\\\\mathrm{g},$ $62\\\\%$ ) as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ ,DMSO- $d_{6}$ ) $\\\\delta$ 9.66 (s, 1H), 9.28 (s, 1H), 7.97 (d, $J = 7.1$ Hz, 1H), 6.81 (dd, $J = 7.1$ $2.1\\\\mathrm{Hz}$ , 1H), 6.30 (d, $J = 2.2\\\\mathrm{Hz}$ , 1H), 4.80 (s, 2H), 4.66 (p, $J = 7.0\\\\mathrm{Hz}$ , 1H), 3.82 (p, $J = 7.1\\\\mathrm{Hz}$ , 1H), 3.28-3.01 (m, 4H), 2.98-2.80 (m, 2H), 2.10 (s, 4H), 2.03-1.87 (m, 2H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 276 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . A solution of this material $(1.19\\\\mathrm{g},$ 3.05 mmol, 1.0 equiv), 4-bromo-6-chloro-pyridazin-3-amine (70, 1.35 g, 6.48 mmol, 2.1 equiv) and DIEA $(1.67\\\\mathrm{g},$ 13.0 mmol, 4.3 equiv) in NMP $(15~\\\\mathrm{mL})$ was stirred at $120^{\\\\circ}\\\\mathrm{C}$ for $2\\\\textrm{h}$ After cooling to room temperature, the reaction mixture was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%$ $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ - 0 to $50\\\\%$ to afford trans-3-((4-(3-(3-amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutan-1-ol $(800~\\\\mathrm{mg},$ $65\\\\%$ ) as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ ,DMSO- $d_{6}$ ) $\\\\delta$ 7.75 (d, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 6.90 (s, 1H), 6.49 (dd, $J = 6.0$ $2.1~\\\\mathrm{Hz}$ , 1H), 6.11 (d, $J = 2.0~\\\\mathrm{Hz}$ , 1H), 5.84 (s, 2H), 5.12 (d, $J = 6.5~\\\\mathrm{Hz}$ , 1H), 4.65 (p, $J = 7.3~\\\\mathrm{Hz}$ , 1H), 4.45 (s, 2H), 3.81 (q, $J = 7.0~\\\\mathrm{Hz}$ , 1H), 3.22-3.13 (m, 2H), 2.87 (d, $J = 11.6~\\\\mathrm{Hz}$ , 2H), 2.76-2.61 (m, 2H), 2.13 (d, $J =$ $7.2~\\\\mathrm{Hz}$ , 2H), 1.98-1.75 (m, 4H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 403 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . A solution of this material $(790~\\\\mathrm{mg},$ $1.96~\\\\mathrm{mmol}$ , 1.0 equiv), $(2-$ methoxymethoxy)phenyl)boronic acid (85, $535~\\\\mathrm{mg}$ , 2.94 mmol, 1.5 equiv), $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ (812 mg, $5.88~\\\\mathrm{mmol}$ , 3.0 equiv) and $\\\\mathrm{Pd(PPh_3)_4}$ (226 mg, 0.196 mmol, 0.10 equiv) in water $(1~\\\\mathrm{mL})$ and 1,4-dioxane $(10~\\\\mathrm{mL})$ was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for $2\\\\textrm{h}$ . The resulting mixture was cooled to room temperature and was extracted with EtOAc $(75~\\\\mathrm{mL} \\\\times 3)$ . The combined organic layers were washed with water $(100~\\\\mathrm{mL})$ and were dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%$ $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ - O to $50\\\\%$ to afford the title compound $(590~\\\\mathrm{mg},$ $60\\\\%$ ) as a yellow solid. $^{1}\\\\mathrm{H}$ NMR $(300~\\\\mathrm{MHz}$ ,DMSO- $d_{6}$ ) $\\\\delta$ 7.74 (d, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 7.59 (dd, $J = 7.6$ $1.8~\\\\mathrm{Hz}$ , 1H), 7.34 (ddd, $J = 8.8$ $7.2$ $1.8~\\\\mathrm{Hz}$ , 1H), 7.19-7.01 (m, 3H), 6.50 (dd, $J = 6.0$ $2.1~\\\\mathrm{Hz}$ , 1H), 6.12 (d, $J = 2.0$ Hz, 1H), 5.72 (s, 2H), $5.13(s,2H)$ ,5.08 (d, $J = 6.3~\\\\mathrm{Hz}$ , 1H),4.64 (p, $J = 7.3~\\\\mathrm{Hz}$ , 1H),4.47 (s, 2H),3.79 (p, $J = 7.1~\\\\mathrm{Hz}$ , 1H),3.22 (s, 3H), $3.20 - 3.09$ (m, 2H),2.86 (d, $J = 11.4~\\\\mathrm{Hz}$ , 2H),2.78-2.62 (m, 2H), $2.29 - 2.11$ (m, 2H), $2.02 - 1.75$ (m,4H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 505 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\"4-(8-(2-((trans-3-((6-lodopyridin-3-yl)oxy)cyclobutoxy)-pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)-6-(2-(methoxymethoxy)phenyl)pyridazin-3-amine (149). To a $0^{\\\\circ}\\\\mathrm{C}$ solution of $\\\\mathrm{PPh}_3$ 264 mg, 1.00 mmol, 4.8 equiv) in THF (5 mL) was added DIAD (202 mg, 1.00 mmol, 4.8 equiv). The mixture was stirred for 5 min at $0^{\\\\circ}\\\\mathrm{C}$ , then 6-iodopyridin-3-ol (221 mg, 1.00 mmol, 4.8 equiv) was added followed by intermediate 148 (105 mg, 0.208 mmol). The resulting mixture was warmed to room temperature and was stirred for a additional 12 h. The reaction was then diluted with EtOAc (100 mL) and the mixture was washed with water (100 mL). The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in \"]","page_idx":"44","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"44","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"44","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"44","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"44","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1306 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"44","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"44","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,481,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ 0 to $60\\\\%$ ) to afford the title compound $(85\\\\mathrm{mg},58\\\\%)$ as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8.06 (d, $J = 3.2~\\\\mathrm{Hz}$ 1H),7.75(d, $J = 6.0~\\\\mathrm{Hz}$ 1H),7.69 (d, $J = 8.7~\\\\mathrm{Hz}$ 1H),7.59dd, $J = 7.6$ $1.8\\\\mathrm{Hz}$ 1H),7.35td $J = 7.3$ $1.8\\\\mathrm{Hz}$ 1H), 7.19-7.02 (m, 4H),6.53dd, $J = 6.1$ $2.0\\\\mathrm{Hz}$ 1H),6.17d $J = 2.0$ $\\\\mathrm{Hz},1\\\\mathrm{H})$ ,5.74s,2H),5.29q, $J = 5.7\\\\mathrm{Hz}$ 1H),5.15s,2H),4.97t, $J = 5.5\\\\mathrm{Hz}$ 1H),4.49s,2H),3.23s,3H),3.16d $J = 10.7\\\\mathrm{Hz}$ 2H), 2.86 d, $J = 11.4\\\\mathrm{Hz}$ 2H),2.58-2.50 m,4H),2.20 d, $J = 7.1~\\\\mathrm{Hz}$ 2H),2.01-1.92 (m, 2H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 708 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\"(2S,4R)-1-((2R)-2-(3-((3-5-(trans-3-((4-3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)pyridin-2-yl)prop-2-yn-1-yl)oxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (24). A solution of intermediate 149 (75.0 mg, 0.106 mmol, 1.0 equiv), intermediate 145 (56.9 mg, 0.106 mmol, 1.0 equiv), CuI (2.0 mg, 0.011 mmol, 0.10 equiv), TEA (32.1 mg, 0.320 mmol, 3.0 equiv), and $\\\\mathrm{Pd}(\\\\mathrm{PPh}_3)_2\\\\mathrm{Cl}_2$ (7.4 mg, 0.010 mmol, 0.10 equiv) in DMF (3 mL) was stirred at $65^{\\\\circ}\\\\mathrm{C}$ for $3\\\\mathrm{~h}$ . The reaction was cooled to room temperature and was diluted with EtOAc (75 mL). The resulting mixture was washed with water (75 mL) and was dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ to afford (2S,4R)-1-(2-(3-((3-(5-(trans-3-((4-(3-(3-amino-6-(2-methoxymethoxy)phenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]-octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)pyridin-2-yl)prop-2-yn-1-yl)oxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide ( $\\\\sim$ 1:1 mixture of isopropyl group isomers, 90.0 mg, $76\\\\%$ ) as a white solid. $^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 9.03–8.89 (m, 1H), 8.45–8.25 (m, 1H), 8.22 (t, $J = 3.3\\\\mathrm{~Hz}$ , 1H), 7.81–7.52 (m, 4H), 7.52–7.22 (m, 6H), 7.22–7.05 (m, 2H), 6.54 (dd, $J = 6.0$ , 2.0 Hz, 1H), 6.28–6.12 (m, 2H), 5.92–5.75 (m, 4H), 5.36–4.83 (m, 6H), 4.56–4.35 (m, 2H), 4.32–4.21 (m, 1H), 3.84–3.57 (m, 2H), 3.57–3.30 (m, 6H), 3.28–3.15 (m, 3H), 2.98–2.85 (m, 1H), 2.58–2.50 (m, 3H), 2.48–2.41 (m, 3H), 2.35–2.15 (m, 3H), 2.08–1.89 (m, 3H), 1.87–1.73 (m, 1H), 1.49–1.31 (m, 3H), 1.01–0.74 (m, 6H). LC-MS $(\\\\mathrm{ES}+)$ : $m/z$ 1116 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . A solution of this material (80.0 mg, 0.0717 mmol) in HCl (4.0 M in MeOH, 2 mL) was stirred at room temperature for $4\\\\mathrm{~h}$ . The resulting mixture was concentrated under reduced pressure, and the residue was purified by preparative HPLC [column: XBridge Prep OBD C18 Column, $30\\\\times 150\\\\mathrm{~mm}^2$ , $5\\\\mu\\\\mathrm{m}$ ; mobile phase A: water (10 mmol/L $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3$ ), mobile phase B: $\\\\mathrm{CH}_3\\\\mathrm{CN}$ ; flow rate: $60\\\\mathrm{~mL/min}$ ; gradient: 21 to $41\\\\%$ B over $10\\\\mathrm{~min}$ ; wavelength: $254/220\\\\mathrm{~nm}$ ; RT: $9.3\\\\mathrm{~min}$ ] to afford $16\\\\mathrm{mg}$ of the MOM-deprotected product as a $\\\\sim$ 1:1 mixture of the two isopropyl group isomers. These compounds were subsequently separated by preparative chiral HPLC [column: CHIRALPAK IA $2\\\\times 25\\\\mathrm{~cm}^2$ , $5\\\\mu\\\\mathrm{m}$ ; mobile phase A: MTBE (0.1% FA), mobile phase B: 1:1 MeOH:DCM; flow rate: $18\\\\mathrm{~mL/min}$ ; gradient: isocratic $40\\\\%$ B; RT:1:57 min; RT:2:20 min; sample solvent: EtOH; injection volume: $1.0\\\\mathrm{~mL}$ ; number of runs: 2] to afford the title compound (slower peak, $2.2\\\\mathrm{mg}$ , $2.9\\\\%$ ) as a white solid. $^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 14.15 (s, 1H), 8.99 (s, 1H), 8.42 (d, $J = 7.6\\\\mathrm{~Hz}$ , 1H), 8.23 (d, $J = 2.8\\\\mathrm{~Hz}$ , 1H), 7.93 (d, $J = 7.9\\\\mathrm{~Hz}$ , 1H), 7.79 (d, $J = 5.9\\\\mathrm{~Hz}$ , 1H), 7.51 (t, $J = 4.3\\\\mathrm{~Hz}$ , 2H), 7.50–7.26 (m, 5H), 7.26–7.18 (m, 1H), 6.90–6.82 (m, 2H), 6.56 (dd, $J = 6.2$ , $1.8\\\\mathrm{~Hz}$ , 1H), 6.24–6.15 (m, 2H), 5.98 (s, 2H), 5.38–5.28 (m, 1H), 5.16 (s, 2H), 5.04 (t, $J = 5.4\\\\mathrm{~Hz}$ , 1H), 4.92 (t, $J = 7.2\\\\mathrm{~Hz}$ , 1H), 4.52 (s, 2H), 4.39 (t, $J = 7.8\\\\mathrm{~Hz}$ , 1H), 4.29 (s, 1H), 3.71 (d, $J = 9.6\\\\mathrm{~Hz}$ , 1H), 3.70–3.45 (m, 3H), 3.30–3.22 (m, 3H), 3.03 (d, $J = 11.6\\\\mathrm{~Hz}$ , 2H), 2.61–2.54 (m, 3H), 2.46 (s, 3H), 2.31–2.12 (m, 3H), 2.09–1.90 (m, 3H), 1.85–1.71(m, 1H), 1.51–1.31 (m, 3H), 1.02–0.75 (m, 6H). LC-MS $(\\\\mathrm{ES}+)$ : $m/z$ $1072[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . The isomer bearing the undesired isopropyl stereocenter $(24e,$ isopropyl isomer corresponding to $^{24}$ structure not shown) was also isolated (faster peak, $3.3\\\\mathrm{mg},$ $4.3\\\\%$ ) as a white solid. $^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz},$ DMSO- $d_6$ ) $\\\\delta$ $14\\\\.13$ (s, $1\\\\mathrm{~Hz}$ ), $8\\\\.98$ (d, $J =$ $9\\\\.8\\\\mathrm{~Hz}$ , $1\\\\mathrm{~Hz}$ ), $8\\\\.43 -8\\\\.8$ (m, $1\\\\mathrm{~Hz}$ ), $8\\\\.22$ (t, $J =$ $9\\\\.1\\\\mathrm{~Hz}$ , $1\\\\mathrm{~Hz}$ ), $7\\\\.92$ (d, $J =$ $7\\\\.9\\\\mathrm{~Hz}$ , $1\\\\mathrm{~Hz}$ ), $7\\\\.78$ (d, $J =$ $5\\\\.9\\\\mathrm{~Hz}$ , $1\\\\mathrm{~Hz}$ ), $7\\\\.54 -7\\\\.38$ (m, $4\\\\mathrm{~Hz}$ ), $7\\\\.37 -7\\\\.17$ \"]","page_idx":"45","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[514,70,915,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"$(\\\\mathrm{m},4\\\\mathrm{H})$ 6.86dd $J = 10.2$ $7.8~\\\\mathrm{Hz}$ 2H),6.56dd $J = 6.0$ $2.0~\\\\mathrm{Hz}$ 1H),6.28-6.15 $\\\\mathrm{(m,2H)}$ 5.98s,2H),5.32 $\\\\mathrm{(t,J = 6.0Hz,1H)}$ ,5.15 $\\\\mathrm{(d,J = 11.4Hz,2H)}$ 5.03 $\\\\mathrm{(d,J = 7.1Hz,1H)}$ 4.90 $\\\\mathrm{(t,J = 7.2Hz}$ 1H),4.52s,2H),4.44 $\\\\mathrm{(t,J = 7.7Hz,1H)}$ 4.27s,1H),3.80 $\\\\mathrm{(d,J =}$ $8.5\\\\mathrm{Hz}$ 1H),3.61-3.45 $\\\\mathrm{(m,3H)}$ 3.29-3.20 $\\\\mathrm{(m,3H)}$ 3.03 $\\\\mathrm{(d,J =}$ $11.6\\\\mathrm{Hz},2\\\\mathrm{H})$ 2.62-2.52 $\\\\mathrm{(m,3H)}$ 2.50-2.40 $\\\\mathrm{(m,3H)}$ 2.36-2.10 $\\\\mathrm{(m,3H)}$ 2.03-1.92 $\\\\mathrm{(m,3H)}$ 1.84-1.70 $\\\\mathrm{(m,1H)}$ 1.47 $\\\\mathrm{(d,J = 7.0Hz}$ 1H),1.35 $\\\\mathrm{(d,J = 7.0Hz,2H)}$ 0.98 $\\\\mathrm{(d,J = 6.6Hz,2H)}$ 0.90-0.69 $\\\\mathrm{(m,4H)}$ .LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 1072 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\"(2S,4S)-1-((R)-2-(3-(2,2-Diethoxyethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (150).DIAD $(263\\\\mathrm{mg},$ $1.30\\\\mathrm{mmol}$ 1.6 equiv) was added to a $0^{\\\\circ}\\\\mathrm{C}$ solution of $\\\\mathrm{PPh}_3$ $(340\\\\mathrm{mg},$ $1.29\\\\mathrm{mmol}$ 1.6 equiv) in THF $(15\\\\mathrm{mL})$ . The reaction was stirred at $0^{\\\\circ}\\\\mathrm{C}$ for $1\\\\textrm{h}$ then intermediate 60 $(500\\\\mathrm{mg},0.814\\\\mathrm{mmol},1.0$ equiv) and AcOH $(80.8\\\\mathrm{mg},1.3\\\\mathrm{mmol},1.6$ equiv) were added sequentially. The reaction was stirred at $0^{\\\\circ}\\\\mathrm{C}$ for $1\\\\textrm{h}$ then was maintained at room temperature for an additional $2\\\\textrm{h}$ . The volatiles were removed under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $55\\\\%$ ) to afford (3S,5S)-1-((R)-2-(3-(2,2-diethoxyethoxy)isoxazol-5- yl)-3-methylbutanoyl)-5-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)- ethyl)carbamoyl)pyrrolidin-3-yl acetate $(170~\\\\mathrm{mg},32\\\\%)$ as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (400 MHz, DMSO- $d_{6}$ 8.99 (s, 1H), 8.53-8.13 (m, 1H), 7.71-7.31 (m, 4H), 6.17 (s, 1H), 5.16-5.06 (m, 1H), 5.00- 4.88 (m, 1H), 4.84-4.71 (m, 1H), 4.49-4.41 (m, 1H), 4.12-4.06 (m, 2H), 3.90-3.77 (m, 1H), 3.77-3.48 (m, 6H), 2.48-2.39 (m, 4H),2.33-2.22 (m, 1H), 2.02-1.93 (m, 1H), 1.80-1.60 (m, 3H), $1.48 - 1.36$ m, 3H), 1.13 t $J = 7.0~\\\\mathrm{Hz}$ 6H), $1.02 - 0.91$ m, 3H), $0.80$ d $J = 6.5~\\\\mathrm{Hz}$ ,3H.LC-MS $(\\\\mathrm{ES + })$ .. $m / z~657[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ .This material $(160~\\\\mathrm{mg},$ $0.244\\\\mathrm{mmol})$ was dissolved in MeOH $(1\\\\mathrm{mL})$ at room temperature and $\\\\mathrm{NH}_3$ $(7.0\\\\mathrm{M}$ in MeOH, $5\\\\mathrm{mL})$ was added. The reaction was stirred at room temperature for $2\\\\textrm{h}$ then the volatiles were removed under reduced pressure. The residue was diluted with DCM $(30~\\\\mathrm{mL})$ , and the resulting mixture was washed with brine (20 mL). The organic layer was dried over sodium sulfate and was filtered. Concentration of the filtrate under reduced pressure afforded the title compound $(120\\\\mathrm{mg},80\\\\%$ yield) as a white solid. $^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_{6}$ ) $\\\\delta$ 8.99 (s, 1H), 8.46 (d, $J = 7.7~\\\\mathrm{Hz}$ , 1H), $7.51 - 7.32$ (m, 4H),6.17 s, 1H),5.39-5.19 (m, 1H),5.01-4.86 (m, 1H),4.86- 4.73 (m, 1H),4.40-4.27 (m, 1H),4.27-4.15 (m, 1H),4.15-3.97 (m, 2H), $3.85 - 3.60$ (m, 4H), $3.60 - 3.46$ (m, 3H),2.46 (s, 3H), $2.41 - 2.18$ m, 2H), $1.71 - 1.58$ (m, 1H), $1.50 - 1.32$ (m, 3H), $1.13$ t $J = 7.1~\\\\mathrm{Hz}$ ,6H),0.96d $J = 6.7~\\\\mathrm{Hz}$ ,3H),0.81d $J = 6.6~\\\\mathrm{Hz}$ ,3H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z~615[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ \",\"(2S,4S)-4-Hydroxy-1-((R)-3-methyl-2-(3-(2-oxoethoxy)-isoxazol-5-yl)butanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (151). A solution of intermediate 150 $(115\\\\mathrm{mg},0.187\\\\mathrm{mmol})$ in formic acid $(2\\\\mathrm{mL})$ and water $(2\\\\mathrm{mL})$ was stirred at $60^{\\\\circ}\\\\mathrm{C}$ for $2\\\\mathrm{h}$ . After cooling to room temperature, the solvent was removed under reduced pressure to afford the crude title compound $(105\\\\mathrm{mg})$ as a white solid. This material was used in the next step without further purification. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 9.61 (s, 1H), 8.99 (s, 1H), 8.50-8.43 (m, 1H), 7.50-7.33 (m, 4H), 6.28-6.08 (m, 1H), 5.33 (s, 1H), 4.95 (d, $J = 9.7\\\\mathrm{Hz}$ , 2H), 4.38-4.16 (m, 2H), 4.07-3.93 (m, 1H), 3.81-3.64 (m, 2H), 3.57-3.46 (m, 1H), 2.46 (d, $J = 5.7\\\\mathrm{Hz}$ , 3H), 2.38-2.17 (m, 2H), 1.70-1.60 (m, 1H), 1.45-1.30 (m, 3H), 1.03-0.89 (m, 3H), 0.89-0.75 (m, 3H). LC-MS $(\\\\mathrm{ES + })$ : $m / z$ 541 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\"(2S,4S)-1-((2R)-2-(3-(2-(4-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)ethoxy)-isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (25). A solution of intermediate 151 $(95.0\\\\mathrm{mg}$ $0.176\\\\mathrm{mmol}$ 1.0 equiv), intermediate 119 (HCl salt, $111\\\\mathrm{mg}$ $0.191\\\\mathrm{mmol}$ 1.1 equiv), and NaOAc $(43.0\\\\mathrm{mg}$ $0.524\\\\mathrm{mmol}$ 3.0 equiv) in DCM $(0.7\\\\mathrm{mL})$ and MeOH $(2.1\\\\mathrm{mL})$ was stirred at room temperature for $^{\\\\textrm{\\\\scriptsize 1h}}$ . $\\\\mathrm{NaBH}_3\\\\mathrm{CN}$ $(16.5\\\\mathrm{mg},0.263\\\\mathrm{mmol}$ 1.5 equiv) was the added and the mixture was stirred at room temperature overnight. The volatiles were removed under reduced pressure, and the residue was purified by preparative \"]","page_idx":"45","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"45","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"45","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"45","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"45","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1307 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"45","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"45","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,71,479,283]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"46","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HPLC [column: XBridge Prep OBD C18 Column, $30 \\times 150 \\mathrm{~mm}^2$ , $5 \\mu \\mathrm{m}$ ; mobile phase A: water(10 mmol/L $\\mathrm{NH}_4\\mathrm{HCO}_3$ ), mobile phase B: $\\mathrm{CH}_3\\mathrm{CN}$ ; flow rate: $60 \\mathrm{~mL} / \\mathrm{min}$ ; gradient: 52 to $69\\%$ B over $10 \\mathrm{~min}$ ; wavelength: $254 / 220 \\mathrm{~nm}$ ; RT: $9.3 \\mathrm{~min}$ ] to afford the title compound (61 mg, $33\\%$ ) as a pink solid. ${}^{1}\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) $\\delta$ 14.15 (s, 1H), 8.99 (s, 1H), 8.44 (d, $J = 7.7 \\mathrm{~Hz}$ , 1H), 8.00-7.88 (m, 1H), 7.77 (d, $J = 5.9 \\mathrm{~Hz}$ , 1H), 7.50 (s, 1H), 7.49-7.43 (m, 2H), 7.43-7.35 (m, 2H), 7.27-7.19 (m, 1H), 6.91-6.80 (m, 2H), 6.57-6.50 (m, 1H), 6.20-6.09 (m, 2H), 5.97 (s, 2H), 5.33 (d, $J = 7.2 \\mathrm{~Hz}$ , 1H), 5.26-5.15 (m, 1H), 4.99-4.88 (m, 1H), 4.49 (d, $J = 4.5 \\mathrm{~Hz}$ , 2H), 4.35-4.25 (m, 2H), 4.25-4.15 (m, 3H), 3.80-3.65 (m, 2H), 3.58-3.48 (m, 1H), 3.31-3.18 (m, 3H), 3.02 (d, $J = 11.6 \\mathrm{~Hz}$ , 2H), 2.74 (d, $J = 11.1 \\mathrm{~Hz}$ , 2H), 2.64 (t, $J = 5.6 \\mathrm{~Hz}$ , 2H), 2.46 (s, 3H), 2.38-2.25 (m, 6H), 2.22-2.09 (m, 4H), 2.01-1.92 (m, 2H), 1.77 (d, $J = 12.3 \\mathrm{~Hz}$ , 2H), 1.69-1.60 (m, 1H), 1.47-1.37 (m, 5H), 1.01-0.91 (m, 3H), 0.82 (t, $J = 7.5 \\mathrm{~Hz}$ , 3H). LC-MS ( $\\mathrm{ES+}$ ): $m/z$ 1068 [M + H]+ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,285,479,720]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"46","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6-Phenyl-4-(8-(2-(trans-3-(piperidin-4-yloxy)cyclobutoxy)-pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)pyridazin-3-amine (152). A solution of intermediate 117 (200 mg, 0.340 mmol, 1.0 equiv), phenylboronic acid (83 mg, 0.680 mmol, 2.0 equiv), $\\mathrm{K}_2\\mathrm{CO}_3$ (141 mg, 1.02 mmol, 3.0 equiv) and $\\mathrm{Pd(PPh_3)_4}$ (39 mg, 0.0341 mmol, 0.10 equiv) in 1,4-dioxane (5 mL) and water (0.5 mL) was stirred at $90^{\\circ}\\mathrm{C}$ for 3 h. The reaction mixture was cooled to room temperature and was diluted with EtOAc (100 mL). The resulting solution was washed with water (100 mL), and the organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% $\\mathrm{NH_4HCO_3}$ ), 0 to 80%) to afford tert-butyl 4-(trans-3-((4-(3-(3-amino-6-phenylpyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)-pyridin-2-yl)oxy)cyclobutoxy)-piperidine-1-carboxylate (130 mg, 61%) as a yellow oil. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\delta$ 8.02–7.93 (m, 2H), 7.76 (d, $J = 5.9~\\mathrm{Hz}$ , 1H), 7.47–7.32 (m, 3H), 7.27 (s, 1H), 6.52 (d, $J = 6.0~\\mathrm{Hz}$ , 1H), 6.13 (s, 1H), 5.74 (s, 2H), 5.25–5.10 (m, 1H), 4.49 (s, 2H), 4.36–4.26 (m, 1H), 3.75–3.56 (m, 2H), 3.49–3.39 (m, 1H), 3.20 (d, $J = 11.5~\\mathrm{Hz}$ , 2H), 3.08–2.85 (m, 4H), 2.40–2.21 (m, 4H), 2.18 (d, $J = 7.1~\\mathrm{Hz}$ , 2H), 2.03–1.87 (m, 2H), 1.83–1.66 (m, 2H), 1.39 (s, 9H), 1.33–1.21 (m, 2H). LC-MS (ES+): m/z 628 [M + H]+. A solution of this material (120 mg, 0.191 mmol) in HCl (4.0 M in MeOH, 4 mL) was stirred at room temperature for 2 h. The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 100%) to afford the title compound (95 mg, 94%) as a yellow oil. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\delta$ 8.02–7.92 (m, 2H), 7.76 (d, $J = 6.0~\\mathrm{Hz}$ , 1H), 7.50–7.31 (m, 3H), 7.27 (s, 1H), 6.52 (dd, $J = 6.1$ , 2.0 Hz, 1H), 6.13 (d, $J = 2.1~\\mathrm{Hz}$ , 1H), 5.74 (s, 2H), 5.26–5.13 (m, 1H), 4.48 (s, 2H), 4.33–4.24 (m, 1H), 3.45–3.33 (m, 1H), 3.20 (d, $J = 11.4~\\mathrm{Hz}$ , 2H), 3.04–2.90 (m, 4H), 2.66–2.54 (m, 2H), 2.37–2.23 (m, 4H), 2.22–2.13 (m, 2H), 1.99–1.92 (m, 2H), 1.86–1.77 (m, 2H), 1.46–1.30 (m, 2H). LC-MS $(\\mathrm{ES+})$ : m/z 528 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,720,479,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"46","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-((2R)-2-(3-(2-(4-(trans-3-((4-(3-(3-Amino-6-phenylpyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (26). A solution of intermediate 152 $(30.0\\mathrm{mg},0.0568\\mathrm{mmol}$ 1.0 equiv), intermediate 61 $(30.7\\mathrm{mg},0.0568\\mathrm{mmol}$ 1.0 equiv), and NaOAc $(14.0\\mathrm{mg},0.170$ mmol, 3.0 equiv) in MeOH $(3\\mathrm{mL})$ was stirred at room temperature for $^{\\textrm{\\scriptsize 1h}}$ . $\\mathrm{NaBH}_3\\mathrm{CN}$ $(5.3\\mathrm{mg},0.084\\mathrm{mmol}$ 1.5 equiv) was then added, and the reaction was stirred at room temperature for $^{\\textrm{\\scriptsize 1h}}$ After quenching at room temperature with water $(2\\mathrm{mL})$ ,the volatiles were removed under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\%$ $\\mathrm{NH_4HCO_3)}$ 0 to $100\\%$ ) to afford $33~\\mathrm{mg}$ of impure product. This material was further purified by preparative HPLC [column: XBridge Prep OBD C18 Column, $30\\times 150\\mathrm{mm}^2$ $5\\mu \\mathrm{m};$ mobile phase A: water $(10\\mathrm{mmol / L}$ $\\mathrm{NH_4HCO_3})$ , mobile phase B: $\\mathrm{CH}_3\\mathrm{CN}$ flow rate: 60 mL/min; gradient: 18 to $42\\%$ B over $10\\mathrm{min}$ wavelength: 254/220 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,71,914,208]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"46","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"nm; RT: $9.6\\mathrm{min}$ to afford the title compound $(6.7\\mathrm{mg},11\\%$ yield) as a white solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 8 8.97 (d, $J = 1.1~\\mathrm{Hz}$ 1H), 8.39 (d, $J = 7.6~\\mathrm{Hz}$ 1H), 8.00-7.91 (m, 2H), 7.75 (d, $J = 5.9$ Hz, 1H), 7.49-7.30 (m, 7H), 7.25 (s, 1H), 6.50 (dd, $J = 6.1$ $2.0\\mathrm{Hz}$ 1H), 6.15-6.05 (m, 2H), 5.71 (s, 2H), 5.25-5.11 (m, 1H), 5.08 (d, $J$ $= 3.7\\mathrm{Hz}$ , 1H), 4.96-4.82 (m, 1H), 4.47 (s, 2H), 4.41-4.15 (m, 5H), 3.74-3.58 (m, 2H), 3.43 (d, $J = 10.8~\\mathrm{Hz}$ , 1H), 3.28-3.13 (m, 3H), 2.94 (d, $J = 11.4~\\mathrm{Hz}$ , 2H), 2.79-2.67 (m, 2H), 2.63 (t, $J = 5.6~\\mathrm{Hz}$ - 2H), 2.44 (s, 3H), 2.36-2.05 (m, 9H), 2.05-1.84 (m, 3H), 1.83- 1.68 (m, 3H), 1.49-1.29 (m, 5H), 0.94 (d, $J = 6.3~\\mathrm{Hz}$ , 3H), 0.85- 0.71 (m, 3H). LC-MS $(\\mathrm{ES + })$ .. $m / z$ 1053 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,208,914,700]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"46","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4S)-1-((R)-2-(3-(4-(Dimethoxymethyl)piperidin-1-yl)-isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (153). To a solution of intermediate 127 (300 mg, 0.469 mmol, 1.0 equiv) and HOAc (56.1 mg, 0.935 mmol, 2.0 equiv) and $\\mathrm{PPh}_3$ (246 mg, 0.935 mmol, 2.0 equiv) in THF (2 mL) was added a solution of DIAD (189 mg, 0.935 mmol, 2.0 equiv) in THF (1 mL) at $0^{\\circ}\\mathrm{C}$ . The reaction was warmed to room temperature and was stirred at that temperature for 1 h. The volatiles were then removed under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc: petroleum ether, 0:100 to 3:1) to afford (3S,SS)-1-((R)-2-(3-(4-(dimethoxymethyl)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-5-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)carbamoyl)-pyrrolidin-3-yl acetate (301 mg, 94% yield) as a white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\delta$ 8.97 (s, 1H), 8.10 (d, $J = 7.8~\\mathrm{Hz}$ , 1H), 7.46-7.27 (m, 4H), 6.14 (s, 1H), 5.16-5.03 (m, 1H), 5.01-4.86 (m, 1H), 4.43 (dd, $J = 9.3$ , 3.4 Hz, 1H), 4.04 (dd, $J = 10.5$ , 6.7 Hz, 1H), 3.82 (dd, $J = 11.3$ , 5.7 Hz, 1H), 3.76-3.54 (m, 4H), 3.25 (d, $J = 2.0~\\mathrm{Hz}$ , 6H), 2.76-2.62 (m, 2H), 2.47-2.36 (m, 4H), 2.31-2.13 (m, 1H), 2.03-1.91 (m, 1H), 1.83-1.68 (m, 4H), 1.64 (d, $J = 13.5~\\mathrm{Hz}$ , 2H), 1.40 (dd, $J = 10.7$ , 7.0 Hz, 3H), 1.32-1.15 (m, 2H), 0.99-0.87 (m, 3H), 0.83-0.74 (m, 3H). LC-MS $(\\mathrm{ES+})$ : $m/z$ 682 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . To a solution of this material (300 mg, 0.440 mmol) in MeOH (4 mL) was added $\\mathrm{NH}_3$ (7.0 M in MeOH, 5 mL) at room temperature. The reaction mixture was stirred at room temperature for $2.5\\mathrm{h}$ then was concentrated under reduced pressure. The residue was adjusted to pH 7 with aqueous $1\\mathrm{M}$ HCl (50 mL), and the resulting solution was extracted with EtOAc $(100~\\mathrm{mL} \\times 3)$ . The combined organic layers were dried over sodium sulfate, filtered, and the filtrate was concentrated under vacuum. The residue was purified by silica gel chromatography (MeOH:DCM, 0:100 to 4:96) to afford the title compound (195 mg, 69%) as a white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\delta$ 8.98 (s, 1H), 8.41 (d, $J = 7.7~\\mathrm{Hz}$ , 1H), 7.48-7.30 (m, 4H), 6.13 (s, 1H), 5.36-5.22 (m, 1H), 4.99-4.85 (m, 1H), 4.29 (dd, $J = 8.9$ , 5.2 Hz, 1H), 4.23-4.13 (m, 1H), 4.05 (d, $J = 6.8~\\mathrm{Hz}$ , 1H), 3.74-3.55(m, 4H), 3.51 (dd, $J = 10.1$ , 4.7 Hz, 1H), 3.22 (d, $J = 3.8~\\mathrm{Hz}$ , 6H), 2.76-2.60 (m, 2H), 2.45 (s, 3H), 2.38-2.14 (m, 2H), 1.77-1.57 (m, 4H), 1.39-1.34 (m, 3H), 1.27-1.19 (m, 2H), 0.98-0.91 (m, 3H), 0.82-0.75 (m, 3H). LC-MS $(\\mathrm{ES+})$ : $m/z$ 640 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,700,914,882]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"46","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4S)-1-((R)-2-(3-(4-Formylpiperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (154). A solution of intermediate 153 $(30\\mathrm{mg},0.0469\\mathrm{mmol})$ in formic acid $(0.5\\mathrm{mL})$ and water $(0.5\\mathrm{mL})$ was stirred at $60^{\\circ}\\mathrm{C}$ for $1\\textrm{h}$ The reaction mixture was then cooled to room temperature and was concentrated under reduced pressure to afford the crude title compound $(32\\mathrm{mg})$ as an off-white solid. ${}^{1}\\mathrm{H}$ NMR $(300\\mathrm{MHz}$ DMSO- $d_{6})$ 89.62s1H8.99 s,1H),8.43d $J = 7.7~\\mathrm{Hz}$ 1H),7.56-7.26 m4H6.17s1H), 5.30 d $J = 7.0~\\mathrm{Hz}$ 1H),5.00-4.87 m,1H),4.30dd $J = 8.8$ 5.2 Hz,1H),4.26-4.14 m,1H),3.76-3.62 m,2H),3.62-3.47 m, 3H),2.96-2.59 m,2H),2.46 s,3H),2.39-2.16 m,2H),2.03- 1.82 m,2H),1.76-1.58 m,2H),1.58-1.42 m,2H),1.40 d $J =$ $7.0~\\mathrm{Hz}$ 3H),1.04-0.88 m,3H),0.88-0.74 m,3H).LC-MS (ES +): $m / z$ 594 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[518,883,914,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"46","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4S)-1-((2R)-2-(3-(4-((4-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)methyl)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-car ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"46","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[532,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"46","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"46","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[484,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"46","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1308 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,953,912,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"46","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[764,962,912,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"46","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,71,482,345]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"boxamide (27). A solution of intermediate 154 $(32\\mathrm{mg},0.054\\mathrm{mmol}$ 1.0 equiv), intermediate 119 (HCl salt, $30~\\mathrm{mg}$ $0.052\\mathrm{mmol}$ 1.0 equiv) and NaOAc $(12.0\\mathrm{mg}$ $0.146\\mathrm{mmol}$ 2.7 equiv) in DCM (0.2 mL) and MeOH $(0.6~\\mathrm{mL})$ was stirred at room temperature for $1\\textrm{h}$ $\\mathrm{NaBH}_3\\mathrm{CN}$ $(6.0\\mathrm{mg}$ $0.095\\mathrm{mmol}$ 1.7 equiv) was then added, and the reaction was stirred at room temperature overnight. The mixture was then concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN)}$ in water $(0.05\\%)$ $\\mathrm{NH_4HCO_3}$ 0 to $100\\%$ ) to afford the title compound $(24\\mathrm{mg},43\\%)$ as a white solid. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ DMSO- $d_{6})$ $\\delta$ 14.15s,1H8.99s,1H8.42d $J = 7.7~\\mathrm{Hz}$ 1H7.92dd $J = 8.0$ $1.6\\mathrm{Hz},1\\mathrm{H})$ 7.77d $J = 5.9~\\mathrm{Hz},$ 1H7.50s,1H7.48-7.42m, 2H7.42-7.32m2H7.27-7.18m1H6.90-6.80m2H 6.56-6.50m1H6.14d $J = 1.9~\\mathrm{Hz},$ 2H5.98s2H5.33d $J$ $= 7.2\\mathrm{Hz},$ 1H),5.24-5.15m1H),5.01-4.89m1H),4.49s2H) 4.29dd $J = 8.9$ $5.0~\\mathrm{Hz},$ 2H),4.19q $J = 5.6~\\mathrm{Hz},$ 1H3.77-3.56 m4H),3.52dd $J = 10.4$ $4.8~\\mathrm{Hz},$ 1H),3.28-3.19m3H3.01d $J = 11.6~\\mathrm{Hz},$ 2H),2.82-2.60m4H),2.46s3H),2.32-2.13m, 9H),2.11s,1H),2.04-1.92m4H),1.83-1.75m2H),1.75- 1.59m4H),1.49-1.35m5H),1.18-1.02m2H),0.95d $J =$ $6.6~\\mathrm{Hz},$ 3H),0.85-0.76m3H).LC-MS $(\\mathrm{ES + })$ .. $m / z$ 1122 $[\\mathbf{M}+$ $\\mathrm{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,346,482,755]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-1-((2R)-2-(3-(4-((4-(trans-3-((4-(3-(3-Amino-6-phenylpyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)methyl)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (28). A solution of intermediate 128 (40 mg, 0.067 mmol, 1.0 equiv), and intermediate 152 (57 mg, 0.108 mmol, 1.6 equiv) and NaOAc (16.5 mg, 0.201 mmol, 3.0 equiv) in DCM (0.2 mL) and MeOH (0.6 mL) was stirred at room temperature for 0.5 h. $\\mathrm{NaBH}_3\\mathrm{CN}$ (8.4 mg, 0.13 mmol, 1.9 equiv) was then added, and the reaction was stirred at room temperature for 1 h. After quenching by the addition of water (10 mL), the resulting mixture was extracted with EtOAc (20 mL × 3). The combined organic layers were dried over sodium sulfate, filtered, and the filtrate was concentrated under vacuum. The residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% $\\mathrm{NH}_4\\mathrm{HCO}_3$ ), 0 to 100%) to afford 32 mg of impure product as a white solid. This material was further purified by preparative HPLC [column: XSelect CSH Fluoro Phenyl $30 \\times 150$ mm², 5 μm; mobile phase A: water (10 mmol/L $\\mathrm{NH}_4\\mathrm{HCO}_3$ ), mobile phase B: CH₃CN; flow rate: 60 mL/min; gradient: 58 to 75% B over 11 min; wavelength: 254 nm; RT: 8.47 min] to afford the title compound (3.2 mg, 6.1% over two steps) as a white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 8.97 (d, $J = 1.4$ Hz, 1H), 8.39 (d, $J = 7.7$ Hz, 1H), 8.00–7.91 (m, 2H), 7.74 (d, $J = 5.9$ Hz, 1H), 7.49–7.32 (m, 6H), 7.34 (s, 1H), 7.25 (s, 1H), 6.54–6.46 (m, 1H), 6.14–6.06 (m, 2H), 5.71 (s, 2H), 5.22–5.13 (m, 1H), 5.09 (d, $J = 3.7$ Hz, 1H), 4.90 (t, $J = 7.2$ Hz, 1H), 4.47 (s, 2H), 4.34 (t, $J = 7.8$ Hz, 1H), 4.27 (s, 2H), 3.69 (d, $J = 7.2$ Hz, 1H), 3.65–3.46 (m, 3H), 3.40 (d, $J = 10.6$ Hz, 1H), 3.27–3.13 (m, 3H), 2.93 (d, $J = 11.4$ Hz, 2H), 2.80–2.59 (m, 4H), 2.44 (s, 3H), 2.35–2.22 (m, 4H), 2.21–2.02 (m, 5H), 2.01–1.87 (m, 5H), 1.80–1.51 (m, 6H), 1.48–1.32 (m, 5H), 1.16–0.99(m, 2H), 0.93 (d, $J = 6.4$ Hz, 3H), 0.87–0.73 (m, 3H). LC–MS $(\\mathrm{ES}+)$ : m/z 1106 $[\\mathbf{M} + \\mathbf{H}]^+$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,755,482,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methyl 2-(2-(2-methoxyethoxy)ethyl)-3-oxo-2,3-dihydroisoxazol-5-yl)-3-methylbutanoate (157). A solution of racemic intermediate 40 $(500\\mathrm{mg},2.51\\mathrm{mmol},1.0$ equiv), 1-bromo-2-(2-methoxyethoxy)ethane $(459\\mathrm{mg},2.51\\mathrm{mmol},1.0$ equiv), and $\\mathrm{K}_2\\mathrm{CO}_3$ $(1.04\\mathrm{g},7.53\\mathrm{mmol},3.0$ equiv) in DMF $(6\\mathrm{mL})$ was stirred at $60^{\\circ}\\mathrm{C}$ for $1\\textrm{h}$ The mixture was cooled to room temperature, and the solids were filtered off. The filtrate was directly purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.05\\% \\mathrm{NH_4HCO_3})$ 0 to $100\\%$ ) to afford the title compound $(612\\mathrm{mg},81\\%)$ as a yellow oil. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ DMSO- $d_{6})$ 6.23s1H4.29-4.23m 2H3.75-3.68m3H3.67s3H3.60-3.53m2H3.48- 3.41m2H)3.24s3H)2.37-2.23m1H)0.94d $J = 6.7~\\mathrm{Hz}$ 3H)0.85d $J = 6.7~\\mathrm{Hz}$ 3H.LC-MS $(\\mathrm{ES + })$ .. $m / z$ 302 $[\\mathbf{M} + \\mathbf{H}]^{+}$ .A small amount of the corresponding isoxazole $N$ -alkylation product (structure not shown) eluted ahead of compound 157 and was ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,71,915,135]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"isolated as a yellow oil (105 mg, 14%). ${}^{1}\\mathrm{H}$ NMR (400 MHz, DMSO- $d_{6}$ ) $\\delta$ 5.84 (s, 1H), 3.95 (t, $J = 5.4\\mathrm{~Hz}$ , 2H), 3.69 (s, 3H), 3.65-3.55 (m, 3H), 3.48 (dd, $J = 5.9$ , 3.7 Hz, 2H), 3.38 (dd, $J = 5.9$ , 3.6 Hz, 2H), 3.22 (s, 3H), 2.34-2.21 (m, 1H), 0.95 (d, $J = 6.7\\mathrm{~Hz}$ , 3H), 0.91 (d, $J = 6.8\\mathrm{~Hz}$ , 3H). LC-MS (ES+): $m/z$ 302 $[\\mathbf{M} + \\mathbf{H}]^{+}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,133,915,281]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2-(3-(2-(2-Methoxyethoxy)ethoxy)isoxazol-5-yl)-3-methylbutanoic acid (158). A solution of intermediate 157 $(300\\mathrm{mg},0.997$ mmol, 1.0 equiv) and LiOH $(47.7\\mathrm{mg},1.99\\mathrm{mmol},2.0$ equiv) in THF $(2.5~\\mathrm{mL})$ and water $(2.5~\\mathrm{mL})$ was stirred at room temperature for $2\\mathrm{h}$ The volatiles were then removed under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\mathrm{(CH_3CN}$ in water $(0.1\\%$ FA), 0 to $100\\%$ ) to afford the title compound $(251\\mathrm{mg},88\\%)$ as a colorless oil. ${}^{1}\\mathrm{H}$ NMR $(400\\mathrm{MHz}$ DMSO- $d_{6})$ 8 12.96s,1H)6.17s1H4.29-4.23m2H3.75- 3.69m2H)3.63-3.53m2H)3.50d $J = 8.6 \\mathrm{Hz}$ 1H)3.48- 3.42m2H)3.24s3H)2.34-2.21m1H)0.96d $J = 6.7 \\mathrm{Hz}$ 3H),0.85d $J = 6.7 \\mathrm{Hz}$ 3H.LC-MS $(\\mathrm{ES + })$ .. $m / z$ 288 $[\\mathbf{M} + \\mathbf{H}]^{+}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,281,915,712]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2S,4R)-4-Hydroxy-1-((R)-2-(3-(2-(2-methoxyethoxy)-ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (155). A solution of intermediate 158 (200 mg, 0.696 mmol, 1.0 equiv), intermediate 57 (HCl salt, 256 mg, 0.695 mmol, 1.0 equiv), DIEA (449 mg, 3.48 mmol, 5.0 equiv), and HATU (397 mg, 1.04 mmol, 1.5 equiv) in DMF (5 mL) was stirred at room temperature for 1 h. The crude mixture was directly purified by prepacked C18 column chromatography (CH $_3$ CN in water (0.05% NH $_4$ HCO $_3$ ), 0 to 100%) to afford 227 mg of a ~1:1 mixture of 155 and 156. This mixture was subsequently separated by preparative chiral HPLC [column: CHIRALPAK IA, $2 \\times 25~\\mathrm{cm}^2$ , 5 μm; mobile phase A: 3:1 hexane:DCM (0.5% 2 M NH $_3$ -MeOH), mobile phase B: EtOH; flow rate: 20 mL/min; gradient: isocratic 10% B; wavelength: 220/254 nm; RT1:5.65 min; RT2:9.19 min; sample solvent: EtOH; injection volume: 1.0 mL; number of runs: 6] to afford the title compound (slower peak, 86 mg, 21%) as a white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 9.00 (d, J = 2.4 Hz, 1H), 8.43 (d, J = 7.6 Hz, 1H), 7.45 (d, J = 8.3 Hz, 2H), 7.37 (d, J = 8.3 Hz, 2H), 6.11 (s, 1H), 5.10 (d, J = 3.7 Hz, 1H), 5.06–4.86 (m, 1H), 4.38 (t, J = 7.9 Hz, 1H), 4.32–4.19 (m, 3H), 3.76–3.61 (m, 4H), 3.57 (dd, J = 5.9, 3.5 Hz, 2H), 3.49–3.40 (m, 3H), 3.25 (s, 3H), 2.47 (d, J = 1.6 Hz, 3H), 2.27–2.16 (m, 1H), 2.09–1.88 (m, 1H), 1.85–1.70 (m, 1H), 1.50–1.31 (m, 3H), 0.96 (d, J = 6.3 Hz, 3H), 0.80 (d, J = 6.7 Hz, 3H). LC-MS (ES+): m/z 601 [M + H]+. The configuration of the isopropyl group was assigned based on the crystal structure shown in Figure S15. Compound 156 (faster peak, 52 mg, 13%) was also isolated as a white solid. ${}^{1}\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 9.03–8.88 (m, 1H), 8.33 (d, J = 7.8 Hz, 1H), 7.47–7.26 (m, 4H), 6.13 (d, J = 15.8 Hz, 1H), 5.11 (d, J = 3.6 Hz, 1H), 5.07–4.85 (m, 1H), 4.55–4.37 (m, 1H), 4.30–4.18 (m, 3H), 3.76 (d, J = 8.7 Hz, 1H), 3.72–3.64 (m, 2H), 3.60–3.38 (m, 6H), 3.23 (d, J = 5.0 Hz, 3H), 2.47 (d, J = 3.4 Hz, 3H), 2.35–2.20 (m, 1H), 2.19–1.97 (m, 1H), 1.97–1.70 (m, 1H), 1.46 (d, J = 6.9 Hz, 1H), 1.36 (d, J = 7.0 Hz, 2H), 1.00–0.69 (m, 6H). LC-MS (ES+): m/z 601 [M + H]+.\\n\\n ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,723,721,737]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ASSOCIATED CONTENT ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[515,741,708,755]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Supporting Information ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,756,915,785]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jmedchem.3c01781. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[551,788,915,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"BRM/BRG1 and VHL Alpha-LISA binding assay details, determination of BRM-10 crystal structure, cell-based assay descriptions, in vitro and in vivo DMPK assay protocols, SPR assay details, crystal structure determination of BRG1-VBC-17 ternary complex, descriptions of in vivo PK/PD and efficacy experiments, BRM $\\mathrm{DC}_{50}$ and $D_{\\mathrm{max}}$ values of more and less potent PROTAC diastereomers (separated via chiral methods), VHL crystal structure of compound 155, depictions of ${}^{1}\\mathrm{H}$ NMR and LC-MS characterization data for new compounds listed in Table 2 (PDF) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1309 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"47","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[118,75,481,103]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Molecular formula strings for new compounds listed in Table 2 (CSV) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,125,293,140]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"AUTHOR INFORMATION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[80,145,245,160]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Corresponding Authors ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[98,161,471,257]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Michael Berlin - Arvinas LLC, New Haven, Connecticut 06511, United States; Phone: 203-535-1456; Email: michael.berlin@arvinas.com \",\"Peter S. Dragovich - Genentech Inc., South San Francisco, California 94080, United States; $\\\\odot$ orcid.org/0000-0001-7372-2862; Phone: 650-467-6854; Email: dragovich.peter@gene.com \"]","page_idx":"48","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[80,266,138,280]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Authors ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[98,282,479,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Jennifer Cantley - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Mark Bookbinder - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Elizabeth Bortolon - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Fabio Broccatelli - Genentech Inc., South San Francisco, California 94080, United States \",\"Greg Cadelina - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Emily W. Chan - Genentech Inc., South San Francisco, California 94080, United States \",\"Huifen Chen - Genentech Inc., South San Francisco, California 94080, United States; $\\\\odot$ orcid.org/0000-0001-8273-9295 \",\"Xin Chen - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Yunxing Cheng - Pharmaron Beijing, Co. Ltd., Beijing 100176, P. R. China \",\"Tommy K. Cheung - Genentech Inc., South San Francisco, California 94080, United States \",\"Kim Davenport - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Dean DiNicola - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Debbie Gordon - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Brian D. Hamman - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Alicia Harbin - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Roy Haskell - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Mingtao He - Pharmaron Beijing, Co. Ltd., Beijing 100176, P.R.China \",\"Alison J. Hole - Evotec (U.K.) Ltd., Abingdon, Oxfordshire OX14 4RY, U.K. \",\"Thomas Januario - Genentech Inc., South San Francisco, California 94080, United States \",\"Philip S. Kerry - Evotec (U.K.) Ltd., Abingdon, Oxfordshire OX14 4RY, U.K. \",\"Stefan G. Koenig - Genentech Inc., South San Francisco, California 94080, United States; orcid.org/0000-0002-1878-614X \",\"Limei Li - Pharmaron Beijing, Co. Ltd., Beijing 100176, P. R. China \",\"Mark Merchant - Genentech Inc., South San Francisco, California 94080, United States \"]","page_idx":"48","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[532,71,914,525]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Inmaculada Pérez-Dorado - Evotec (U.K.) Ltd., Abingdon, Oxfordshire OX14 4RY, U.K. \",\"Jennifer Pizzano - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Connor Quinn - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Christopher M. Rose - Genentech Inc., South San Francisco, California 94080, United States; $\\\\text{©}$ orcid.org/0000-0002-7502-3368 \",\"Emma Rousseau - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Leofal Soto - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Leanna R. Staben - Genentech Inc., South San Francisco, California 94080, United States \",\"Hongming Sun - Pharmaron Beijing, Co. Ltd., Beijing 100176, P. R. China \",\"Qingping Tian - Genentech Inc., South San Francisco, California 94080, United States \",\"Jing Wang - Arvinas LLC, New Haven, Connecticut 06511, United States \",\"Weifeng Wang - Pharmaron Beijing, Co. Ltd., Beijing 100176, P. R. China \",\"Crystal S. Ye - Genentech Inc., South San Francisco, California 94080, United States \",\"Xiaofen Ye - Genentech Inc., South San Francisco, California 94080, United States \",\"Penghong Zhang - Pharmaron Beijing, Co. Ltd., Beijing 100176, P. R. China \",\"Yuhui Zhou - Genentech Inc., South San Francisco, California 94080, United States \",\"Robert Yauch - Genentech Inc., South San Francisco, California 94080, United States \"]","page_idx":"48","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[514,530,856,560]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Complete contact information is available at: https://pubs.acs.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,571,558,583]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Notes ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,586,853,600]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The authors declare no competing financial interest. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,613,711,627]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ACKNOWLEDGMENTS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,633,915,703]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The authors acknowledge the use of the Diamond Light Source and the Swiss Light Source for structural data collection and thank the staff for their support. They also thank Drs. James Kiefer and Yoana Dimitrova for many helpful discussions regarding the manuscript. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,715,716,730]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABBREVIATIONS USED ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,735,915,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"AcOH, acetic acid; Alpha-LISA, amplified luminescent proximity homogeneous assay-linked immunosorbent assay; Boc, tert-butyloxycarbonyl; BRM, Brahma homologue; BRG1, Brahma-related gene 1; Cbz, benzyloxycarbonyl; DCM, dichloromethane; DIAD, diisopropyl azodicarboxylate; DIEA, N,N-diisopropylethylamine; DMA, N,N-dimethylacetamide; DMAP, 4-dimethylaminopyridine; DME, dimethoxyethane; DMF, N,N-dimethylformamide; DMSO, dimethyl sulfoxide; EEDQ, N-ethoxycarbonyl-2-ethoxy-1,2-dihydroquinoline; EtOAc, ethyl acetate; EtOH, ethanol; FA, formic acid; HATU, 1-[bis(dimethylamino)methylene]-1H-1,2,3-triazolo[4,5-b]pyridinium 3-oxide hexafluorophosphate; HP-beta-CD, 2-hydroxypropyl- $\\beta$ -cyclodextrin; HPLC, high-performance liquid chromatography; IP, intraperitoneal; IV, intravenous; LC-MS, liquid chromatography-mass spectrometry; LDA, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,46,311,61]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[530,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[864,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[482,952,512,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1310 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,952,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"48","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[77,71,482,293]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"49","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"lithium diisopropylamide; MeOH, methanol; MOM, methoxymethyl; MTBE, methyl tert-butyl ether; NMP, $N$ -methyl-2-pyrrolidone; PEG, polyethylene glycol; PK/PD, pharmacokinetic-pharmacodynamic; PROTAC, proteolysis targeting chimera (PROTAC is a registered trademark of Arvinas Operations, Inc.); rt, room temperature; SFC, supercritical fluid chromatography; SMARCA2, SWI/SNF-related, matrix-associated, actin-dependent regulator of chromatin subfamily A member 2; SMARCA4, SWI/SNF-related, matrix-associated, actin-dependent regulator of chromatin subfamily A member 4; SPR, surface plasmon resonance; T3P, propanephosphonic acid anhydride; TEA, triethylamine; TEMPO, 2,2,6,6-tetramethylpiperidine-1-oxyl radical; TFA, trifluoroacetic acid; THF, tetrahydrofuran; TLC, thin-layer chromatography; VBC, VHL, elongin B, and elongin C complex; VHL, Von Hippel-Lindau tumor suppressor ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,307,207,322]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"49","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"REFERENCES ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[80,327,481,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(1) Wanior, M.; 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Rev. 2009, 109, 2551-2651. \"]","page_idx":"51","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[80,46,311,61]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"51","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Medicinal Chemistry ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[532,48,632,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"51","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pubs.acs.org/jmc ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,48,904,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"51","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[484,952,512,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"51","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1313 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[716,953,914,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"51","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1021/acs.jmedchem.3c01781 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[762,962,914,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"51","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Med.Chem.2024,67,1262-1313 ","text_format":null,"text_level":null,"type":"footer"}],"string":"[\n {\n \"bbox\": \"[79,135,915,203]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PROTACs Targeting BRM (SMARCA2) Afford Selective In Vivo Degradation over BRG1 (SMARCA4) and Are Active in BRG1 Mutant Xenograft Tumor Models \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,210,889,351]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Michael Berlin,\\\\* Jennifer Cantley, Mark Bookbinder, Elizabeth Bortolon, Fabio Broccatelli, Greg Cadelina, Emily W. Chan, Huifen Chen, Xin Chen, Yunxing Cheng, Tommy K. Cheung, Kim Davenport, Dean DiNicola, Debbie Gordon, Brian D. Hamman, Alicia Harbin, Roy Haskell, Mingtao He, Alison J. Hole, Thomas Januario, Philip S. Kerry, Stefan G. Koenig, Limei Li, Mark Merchant, Inmaculada Perez-Dorado, Jennifer Pizzano, Connor Quinn, Christopher M. Rose, Emma Rousseau, Leofal Soto, Leanna R. Staben, Hongming Sun, Qingping Tian, Jing Wang, Weifeng Wang, Crystal S. Ye, Xiaofen Ye, Penghong Zhang, Yuhui Zhou, Robert Yauch, and Peter S. Dragovich\\\\* \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,358,116,386]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/1023/495c0ee0ad5421084bfb3978d11d23294d8be1088b909fc24b192d01c5085d7a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[120,365,380,380]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Cite This: J. Med. Chem. 2024, 67, 1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,358,550,386]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0937/8e773d004368857f6e11eca166d679db032d9f05ec733678769f802cc6f411c7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[551,366,635,380]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Read Online \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": 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\"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Supporting Information \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[205,440,790,555]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/1015/c51e2c04935c0a2df39009ecc4523a27d18033f4de276e17d41f4166ca42b6fc.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,560,915,686]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABSTRACT: The identification of VHL-binding proteolysis targeting chimeras (PROTACs) that potently degrade the BRM protein (also known as SMARCA2) in SW1573 cell-based experiments is described. These molecules exhibit between 10- and 100-fold degradation selectivity for BRM over the closely related paralog protein BRG1 (SMARCA4). They also selectively impair the proliferation of the H1944 \\\"BRG1-mutant\\\" NSCLC cell line, which lacks functional BRG1 protein and is thus highly dependent on BRM for growth, relative to the wild-type Calu6 line. In vivo experiments performed with a subset of compounds identified PROTACs that potently and selectively degraded BRM in the Calu6 and/or the HCC2302 BRG1 mutant NSCLC xenograft models and also afforded antitumor efficacy in the latter system. Subsequent PK/PD analysis established a need to achieve strong BRM degradation ( $>95\\\\%$ ) in order to trigger meaningful antitumor activity in vivo. Intratumor quantitation of mRNA associated with two genes whose transcription was controlled by BRM (PLAU and KRT80) also supported this conclusion. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,713,230,727]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"INTRODUCTION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,733,481,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The SWI/SNF chromatin remodeling complexes were originally identified in yeast where they were observed to impact mating-type switch (SWI) and sucrose fermentation $(\\\\mathrm{SNF} = \\\\mathrm{succrose}$ nonfermenting) phenotypes. Since these initial discoveries, homologues of these multiprotein entities were characterized in many additional eukaryotic organisms suggesting a strong evolutionary conservation. In mammals, three SWI/SNF complexes have been identified to date: BAF (BRG1/BRM-associated factor; also known as SWI/SNF-A), PBAF (polybromo-associated BAF, also known as SWI/SNF-B), and, more recently, noncanonical BAF (ncBAF or GBAF). These complexes open tightly packed chromatin structures in cell nuclei to enable the binding of transcription factors and associated proteins and thereby initiate gene \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,713,915,830]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"expression. $^{1-4}$ They require the catalytic activity of an ATPase which is provided in a mutually exclusive manner by one of two protein subunits: BRM (Brahma homologue; also known as SWI/SNF-related, matrix-associated, actin-dependent regulator of chromatin subfamily A member 2 or SMARCA2) or BRG1 (Brahma-related gene 1; SMARCA4). $^{5}$ The remaining subunits present in each complex are selected from nearly 30 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,847,706,860]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received: September 25, 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,861,705,873]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Revised: November 25, 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,875,703,887]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Accepted: December 18, 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,888,682,901]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Published: January 5, 2024 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[843,841,914,918]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": 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null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1262 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,948,912,958]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,958,912,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": 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Chemical structures of representative known BRM/BRG1 ATPase inhibitors. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0333/aae9076928b4eb3db33a336b1c21342d8463f902a75466b27fbc9ecbc991d5c3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[199,238,388,378]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0362/3e771861e9294e18bf42d2ac3499dd5ddb470960fd4c2626e0827e1fc0c78fa6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[398,257,594,378]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0844/9d6dc49ea26b5b96fd5f3c6b16de03357bca1e7af1fa0984e3fccfecfb588f7f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[627,240,795,378]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0574/cf4b857d175daf053ffcd142e6d8ec0fa0f05ccc11f7c511488cf00e1e66152b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[327,385,680,621]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0873/11cf29a8961db8e213585fa992ac04252c3dfdd23f8b82bcc4151658661936d3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[220,627,789,760]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 2. Chemical structures of representative known BRM/BRG1 bromodomain binders and PROTACs. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0699/865b691555a38a2fd876439ed0d3b0067eaea6ea19f11ae1381b4ff8cda69122.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[79,792,479,822]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"possibilities with the final composition determining the precise biological role of each multicomponent entity. $^{1-4}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,822,482,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Alterations in mammalian SWI/SNF complexes have been characterized in multiple human cancers, and many efforts are currently underway to develop new therapies which exploit these potential vulnerabilities. $^{1-6}$ In particular, cancer cells which harbor homozygous loss-of-function mutations in the BRG1 protein are known to be highly dependent on BRM for their growth and proliferation. $^{7,8}$ These observations have spurred numerous endeavors to develop inhibitors of BRM \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,792,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ATPase activity. Accordingly, an optimized example which exhibited in vivo antitumor efficacy was previously disclosed (1, Figure 1), and another compound was recently advanced to Phase 1 clinical trials (2, Figure 1; for other examples of BRM/BRG1 ATPase inhibitors, see refs 10-13). However, genetic studies indicate that loss of BRG1 (or both BRM and BRG1) may be detrimental to the health of normal cells and tissues.[14-16] Consistent with these findings, preclinical dose-escalation of compound 1 and related molecules which potently inhibit both BRM and BRG1 ATPase activity in \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,313,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1263 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,71,479,98]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"mouse xenograft efficacy studies was limited by tolerability issues. $^{9,17}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,100,481,332]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As an alternate approach to targeting BRM for the treatment of BRG1 mutant cancers, we focused on the bromodomain present in the C-terminal region of the protein. Potent small molecule binders/inhibitors of many bromodomain-containing proteins have been identified in recent years, and some of these compounds have advanced into clinical-stage testing.[18,19] In the case of BRM, several distinct series of potent bromodomain-binding molecules have been reported in the literature by multiple research groups (compounds 3-5, Figure 2).[20-25] However, biological studies employing these compounds demonstrated that simply blocking the bromodomain present in BRM with a potent inhibitor did not afford meaningful antiproliferation effects in cell-based experiments.[26] In contrast, intracellular knock-down of the BRM protein via biological methods potently inhibited the growth and proliferation of BRM-dependent (BRG1 mutant) cancer cells.[26] \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,333,482,610]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Informed by these results, we sought to transform simple BRM bromodomain binders into chimeric entities that could simultaneously recognize an E3 ligase protein and thereby induce BRM degradation via ternary complex formation, BRM ubiquitination, and subsequent destruction via the cellular proteasome. Such heterobifunctional molecules are often termed PROTACs (proteolysis targeting chimeras), and they are becoming an increasingly important component of medicinal and biological chemistry research.[27-29] Several BRM-targeting PROTACs have been disclosed by others in the scientific literature (e.g., compounds 6 and 7, Figure 2),[30-32] and some of these molecules display good degradation selectivity for BRM over BRG1 and/or the potential for oral administration (for other examples of BRM/BRG1 degraders, see refs 33-41). In this report, we describe the initial findings from our own efforts to identify potent and selective chimeric BRM degraders which incorporate BRM bromodomain-binding moieties. These studies significantly expand on our earlier disclosure regarding the detailed biology associated with one of our degrader molecules.[42] \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,620,317,635]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"RESULTS AND DISCUSSION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,638,482,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We began our search for BRM-targeting PROTACs by first identifying several potent BRM bromodomain ligands that protruded away from the protein's surface in a variety of distinct conformations. We envisioned employing the solvent-exposed portion of these compounds for subsequent elaboration into the desired heterobifunctional degraders. As shown in Figure 3 and Table 1, the 3-amino-pyridazine-containing compound 8, which was originally discovered as part of a research collaboration between Genentech and Constellation Pharmaceuticals,[23,24] displayed potent binding affinity to both BRM and BRG1 in Alpha-LISA assessments employing the proteins' bromodomain regions and a biotinylated BRM/BRG1-binding probe (see Supporting Information for details). The near-equal affinities exhibited by 8 for both BRM and BRG1 were consistent with the high degree of amino acid conservation among the two proteins in the compound's binding region.[20] At this point in our research endeavors, we did not know whether PROTACs derived from ligands with similar BRM/BRG1 binding affinities could exhibit selective degradation of one protein relative to the other. Encouragingly, however, PROTACs constructed from a relatively promiscuous and nonselective kinase inhibitor \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,71,911,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 3. BRM/BRG1 binding ligands employed in this work (9 and 10) and reference ligand 8. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0681/70452455be3d2dac8c86e205bc16ab72ab31eeffddb272a28021ebb26dd3c4f4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[515,410,915,480]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0745/3ec78eed18a83c88d0406874cc82364723a530b87787ec817d471d96d4b03ba1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Cmpd</td><td>BRM IC50(nM)a</td><td>BRG1 IC50(nM)b</td><td>H1944 GI50(nM)c</td><td>Calu6 GI50(nM)d</td></tr><tr><td>8</td><td>18</td><td>16</td><td>>300</td><td>>300</td></tr><tr><td>9</td><td>1.2</td><td>3.3</td><td>>300</td><td>>300</td></tr><tr><td>10</td><td>2.7</td><td>2.8</td><td>ND</td><td>ND</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. BRM/BRG1 Binding Affinities and Antiproliferation Properties of Compounds 8-10 \\\"]\",\n \"table_footnote\": \"[\\\"${}^{a}$ BRM binding affinity (bromodomain protein fragment). ${}^{b}$ BRG1 binding affinity (bromodomain protein fragment). ${}^{c}$ H1944 antiproliferation activity (BRM-dependent cell line,time point = 7 days). ${}^{d}$ Calu6 antiproliferation activity (time point = 7 days). ND = not determined. See Supporting Information for additional details and discussion of error associated with each assay. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[510,583,915,665]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"scaffold were previously reported to exhibit selective kinase degradation in cell-based experiments.[43] Similarly, selective degradation of BRD4 over the related BRD2 and BRD3 entities was achieved by a chimeric degrader constructed from a ligand which nonselectively bound to the proteins' respective bromodomains.[44] \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,666,915,898]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Further exploration identified the 3,8-diazabicyclo[3.2.1]-octane-containing molecule 9 and the related analog 10 which both displayed improved BRM/BRG1 binding affinities relative to 8 (Figure 3, Table 1, Figure S1). The ability of 8 and 9 to impact the growth and proliferation of BRMDependent (BRG1 mutant) and non-BRM-dependent (BRG1 \\\"wild type\\\") cancers in vitro was respectively assessed using the H1944 and Calu6 cell lines (see Supporting Information for full details). As depicted in Table 1, none of these molecules afforded meaningful antiproliferation effects against either of these lines up to the highest tested concentration $(300\\\\mathrm{nM})$ These results were consistent with prior literature reports describing the inactivity of other potent BRM-bromodomainbinding compounds in related cell growth experiments (e.g., compound 2).26 They also reinforced our desire to impart BRM degradation properties to the depicted ligands in order to enhance their anticancer characteristics. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,900,914,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To guide transformation of the BRM-binding ligands into the desired heterobifunctional degraders, we obtained high-resolution crystal structures of compound 10 bound to the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1264 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[163,72,833,445]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 4. X-ray crystal structure of compound 10 bound to BRM. Compound 10 (pink): PDB code = 8QJT. Dashed green lines are hydrogen bonds observed between the ligand and the BRM protein. The pink arrow depicts the exit vector from the BRM binding pocket. Resolution = 2.57 Å. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0966/c55e2a7c976fbf0013559e37127d7fe0e2d35609891b63f5712d6dbfc0190cf8.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,503,481,658]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"BRM protein. As shown in Figure 4, the ligand formed key hydrogen bonds with the protein that included contacts between the phenol moiety and Tyr1421 as well as H-bonds between the amino-pyridazine fragment and the Asn1464 BRM residue. The 3,8-diazabicyclo[3.2.1]octane group appended to the amino-pyridazine core of the compound afforded a vector that extended away from the BRM protein surface and into solvent (Figure 4). We were therefore curious to learn whether ligand 10 could be elaborated into functionally active BRM degraders with biological potencies similar to those depicted by 6. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,660,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We began our exploration of novel BRM degrader PROTACs by tethering compound 10 via a polyethylene glycol (PEG) linker to a peptidomimetic ligand that was known to efficiently bind to the Von Hippel-Lindau (VHL) E3 ubiquitin ligase.45 As shown in Figure 5 and Table 2, the resulting heterobifunctional molecule (11) displayed potent and extensive $(>85\\\\%)$ degradation of the targeted BRM protein when assessed in SW1573 cells after a $22\\\\mathrm{h}$ incubation period (see Supporting Information for full details). Encouragingly, the molecule degraded the BRG1 protein with reduced potency relative to the effect on BRM in the same cell line, although significant protein loss was ultimately achieved at high concentrations (Table 2, cf., Figure S4). Interestingly, compound 11 displayed binding affinities for the BRM and BRG1 proteins that were 20-50-fold weaker than those exhibited by the bromodomain-binding ligands 9 and 10 (61 and $139\\\\mathrm{nM}$ , respectively; cf., Table 1). These differences may be due to the appended VHL ligand partially interfering with BRM/BRG1 recognition by the PROTAC and/or increased entropic penalties associated with the binding of 11 relative to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,503,915,560]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the simple bromodomain ligands. Similar BRM bromodomain affinity differences between a ligand/inhibitor and the corresponding PROTACs were noted by others during the identification of compound 6.[30] \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,560,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Replacement of the acetylated tert-butyl glycine moiety present in 11 with an isoxazole-containing fragment inspired by previously disclosed VHL-binding ligands significantly improved the BRM degradation activity of the resulting compound (12) relative to its precursor (11) (Figure 5, Table 2).46,47 Unfortunately, this improvement was also accompanied by a strengthening of BRG1 degradation activity which resulted in a poorer BRG1/BRM degradation selectivity ratio for compound 12 as compared to 11 (7.8 and 22, respectively; Table 2). Encouragingly, rigidification of the PEG linker contained in 12 by the introduction of a piperazine moiety afforded a new PROTAC (13) which improved both BRM degradation potency and BRG1 selectivity relative to 12 (Figure 5, Table 2). Compound 13 also potently impeded the growth of the H1944 BRM-dependent (BRG1 mutant) nonsmall cell lung cancer cell line in a 7-day in vitro antiproliferation experiment (Table 2; see Supporting Information for full details). Importantly, and consistent with its weakened degradation activity toward the BRG1 protein relative to BRM, compound 13 was $>10$ -fold less active in suppressing the growth of the non-BRM-dependent (BRG1 wild-type) Calu6 cell line compared to its H1944 potency (Table 2). These observations reassuringly indicated that the BRG1/BRM degradation selectivity measured in SW1573 cells could translate into differentiated antiproliferation effects in cancer cell lines bearing mutant or wild-type forms of the BRG1 protein. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[532,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1265 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[222,70,774,205]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0115/e33a8e37d443f6edd95323639ab0947a35d41ac36d86193124a9df707d6b4220.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[222,236,775,383]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0004/77e7e0828ed51f2c2744988ed0efc4862c23b66a1f904cd8935ffed7e550d099.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[230,410,764,576]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 5. Structures of PROTACs 11-13. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0748/4b0cae74c26fc10595391c70a2eda3eed437f3b888c076c5a96e0dacab04075d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,611,482,811]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Having completed our initial identification of VHL-binding BRM/BRG1-degraders, we next turned to assessing and improving the in vivo pharmacokinetic properties of the PROTACs under study. The initial objective in this portion of our explorations was the identification of at least one in vivo tool compound that could be used to probe BRM-related biologies in PK/PD and/or efficacy experiments. At this juncture, we did not know which route of in vivo administration would be most appropriate for the compounds being evaluated (e.g., oral, intravenous, intraperitoneal, or subcutaneous). Accordingly, we sought to enhance the murine in vivo clearance and half-life properties of the PROTACs with the expectation that such improvements would benefit all of the possible administration routes under consideration. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,811,482,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As shown in Table 2, introduction of a benzylic (S)-methyl group into the PROTAC design significantly improved BRM/BRG1 binding, BRM degradation, and H1944 antiproliferation activity while maintaining degradation selectivity over BRG1 (compare 14 with 13; see also Figure S5). This modification has been successfully incorporated into many other VHL-based PROTAC compounds that are described in the scientific literature.[48,49] Compound 14 was highly labile in an in vitro mouse liver microsome stability assessment, and this \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,611,915,855]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"undesirable characteristic was not improved by simple methyl substitution of the central piperazine contained in the molecule (compounds 15 and 16). However, introduction of a linker derived from a trans-1,3-cyclobutane-diol fragment and simultaneous replacement of the piperazine moiety with a piperidine group afforded a new PROTAC (17) that maintained favorable BRM degradation activity and noticeably improved mouse microsome stability outcomes (Table 2). This compound also exhibited a relatively low (stable) in vivo clearance value and a moderate half-life when administered to mice via IV injection (Table 2). In vitro metabolite identification experiments performed with 17 using mouse hepatocytes determined that piperidine N-dealkylation was a major contributor to the compound's murine metabolism (Figure 6, 17a and 17b). Accordingly, we explored additional linker modifications which altered the piperidine moiety in an effort to further improve in vivo pharmacokinetic properties. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,855,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Incorporation of a piperazine group or a second piperidine moiety adjacent to the VHL-binding portion of 16 improved in vitro and/or in vivo DMPK characteristics (Table 2, 18 and 19). Reversing the orientation of the central piperidine present in the linker relative to its positioning in compound 18 provided a potent PROTAC with acceptable in vitro and/or in \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1266 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[296,91,698,215]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Table 2. Exploration of PROTAC In Vitro and In Vivo DMPK Properties \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0209/a93c2d174de61ddb8ae52e2e8a57ed5fa36d1f5c4b6c37585c9afa2602f12d8e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[189,220,805,685]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0011/f176c976a136dd1bd94495bf5e2a3e713bb9d7e58cbd262e999ccf0e5bb234c4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Cmpd</td><td>Linker</td><td>BRM DC50 (nM)a</td><td>BRG1 DC50 (nM)b</td><td>H1944 GI50 (nM)c</td><td>Calu6 GI50 (nM)d</td><td>MLM (ER)e</td><td>Mouse PPB (%)f</td><td>Mouse IV Cl (mL/min/kg)g</td><td>Mouse IV t1/2 (h)h</td></tr><tr><td>6</td><td>Figure 2</td><td>8.2</td><td>32</td><td>17</td><td>41</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td></tr><tr><td>11</td><td>Figure 5</td><td>32</td><td>703i</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td></tr><tr><td>12</td><td>Figure 5</td><td>0.76</td><td>5.9</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td><td>ND</td></tr><tr><td>13</td><td>Figure 5</td><td>0.39</td><td>9.5</td><td>3.6</td><td>62</td><td>0.65</td><td>98.5</td><td>ND</td><td>ND</td></tr><tr><td>14</td><td>OCHNCH2O-</td><td>0.068</td><td>1.5</td><td>0.17</td><td>7.0</td><td>0.72</td><td>98.4</td><td>ND</td><td>ND</td></tr><tr><td>15</td><td>OCHNCH2O-</td><td>0.055</td><td>0.71</td><td>0.26</td><td>12</td><td>0.83</td><td>98.5</td><td>ND</td><td>ND</td></tr><tr><td>16</td><td>OCHNCH2O-</td><td>0.11</td><td>2.7</td><td>0.72</td><td>38</td><td>0.83</td><td>ND</td><td>ND</td><td>ND</td></tr><tr><td>17</td><td>OCHNCH2O-</td><td>0.093</td><td>4.9</td><td>0.64</td><td>24</td><td>0.53</td><td>97.3</td><td>22</td><td>2.6</td></tr><tr><td>18</td><td>OCHNCH2O-</td><td>0.085</td><td>3.2</td><td>1.3</td><td>11</td><td>0.40</td><td>96.6</td><td>9.6</td><td>13</td></tr><tr><td>19</td><td>OCHNCH2O-</td><td>0.039</td><td>1.1</td><td>0.58</td><td>6.5</td><td>0.44</td><td>95.2</td><td>9.6</td><td>16</td></tr><tr><td>20</td><td>OCHNCH2O-</td><td>0.062</td><td>1.4</td><td>0.72</td><td>10</td><td>0.15</td><td>96.5</td><td>12</td><td>17</td></tr><tr><td>21</td><td>OCHNCH2O-</td><td>0.14</td><td>1.8</td><td>0.30</td><td>4.4</td><td>0.14</td><td>98.1</td><td>9.2</td><td>1.4</td></tr><tr><td>22</td><td>OCHNCH2O-</td><td>0.09</td><td>1.3</td><td>0.45</td><td>6.8</td><td>0.27</td><td>98.9</td><td>11</td><td>3.7</td></tr><tr><td>23</td><td>OCHNCH2O-</td><td>0.053</td><td>0.99</td><td>0.23</td><td>3.7</td><td>0.41</td><td>99.4</td><td>6.7</td><td>6.7</td></tr><tr><td>24</td><td>OCHNCH2O-</td><td>0.27</td><td>5.1</td><td>0.70</td><td>28</td><td>0.15</td><td>98.4</td><td>22</td><td>1.5</td></tr></table>\",\n \"table_caption\": \"[]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[77,690,915,780]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"${}^{a}$ BRM degradation potency (SW1573 cells,time point $= {22}\\\\mathrm{\\\\;h}$ ). ${}^{b}$ BRG1 degradation potency (SW1573 cells,time point $= {22}\\\\mathrm{\\\\;h}$ ). Extent of BRM and BRG1 degradation $\\\\left( {D}_{\\\\max }\\\\right) > {85}\\\\%$ unless otherwise indicated; see Table S4 for exact values. ${}^{c}$ H1944 antiproliferation activity (BRM-dependent cell line,time point $= 7$ days). ${}^{d}$ Calu6 antiproliferation activity (time point $= 7$ days). ${}^{e}$ In vitro mouse liver microsome stability [ER = extraction ratio; range $= 0$ (stable) to 1 (labile)]. ${}^{f}$ In vitro binding to mouse plasma proteins (number indicates % bound). ${}^{g}$ In vivo mouse clearance value determined following IV administration at $1\\\\mathrm{{mg}}/\\\\mathrm{{kg}}$ . ${}^{h}$ In vivo mouse half-life determined following IV administration at $1\\\\mathrm{{mg}}/\\\\mathrm{{kg}}$ . ${}^{i}{D}_{\\\\max } = {78}\\\\%$ . ND = not determined. See Supporting Information for discussion of experimental details and error associated with each assay. Literature compound 6 included for comparison purposes. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,795,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"vivo DMPK attributes (Table 2, 20). Combining a central piperazine moiety with other linker fragments identified during exploration of piperidine-containing molecules was also tolerated (22) as was a slight truncation of linker length (Table 2, 21 and 23). In addition, a heteroaromatic moiety could be introduced into the central region of the linker without significantly compromising BRM degradation and/or DMPK properties (compound 24). The propensity for the described PROTACs to bind to mouse plasma proteins was assessed for many of the molecules depicted in Table 2. All \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,795,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tested compounds displayed similar binding characteristics that ranged from 95.2 to $99.4\\\\%$ bound. In addition, the compounds which exhibited the longest in vivo half-lives typically contained strongly basic amines (calculated $\\\\mathrm{pK_a} > 8.5$ ; e.g., 18, 19, and 20). These structural attributes afforded relatively large volumes of distribution to these molecules ( $>1~\\\\mathrm{L / kg}$ ) which, when combined with their low in vivo clearances, resulted in the long half-lives. Additional discussion regarding the BRG1/BRM degradation and Calu6/H1944 antiproliferation selectiv \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1267 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[110,70,884,200]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 6. In vitro MetID assessment of compound 17 using mouse hepatocytes. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0696/74cdbcdf321be90eb091caf4e25d454c89712b3c9d50ef75f840344df70d3d47.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[80,252,915,328]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0195/ef1b565e59e1593e287c504eec41652026fa214e50da052106c518e946f95806.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=\\\"2\\\">Cmpd</td><td>Degradation</td><td colspan=\\\"3\\\">SPR Bromodomains Only</td><td colspan=\\\"3\\\">SPR Full-Length Proteins</td></tr><tr><td>BRG1/BRMa</td><td>BRMT1/2(s)b</td><td>BRGT1(t1/2)(s)c</td><td>BRG1/BRMd</td><td>BRMT1/2(s)e</td><td>BRGT1(t1/2)(s)e</td><td>BRG1/BRMe</td></tr><tr><td>14</td><td>22</td><td>6.0</td><td>2.0</td><td>0.33</td><td>ND</td><td>ND</td><td>ND</td></tr><tr><td>17</td><td>53</td><td>13.3</td><td>9.5</td><td>0.71</td><td>346</td><td>1174</td><td>3.4</td></tr><tr><td>19</td><td>28</td><td>4.0</td><td>9.0</td><td>2.25</td><td>462</td><td>1386</td><td>3</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 3. Half-Lives of Ternary Complexes Formed between Representative PROTACs and the VHL and BRM/BRG1 Proteins \\\"]\",\n \"table_footnote\": \"[\\\"${}^{a}$ Ratio of BRG1 and BRM degradation ${\\\\\\\\mathrm{{DC}}}_{50}$ values (determined in SW1573 cells and depicted in Table 2). ${}^{b}$ SPR half-lives of BRM/PROTAC/ VHL ternary complex determined using bromodomain fragment. ${}^{c}$ SPR half-lives of BRG1/PROTAC/VHL ternary complex determined using bromodomain fragment. ${}^{d}$ Ratio of BRG1/BRM ternary complex half-lives (bromodomain fragments). ${}^{e}$ Ternary complex half-lives and ratios determined using full length BRM or BRG1 proteins. ND = not determined. See Supporting Information for discussion of experimental details and error associated with each assay. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[222,411,775,797]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 7. BRG1/BRM degradation potencies $\\\\\\\\left(\\\\\\\\mathrm{DC}_{50}\\\\\\\\right.$ values) and Calu6/H1944 antiproliferation selectivity ratios of compounds described in Table 2. BRM and BRG1 degradation activity was measured in SW1573 cells (time point $= 22\\\\\\\\mathrm{h}$ ). Extent of BRM and BRG1 degradation $\\\\\\\\left(D_{\\\\\\\\max}\\\\\\\\right) > 85\\\\\\\\%$ for all compounds (see Table 2 legend for one exception). The Calu6/H1944 $\\\\\\\\mathrm{GI}_{50}$ ratio is a unitless parameter. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0807/bc967128dad3f3ca2d8a21a2f64632090012f57ee9cce812d8810a4f57690f94.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[79,855,481,882]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ities of the Table 3 compounds is provided below (cf., Figure 7). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,883,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The BRM and BRG1 degradation $\\\\mathrm{DC}_{50}$ values for the compounds shown in Table 2 are graphically depicted in Figure 7 along with the associated ratios of Calu6 and H1944 antiproliferation potencies. As described in the Table 2 legend, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,855,917,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"nearly all of the molecules afforded extensive BRM and BRG1 degradation outcomes ( $D_{\\\\mathrm{max}}$ values $>85\\\\%$ ; see Table S4 for exact values). As can be seen in this illustration, the compounds clustered within a relatively narrow range of BRG1/BRM degradation selectivity (10 to 100-fold) and BRM degradation potency ( $\\\\mathrm{DC}_{50} = 0.03$ to $0.55 \\\\mathrm{nM}$ ). Compounds \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,61]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1268 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,72,482,457]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"which resided at the extremes of these ranges were likely differentiated from each other, but those closer to the range medians were not easily distinguished on account of experimental error (even with the multireplicate testing that was typically employed in their characterizations; see Supporting Information for additional discussion). A partial correlation was observed between BRG1/BRM degradation and Calu6/H1944 selectivity ratios (Figure 7, higher on $y$ -axis = more likely to be green versus yellow). However, the relationship was not absolute, and several exceptions were noted in the Figure 7 depiction (e.g., compounds 14, 15, and 18). We do not currently understand the scientific reasons which underlie these selectivity ratio variations. However, they may involve different BRM, BRG1, and/or VHL protein expression levels in the Calu6 and/or H1944 cells employed in the antiproliferation assessments relative to those present in the SW1573 line used for the degradation assay. The time points associated with the two types of biological profilings were also dramatically different: $22\\\\mathrm{h}$ for the degradation assessments and 7 days for the antiproliferation readouts. In addition, the BRG1/BRM half-lives likely did not influence the described outcomes as they were shown by others to be similar across a range of different cell lines.[50] Given these uncertainties, we advanced compounds which exhibited either promising BRG1/BRM degradation or Calu6/H1944 antiproliferation selectivity (sometimes both) into in vivo PK/PD experiments to better define the in vitro to in vivo translation of these parameters. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,458,482,761]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As is now relatively common in PROTAC-related research, we employed surface plasmon resonance (SPR) biophysical methods to characterize the ternary complexes formed between representative chimeric degraders from Table 2 and the VHL and BRM/BRG1 proteins. Encouragingly, these assessments could readily detect the association of the expected three-component entities when representative examples of the PROTACs under study were tested using the bromodomain fragments of either the BRM or BRG1 proteins (Table 3). However, in contrast to prior literature reports involving BRD4-targeting PROTACs,[51,52] the stabilities of these ternary complexes did not correlate strongly with the corresponding PROTAC degradation activities. As a result, the BRG1/BRM selectivity ratios determined by the ability of the tested PROTACs to form stable (long-lived) ternary complexes with the two proteins did not match well with the BRG1/BRM degradation selectivities measured in the SW1573 cell-based assessments (Table 3). Expanding the SPR-based biophysical half-life characterizations to include full-length BRM and BRG1 proteins did not improve these correlations, although only a relatively small number of PROTACs was assessed via these methods (Table 3, Figures S6 and S7). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,762,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In an alternative approach to characterizing ternary complex formation, we examined the affinities of selected PROTAC molecules for the VHL protein by SPR alone and following precomplexation with BRM or BRG1. Similar to the half-life determinations described above, both BRM/BRG1 bromodomain fragments and full-length proteins were employed in these assessments. In general, these experiments revealed similar or weaker (negative cooperativity) VHL affinities for the bromodomain-PROTAC complexes relative to those determined for the isolated degraders (Table S2). In contrast, stronger (positive cooperativity) VHL binding was generally observed for the same compounds when the assessments were performed using the full-length BRM/BRG1 proteins (Table \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,306]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S2). Similar positive cooperativity behavior was noted by others during the biological profiling of the related BRM/BRG1 degrader 6.30 Unfortunately, the ratios of VHL affinities determined for the BRG1 and BRM PROTAC complexes in these studies did not correlate well with the measured BRG1/BRM degradation selectivities for the isolated compounds determined in SW1573 cells (Table S2). This lack of correlation, as well as the related outcomes in the half-life experiments described above, may be due to an incorrect representation of the BRM/BRG1 proteins in the biophysical assessments relative to the intracellular environment. In particular, it is currently unknown which (if any) BAF complex members are associated with BRM and/or BRG1 when the proteins are engaged intracellularly by the described PROTAC molecules. An alternate possibility involves significantly different ubiquitin transfer rates being associated with the various ternary complexes once they are formed. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,307,915,665]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We also obtained crystal structures of the ternary complexes formed between the chimeric degraders under study and the VHL and BRM or BRG1 proteins. These experiments were conducted using the BRM/BRG1 bromodomain fragments, and both proteins were separately assessed in crystallization studies to increase the likelihood of obtaining crystals and determining structures. These activities successfully afforded multiple structures of various PROTACs bound to both VHL and either BRM or BRG1 from purified ternary complexes. However, few contacts between the proteins were observed in these structures, possibly due to the transient nature of any such interactions that could be disrupted during crystal formation. Figure S8 depicts the solved ternary complex structure formed between VHL, compound 17, and BRG1 and is a good representation of the other examples that were obtained. The described difficulty in obtaining ternary structures which illuminate close contacts between VHL and BRM or BRG1 may be due to the nature of the PROTACs we employed in the experiments (i.e., the compounds contain long and rather rigid linkers). Others have described ternary complexes formed between BRM, VHL, and PROTACs related to compounds 6 and 7 in which the two proteins do closely associate.[30,31] The alternate attachment location of the PROTAC linker to the VHL-binding fragment in compounds 6 and 7 relative to the molecules described in this work may have contributed to the disparate structural outcomes. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,665,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We next progressed promising PROTACs into single-administration in vivo PK/PD experiments in xenograft bearing mice so as to better understand (1) the drivers of in vivo BRM degradation and BRG1 selectivity and (2) the relationships between the various in vitro and in vivo biological parameters under study. We began this phase of our endeavors by employing intraperitoneal (IP) dosing to deliver the assessed compounds. We selected a diverse panel of molecules for such testing that were purposefully chosen to span a range of BRM degradation potencies, BRG1/BRM degradation selectivities, H1944 antiproliferation potencies, Calu6/H1944 antiproliferation selectivities, and stabilities toward mouse liver microsomes. In addition, Calu6 tumors (BRG1 wild-type) were utilized for these initial PK/PD experiments. Although these cancers were not dependent on BRM activity for growth, their use enabled intratumor degradation measurements of both the BRM and BRG1 proteins and thereby facilitated assessment of in vivo BRG1/BRM degradation selectivity outcomes. In contrast, a functional version of the BRG1 protein would presumably be absent in a BRM-dependent xenograft model \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[532,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[484,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1269 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[227,73,769,448]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 8. In vivo BRM and BRG1 degradation observed for selected PROTACs in Calu6 tumors following single IP administration (dose = 10 mg/kg). BRM and BRG1 degradation was measured in Calu6 tumors (time point = 24 h). Compound plasma concentrations were measured at the 24 h time point; [Plasma]/BRM $\\\\\\\\mathrm{DC}_{50}$ ratios were subsequently calculated using $\\\\\\\\mathrm{DC}_{50}$ data contained in Table 2 (unitless parameter) and are uncorrected for protein binding effects. BRG1 $\\\\\\\\mathrm{DC}_{50}$ /BRM $\\\\\\\\mathrm{DC}_{50}$ ratios were calculated from the $\\\\\\\\mathrm{DC}_{50}$ data contained in Table 2 (unitless parameter). Numbers associated with symbols refer to compounds from Table 2. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0479/f519499598e97dfd6ff1a803b98d0dc1128bc17925dab0c446d7844a3e3e8450.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[80,565,914,680]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0054/dc4419c69743bfcc2205e0b8759cc479cdfd0b3cd1528d5625388ab0d181ae86.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Cmpd</td><td>BRM DC50 (nM)a</td><td>BRG1 DC50/BRM DC50b</td><td>BRM deg. (%)c</td><td>BRG1 deg. (%)d</td><td>[Plasma] (nM)e</td><td>[Plasma]/BRM DC50f</td></tr><tr><td>15</td><td>0.055</td><td>13</td><td>64 ± 14</td><td>14 ± 11</td><td>22 ± 2.1</td><td>400</td></tr><tr><td>16</td><td>0.11</td><td>25</td><td>46 ± 5.5</td><td>0 ± 11</td><td>ND</td><td>NA</td></tr><tr><td>17</td><td>0.093</td><td>53</td><td>83 ± 9.8</td><td>27 ± 23</td><td>26 ± 6.5</td><td>280</td></tr><tr><td>18</td><td>0.085</td><td>38</td><td>81 ± 15</td><td>ND</td><td>108 ± 10</td><td>1270</td></tr><tr><td>19</td><td>0.039</td><td>28</td><td>87 ± 8</td><td>0 ± 17</td><td>71 ± 14</td><td>1820</td></tr><tr><td>21</td><td>0.14</td><td>13</td><td>67 ± 23</td><td>30 ± 28</td><td>112 ± 31</td><td>800</td></tr><tr><td>24</td><td>0.27</td><td>19</td><td>95 ± 2.5</td><td>49 ± 13</td><td>129 ± 65</td><td>478</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 4. In Vivo BRM and BRG1 Degradation Observed for Selected PROTACs in Calu6 Tumors Following Single IP Administration (Dose = 10 mg/kg) \\\"]\",\n \"table_footnote\": \"[\\\"${}^{a}$ BRM degradation measured in SW1573 cells (Table 2). ${}^{b}$ Ratio of BRG1 and BRM degradation ${\\\\\\\\mathrm{{DC}}}_{50}$ values measured in SW1573 cells and calculated from data contained in Table 2. ${}^{c}$ BRM degradation measured in Calu6 tumors (time point $= {24}\\\\\\\\mathrm{\\\\\\\\;h}$ ). ${}^{d}$ BRG1 degradation measured in Calu6 tumors (time point $= {24}\\\\\\\\mathrm{\\\\\\\\;h}$ ). ${}^{e}$ Compound plasma concentration measured at the ${24}\\\\\\\\mathrm{\\\\\\\\;h}$ time point. ${}^{f}$ [Plasma]/BRM ${\\\\\\\\mathrm{{DC}}}_{50}$ ratio calculated using BRM ${\\\\\\\\mathrm{{DC}}}_{50}$ data (unitless parameter). ND = not determined. NA = not applicable. Reported error = standard deviation. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[79,745,479,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(see below for alternate BRG1 quantitation methods that were employed in such situations). To simplify comparisons among the tested compounds, all PROTACs were administered in solution at a fixed dose of $10\\\\mathrm{mg / kg}$ using a formulation composed of $10\\\\%$ EtOH, $10\\\\%$ DMSO, $20\\\\%$ Solutol/Kolliphor HS15 in $60\\\\%$ $10\\\\mathrm{mM}$ , $\\\\mathrm{pH}5$ , citrate buffer. BRM and BRG1 protein levels were subsequently quantitated in the tumors 24 h following the administration of each test molecule, and compound plasma concentrations in the mice were also measured at the same time point. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,885,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The collective PK/PD data obtained from the above experiments are depicted in Figure 8 and Table 4. As evident in the tabulated results and somewhat anticipated given the in vivo nature of the studies, considerable variability was observed \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,745,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"in the quantitation of both BRM and BRG1 protein levels during these assessments. Based on these observations, we defined a $>30\\\\%$ reduction in measured protein levels as significant enough to impact conclusions regarding the performance of a given molecule, and this cutoff is depicted for BRG1 degradation in Figure 8 as a dotted blue line. In addition, we were aware of literature reports suggesting that near-complete BRM degradation might be required to obtain favorable outcomes in our planned antitumor efficacy experiments.[53] We therefore sought to identify compounds which afforded $>80\\\\%$ BRM degradation in these screening studies (vertical pink line in Figure 8) with the expectation that such protein suppression could be maintained long-term via once-daily administrations if needed. Since we wanted to progress \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[532,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1270 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[140,71,472,265]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0394/45744e5f78e5c79183302badb2910d05be77f40818622784a0d4ec23c3452405.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[518,71,859,266]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 9. In vivo efficacy study employing compound 17 in the HCC2302 BRM-dependent xenograft model. A = tumor volumes; B = body weight changes. Compound 17 was administered once daily via IP injection on days 0 through 11. See Figure S11 for significance analysis. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0757/bbe3710ecff19c098ecfe51dc73018f662066575f0827f48b006e05734e38d7d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[294,335,700,458]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0993/13810b9e96d60dee7a6a3483c5d5edaa4e32e06a7481e0e961704000e32a303b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[192,462,803,608]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0239/a5e17999b40d602cce296e45b3d2f8fbfe518d5ab6f4f6131e380063918c04c7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Cmpd</td><td>Linker</td><td>R1</td><td>R2</td><td>BRM Kd (nM)a</td><td>BRG1 Kd (nM)b</td><td>VHL Kd (nM)c</td><td>BRM DC50 (nM)d</td><td>BRG1 DC50 (nM)e</td><td>H1944 GI50 (nM)f</td></tr><tr><td>17</td><td>O=O, O=OCH2N=O-</td><td>OH</td><td>(R)-OH</td><td>72</td><td>108</td><td>3.4</td><td>0.093</td><td>4.9</td><td>0.64</td></tr><tr><td>25</td><td>same as above</td><td>OH</td><td>(S)-OH</td><td>ND</td><td>ND</td><td>~4700</td><td>>30</td><td>>300</td><td>>300</td></tr><tr><td>26</td><td>same as above</td><td>H</td><td>(R)-OH</td><td>10280</td><td>12620</td><td>ND</td><td>>5000</td><td>>5000</td><td>>5000</td></tr><tr><td>19</td><td>O=O, O=OCH2N=O</td><td>OH</td><td>(R)-OH</td><td>93</td><td>65</td><td>350</td><td>0.039</td><td>1.1</td><td>0.58</td></tr><tr><td>27</td><td>same as above</td><td>OH</td><td>(S)-OH</td><td>ND</td><td>ND</td><td>~4000</td><td>>30</td><td>>300</td><td>>300</td></tr><tr><td>28</td><td>same as above</td><td>H</td><td>(R)-OH</td><td>8540</td><td>5220</td><td>ND</td><td>>5000</td><td>>5000</td><td>>5000</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 5. Inactive Control PROTACs Employed in Mouse Tolerability Assessments \\\"]\",\n \"table_footnote\": \"[\\\"${}^{a}$ BRM binding affinity (bromodomain protein fragment). ${}^{b}$ BRG1 binding affinity (bromodomain protein fragment). ${}^{c}$ VHL binding affinity. ${}^{d}$ BRM degradation potency (SW1573 cells, time point = 22 h). ${}^{e}$ BRG1 degradation potency (SW1573 cells, time point = 22 h). ${}^{f}$ H1944 antiproliferation activity (BRM-dependent cell line, time point = 7 days). ND = not determined. See Supporting Information for discussion of error associated with each assay. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[77,681,481,797]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"molecules with relatively high in vivo BRG1/BRM degradation selectivities into multiadministration efficacy studies, we targeted a $< 40\\\\%$ BRG1 degradation outcome in the PK/PD assessment as an additional PROTAC attribute required for such advancement (horizontal pink line in Figure 8). Importantly, all compounds were well-tolerated in these single-administration experiments with minimal impacts observed on animal body-weights and general health. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,797,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As can be seen in the summarized information, several tested PROTACs exhibited meaningful BRM degradation in the Calu6 tumors with several exceeding our $>80\\\\%$ threshold (17, 18, 19, and 24). The majority of these molecules also afforded the desired $<40\\\\%$ BRG1 degradation levels (24 was the exception). Somewhat surprisingly, the extent of BRM degradation observed in the tumors did not correlate well with $24\\\\mathrm{h}$ compound plasma exposures that were normalized using the corresponding in vitro BRM degradation $\\\\mathrm{DC}_{50}$ values (Table 4; Figure 8, two yellow symbols afforded $>80\\\\%$ BRM \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,681,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"degradation). The [plasma]/BRM $\\\\mathrm{DC}_{50}$ ratios were not adjusted for compound interactions with mouse plasma proteins, but the similar binding behavior for all tested PROTACs suggested that such inclusion would not significantly alter the lack of correlation (cf., Table 2). We do not currently understand why stronger relationships were not observed between the normalized plasma exposures of the tested molecules and their in vivo BRM degradation outcomes. It was possible that the BRM degradation potencies varied somewhat between the SW1573 cell lines used for the in vitro assessments and the in vivo Calu6 tumor models and thereby skewed the analyses. Alternatively, measuring compound levels in the tumors as opposed to plasma might have afforded stronger correlations (see discussion of the IV-based PK/PD studies below for implementation of this approach). Reassuringly, however, the in vitro BRG1/BRM degradation selectivities measured in the SW1573 cells translated relatively well to the in vivo setting. Accordingly, the compounds that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1271 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[181,72,813,388]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 10. In vitro proteomics profiling of compound 17 in SW1573 cells. Each axis depicts the change in expression of a given protein in response to treatment with $100\\\\\\\\mathrm{nM}$ compound 17 relative to DMSO control (two independent replicates). Time point $= 8\\\\\\\\mathrm{h}$ . Negative values depict protein reductions, and outcomes which exceed $\\\\\\\\pm 1$ log2 fold-change are considered outside the error of the experiment. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0045/7a781240de51178983d3b3de2790120b05e17b7ce75e09948007328acd8d20ec.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,446,481,658]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"exhibited $>80\\\\%$ BRM degradation and $<40\\\\%$ BRG1 reductions in the Calu6 assessments also displayed relatively high in vitro BRG1/BRM ratios ( $>28$ , larger symbols in Figure 8, compounds 17 and 19; BRG1 degradation in Calu6 tumors was not measured for 18). Based on the collective PK/PD data, we selected compounds 17 and 19 to advance into multiadministration antitumor efficacy studies employing IP delivery. Both molecules afforded strong in vivo BRM degradation outcomes, and the former PROTAC exhibited one of the highest in vitro BRG1/BRM degradation ratios of the tested entities. In contrast, compound 19 displayed the highest [plasma]/BRM $\\\\mathrm{DC}_{50}$ ratio of the molecules depicted in Table 4. We were therefore curious to learn how these compounds with somewhat differing biological profiles would perform in multiadministration efficacy studies. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,660,481,898]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the subsequent experiments, compound 17 was administered via IP injection to mice bearing BRM-dependent (BRG1 mutant) HCC2302 xenografts once-daily at both 10 and $30\\\\mathrm{mg / kg}$ using a solution-based formulation. As shown in Figure 9A, both administration regimens afforded a minor impact on tumor growth relative to vehicle control over 11 days of continuous dosing (no dose-response was detected). Unfortunately, as shown in Figure 9B, extensive body weight loss was observed in the mice in response to these treatments. Such trends were partially reversed by additional feeding initiated on day 9 of the experiment, but all test animals ultimately died or were euthanized by day 13 due to their poor overall health. In addition, a separate pharmacokinetic assessment performed with compound 17 in nonxenograft-bearing mice afforded a relatively flat plasma exposure profile following IP dosing at $10\\\\mathrm{mg / kg}$ with minimal animal-to-animal variability (Figure S10). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,898,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In an effort to better understand the poor tolerability displayed by the relatively selective compound 17, we prepared the control molecules 25 and 26 (Table 5). The former entity \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,446,915,728]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"inverted the stereochemistry of the hydroxyl group present in the VHL-binding portion of 17 and thereby lost significant affinity for the VHL protein and corresponding BRM degradation properties (compare 25 with 17, Table 5). Compound 26 lacked the phenol moiety present in the BRM-binding portion of 17 and thus exhibited dramatically worsened BRM-binding and degradation characteristics relative to the latter molecule (compare 26 with 17, Table 5). Both 25 and 26 were well tolerated in mice bearing HCC2302 xenografts when administered once-daily via IP injections at $10\\\\mathrm{mg / kg}$ using the same solution-based formulation previously employed for 17. In each of these experiments, only $1 / 6$ mice exhibited $>10\\\\%$ body-weight loss during 15 days of continuous dosing, and all animals survived to day 15 (results similar to vehicle control; data not shown). Compound 17 was included in this follow-on experiment for side-by-side comparison purposes and again exhibited poor tolerability when administered IP once-daily at $10\\\\mathrm{mg / kg}$ (6/6 mice euthanized by day 15 due to poor condition; data not shown). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,730,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Collectively, these results indicated that the poor tolerability exhibited by compound 17 did not result from the molecule's physicochemical properties or from nondegradation-related off-target biological activities. To probe the degradation selectivity of the PROTAC, we performed in vitro proteomics experiments in SW1573 cells using a fixed compound concentration of $100\\\\mathrm{nM}$ and an $8\\\\mathrm{h}$ time point. As shown in Figure 10, these studies determined that 17 was a relatively selective degrader across the broad cellular proteome but that the molecule significantly impacted a few proteins in addition to BRM and BRG1 [e.g., PALS1, B4E2N5, PATJ, and smaller effects on MAPKAPK3, PLAU, and PBRM1; PLAU is known to be modulated by BRM (see below), and PBRM1 contains a bromodomain with high homology to that present in BRM/BRG1]. It was not obvious that reductions in these proteins \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[532,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1272 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,105,915,235]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0044/6641f4d4c6cbb6859a190ab6697bdaf247bf4ea37796250e0ab9658b2f4d9f61.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Cmpd</td><td>BRM DC50 (nM)a</td><td>BRG1 DC50/BRM DC50b</td><td>BRM deg. (%)c</td><td>BRG1 deg. (%)d</td><td>[Tumor] (ng/g)e</td><td>[Tumor]/BRM DC50f</td></tr><tr><td>15</td><td>0.055</td><td>13</td><td>0 ± 8</td><td>0 ± 16</td><td>76 ± 23</td><td>1380</td></tr><tr><td>17g</td><td>0.093</td><td>53</td><td>64 ± 10</td><td>4 ± 12</td><td>158 ± 33</td><td>1700</td></tr><tr><td>18</td><td>0.085</td><td>38</td><td>56 ± 23</td><td>28 ± 16</td><td>840 ± 1250</td><td>9880</td></tr><tr><td>19h</td><td>0.039</td><td>28</td><td>82 ± 3</td><td>22 ± 5</td><td>483 ± 175</td><td>12,380</td></tr><tr><td>20</td><td>0.062</td><td>23</td><td>95 ± 1.5</td><td>83 ± 12</td><td>ND</td><td>NA</td></tr><tr><td>21</td><td>0.14</td><td>13</td><td>70 ± 33</td><td>22 ± 28</td><td>175 ± 167</td><td>1250</td></tr><tr><td>22</td><td>0.09</td><td>14</td><td>87 ± 13</td><td>53 ± 14</td><td>75 ± 47</td><td>833</td></tr><tr><td>23</td><td>0.053</td><td>19</td><td>83 ± 5</td><td>59 ± 5</td><td>774 ± 400</td><td>14,600</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 6. In Vivo BRM and BRG1 Degradation Observed for Selected PROTACs in HCC2302 Tumors Following Single IV Administration (Dose = 20 mg/kg) \\\"]\",\n \"table_footnote\": \"[\\\"${}^{a}$ BRM degradation measured in SW1573 cells (Table 2). ${}^{b}$ Ratio of BRG1 and BRM degradation ${\\\\\\\\mathrm{{DC}}}_{50}$ values measured in SW1573 cells and calculated from data contained in Table 2. ${}^{c}$ BRM degradation measured in HCC2302 tumors (time point = 96 h). ${}^{d}$ BRG1 degradation measured in mouse stroma cells (time point = 96 h). ${}^{e}$ Compound tumor concentration measured at the ${96}\\\\\\\\mathrm{\\\\\\\\;h}$ time point. ${}^{f}$ [Tumor]/BRM ${\\\\\\\\mathrm{{DC}}}_{50}$ ratio calculated using BRM ${\\\\\\\\mathrm{{DC}}}_{50}$ data (units $= \\\\\\\\mathrm{{ng}}/\\\\\\\\mathrm{g}/\\\\\\\\mathrm{{nM}}$ ). ${}^{g}$ Dose $= {40}\\\\\\\\mathrm{{mg}}/\\\\\\\\mathrm{{kg}}$ . ${}^{h}$ Dose $= {10}\\\\\\\\mathrm{{mg}}/\\\\\\\\mathrm{{kg}}$ . ND $=$ not determined. NA $=$ not applicable. Reported error $=$ standard deviation. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[212,312,779,698]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 11. In vivo BRM degradation observed in HCC2302 tumors for selected PROTACs following single IV administration (dose = 20 mg/kg). BRM degradation was measured in HCC2302 tumors (time point = 96 h). BRG1 degradation was measured in mouse stromal cells (time point = 96 h). Compound tumor concentrations were measured at the 96 h time point; [Tumor]/BRM $\\\\\\\\mathrm{DC}_{50}$ ratios were subsequently calculated using $\\\\\\\\mathrm{DC}_{50}$ data contained in Table 2 (units = ng/g/nM) and are uncorrected for protein binding effects. BRG1 $\\\\\\\\mathrm{DC}_{50}$ /BRM $\\\\\\\\mathrm{DC}_{50}$ ratios were calculated from the $\\\\\\\\mathrm{DC}_{50}$ data contained in Table 2 (unitless parameter). Numbers associated with symbols refer to compounds from Table 2. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0024/5a1a815f6c0592d5dbd95005195dbc236ef109cd20477831522e167195717f50.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,785,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"would result in the poor short-term mouse tolerability outcomes, but we also cannot exclude such possibilities. Based on these observations, the most plausible explanation for the undesired compound 17 tolerability profile was that the IP administration route afforded high concentrations of the molecule in the intraperitoneal cavities and/or gastrointestinal tracts of the animals that produced robust degradation of both the BRM and BRG1 proteins. This hypothesis was consistent with literature reports indicating that BRG1 is required to maintain the intestinal epithelium in mice.[15,16] Our data also aligned with disclosures by others involving nonselective \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,785,915,827]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"BRM/BRG1 ATPase inhibitors which were similarly associated with mouse tolerability issues during oral dose-escalation in vivo studies (cf., compound 1, Figure 1).<sup>9,17</sup> \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,827,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To bolster our understanding, we also performed HCC2302 xenograft efficacy experiments with compound 19 employing once-daily IP administrations of $10\\\\mathrm{mg / kg}$ and a solution formulation ( $10\\\\%$ EtOH, $10\\\\%$ DMSO, $20\\\\%$ Solutol/Kolliphor HS15 in $60\\\\%$ $10~\\\\mathrm{mM}$ $\\\\mathsf{pH}5,$ citrate buffer). Once again, significant mouse body weight losses were noted in these studies along with deteriorations in the overall health of the animals. As a result, all animals (6/6 mice) either died or were \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[532,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1273 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,71,481,223]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"euthanized by day 7 of the experiment with minimal impact observed on the rate of HCC2302 tumor growth (data not shown). At this juncture, we did not believe that other apparently selective degraders from Table 4 and/or Figure 8 were likely to afford improved outcomes in IP-based, multiadministration xenograft efficacy. We therefore shifted our focus to delivering promising PROTACs via IV administration, which would avoid high compound concentrations in the intraperitoneal cavity, in an effort to achieve in vivo exposures sufficient to drive antitumor activity without triggering unwanted tolerability issues. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,225,479,610]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As was done for the IP-administered studies described above, we again selected a diverse panel of BRM degrader PROTACs for testing in IV-based PK/PD experiments. Since our animal welfare protocols dictated that a maximum of two IV injections could be administered to a given mouse during a one-week period, we primarily chose compounds that exhibited low in vivo mouse clearance values and/or long half-lives in earlier in vivo DMPK profiling (cf., Table 2). In addition, we conducted the IV-administered PK/PD assessments in BRM-dependent HCC2302 xenografted tumors to better align with subsequent efficacy experiments anticipated for the most promising compounds in that model. Since a functional version of the BRG1 protein was not present in the HCC2302 xenografts, we quantitated this entity in the murine stroma cells that were harvested alongside the tumors in this phase of our studies. Given the maximal twice-weekly IV-dosing frequency that could be employed in multiadministration efficacy studies, we measured BRM and BRG1 protein levels $96\\\\mathrm{h}$ after each compound was dosed in the PK/PD experiments. To facilitate comparisons among the different tested PROTACs, all molecules were administered using a solution formulation (10% 2-hydroxypropyl-beta-cyclodextrin, $40~\\\\mathrm{mM}$ sodium acetate, $40~\\\\mathrm{mMNaCl}$ in $\\\\mathsf{pH}4.5$ water) with the majority dosed at $20\\\\mathrm{mg / kg}$ (a few exceptions are noted below). As the $96\\\\mathrm{h}$ mouse plasma concentrations of the assessed molecules were anticipated to be very low, we instead quantitated the amounts of each compound present in the HCC2302 tumors at this time point. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,610,479,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The collective data from this round of PK/PD studies are depicted in Table 6 and Figure 11. As can be seen in the plotted results, several tested PROTACs afforded strong $(>80\\\\%)$ BRM degradation in the HCC2302 tumors $96\\\\mathrm{h}$ after their initial IV administrations. The extent of BRM degradation observed in these studies correlated reasonably well with the amount of test compound detected in the tumors at the $96\\\\mathrm{h}$ time point normalized by in vitro BRM degradation potency (color coding in Figure 11, green symbols afford stronger in vivo BRM degradation relative to other colors; compound 22 was an exception). In addition, the BRG1/BRM degradation selectivity measured in the SW1573 cell based assessments also correlated relatively well with in vivo selectivity (larger symbols typically lower on y-axis in Figure 11). As was the case with the single-administration IP-based PK/PD experiments described above, all compounds tested in this phase of our research were well-tolerated with minimal impacts observed on animal body-weights and general health. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,860,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Since compound 19 was the only example among the molecules depicted in Figure 11 that met our desired in vivo BRM and BRG1 degradation criteria, it was selected for profiling in multiadministration efficacy studies. Accordingly, the degrader was administered twice-per-week (on days 4 and 7) to mice bearing HCC2302 BRM-dependent xenografts via \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,142]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IV injection at $20\\\\mathrm{mg / kg}$ using the same solution formulation employed for the IV-based PK/PD studies described above. During the majority of the assessment period, this regimen afforded significant tumor growth inhibition with generally acceptable mouse body weight loss (Figures 12 and S13). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[520,155,911,400]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 12. In vivo efficacy study employing compound 19 in the HCC2302 BRM-dependent xenograft model. Compound 19 was administered twice-per-week via IV injection on days 0 through 21. See Figure S12 for significance analysis. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0839/eaddf29feadd7850059a8e79ef659fbe803f552d96712c87a15838f46a64514b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[512,473,915,857]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, weight loss reached concerning levels on day 18, and nutritional supplementation was therefore initiated. In spite of these interventions, $2/10$ mice involved in the study were found dead on day 21, and the experiment was concluded on day 22 due to the deteriorating condition of the remaining animals. The control compounds 27 and 28 (Table 5) which respectively attenuated VHL and BRM binding affinity relative to 19 and thereby lost significant BRM degradation potency were also examined in mice bearing HCC2302 xenografts (the origin of the relatively weak VHL affinity displayed by 19 compared to PROTAC 17 is not currently understood). Twice-weekly IV administration of both compounds at $20\\\\mathrm{mg}/$ kg over a 21 day period using the same formulation employed for 19 was well-tolerated with $0/6$ mice associated with each molecule exhibiting $>10\\\\%$ body weight loss (results similar to vehicle; data not shown). These outcomes collectively suggested that, despite the favorable in vivo BRG1/BRM selectivity displayed by 19 in the IV-based single-administration PK/PD studies above, concentrations of the compound likely reached sufficient levels in certain (sensitive) mouse tissues which degraded both proteins during the latter phase of the repeat-administration efficacy experiments. Importantly, broad-spectrum proteomics studies performed with 19 in SW1573 cells indicated that the compound was a highly selective degrader which only impacted BRM, BRG1, and PBRM1.42 These data supported our hypothesis that loss of both BRM and BRG1 contributed to the mouse tolerability issues observed with the molecule. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,858,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The preceding data highlighted a key challenge associated with the compounds described in this work which exhibited relatively high but finite in vitro BRG1/BRM degradation selectivity ratios. Such molecules needed to achieve in vivo exposures in multiadministration antitumor studies sufficient to produce strong BRM degradation outcomes and the desired \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[532,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1274 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[174,72,823,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 13. In vivo CD1 mouse PK profiles for compound 19 following IV administration at 10 and $30\\\\\\\\mathrm{mg / kg}$ $(n = 3)$ . \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0844/333ac16a92a62306938b2359fda13223d0f8225bb169c48960e4551bd96bd157.jpg\",\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[80,398,915,445]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0898/d37c4303bd17586ad4dc938ec026c12bdecc35fa2e97344666fbdc240ae799f5.jpg\",\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Dose (mg/kg)</td><td>Cl (mL/min/kg)a</td><td>Vss (L/kg)b</td><td>t1/2 (h)c</td><td>C0 (ng/mL)d</td><td>AUClast (h ng/mL)e</td></tr><tr><td>10</td><td>16 ± 4.0</td><td>6.3 ± 0.39</td><td>6.6 ± 1.1</td><td>12,630 ± 1700</td><td>10,160 ± 2600</td></tr><tr><td>30</td><td>15 ± 3.1</td><td>8.7 ± 2.0</td><td>8.9 ± 1.2</td><td>58,000 ± 28,400</td><td>30,850 ± 8650</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 7. In Vivo PK Parameters Obtained for Compound 19 Following IV Administration to CD1 Mice at 10 and ${30}\\\\\\\\mathrm{{mg}}/\\\\\\\\mathrm{{kg}}\\\\\\\\left( {n = 3}\\\\\\\\right)$ \\\"]\",\n \"table_footnote\": \"[\\\"${}^{a}$ In vivo clearance value. ${}^{b}$ In vivo volume of distribution. ${}^{c}$ In vivo half-life. ${}^{d}$ Initial in vivo plasma concentration. ${}^{e}$ In vivo exposure measured over ${24}\\\\\\\\mathrm{\\\\\\\\;h}$ time period. Formulation $= {10}\\\\\\\\%$ HP-beta-CD, ${40}\\\\\\\\mathrm{{mM}}\\\\\\\\mathrm{{NaOAc}}$ ,and ${40}\\\\\\\\mathrm{{mM}}\\\\\\\\mathrm{{NaCl}}$ in water pH 4.0. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[80,520,914,578]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0653/4d2abd1bbaf92ee4007b11f32136d44c0a2b9b59ae095187e64e6b88596cad6b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Dose (mg/kg)a</td><td>#admin.b</td><td>Time point (h)c</td><td>BRM deg. (%)d</td><td>BRG1 deg. (%)e</td><td>PLAU supp. (%)f</td><td>KTR80 supp. (%)g</td><td>Approx. TGI (%)h</td></tr><tr><td>10</td><td>7</td><td>24</td><td>81 ± 8</td><td>30 ± 20</td><td>91 ± 22</td><td>25 ± 27</td><td>1</td></tr><tr><td>20</td><td>7</td><td>24</td><td>99 ± 2</td><td>47 ± 16</td><td>98 ± 19</td><td>71 ± 27</td><td>62</td></tr><tr><td>30</td><td>3</td><td>96</td><td>97 ± 2</td><td>84 ± 6</td><td>97 ± 22</td><td>72 ± 25</td><td>(strong)i</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 8. Pharmacodynamic Effects Observed in HCC2302 Xenografts at the Conclusion of Efficacy Experiments Involving Compound 19 \\\"]\",\n \"table_footnote\": \"[\\\"${}^{a}$ Dose of 19 administered twice-weekly via IV injection. ${}^{b}$ Number of administrations prior to obtaining PD readouts. ${}^{c}$ Time after last compound administration before obtaining PD readouts. ${}^{d}$ BRM degradation measured in HCC2302 tumors. ${}^{e}$ BRG1 degradation measured in mouse stroma cells. ${}^{f}$ Suppression of PLAU mRNA transcript in HCC2302 tumors. ${}^{g}$ Suppression of KRT80 mRNA transcript in HCC2302 tumors. ${}^{h}$ Approximate tumor growth inhibition (TGI) observed at end of each study. ${}^{i}$ Tumor growth inhibition was strong (>65%) but was not quantitated due to poor tolerability. Reported error = standard deviation. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[77,656,482,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"anticancer efficacy without exceeding levels which simultaneously degraded BRG1 in sensitive animal tissues (see below for discussion regarding the amount of BRM degradation required to afford meaningful antitumor effects). Several additional efficacy studies conducted with 19 in mice bearing HCC2302 xenografts exemplified these challenges. Administering the compound twice-weekly IV at $10\\\\mathrm{mg / kg}$ was well-tolerated over 21 days but had no impact on tumor growth (tumors in the treatment group grew similar to vehicle control; data not shown). Similarly, increasing the IV dose of 19 to 30 $\\\\mathrm{mg / kg}$ twice-weekly afforded strong antitumor efficacy, but the regimen could not be sustained for more than 11 days due to poor tolerability (note: these studies were both performed before the $20\\\\mathrm{mg / kg}$ BIW IV experiment described above was conducted). Strikingly, the in vivo mouse PK profiles for compound 19 obtained following IV administration at 10 and $30\\\\mathrm{mg / kg}$ to nontumor-bearing mice illustrated that relatively small (within 3-fold) differences in $C_{\\\\mathrm{max}}$ and AUC values resulted in the disparate efficacy and tolerability outcomes (Figure 13, Table 7). Continued experimentation with 19 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,656,915,798]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(A947) ultimately determined that IV administration of the molecule at $40\\\\mathrm{mg / kg}$ once every other week provided the optimal balance between strong antitumor efficacy and acceptable tolerability (data not shown). The molecule was subsequently profiled in multiple additional in vivo biological studies employing that regimen, and these data, along with extensive in vitro characterizations of the compound (e.g., degradation potency via Western blot, degradation kinetics, and degradation mechanism of action), were recently communicated in a separate disclosure.[42] \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,800,915,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As part of the above efficacy experiments, we measured the degree of BRM and BRG1 degradation in the tumors at the end of each study period. Such assessments were typically performed $24\\\\mathrm{h}$ after the final dosing of the compound under study (i.e., measured on day 22 of a 21-day experiment following 7 IV administrations). An alternate time point was employed for degrader 19 dosed at $30~\\\\mathrm{mg / kg}$ on account of the poor tolerability that led to early study termination after only 3 injections. As shown in Table 8, strong $(>80\\\\%)$ BRM degradation was observed in all of these assessments. However, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1275 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,561,87]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 1. Preparation of Various Isoxazole-Containing Intermediates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,91,774,283]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0272/83fbeb646b739d7b7dd376ebfad2f18b86aacd2ad2de2ba66c3a4cf65bac26d5.jpg\",\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[314,321,719,540]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions $\\\\\\\\left( {\\\\\\\\mathrm{{Bn}} = {\\\\\\\\mathrm{{CH}}}_{2}\\\\\\\\mathrm{{Ph}}}\\\\\\\\right)$ : (a) ${\\\\\\\\mathrm{{KHCO}}}_{3},{10} : 1\\\\\\\\mathrm{{EtOAc}} : {\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O},\\\\\\\\mathrm{{rt}},{16}\\\\\\\\mathrm{\\\\\\\\;h},{98}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{b}\\\\\\\\right) {\\\\\\\\mathrm{{CrO}}}_{3},{6.0}\\\\\\\\mathrm{M}{\\\\\\\\mathrm{H}}_{2}{\\\\\\\\mathrm{{SO}}}_{4}$ ,acetone,0to ${25}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{12}\\\\\\\\mathrm{\\\\\\\\;h},{90}\\\\\\\\%$ ; (c) con. ${\\\\\\\\mathrm{H}}_{2}{\\\\\\\\mathrm{{SO}}}_{4}$ ,MeOH, ${70}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h},{65}\\\\\\\\%$ ; (d) t-BuOK, 2-Iodopropane,THF,0to ${25}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{16}\\\\\\\\mathrm{\\\\\\\\;h},{56}\\\\\\\\%$ ; (e) KOH,MeOH,reflux,4 h,66%; (f) ${\\\\\\\\mathrm{K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ , Benzyl bromide,NMP, ${60}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{4.5}\\\\\\\\mathrm{\\\\\\\\;h},{46}\\\\\\\\%$ ; (g) LDA, Dimethyl carbonate, $- {78}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},3\\\\\\\\mathrm{\\\\\\\\;h},{33}\\\\\\\\%$ ; (h) t-BuOK, 2-Iodopropane, 2:1 DMF:THF, ${20}^{ \\\\\\\\circ }\\\\\\\\mathrm{C}$ , ${12}\\\\\\\\mathrm{\\\\\\\\;h},{82}\\\\\\\\%$ ; (i) ${\\\\\\\\mathrm{{TiCl}}}_{4}$ ,DCM, ${25}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{13}\\\\\\\\mathrm{\\\\\\\\;h},{94}\\\\\\\\%$ ; (j) 2-Bromo-1,1-diethoxyethane, ${\\\\\\\\mathrm{K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,DMF, ${70}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},8\\\\\\\\mathrm{\\\\\\\\;h},{49}\\\\\\\\%$ ; (k) LiOH, MeOH, ${40}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h}$ . \\\"]\",\n \"img_path\": \"images/0006/ff8c50cc0dbf2b23fd046c50c54597c61f5fa1c47c5a5f6b7f7762bfcdcdd8ac.jpg\",\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,611,482,898]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"only experiments in which such BRM alterations exceeded $95\\\\%$ degradation were associated with tumor growth inhibition outcomes that meaningfully differentiated from vehicle control groups. These results were consistent with reports from others which suggested that near-complete loss of the BRM protein was required to impact the proliferation of BRM-dependent cell lines and tumors.[53] They also paralleled our own observations during the detailed in vitro and in vivo characterizations of compound 19 (A947) that were disclosed in a separate publication.[42] In addition, BRG1 protein levels in mouse stroma cells were monitored as part of the above experiments. The compound 19 dose which afforded the strongest BRG1 reductions was associated with the poorest tolerability results (Table 8, $30~\\\\mathrm{mg / kg}$ ). These data supported our desire to avoid strong degradation of both the BRM and BRG1 proteins so as to minimize unwanted impacts on noncancerous cells and tissues.[14-17] Given the small number of experiments, additional studies are required to fully define the relationships between BRM/BRG1 degradation and both efficacy and tolerability outcomes. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,898,482,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In addition to measuring the BRM and BRG1 protein levels, we also profiled PLAU and KRT80 mRNA transcripts in the end-of-study HCC2302 tumors to understand the impact of \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,611,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the tested compounds on BRM-related gene expression. We selected PLAU and KRT80 transcripts for this purpose as production of both entities was previously associated with BRM activity via our own research and by disclosures from others.[9,42] As shown in Table 8, both transcripts were significantly suppressed by treatment with degrader 19 with KRT80 mRNA levels providing the better means to differentiate the tested doses. Accordingly, $>70\\\\%$ suppression of the KRT80 transcript was required to obtain antitumor efficacy outcomes that meaningfully differed from vehicle control. Importantly, the association between alteration of a particular gene transcript and tumor growth inhibition is likely to be dependent on the specific tumor being studied, and these relationships need to be independently assessed and characterized for each individual situation. In addition, although the preceding experiments established a need to achieve strong BRM degradation $(>95\\\\%)$ to drive meaningful antitumor efficacy, they did not address the duration for which such alterations needed to be maintained. Additional experiments are therefore needed to better define the temporal relationships between BRM degradation and antitumor efficacy. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1276 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,72,561,87]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 2. Preparation of Various Isoazole-Containing Intermediates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[187,90,817,276]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0459/d40c4c15558f84975c5ab0f1dd79cfba6beac1287941e3be949a94123dbba3ea.jpg\",\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[177,305,799,468]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions ${\\\\\\\\left( \\\\\\\\mathrm{{Boc}} = \\\\\\\\mathrm{C}\\\\\\\\left( \\\\\\\\mathrm{O}\\\\\\\\right) \\\\\\\\mathrm{{OC}}{\\\\\\\\left( {\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\right) }_{3},\\\\\\\\mathrm{{Cbz}} = \\\\\\\\mathrm{C}\\\\\\\\left( \\\\\\\\mathrm{O}\\\\\\\\right) {\\\\\\\\mathrm{{OCH}}}_{2}\\\\\\\\mathrm{{Ph}}\\\\\\\\right) }$ : (a) Perfluorobutyl sulfonyl chloride, ${\\\\\\\\mathrm{K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3},{\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\mathrm{{CN}},2{5}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h},{90}\\\\\\\\%$ ; (b) tert-Butyl piperazine-1-carboxylate (44),DMF, ${130}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},4\\\\\\\\mathrm{\\\\\\\\;h},{35}\\\\\\\\%$ ; (c) LiOH,1:1 THF: ${\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O},\\\\\\\\mathrm{{rt}},1 - 2\\\\\\\\mathrm{\\\\\\\\;h},{70} - {99}\\\\\\\\%$ ; (d) ${4.0}\\\\\\\\mathrm{M}\\\\\\\\mathrm{{HCl}},1,4$ -dioxane, ${25}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h},{84}\\\\\\\\%$ ; (e) benzyl chloroformate, TEA, DCM, ${25}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{15}\\\\\\\\mathrm{\\\\\\\\;h},{44}\\\\\\\\%$ ; (f) Trimethoxymethane, $p$ -TsOH, ${25}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{2.0}\\\\\\\\mathrm{\\\\\\\\;h},{63}\\\\\\\\%$ ; (g) Pd/C, ${\\\\\\\\mathrm{H}}_{2}$ , THF, ${25}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{12}\\\\\\\\mathrm{\\\\\\\\;h},{85}\\\\\\\\%$ ; (h) Intermediate 43, DIEA, DMF, ${80}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{12}\\\\\\\\mathrm{\\\\\\\\;h},{26}\\\\\\\\%$ . \\\"]\",\n \"img_path\": \"images/0057/23fd6a075d14d7be2927dbd55db102ff53c0de8ceaac0c55afb0b790318c3041.jpg\",\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,537,482,745]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The compounds described in this work were prepared by a variety of related synthetic methods. The generation of several key intermediates is detailed below, and these descriptions also highlight numerous important commercially available building blocks that are widely utilized in subsequent syntheses. These preparations are then followed by the syntheses of the specific final compounds that were profiled in the biological assays described above. Salts of amine-containing products (including final PROTAC molecules) are typically not shown in the various synthetic schemes even though they may have been generated by the synthesis and/or purification conditions employed. All reagents and starting materials were derived from commercial sources unless otherwise indicated. The BRM-binding molecules 8-10 were synthesized using preparations derived from the literature.[23] \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,746,482,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 1 depicts the preparation of several isoxazole-containing intermediates in racemic form. Hydroxycarbonimidic dibromide (29) was condensed with but-3-yn-1-ol (30) at room temperature to give isoxazole 31. Jones oxidation and subsequent esterification under acidic conditions then afforded intermediate 33 (via carboxylic acid 32). Alkylation of this compound with 2-iodopropane provided racemic ester 34, and this entity was then transformed into carboxylic acid 35 via exposure to basic methanol at elevated temperature. Separately, 5-methylisoxazol-3-ol (36) was protected as the corresponding benzyl ether (37). This material was deprotonated with lithium diisopropylamide, and the resulting anion was condensed with dimethyl carbonate to give ester 38. Alkylation of this entity with 2- \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,537,915,635]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"iodopropane then afforded racemic intermediate 39, and the benzyl moiety present in this material was subsequently removed via treatment with titanium tetrachloride to give ester 40. Alkylation of this intermediate with 2-bromo-1,1-diethoxyethane generated acetal 41, and the ester contained in this entity was subsequently hydrolyzed under basic conditions to give carboxylic acid 42. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,635,915,871]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The preparation of several additional racemic isoxazole-containing intermediates is shown in Scheme 2. Ester 40 (Scheme 1) was condensed with perfluorobutyl sulfonyl chloride to give compound 43. This entity was coupled with tert-butyl piperazine-1-carboxylate (44) to provide ester 45, and this material was subsequently hydrolyzed under basic conditions to give carboxylic acid 46. Separately, commercially available tert-butyl 4-formylpiperidine-1-carboxylate (47) was converted to the corresponding Cbz-protected analog 49 by acidic deprotection (to give intermediate 48) and subsequent condensation with benzyl chloroformate. The aldehyde moiety present in 49 was then transformed into the related dimethyl acetal 50, and the Cbz protecting group was removed via hydrogenation to provide intermediate 51. This entity was coupled with compound 43, and the ester contained in the resulting product (52) was hydrolyzed under basic conditions to give carboxylic acid 53. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,872,914,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Several VHL-binding fragments required for the preparation of final PROTAC compounds were synthesized as illustrated in Scheme 3. Commercially available (2S,4R)-4-hydroxy- $N\\\\cdot$ (4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide $(54)^{46,54}$ was coupled with intermediate 35 (Scheme 1), and the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1277 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,72,464,86]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 3. Preparation of Intermediates 56, 59, and $61^{a}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[151,92,848,291]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0112/0a4dd1e4bc9b5ceb0ac11da8751345f89c1dde0f582e4ea26ccaa4788956577d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[153,332,830,506]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions: (a) Intermediate 35, HATU, DIEA, DMF, rt, $1 - 2\\\\\\\\mathrm{\\\\\\\\;h},{47} - {75}\\\\\\\\%$ ; (b) ${40}\\\\\\\\%$ aq. HBr, ${60}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},4 - {4.5}\\\\\\\\mathrm{\\\\\\\\;h},{55} - {98}\\\\\\\\%$ ; (c) 1,2- dibromoethane, ${\\\\\\\\mathrm{{Cs}}}_{2}{\\\\\\\\mathrm{{CO}}}_{3},{\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\mathrm{{CN}},{70}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2 - 3\\\\\\\\mathrm{\\\\\\\\;h},{38} - {58}\\\\\\\\%$ ; (d) Intermediate 42, Intermediate 57, HATU, DIEA, DMF, rt, ${0.5}\\\\\\\\mathrm{\\\\\\\\;h}$ ; (e) chiral SFC separation, ${31}\\\\\\\\%$ (over two steps); (f) 1:1 THF: ${\\\\\\\\mathrm{H}}_{2}{\\\\\\\\mathrm{{SO}}}_{4}\\\\\\\\left( {{1.0}\\\\\\\\mathrm{M}}\\\\\\\\right) ,{50}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},5\\\\\\\\mathrm{\\\\\\\\;h}$ ,used crude. \\\"]\",\n \"img_path\": \"images/0134/6c4abbc9f6a68ceada40e8cd9882b47fb1a56cba1a27ba6a129cb54be06ed0ed.jpg\",\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,563,482,828]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"methoxy group present in the resulting product (not shown) was subsequently cleaved by exposure to aqueous HBr to give compound 55. This material was then alkylated with 1,2-dibromoethane to afford intermediate 56. A similar sequence of reactions was applied to $(2S,4R)$ -4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (57) that was prepared by acidic deprotection of the corresponding $N$ -Boc derivative (not shown)[48,55] to provide compound 59 (via intermediate 58). Separately, intermediates 42 (Scheme 1, racemic) and 57 were coupled to give the corresponding product as a $\\\\sim 1:1$ mixture of diastereomers. This mixture was separated using chiral SFC methods to afford acetal 60 and the related isopropyl epimer (60e, structure not shown). The separated acetals were then deprotected under acidic conditions to provide the corresponding aldehydes (61, shown in Scheme 3, and 61e). The absolute configuration of the isopropyl stereocenter contained in aldehyde 61 (and in acetal 60 by inference) was established as described below in Scheme 9. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,830,482,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The preparation of PROTAC 11 is depicted in Scheme 4. The fluorine group present in 4-bromo-2-fluoropyridine (62) was displaced with 3,6,9-trioxaundecane-1,11-diol (63) under basic conditions to give the ether coupling product (64). The alcohol contained in this intermediate was oxidized to a carboxylic acid moiety (65) by exposure to TEMPO/ $\\\\mathrm{PhI(OAc)}_2$ ,[56] and this entity was converted to the corresponding methyl ester (66) by treatment with thionyl chloride in \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,563,915,828]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MeOH. Xantphos-mediated coupling of 66 with tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, Scheme 1) provided the corresponding Boc-protected coupling product (68).57 Boc-deprotection was then effected under acidic conditions and the resulting amine (69) was condensed with 4-bromo-6-chloropyridazin-3-amine (70) to afford aminochloro-pyridazine 71 as the major product. This intermediate was subsequently coupled with 2-hydroxyphenylboronic acid (72) to provide 73, and the methyl ester present in this entity was then hydrolyzed under basic conditions to give carboxylic acid 74. HATU-mediated amide formation using the known VHL-binding fragment $75^{48}$ then provided PROTAC 11. Importantly, attempts to improve the convergence of the depicted route via the coupling of preassembled intermediates related to 76 with pyridyl-halides (77) resulted in the unwanted and near-exclusive derivatization of the pyridazine $\\\\mathrm{NH}_2$ moiety (Scheme 5, product 78) instead of the desired 3,8-diazabicyclo[3.2.1]octane amino group (Scheme 5, product 79). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,830,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 6 describes the synthesis of PROTAC 12. 4-Bromo-2-fluoropyridine (62, Scheme 4) was coupled with 3,6-dioxaoctane-1,8-diol (80) and the resulting bromine-containing intermediate (81) was transformed into alcohol 86 using a sequence of reactions that were analogous to those shown in Scheme 4 to convert ester 66 into phenol 73. In this instance, coupling of 81 with tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, Scheme 4) followed by acidic deprotection of \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1278 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,355,86]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 4. Preparation of PROTAC $11^{a}$ \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[108,92,884,335]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0931/648bfa80357e9da2bd22763d12cdb33989ef18afca246693f376d2743f7c5bf7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[140,368,336,421]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0694/486e44de7d664b85d5f462f06abe6a4b36a363173faf31b105a43b06db1ea759.jpg\",\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[347,367,423,420]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0802/149db31eb96e4c573a15da6bbf60aac30958f1df5149ceec5d205b8fe2e2accd.jpg\",\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[444,367,525,420]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0136/b3bede3ad03fcdf8ec5fe09179306c456d9e69bb16599e6c2a45a23f853b2f31.jpg\",\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[548,363,619,421]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0032/6e940a11b34491bbd9273b6f08e7751e84215289d9d30277153dc3ebdfe9145b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[637,358,833,437]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions ${\\\\\\\\left( \\\\\\\\mathrm{{Boc}} = \\\\\\\\mathrm{C}\\\\\\\\left( \\\\\\\\mathrm{O}\\\\\\\\right) \\\\\\\\mathrm{{OC}}{\\\\\\\\left( {\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\right) }_{3}\\\\\\\\right) }$ : (a) 3,6,9-Trioxaundecane-1,11-diol (63),NaH,DMF,75 °C,2 h,70%; (b) TEMPO, $\\\\\\\\mathrm{{PhI}}{\\\\\\\\left( \\\\\\\\mathrm{{OAc}}\\\\\\\\right) }_{2}$ ,DCM, ${\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O}$ ,rt, $2\\\\\\\\mathrm{\\\\\\\\;h},{46}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{c}\\\\\\\\right) {\\\\\\\\mathrm{{SOCl}}}_{2}$ ,MeOH,rt, $4\\\\\\\\mathrm{\\\\\\\\;h},{73}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{d}\\\\\\\\right)$ tert-Butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67),RuphosPd G2, ${\\\\\\\\mathrm{{Cs}}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,toluene, ${90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},4\\\\\\\\mathrm{\\\\\\\\;h},{85}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{e}\\\\\\\\right) 1 : 5$ TFA:DCM,rt, $2\\\\\\\\mathrm{\\\\\\\\;h},{85}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{f}\\\\\\\\right) 4$ -Bromo-6-chloropyridazin-3-amine (70),NMP,DIEA, ${120}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},3\\\\\\\\mathrm{\\\\\\\\;h}$ , 50%; (g) 2-Hydroxyphenylboronic acid (72), $\\\\\\\\mathrm{{Pd}}{\\\\\\\\left( {\\\\\\\\mathrm{{PPh}}}_{3}\\\\\\\\right) }_{4},{\\\\\\\\mathrm{\\\\\\\\;K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h},{37}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{h}\\\\\\\\right)$ LiOH,1:1 THF: ${\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O}$ ,rt,1 h,94%; (i) Intermediate 75,HATU,DIEA,DMF,rt,2 h,26%. \\\"]\",\n \"img_path\": \"images/0493/7ced20e36c26c3cd4f0149c638c3713120dd65b42b03022665829edd65a85684.jpg\",\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[80,527,434,542]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 5. Unwanted Coupling of Pyridazine Amine \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[98,550,897,715]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0703/3e3e57acf92dfd10e2daab1935a153f6d7c5b9df95cdb41fcfe632093692cc75.jpg\",\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,727,482,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the resulting product (82) and subsequent condensation of the amine thus obtained (83) with 4-bromo-6-chloropyridazin-3-amine (70, Scheme 4) afforded intermediate 84. This entity was then coupled with (2-(methoxymethoxy)phenyl)boronic acid (85) to provide alcohol 86. Conversion of this alcohol to the corresponding tosylate (87) followed by subsequent alkylation with intermediate 55 (Scheme 2) afforded the coupled product as a mixture of diastereomers (epimeric at the isopropyl center). Removal of the methoxymethoxy protecting groups under acidic conditions and separation of the resulting phenol-containing compounds by chiral HPLC then gave PROTAC 12 along with the corresponding isopropyl epimer (12e, structure not shown). The BRM-degradation activities of both molecules were subsequently assessed, and the molecule with the more potent activity (ca. 100-fold more potent than \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,727,915,770]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the other isopropyl epimer, Table S4) was assigned the absolute configuration depicted for PROTAC 12 in Figure 5 and Table 2. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,770,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The described approach of synthesizing closely related diastereomeric compound pairs, separating the two molecules using chromatographic methods (typically chiral), and testing the purified entities for biological activity was employed in the preparation of the majority of isoxazole-containing PROTACs described in this work. As illustrated in the example of compound 12, the most potent member of each PROTAC pair so evaluated was assigned the absolute isopropyl group configuration shown in Table 2 (as well as Figure 5). In most cases, the alternate diastereomer was at least 100-fold less potent than the more active member of a given compound pair (Table S4). Interestingly, it was not always possible to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1279 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[108,92,887,583]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Scheme 6. Preparation of PROTAC $12^{a}$ \\\"]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions $\\\\\\\\left( {\\\\\\\\mathrm{{Ts}} = {\\\\\\\\mathrm{{SO}}}_{2}\\\\\\\\mathrm{{Ph}}\\\\\\\\left( {4 - \\\\\\\\mathrm{{Me}}}\\\\\\\\right) ,\\\\\\\\mathrm{{Boc}} = \\\\\\\\mathrm{C}\\\\\\\\left( \\\\\\\\mathrm{O}\\\\\\\\right) \\\\\\\\mathrm{{OC}}{\\\\\\\\left( {\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\right) }_{3}}\\\\\\\\right)$ : (a) 3,6-Dioxoctane-1,8-diol (80),NaH,DMF,rt,1h,69%; (b) tert- Butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67),RuphosPd G3, ${\\\\\\\\mathrm{{Cs}}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h},{97}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{c}\\\\\\\\right) {4.0}\\\\\\\\mathrm{M}\\\\\\\\mathrm{{HCl}},\\\\\\\\mathrm{{MeOH}},\\\\\\\\mathrm{{rt}},4\\\\\\\\mathrm{\\\\\\\\;h}$ ; (d) 4-Bromo-6-chloropyridazin-3-amine (70),NMP,DIEA, ${120}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},8\\\\\\\\mathrm{\\\\\\\\;h},{44}\\\\\\\\%$ over 2 steps;(e)(2-(Methoxymethoxy)phenyl)boronic acid (85), Pd ${\\\\\\\\left( {\\\\\\\\mathrm{{PPh}}}_{3}\\\\\\\\right) }_{4},{\\\\\\\\mathrm{K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O},{100}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},4\\\\\\\\mathrm{\\\\\\\\;h},{73}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{f}\\\\\\\\right)$ TsCl,TEA,DMAP,DCM,rt,10 h,85%; (g) Intermediate 55, ${\\\\\\\\mathrm{K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,DMF, ${60}^{ \\\\\\\\circ }\\\\\\\\mathrm{C}$ ,4 h,31%; (h)) ${4.0}\\\\\\\\mathrm{M}\\\\\\\\mathrm{{HCl}}$ ,MeOH,rt,8 h,(i) chiral HPLC separation, 26% over 2 steps. \\\"]\",\n \"img_path\": \"images/0083/637d82e07a32e795eb23ca57b95846c99ba96d4c4c757fd833e894e25a14e969.jpg\",\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,667,484,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"correctly assign the stereocenters using separation retention times and/or ${}^{1}\\\\mathrm{H}$ NMR spectra comparisons. The accuracy of such structural assignments was supported by the solved crystal structure of the ternary complex formed between PROTAC 17, BRG1, and VHL which verified the configuration of the isopropyl group (see above discussion as well as Figures S8, S9, and S14). The assignments were also consistent with the solved crystal structure of a potent VHL-binding isoxazole-containing moiety in which the isopropyl group stereochemistry corresponded to that shown in Table 2 and Figure 5 (Figures S14-S16). Importantly, the isopropyl stereocenters present in the separated single diastereomers were configurationally stable when subjected to physiological assay conditions and routine solid-state storage and handling procedures. However, they could be racemized by exposure to strongly basic conditions $(\\\\mathrm{pH} > 9)$ , and their configurational stability during long-term solution-based storage (e.g., DMSO) remains to be determined. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,667,917,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The preparation of PROTACs 13 and 14 is shown in Scheme 7. Commercially available benzyl 4-(2-hydroxyethyl)-piperazine-1-carboxylate (90) was coupled with 5-bromo-2-fluoropyridine (62, Scheme 4) via nucleophilic fluoride displacement to give intermediate 91. This entity was then coupled with Boc-protected 3,8-diazabicyclo[3.2.1]octane 67 (Scheme 4),[57] and the resulting product (not shown) was deprotected under acidic conditions to afford 92. This intermediate was condensed with 4-bromo-6-chloropyridazin-3-amine (70, Scheme 4) to provide 93. Subsequent coupling of 93 with (2-(methoxymethoxy)phenyl)boronic acid (85, Scheme 6) via Pd-mediated catalysis[58] followed by removal of the Cbz moiety present in the resulting product (not shown) then afforded key intermediate 94. This entity was coupled with bromide 56 (Scheme 3; ca. 1:1 mixture of diastereomers) via transient formation of the corresponding iodide. The MOM protecting groups present in coupled diastereomeric products (95) were then removed under acidic conditions, and the compounds thus obtained were separated \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1280 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[108,91,887,553]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Scheme 7. Preparation of PROTACs 13 and $14^{a}$ \\\"]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions ${\\\\\\\\left( \\\\\\\\mathrm{{Boc}} = \\\\\\\\mathrm{C}\\\\\\\\left( \\\\\\\\mathrm{O}\\\\\\\\right) \\\\\\\\mathrm{{OC}}{\\\\\\\\left( {\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\right) }_{3};\\\\\\\\mathrm{{Cbz}} = \\\\\\\\mathrm{C}\\\\\\\\left( \\\\\\\\mathrm{O}\\\\\\\\right) {\\\\\\\\mathrm{{OCH}}}_{2}\\\\\\\\mathrm{{Ph}}\\\\\\\\right) :$ (a) 4-Bromo-2-fluoropyridine (62),NaH,DMF,rt,0.5 h,83%; (b) tert-Butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67),RuPhosPd G2, ${\\\\\\\\mathrm{{Cs}}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,toluene, ${90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},5\\\\\\\\mathrm{\\\\\\\\;h},{56}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{c}\\\\\\\\right)$ TFA,DCM,rt,1 h,93%; (d) 4- Bromo-6-chloropyridazin-3-amine (70),DMP,DIEA,130 °C,3 h,84%; (e) (2-(Methoxymethoxy)phenyl)boronic acid (85),Pd(dppf)- ${\\\\\\\\mathrm{{Cl}}}_{2} \\\\\\\\bullet {\\\\\\\\mathrm{{CH}}}_{2}{\\\\\\\\mathrm{{Cl}}}_{2},{\\\\\\\\mathrm{\\\\\\\\;K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3},1,4$ -dioxane, ${\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O},{90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{1.5}\\\\\\\\mathrm{\\\\\\\\;h},{72}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{f}\\\\\\\\right) \\\\\\\\mathrm{{Pd}}$ on $\\\\\\\\mathrm{C},{\\\\\\\\mathrm{H}}_{2}$ ,MeOH,rt,5 h,59%; (g) Intermediate 56, ${\\\\\\\\mathrm{K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,KI, ${\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\mathrm{{CN}},{70}^{ \\\\\\\\circ }\\\\\\\\mathrm{C}$ , ${12}\\\\\\\\mathrm{\\\\\\\\;h},{49}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{h}\\\\\\\\right)$ Intermediate 59, ${\\\\\\\\mathrm{K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,NaI, ${\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\mathrm{{CN}},{70}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{12}\\\\\\\\mathrm{\\\\\\\\;h},{68}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{i}\\\\\\\\right) {4.0}\\\\\\\\mathrm{M}\\\\\\\\mathrm{{HCl}},\\\\\\\\mathrm{{MeOH}},\\\\\\\\mathrm{{rt}},3 - {12}\\\\\\\\mathrm{\\\\\\\\;h};\\\\\\\\left( \\\\\\\\mathrm{j}\\\\\\\\right)$ Chiral HPLC separation, ${15} - {27}\\\\\\\\%$ over 2 steps. \\\"]\",\n \"img_path\": \"images/0113/645fe20ae1f8dab53d4766b43944507dfd3652253c64fdf3a8fdd2b41b9f7a7b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,648,481,733]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"by chiral HPLC methods and tested for biological activity. As described above, the more potent diastereomer was assigned the absolute stereochemistry shown for PROTAC 13 in Table 2 (cf., Table S4). Similar derivatization of 94 with bromide 59 (Scheme 3; ca. 1:1 mixture of diastereomers) and subsequent processing of the coupled products afforded PROTAC 14. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,732,482,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The syntheses of several additional PROTAC compounds are illustrated in Scheme 8. 4-Bromo-2-fluoropyridine (62, Scheme 4) was coupled with 2,2-diethoxyethan-1-ol under mildly basic conditions to afford intermediate 97. This entity was condensed with benzyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (98) to give compound 99, and the Cbz protecting group present in this material was subsequently removed via hydrogenation. Elaboration of the resulting amine (100) to intermediate 101 was then accomplished using sequential coupling reactions that were analogous to those employed above to convert 69 to 73 (Scheme 4). Acidic deprotection of the acetal present in 101 gave the corresponding aldehyde (102), and this intermediate was reductively coupled with commercially available tert-butyl-(R)-3-methylpiperazine-1-carboxylate (103) to provide compound 104. Related \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,650,915,746]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"transformation of 102 involving commercially available tert-butyl-(S)-2-methylpiperazine-1-carboxylate (105) afforded compound 106. Independent removal of the Boc protecting groups present in 104 and 106 under acidic conditions followed by reductive amination of the resulting amine products (not shown) using chiral-pure aldehyde 61 (Scheme 3) then respectively provided PROTACs 15 and 16. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,746,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 9 depicts the synthesis of PROTAC 17. Commercially available 3-(benzyloxy)cyclobutan-1-one (107) was reduced to give benzyl-protected-cis-1,3-cyclobutanediol (108).59 This entity was coupled with pyridin-4-ol (4-hydroxypyridine) using Mitsunobu conditions,60 and the resulting trans-cyclobutane product (109) was alkylated with benzyl bromide to give pyridinium salt 110. This material was subsequently reduced to the corresponding 1,2,3,6-tetrahydropyridine (111) by treatment with sodium borohydride. The benzyl alcohol protecting group present in 111 was removed via hydrogenation over a palladium catalyst, and this process also reduced the 1,2,3,6-tetrahydropyridine moiety to a piperidine group (112). This deprotected material was subjected to a second hydrogenation employing a palladium \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1281 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,395,86]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 8. Synthesis of PROTACs 15 and $16^{a}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[181,92,810,561]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0217/befffb78a8c023c74f52b4f146c9868d14b547e994968a8ec6c0aae5a4fb5edc.jpg\",\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[286,570,698,667]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions ${\\\\\\\\left( \\\\\\\\mathrm{{Boc}} = \\\\\\\\mathrm{C}\\\\\\\\left( \\\\\\\\mathrm{O}\\\\\\\\right) \\\\\\\\mathrm{{OC}}{\\\\\\\\left( {\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\right) }_{3},\\\\\\\\mathrm{{Cbz}} = \\\\\\\\mathrm{C}\\\\\\\\left( \\\\\\\\mathrm{O}\\\\\\\\right) {\\\\\\\\mathrm{{OCH}}}_{2}\\\\\\\\mathrm{{Ph}}\\\\\\\\right) :$ (a) 2,2-Diethoxyethan-1-ol,NaH,DMF,rt,2h,59%; (b) Intermediate 98,RuPhosPd G2,Cs ${}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,toluene, ${90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h},{94}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{c}\\\\\\\\right)$ Pd on $\\\\\\\\mathrm{C},{\\\\\\\\mathrm{H}}_{2}$ ,EtOAc,rt,12 h,92%; (d) 4-Bromo-6-chloropyridazin-3-amine (70), DIEA, NMP, ${120}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h},{74}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{e}\\\\\\\\right) 2 -$ Hydroxyphenylboronic acid (72),Pd(PPh ${}_{3}{)}_{4},{\\\\\\\\mathrm{\\\\\\\\;K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O},{90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h}{70}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{f}\\\\\\\\right) {1.0}\\\\\\\\mathrm{M}{\\\\\\\\mathrm{H}}_{2}{\\\\\\\\mathrm{{SO}}}_{4}$ ,THF, ${60}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},4\\\\\\\\mathrm{\\\\\\\\;h},{24}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{g}\\\\\\\\right)$ Intermediate 103,NaBH(OAc) ${}_{3}$ , ${\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\mathrm{{CN}}$ ,rt, $2\\\\\\\\mathrm{\\\\\\\\;h},{91}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{h}\\\\\\\\right)$ Intermediate 105,NaBH(OAc) ${}_{3}$ , ${\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\mathrm{{CN}}$ ,rt, $8\\\\\\\\mathrm{\\\\\\\\;h},{37}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{i}\\\\\\\\right) {4.0}\\\\\\\\mathrm{M}$ HCl, MeOH, rt, $2 - 8\\\\\\\\mathrm{\\\\\\\\;h},{90} - {91}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{j}\\\\\\\\right)$ Intermediate 61,NaBH(OAc) ${}_{3}$ , ${\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\mathrm{{CN}}$ ,rt, ${10} - {12}\\\\\\\\mathrm{\\\\\\\\;h},3 - {8}\\\\\\\\%$ . \\\"]\",\n \"img_path\": \"images/0762/7125fbb4a3c1e8373c42af6298549436b982980d4c16390adb95be6551095174.jpg\",\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,751,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"hydroxide catalyst in the presence of di-tert-butyl dicarbonate to give Boc-protected piperidine 113. Coupling of this intermediate with 4-bromo-2-fluoro-pyridine (62, Scheme 4) then provided 114, and material was converted to intermediate 115 via condensation with benzyl 3,8-diazabicyclo[3.2.1]-octane-3-carboxylate (97, Scheme 8). Removal of the Cbz protecting group from 115 was accomplished via hydrogenation, and the resulting amine (116) was coupled with 4-bromo-6-chloropyridazin-3-amine (70, Scheme 4) to give intermediate 117. Reaction of 117 with (2-hydroxyphenyl)-boronic acid (72, Scheme 4) then provided compound 118, and the Boc protecting group contained in this material was subsequently removed under acidic conditions to afford amine \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,751,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"119. Coupling of 119 with the chiral-pure VHL-binding fragment 61 (Scheme 3) then provided PROTAC 17. As was described above, the alternate chiral-pure isopropyl epimer corresponding to 61 that was obtained via chiral separation in Scheme 3 (61e, structure not shown) was also converted to the corresponding PROTAC compound (17e, the isopropyl epimer corresponding to 17, not shown). Subsequent biological testing of the two diastereomeric PROTAC molecules was employed to assign the absolute stereochemistries of the isopropyl centers in 17 and, by inference, intermediate 61 (cf., Table S4; more potent diastereomers = isopropyl stereochemistries shown in Table 2 and Schemes 3 and 9). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1282 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,337,86]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 9. Synthesis of PROTAC $17^{a}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[108,90,887,652]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions $\\\\\\\\left( {\\\\\\\\mathrm{{Bn}} = {\\\\\\\\mathrm{{CH}}}_{2}\\\\\\\\mathrm{{Ph}},\\\\\\\\mathrm{{Boc}} = \\\\\\\\mathrm{C}\\\\\\\\left( \\\\\\\\mathrm{O}\\\\\\\\right) \\\\\\\\mathrm{{OC}}{\\\\\\\\left( {\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\right) }_{3},\\\\\\\\mathrm{{Cbz}} = \\\\\\\\mathrm{C}\\\\\\\\left( \\\\\\\\mathrm{O}\\\\\\\\right) {\\\\\\\\mathrm{{OCH}}}_{2}\\\\\\\\mathrm{{Ph}}}\\\\\\\\right)$ : (a) ${\\\\\\\\mathrm{{NaBH}}}_{4}$ ,MeOH, $0{}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},1\\\\\\\\mathrm{\\\\\\\\;h},{97}\\\\\\\\%$ ; (b) Pyridin-4-ol, DIAD, PPh ${}_{3}$ ,THF, ${50}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{12}\\\\\\\\mathrm{\\\\\\\\;h},{55}\\\\\\\\%$ ; (c) BnBr,toluene, ${80}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{12}\\\\\\\\mathrm{\\\\\\\\;h},{92}\\\\\\\\%$ ; (d) ${\\\\\\\\mathrm{{NaBH}}}_{4}$ ,EtOH, ${15}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},4\\\\\\\\mathrm{\\\\\\\\;h},{84}\\\\\\\\%$ ; (e) ${\\\\\\\\mathrm{H}}_{2}$ (50 psi),Pd/C,THF, EtOH, ${35}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{12}\\\\\\\\mathrm{\\\\\\\\;h};{83}\\\\\\\\%$ ; (f) ${\\\\\\\\mathrm{H}}_{2}$ (50 psi), $\\\\\\\\mathrm{{Pd}}{\\\\\\\\left( \\\\\\\\mathrm{{OH}}\\\\\\\\right) }_{2}/\\\\\\\\mathrm{C}$ ,MeOH, ${\\\\\\\\left( \\\\\\\\text{Boc}\\\\\\\\right) }_{2}\\\\\\\\mathrm{O}$ ,rt, ${12}\\\\\\\\mathrm{\\\\\\\\;h},{71}\\\\\\\\%$ ; (g) 4-Bromo-2-fluoro-pyridine (62), ${\\\\\\\\mathrm{{Cs}}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ , ${\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\mathrm{{CN}}$ ,90 ${}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{12}\\\\\\\\mathrm{\\\\\\\\;h},{86}\\\\\\\\%$ ; (h) Benzyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (98), RuphosPd-G2, ${\\\\\\\\mathrm{{Cs}}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,toluene, ${110}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{12}\\\\\\\\mathrm{\\\\\\\\;h},{71}\\\\\\\\%$ ; (i) $\\\\\\\\mathrm{{Pd}}{\\\\\\\\left( \\\\\\\\mathrm{{OH}}\\\\\\\\right) }_{2}/\\\\\\\\mathrm{C}$ , ${\\\\\\\\mathrm{H}}_{2}$ (50 psi),THF, EtOH, ${60}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{12}\\\\\\\\mathrm{\\\\\\\\;h},{89}\\\\\\\\%$ ; (j) 4-Bromo-6-chloropyridazin-3-amine (70), DIEA, DMSO, ${130}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},3\\\\\\\\mathrm{\\\\\\\\;h},{64}\\\\\\\\%$ ; (k) 2-Hydroxyphenyl boronic acid (72), $\\\\\\\\mathrm{{Pd}}{\\\\\\\\left( {\\\\\\\\mathrm{{PPh}}}_{3}\\\\\\\\right) }_{4},{\\\\\\\\mathrm{\\\\\\\\;K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O},{90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{10}\\\\\\\\mathrm{\\\\\\\\;h},{54}\\\\\\\\%$ ; (l) ${4.0}\\\\\\\\mathrm{M}\\\\\\\\mathrm{{HCl}},1,4$ -dioxane,DCM,rt, $2\\\\\\\\mathrm{\\\\\\\\;h}$ ; (m) Intermediate 61, ${\\\\\\\\mathrm{{NaBH}}}_{3}\\\\\\\\mathrm{{CN}},\\\\\\\\mathrm{{NaOAc}},\\\\\\\\mathrm{{MeOH}},\\\\\\\\mathrm{{DCM}},\\\\\\\\mathrm{{rt}},{10}\\\\\\\\mathrm{\\\\\\\\;h};{45}\\\\\\\\%$ over two steps. \\\"]\",\n \"img_path\": \"images/0838/cafd3c7085ff98f1c319211e4577384d495fe748d7ccedf0b37a69d30ff27bf7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,760,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The preparation of PROTACs 18-20 is illustrated in Scheme 10. Intermediate 119 (Scheme 9) was alkylated with 2-bromo-1,1-diethoxyethane and the resulting acetal (120) was deprotected under acidic conditions to give aldehyde 121. Separately, racemic isoxazole-containing carboxylic acid 46 (Scheme 2) was coupled with chiral-pure amine 57 (Scheme 3), and subsequent separation of the diastereomeric products via chiral HPLC provided intermediate 122 and the corresponding isopropyl epimer (122e, structure not shown). Intermediate 122 was deprotected under acidic conditions to give amine 123, and this entity was coupled with aldehyde 121 via reductive amination to afford PROTAC 18. The isopropyl epimer corresponding to intermediate 122 obtained via the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,760,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"chiral separation (122e) was similarly transformed into a closely related diastereomeric PROTAC (18e, the isopropyl epimer corresponding to 18, structure not shown) via the same sequence of reactions. Biological testing of both compounds subsequently established the absolute configuration for PROTAC 18 as that shown in Table 2 and, by inference, the configuration of intermediates 122 and 123 depicted in Scheme 10 (cf., Table S4). In an independent synthesis, enantiomerically pure intermediate 123 was condensed with tert-butyl-4-formylpiperidine-1-carboxylate (124) via a reductive amination process, and the Boc group contained in the resulting product (125) was removed via exposure to acidic \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1283 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,380,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 10. Synthesis of PROTACs $18 - 20^{a}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[222,90,742,610]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0837/4dd35af820bcb1b3a2e768d27a778f5aed1f60ad784ab0bce7a2f8f8bc89b971.jpg\",\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[233,668,733,818]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions $\\\\\\\\left( {\\\\\\\\mathrm{{Boc}} = \\\\\\\\mathrm{C}\\\\\\\\left( \\\\\\\\mathrm{O}\\\\\\\\right) \\\\\\\\mathrm{{OC}}{\\\\\\\\left( {\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\right) }_{3}}\\\\\\\\right)$ : (a) 2-Bromo-1,1-diethoxyethane,NaI, DIEA, DMF, ${70}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{12}\\\\\\\\mathrm{\\\\\\\\;h},{35}\\\\\\\\%$ ; (b) ${1.0}\\\\\\\\mathrm{M}{\\\\\\\\mathrm{H}}_{2}{\\\\\\\\mathrm{{SO}}}_{4}$ , THF, ${60}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{12}\\\\\\\\mathrm{\\\\\\\\;h}$ ; (c) Intermediate 57,HATU,DIEA,DMF,rt,1 h;(d) Chiral HPLC; 24-28% over 2 steps; (e) TFA, DCM, rt, 1 h; (f) Intermediate 121, ${\\\\\\\\mathrm{{NaBH}}}_{3}\\\\\\\\mathrm{{CN}},2 : 1\\\\\\\\mathrm{{MeOH}} : \\\\\\\\mathrm{{DCM}},\\\\\\\\mathrm{{rt}},{24}\\\\\\\\mathrm{\\\\\\\\;h},{13}\\\\\\\\%$ over 2 steps;(g) Intermediate 124, NaOAc, ${\\\\\\\\mathrm{{NaBH}}}_{3}\\\\\\\\mathrm{{CN}},3 : 1\\\\\\\\mathrm{{MeOH}} : \\\\\\\\mathrm{{DCM}},\\\\\\\\mathrm{{rt}},1\\\\\\\\mathrm{\\\\\\\\;h},3\\\\\\\\%$ ; (i) Intermediate 57,HATU,DIEA,DMF,rt,2 h; (j) Chiral HPLC; 11-13% over 2 steps; (k) HCOOH, ${\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O},{60}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},1\\\\\\\\mathrm{\\\\\\\\;h}$ ; (l) Intermediate 119,NaOAc, ${\\\\\\\\mathrm{{NaBH}}}_{3}\\\\\\\\mathrm{{CN}},1 : 1\\\\\\\\mathrm{{MeOH}} : \\\\\\\\mathrm{{DCM}},\\\\\\\\mathrm{{rt}},1\\\\\\\\mathrm{\\\\\\\\;h},{34}\\\\\\\\%$ over 2 steps. \\\"]\",\n \"img_path\": \"images/0099/0614435a61cc7921f9d3b6a516589ddacae2c61ae695dc49e45c3b7bae230813.jpg\",\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[79,913,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"conditions to give 126. This entity was subsequently coupled with aldehyde 138 (Scheme 12) to give PROTAC 20. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,913,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Separately, racemic isoxazole-containing carboxylic acid 53 (Scheme 2) was coupled with enantiomerically pure amine 57 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1284 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,345,86]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 11. Synthesis of PROTAC $21^{a}$ \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[138,92,859,356]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions: (a) TFA,DCM,rt,1 h,80-90%; (b) Intermediate 43, DIEA, DMF, ${130}{}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},1\\\\\\\\mathrm{\\\\\\\\;h},{71}\\\\\\\\%$ ; (c) tert-Butyl 3,8- diazabicyclo[3.2.1]octane-3-carboxylate (67),RuPhosPd G3, ${\\\\\\\\mathrm{{Cs}}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},1\\\\\\\\mathrm{\\\\\\\\;h},{42}\\\\\\\\%$ ; (d) 4-Bromo-6-chloropyridazin-3-amine (70), DMSO, DIEA, ${130}{}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},5\\\\\\\\mathrm{\\\\\\\\;h},{52}\\\\\\\\%$ ; (e) (2-Hydroxyphenyl)boronic acid (72), $\\\\\\\\mathrm{{Pd}}{\\\\\\\\left( {\\\\\\\\mathrm{{PPh}}}_{3}\\\\\\\\right) }_{4},{\\\\\\\\mathrm{\\\\\\\\;K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O},{90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},1\\\\\\\\mathrm{\\\\\\\\;h},{68}\\\\\\\\%$ ; (f) LiOH, THF, ${\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O}$ ,rt, $1\\\\\\\\mathrm{\\\\\\\\;h},{95}\\\\\\\\%$ ; (g) Intermediate 57,HATU,DIEA,DMF,rt,1 h;(h) Chiral HPLC; 4% over 2 steps. \\\"]\",\n \"img_path\": \"images/0626/b0acba7708620e1369dc5191dd643a1ff29a11bb6216d48d8511a149f7d5af79.jpg\",\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,425,481,635]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(Scheme 3), and the diastereomeric products thus obtained were separated by chiral HPLC methods to give intermediate 127 and the corresponding isopropyl epimer (127e, structure not shown). Deprotection of the acetal present in 127 under acidic conditions and reductive coupling of the aldehyde thus obtained (128) with intermediate 119 (Scheme 9) afforded PROTAC 19. Similar to the example of PROTAC 18 above, the isopropyl epimer corresponding to intermediate 127 (i.e., 127e) was converted into a diastereomer of PROTAC 19 (19e, the isopropyl epimer corresponding to 19, structure not shown) via the same two-step sequence. Biological testing of both PROTAC molecules subsequently established the absolute configurations shown for PROTAC 19 and (by inference) intermediates 127 and 128, respectively, shown in Table 2 and Scheme 10 (cf., Table S4). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,635,481,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 11 depicts the synthesis of PROTAC 21. Intermediate 114 (Scheme 9) was deprotected under acidic conditions to provide amine 129. This entity was coupled with racemic intermediate 43 (Scheme 2) to give compound 130. Multistep elaboration of the bromide present in 130 using chemistries analogous to those employed in Scheme 4 above to transform intermediate 69 into compound 73 then provided ester 131 (several synthetic intermediates are not shown in Scheme 11 but are described in the Experimental Section). Hydrolysis of 131 under basic conditions afforded carboxylic acid 132, and this entity was subsequently coupled with enantiomerically pure intermediate 57 (Scheme 3). Separation of the resulting diastereomeric products by chiral HPLC methods then gave PROTAC 21 and the corresponding isopropyl epimer (21e, not shown). As was performed elsewhere in this work, biological testing of the separated diastereomers was employed to assign the absolute configurations of these compounds (cf., Table S4). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,885,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PROTAC 22 was prepared using the method shown in Scheme 12. Commercially available alcohol 133 was coupled with 4-bromopyridin-2-ol to afford intermediate 134 This entity was transformed into compound 135 using a sequence \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,445,917,752]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Scheme 12. Synthesis of PROTAC $22^{a}$ \\\"]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions: (a) 4-Bromopyridin-2-ol, ${\\\\\\\\mathrm{{PPh}}}_{3}$ ,DIAD, THF,rt,1 h,68%; (b) tert-Butyl 3,8-diazabicyclo[3.2.1]octane-3- carboxylate (67), RuPhosPd G3, ${\\\\\\\\mathrm{{Cs}}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},1\\\\\\\\mathrm{\\\\\\\\;h}$ , 80%; (c) TFA,DCM,rt,1 h,79%; (d) 4-Bromo-6-chloropyridazin-3- amine (70),DMSO,DIEA, ${130}{}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},1\\\\\\\\mathrm{\\\\\\\\;h},{65}\\\\\\\\% ;\\\\\\\\;\\\\\\\\left( \\\\\\\\mathrm{e}\\\\\\\\right) \\\\\\\\;\\\\\\\\left( {2 - }\\\\\\\\right.$ Hydroxyphenyl)boronic acid (72), $\\\\\\\\mathrm{{Pd}}{\\\\\\\\left( {\\\\\\\\mathrm{{PPh}}}_{3}\\\\\\\\right) }_{4},{\\\\\\\\mathrm{\\\\\\\\;K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3},1,4$ -dioxane, ${90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h},{56}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{f}\\\\\\\\right)$ LiOH,THF, ${\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O},\\\\\\\\mathrm{{rt}},1\\\\\\\\mathrm{\\\\\\\\;h};\\\\\\\\left( \\\\\\\\mathrm{g}\\\\\\\\right) {\\\\\\\\mathrm{{CH}}}_{3}{\\\\\\\\mathrm{{ONHCH}}}_{3}$ . HCl,HATU,DIEA,DMF,rt,1 h,33%; (h) ${\\\\\\\\mathrm{{LiAlH}}}_{4}$ ,THF,0 to ${25}^{ \\\\\\\\circ }\\\\\\\\mathrm{C}$ , 1 h,41%; (i) Intermediate 123, ${\\\\\\\\mathrm{{NaBH}}}_{3}\\\\\\\\mathrm{{CN}}$ ,NaOAc,3:1 MeOH:DCM,rt,1 h,6%. \\\"]\",\n \"img_path\": \"images/0873/09067e4f9f7a1cf6c57bb3e954a954fe6c795d4217e50e43a5a3405b1558bd84.jpg\",\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[512,900,915,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"of reactions that was similar to those employed in Scheme 4 above to transform intermediate 69 into compound 73 (several synthetic intermediates are not shown in Scheme 12 but are \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1285 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,345,86]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 13. Synthesis of PROTAC $23^{a}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[187,90,807,468]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions $\\\\\\\\left( {\\\\\\\\mathrm{{Boc}} = \\\\\\\\mathrm{C}\\\\\\\\left( \\\\\\\\mathrm{O}\\\\\\\\right) \\\\\\\\mathrm{{OC}}{\\\\\\\\left( {\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\right) }_{3}}\\\\\\\\right)$ : (a) Intermediate 57,HATU,DIEA,DMF,rt,1 h,33%; (b) ${1.0}\\\\\\\\mathrm{M}{\\\\\\\\mathrm{H}}_{2}{\\\\\\\\mathrm{{SO}}}_{4}$ ,THF,60°C,2 h, 74%; (c) tert-Butyl 4-hydroxypiperidine-1-carboxylate (141),NaH,DMF,0 to ${25}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},1\\\\\\\\mathrm{\\\\\\\\;h},{76}\\\\\\\\%$ ; (d) Benzyl 3,8-diazabicyclo[3.2.1]octane-3- carboxylate (98), RuPhosPd G2, ${\\\\\\\\mathrm{{Cs}}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,toluene, ${90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h},{50}\\\\\\\\%$ ; (e) Pd/C, ${\\\\\\\\mathrm{H}}_{2}$ ,EtOAc,rt,4 h,64%; (f) 4-Bromo-6-chloropyridazin-3-amine (70),NMP,DIEA, ${120}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h},{91}\\\\\\\\%$ ; (g) (2-Hydroxyphenyl)boronic acid (72),Pd(PPh ${}_{3}$ ), ${\\\\\\\\mathrm{K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,1,4-dioxane, ${90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h},{54}\\\\\\\\%$ ; (h) TFA,DCM, rt,4 h,73%; (i) Intermediate 140, NaBH(OAc), ${\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\mathrm{{CN}}$ ,rt,4 h; (j) chiral HPLC,2% over 2 steps. \\\"]\",\n \"img_path\": \"images/0098/bcaaf2cdb07a3905608518a119f2598a5142023e55ed7ae8e408a9bc241f8d08.jpg\",\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,552,481,636]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"described in full in the Experimental Section). Hydrolysis of the ester present in 135 was effected under basic conditions, and the resulting acid (136) was converted to aldehyde 138 by reduction of the corresponding Weinreb amide (137). Reductive coupling of 138 with chiral-pure intermediate 123 (Scheme 10) then provided PROTAC 22. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,636,482,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The synthesis of PROTAC 23 is illustrated in Scheme 13. Intermediate 53 (Scheme 2) was coupled with intermediate 57 (Scheme 3) to give compound 139 as a $\\\\sim 1:1$ mixture of diastereomers (epimeric at the isopropyl group). The acetal present in 139 was then converted to the corresponding aldehyde (140, $\\\\sim 1:1$ mixture of diastereomers) under acidic conditions. Separately, 4-bromo-2-fluoro-pyridine (62, Scheme 4) was coupled with tert-butyl 4-hydroxypiperidine-1-carboxylate (141) to provide intermediate 142. This entity was subsequently transformed into compound 143 using a sequence of reactions that was analogous to that employed in Scheme 8 above to convert intermediate 97 into compound 101 (several synthetic intermediates are not shown in Scheme 13 but are fully described and characterized in the Experimental Section). Removal of the Boc group present in 143 under acidic conditions followed by reductive coupling of the resulting amine (144) with aldehyde 140 afforded the desired product as a $\\\\sim 1:1$ mixture of diastereomers (epimeric at the isopropyl group, structure not shown). These molecules were separated by preparative chiral HPLC to afford PROTAC 23 and the corresponding isopropyl epimer (23e, structure not shown). As described elsewhere in this work, the biological \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,552,914,595]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"activities of the separated compounds were assessed, and the more potent entity was assigned the chemical structure depicted for 23 (cf., Table S4). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,595,915,912]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PROTAC 24 was prepared using the methods shown in Scheme 14. Intermediate 58 (Scheme 3) was alkylated with 3-bromoprop-1-yne under mildly basic conditions to give compound 145 ( $\\\\sim$ 1:1 mixture of diastereomers). Separately, intermediate 108 (Scheme 9) was coupled with 4-bromo-2-fluoropyridine (62, Scheme 4) to afford 146, and this entity was transformed into intermediate 147 via coupling with tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, Scheme 4) and debenzylation. Intermediate 147 was deprotected under acidic conditions, and the resulting amine (not shown) was converted to compound 148 via sequential coupling with 4-bromo-6-chloropyridazin-3-amine (70) and (2-(methoxymethoxy)phenyl)boronic acid (85). Intermediate 148 was condensed with 6-iodopyridin-3-ol under Mitsunobu conditions to afford the trans-cyclobutane product (149).[60] This compound was subsequently coupled with the alkyne-containing intermediate 145 and the resulting products were deprotected under acidic conditions to afford PROTAC 24 and the corresponding isopropyl epimer (24e, not shown). Separation of these two PROTACs via preparative chiral HPLC and biological testing of the individual diastereomers enabled assignment of the absolute configuration of 24 as that shown in Table 3 (cf., Table S4). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,913,914,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The syntheses of control PROTACs 25-28 are described in Scheme 15 below. Inversion of the secondary alcohol present \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1286 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[329,92,650,225]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Scheme 14. Synthesis of PROTAC $24^{a}$ \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0377/df00c42ef99d011c519b3e616ca2dae683c67addbbc9e032ae0948dd42b21763.jpg\",\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[151,268,848,533]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions $\\\\\\\\left( {\\\\\\\\mathrm{{Bn}} = {\\\\\\\\mathrm{{CH}}}_{2}\\\\\\\\mathrm{{Ph}},\\\\\\\\mathrm{{Boc}} = \\\\\\\\mathrm{C}\\\\\\\\left( \\\\\\\\mathrm{O}\\\\\\\\right) \\\\\\\\mathrm{{OC}}{\\\\\\\\left( {\\\\\\\\mathrm{{CH}}}_{3}\\\\\\\\right) }_{3}}\\\\\\\\right)$ : (a) Propargyl bromide, ${\\\\\\\\mathrm{K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,DMF,rt, $2\\\\\\\\mathrm{\\\\\\\\;h},{44}\\\\\\\\%$ ; (b) 4-Bromo-2-fluoropyridine (62),NaH,DMF,0 to ${25}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},1\\\\\\\\mathrm{\\\\\\\\;h},{72}\\\\\\\\%$ ; (c) tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67),RuPhosPd G2, ${\\\\\\\\mathrm{{Cs}}}_{2}{\\\\\\\\mathrm{{CO}}}_{3},{90}{}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2$ h, 79%; (d) Pd/C, ${\\\\\\\\mathrm{H}}_{2}$ ,MeOH,rt,12 h,56%; (e) TFA,DCM,,rt,4 h,62%; (f) 4-Bromo-6-chloro-pyridazin-3-amine (70), DIEA,NMP, ${1200}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2$ h, 65%; (g) (2-(Methoxymethoxy)-phenyl)boronic acid (85),Pd(PPh ${}_{3}{)}_{4},{\\\\\\\\mathrm{\\\\\\\\;K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,10:1 1,4-dioxane: ${\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O},{90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},2\\\\\\\\mathrm{\\\\\\\\;h},{60}\\\\\\\\%$ ; (h) 6-Iodopyridin-3-ol, PPh ${}_{3}$ ,DIAD,0 to ${25}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},{12}\\\\\\\\mathrm{\\\\\\\\;h},{58}\\\\\\\\%$ ; (i) Intermediate 145,TEA,Pd(PPh ${}_{3}{)}_{2}{\\\\\\\\mathrm{{Cl}}}_{2}$ ,CuI,DMF, ${65}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},3\\\\\\\\mathrm{\\\\\\\\;h},{76}\\\\\\\\%$ ; (j) ${4.0}\\\\\\\\mathrm{M}\\\\\\\\mathrm{{HCl}}$ in $\\\\\\\\mathrm{{MeOH}},\\\\\\\\mathrm{{rt}},4\\\\\\\\mathrm{\\\\\\\\;h};\\\\\\\\left( \\\\\\\\mathrm{k}\\\\\\\\right)$ chiral HPLC, $3\\\\\\\\%$ over 2 steps. \\\"]\",\n \"img_path\": \"images/0371/b8002d9d770f581c009fba241aef8042c6ad270648804eed092883a61f55cae9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,630,482,870]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"in enantiopure intermediate 60 (Scheme 3) via a Mitsunobu process provided intermediate 150. This entity was then deprotected by exposure to aqueous acid, and the resulting aldehyde (151) was reductively coupled with intermediate 119 (Scheme 9) to afford PROTAC 25. Alternatively, intermediate 117 (Scheme 9) was coupled with phenylboronic acid, and the resulting product (not shown) was deprotected under acidic conditions to give amine 152. This entity was then reductively coupled with enantiopure aldehyde 61 (Scheme 3) to afford PROTAC 26. Similarly, inversion of the secondary hydroxyl group present in enantiopure intermediate 127 (Scheme 10) provided intermediate 153. Conversion of this material to the corresponding aldehyde (154) and subsequent reductive coupling with intermediate 119 (Scheme 9) then gave PROTAC 27. To complete these syntheses, enantiopure aldehyde 128 (Scheme 10) was reductively coupled with intermediate 152 to afford control compound 28. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,870,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, the preparation of VHL binding fragments 155 and 156 that were employed to confirm the stereochemistries of the majority of the degrader compounds described in this work is shown in Scheme 16. Racemic intermediate 40 (Scheme 1) was condensed with 1-bromo-2-(2-methoxyethoxy)ethane \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,630,917,770]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"under mildly basic conditions to give ester 157. This material was subsequently hydrolyzed, and the resulting carboxylic acid (158) was coupled with enantiomerically pure intermediate 57 (Scheme 3) to afford a mixture of compounds 155 and 156 ( $\\\\sim$ 1:1). These molecules were then separated using preparative chiral HPLC to afford the individual compounds. VHL binding assessments and crystal structure determination of the complex formed between 155 and VHL (Figures S14-S16) then enabled assignment of the isopropyl group stereocenters contained in the two compounds. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,783,658,797]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CONCLUSIONS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,803,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This work describes the identification and subsequent exploration of novel PROTAC molecules which utilize the VHL E3 ubiquitin ligase to potently and extensively degrade the BRM (SMARCA2) protein. These compounds were derived from a 3,8-diazabicyclo[3.2.1]octane BRM-binding fragment that extended from the protein into solvent. The majority of the PROTACs depicted in these studies exhibited some degree of degradation selectivity for BRM over the closely related BRG1 paralog in in vitro assessments. Enhancement of in vivo DMPK properties, in particular \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1287 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,380,86]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 15. Synthesis of PROTACs $25 - 28^{a}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[153,90,835,250]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0656/238964dc05d54e4e9edc8150e83cd2607a44f3217d250548c395cb83f2bc288a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[153,282,739,396]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0066/f4ce988e67f856b26c18b49894fa99c4ddb4180918bbcd222d3c71b1a0393a75.jpg\",\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[153,418,840,578]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0867/3dabbf883541335d3e799756473334629932b4ca4046a560e943cd3703753bf6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[362,623,515,646]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions: (a) ${\\\\\\\\mathrm{{PPh}}}_{3}$ ,DIAD,AcOH,THF,0 to ${25}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},1 - 3\\\\\\\\mathrm{\\\\\\\\;h},{32} - {94}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{b}\\\\\\\\right) {\\\\\\\\mathrm{{NH}}}_{3}$ ,MeOH,rt,2 h,69-80%; (c) ${\\\\\\\\mathrm{{HCO}}}_{2}\\\\\\\\mathrm{H},{\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O},{60}$ ${}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},1 - 2\\\\\\\\mathrm{\\\\\\\\;h}$ ; (d) Intermediate 119, NaOAc, ${\\\\\\\\mathrm{{NaBH}}}_{3}\\\\\\\\mathrm{{CN}},3 : 1\\\\\\\\mathrm{{MeOH}} : \\\\\\\\mathrm{{DCM}},\\\\\\\\mathrm{{rt}},{12}\\\\\\\\mathrm{\\\\\\\\;h},{33} - {43}\\\\\\\\%$ over 2 steps; (e) Phenylboronic acid, $\\\\\\\\mathrm{{Pd}}{\\\\\\\\left( {\\\\\\\\mathrm{{PPh}}}_{3}\\\\\\\\right) }_{4}$ , ${\\\\\\\\mathrm{K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3},{90}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},3\\\\\\\\mathrm{\\\\\\\\;h},{61}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{f}\\\\\\\\right) {4.0}\\\\\\\\mathrm{M}\\\\\\\\mathrm{{HCl}}$ in $\\\\\\\\mathrm{{MeOH}},\\\\\\\\mathrm{{rt}},2\\\\\\\\mathrm{\\\\\\\\;h},{94}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{g}\\\\\\\\right)$ Intermediate 61, NaOAc, ${\\\\\\\\mathrm{{NaBH}}}_{3}\\\\\\\\mathrm{{CN}},\\\\\\\\mathrm{{MeOH}},\\\\\\\\mathrm{{rt}},3\\\\\\\\mathrm{\\\\\\\\;h},{11}\\\\\\\\% ;\\\\\\\\left( \\\\\\\\mathrm{h}\\\\\\\\right)$ Intermediate 152, NaOAc, ${\\\\\\\\mathrm{{NaBH}}}_{3}\\\\\\\\mathrm{{CN}},3 : 1\\\\\\\\mathrm{{MeOH}} : \\\\\\\\mathrm{{DCM}},\\\\\\\\mathrm{{rt}},1\\\\\\\\mathrm{\\\\\\\\;h},6\\\\\\\\%$ . \\\"]\",\n \"img_path\": \"images/0499/ed6df892aea495b8f3b857874c6fe2f5e45ca6e273515e9da935ebb74f2fafff.jpg\",\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[80,718,515,735]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scheme 16. Synthesis of VHL Binding Fragments 155 and $156^{a}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[144,738,851,880]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[\\\"${}^{a}$ Reagents and conditions: (a) 1-Bromo-2-(2-methoxyethoxy)ethane, ${\\\\\\\\mathrm{K}}_{2}{\\\\\\\\mathrm{{CO}}}_{3}$ ,DMF, ${60}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},1\\\\\\\\mathrm{\\\\\\\\;h},{81}\\\\\\\\%$ ; (b) LiOH, 1:1 THF: ${\\\\\\\\mathrm{H}}_{2}\\\\\\\\mathrm{O}$ ,rt, $2\\\\\\\\mathrm{\\\\\\\\;h},{88}\\\\\\\\%$ ; (c) Intermediate 57,HATU,DIEA, ${25}^{ \\\\\\\\circ }\\\\\\\\mathrm{C},1\\\\\\\\mathrm{\\\\\\\\;h}$ ; (d) Chiral HPLC, ${20}\\\\\\\\%$ over 2 steps. \\\"]\",\n \"img_path\": \"images/0754/3ffc1f9e5e026fe81f1e68abb060b25b9bd94be8edcb6f0ed17677876cfb1266.jpg\",\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1288 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,481,250]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"mouse IV clearance and half-life parameters, afforded multiple compounds which displayed selective in vivo BRM degradation activity in single-administration PK/PD experiments (both IP and IV dosing; for other recent examples of in vivo exploration of a BRM-targeting PROTAC, see refs31, 32). Quantitation of mRNA associated with two genes whose transcription was controlled by BRM (PLAU and KRT80) provided additional differentiation of tested compounds beyond the protein degradation results. These studies, coupled with the associated in vitro characterization data, enabled the successful identification of an in vivo tool compound that was progressed into multiadministration efficacy experiments (compound 19; A947). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,250,479,692]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"These endeavors demonstrated the ability of compound 19 to afford meaningful in vivo antitumor activity against the HCC2302 BRM-dependent xenograft model. They also illustrated a need for near-complete BRM degradation in order to achieve the desired efficacy results, although the time course associated with such suppression was not explored. In addition, the multiadministration in vivo studies revealed that, in spite of the selective BRM degradation activity mentioned above, long-term dosing of the compound was often associated with suboptimal mouse tolerability outcomes. Several in vivo control experiments demonstrated that the poor tolerability results were not due to the physicochemical properties of the tested molecules and were also likely not related to degradation and/or inhibition of proteins other than BRM and/or BRG1. We currently suspect that the finite BRG1/BRM degradation selectivities exhibited by the identified PROTACs were eroded by high local concentrations of the compounds in sensitive tissues during the multiadministration efficacy experiments. Accordingly, it was important to independently customize the doses and administration frequencies so as to maximize antitumor effects while retaining acceptable tolerability results (see ref 42 for additional descriptions of such explorations for PROTAC 19). For the degraders described in this work, IV administration afforded improved in vivo efficacy performance relative to IP dosing, and the former dosing route was employed to achieve the antitumor effects associated with compound 19. Collectively, the results described in this work suggest that the identification of BRM-degrader PROTACs with further improved BRG1/BRM degradation selectivity properties and/or the use of alternate in vivo delivery strategies may be required to afford robust development candidates. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,710,296,722]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"EXPERIMENTAL SECTION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,730,481,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"General Chemistry Methods. All chemicals, reagents, and solvents were at least reagent grade and were obtained from various commercial sources. The general removal of solvents was conducted by using a rotary evaporator. Residual solvents were then removed from the compounds using a vacuum manifold with $< 10 \\\\mathrm{mmHg}$ pressure and/or via compound lyophilization. ${}^{1}\\\\mathrm{H}$ NMR spectra were recorded on spectrometers operating at 500, 400, or $300\\\\mathrm{MHz}$ and are reported in parts per million (ppm) using signals from nondeuterated solvent components as references. LC-MS spectral data were obtained using standard electrospray ionization mass spectrometry. Normal phase silica gel chromatography, both flash column and preparatory thin-layer, was conducted using Merck silica gel 60 as specifically indicated. Reverse phase and chiral chromatographic separations were conducted using columns and conditions specifically indicated in the experimental procedures below. All reagents and starting materials were derived from commercial sources unless otherwise indicated. All reactions were conducted under a nitrogen \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,71,915,158]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"atmosphere unless otherwise indicated. Salts of amine-containing products (including final PROTAC molecules) are typically not mentioned in the various experimental descriptions even though they may have been generated by the synthesis and/or purification conditions employed. Chemical purities were $\\\\geq 95\\\\%$ for all Table 2 compounds as assessed by LC-MS analysis at UV $254~\\\\mathrm{nm}$ (exception $= 22$ ; $93\\\\%$ pure). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,158,915,343]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(3-Bromoisoxazol-5-yl)ethan-1-ol (31). A solution of hydroxycarbonimidic dibromide (29, 20.0 g, 98.6 mmol, 1.0 equiv) in EtOAc (50 mL) was added dropwise at room temperature to a solution of but-3-yn-1-ol (30, 28.0 g, 399 mmol, 4.0 equiv) and potassium bicarbonate (30.0 g, 300 mmol, 3.0 equiv) in EtOAc:water (200:20 mL). The resulting mixture was stirred at room temperature for 16 h then was diluted with water (100 mL). The organic layer was separated, and the aqueous layer was extracted with EtOAc (100 mL × 2). The combined organic layers were washed with brine (150 mL), dried over anhydrous sodium sulfate, and were concentrated under reduced pressure. The residue was purified by silica gel chromatography eluting with EtOAc:petroleum ether (0:100 to 25:75) to give the title compound 31 (18.5 g, 98%) as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(\\\\mathrm{CD}_3\\\\mathrm{OD}, 400\\\\mathrm{MHz})$ $\\\\delta$ 6.23 (s, 1H), 3.96 (t, $J = 6.1\\\\mathrm{Hz}$ , 2H), 3.03 (t, $J = 6.1\\\\mathrm{Hz}$ , 2H). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,345,914,480]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(3-Bromoisoxazol-5-yl)-3-methylbutanoic acid (32). 2-(3-Bromoisoxazol-5-yl)ethan-1-ol (31, $18.5\\\\mathrm{g}$ , $96.3\\\\mathrm{mmol}$ ) was dissolved in acetone $(220~\\\\mathrm{mL})$ at $0^{\\\\circ}\\\\mathrm{C}$ , and Jones reagent $(19.2\\\\mathrm{g}$ $\\\\mathrm{CrO}_3$ dissolved in $90~\\\\mathrm{mL}$ of $6.0\\\\mathrm{M}$ $\\\\mathrm{H}_2\\\\mathrm{SO}_4$ at $0^{\\\\circ}\\\\mathrm{C}$ ) was added dropwise. The resulting solution was stirred at $25^{\\\\circ}\\\\mathrm{C}$ for $12\\\\mathrm{h}$ then was diluted with water $(100~\\\\mathrm{mL})$ and extracted with EtOAc $(200~\\\\mathrm{mL} \\\\times 3)$ . The combined organic layers were washed with brine, dried over anhydrous sodium sulfate, and were concentrated under reduced pressure to afford the crude title compound 32 $(17.9\\\\mathrm{g}, 90\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ , $\\\\mathrm{CDCl}_3$ $\\\\delta 6.43$ (s, 1H), 3.81-3.74 (m, 2H). LC-MS $(\\\\mathrm{ES+}): m/z 205.9$ $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,481,914,641]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methyl 2-(3-bromoisoxazol-5-yl)-3-methylbutanoate (33). A solution of 2-(3-bromoisoxazol-5-yl)-3-methylbutanoic acid (32, 17.9 g, 86.9 mmol) and concentrated $\\\\mathrm{H}_2\\\\mathrm{SO}_4$ (1.5 mL, 28.1 mmol) in MeOH (150 mL) was stirred at $70^{\\\\circ}\\\\mathrm{C}$ for 2 h. The resulting mixture was cooled to room temperature and was concentrated under reduced pressure. The residue was diluted with water (100 mL) and then extracted with EtOAc (200 mL × 3). The combined organic layers were washed with brine (100 mL), dried over anhydrous sodium sulfate, and were concentrated under reduced pressure. The residue was purified by silica gel chromatography eluting with EtOAc:petroleum ether (0:100 to 25:75) to give the title compound 33 (12.4 g, 65%) as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR (400 MHz, CDCl₃) δ 6.39 (s, 1H), 3.84 (s, 2H), 3.76 (s, 3H). LC-MS (ES+): m/z 221.9 $[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,641,914,840]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methyl 2-(3-bromoisoxazol-5-yl)-3-methylbutanoate (34). Methyl 2-(3-bromoisoxazol-5-yl)-3-methylbutanoate (33, $12.4\\\\mathrm{g}$ 56.3 mmol, 1.0 equiv) was dissolved in THF $(120~\\\\mathrm{mL})$ at $0^{\\\\circ}\\\\mathrm{C}$ and t-BuOK $(9.17\\\\mathrm{g},81.7\\\\mathrm{mmol},1.45\\\\mathrm{equiv})$ was added. After stirring for $10\\\\mathrm{min}$ at $0^{\\\\circ}\\\\mathrm{C}$ , a solution of 2-iodopropane $(12.2\\\\mathrm{g},71.7\\\\mathrm{mmol},$ 1.27 equiv) in THF was added dropwise. The reaction mixture was stirred at room temperature for $16\\\\mathrm{h}$ then was quenched with ice water $(200~\\\\mathrm{mL})$ . The resulting mixture was extracted with EtOAc $(200~\\\\mathrm{mL}\\\\times 3)$ , and the combined organic layers were washed with brine $(100~\\\\mathrm{mL})$ , dried over anhydrous sodium sulfate, and were concentrated under reduced pressure. The residue was purified by silica gel chromatography eluting with EtOAc:petroleum ether (0:100 to 20:80) to afford the title compound 34 $(8.2\\\\mathrm{g},56\\\\%)$ as a yellow oil. ${}^{1}\\\\mathbf{H}$ NMR $\\\\mathrm{(CD_3OD}$ $400\\\\mathrm{MHz}$ $\\\\delta 6.38$ s,1H)3.74s3H)3.65d $J$ $= 8.4\\\\mathrm{Hz}$ 1H)2.44-2.31 m,1H)1.01 d $J = 2.4\\\\mathrm{Hz}$ 3H)0.92 d $J = 6.8\\\\mathrm{Hz}$ 3H). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,841,914,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(3-Methoxyisoxazol-5-yl)-3-methylbutanoic acid (35). To a room temperature solution of a portion of methyl 2-(3-bromoisoxazol-5-yl)-3-methylbutanoate prepared above (34, $3.0\\\\mathrm{g}$ , $11.4\\\\mathrm{mmol}$ , $1.0\\\\mathrm{equiv}$ ) in $\\\\mathrm{MeOH}$ ( $22\\\\mathrm{mL}$ ) was added KOH ( $6.6\\\\mathrm{g}$ , $115\\\\mathrm{mmol}$ , $10\\\\mathrm{equiv}$ ). The reaction mixture was refluxed for $4\\\\mathrm{h}$ then was cooled to room temperature. The resulting solution was acidified to $\\\\mathrm{pH} \\\\approx 5$ with HCl ( $1.0\\\\mathrm{M}$ aqueous solution) and then was concentrated under reduced pressure. The residue was purified by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[532,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[485,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1289 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,953,912,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[764,962,912,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,71,481,135]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"reverse phase chromatography (gradient: $5\\\\% -40\\\\%$ $\\\\mathrm{CH}_3\\\\mathrm{CN}$ in water $(0.1\\\\%$ formic acid)) to yield the title compound 35 $(1.51\\\\mathrm{g},66\\\\%)$ as a colorless thick oil. ${}^{1}\\\\mathrm{H}$ NMR $(\\\\mathrm{CD}_3\\\\mathrm{OD},400\\\\mathrm{MHz})$ $\\\\delta$ 5.93s,1H),3.97 s,3H),3.53d $J = 8.4 \\\\mathrm{Hz}$ 1H2.44-2.35m1H)1.06d $J = 6.8$ Hz,3H),0.96d $J = 6.4 \\\\mathrm{Hz}$ 3H). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,133,481,308]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3-(Benzyloxy)-5-methylisoxazole (37). To a stirred mixture of 5-methylisoxazol-3-ol $(36,50\\\\mathrm{g},505\\\\mathrm{mmol},1.0$ equiv) and potassium carbonate $(105\\\\mathrm{g},757\\\\mathrm{mmol})$ in 1-methyl-2-pyrrolidinone $(400~\\\\mathrm{mL})$ was added benzyl bromide $(72~\\\\mathrm{mL}$ $605~\\\\mathrm{mmol}$ 1.2 equiv) in 1- methyl-2-pyrrolidinone $(100~\\\\mathrm{mL})$ dropwise at $60^{\\\\circ}\\\\mathrm{C}$ over $4\\\\mathrm{h}$ The mixture was stirred at $60^{\\\\circ}\\\\mathrm{C}$ for an additional $0.5\\\\mathrm{h}$ then was cooled to room temperature and was diluted with EtOAc $(500~\\\\mathrm{mL})$ .The diluted mixture was washed with water $(200~\\\\mathrm{mL}\\\\times 2)$ and brine (300 $\\\\mathrm{mL}\\\\times 3)$ , and the organic layer was dried over sodium sulfate and concentrated under reduced pressure. The residue was purified by chromatography on silica gel (solvent gradient: $0 - 5\\\\%$ EtOAc in petroleum ether) to afford the title compound 37 $(44\\\\mathrm{g},46\\\\%)$ as colorless oil. ${}^{1}\\\\mathrm{H}$ NMR $(\\\\mathrm{CDCl}_3,400\\\\mathrm{MHz})$ $\\\\delta 7.29 - 7.53$ m5H),5.66 $(d,J = 0.8\\\\mathrm{Hz},1\\\\mathrm{H})$ 5.25s2H2.34d $J = 0.8 \\\\mathrm{Hz}$ 3H). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,308,481,507]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methyl 2-(3-(benzyloxy)isoxazol-5-yl)acetate (38). To a mixture of 3-(benzyloxy)-5-methylisoxazole (37, 44 g, 233 mmol, 1.0 equiv) in THF (770 mL) was added lithium diisopropylamide (2.0 M in THF, 128 mL, 256 mmol, 1.1 equiv) dropwise at $-78^{\\\\circ}\\\\mathrm{C}$ . The mixture was stirred at $-78^{\\\\circ}\\\\mathrm{C}$ for $0.5\\\\mathrm{h}$ then dimethyl carbonate (23.5 mL, 279 mmol, 1.2 equiv) in THF (66 mL) was added dropwise, and stirring was continued at $-78^{\\\\circ}\\\\mathrm{C}$ for an additional $3\\\\mathrm{h}$ . The mixture was quenched at $-78^{\\\\circ}\\\\mathrm{C}$ with saturated aqueous $\\\\mathrm{NH}_4\\\\mathrm{Cl}$ (100 mL), diluted with EtOAc (300 mL), and was washed sequentially with water (300 mL × 2) and brine (200 mL). The organic layer was dried over sodium sulfate and was concentrated under reduced pressure. The residue was purified by chromatography on silica gel (solvent gradient: $0 - 20\\\\%$ EtOAc in petroleum ether) to afford the title compound 38 (19 g, 33%). ${}^{1}\\\\mathrm{H}$ NMR $(\\\\mathrm{CDCl}_3, 400\\\\mathrm{MHz})$ $\\\\delta$ 7.31–7.50 (m, 5H), 5.95 (s, 1H), 5.27 (s, 2H), 3.76 (s, 3H), 3.74 (s, 2H). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,507,481,706]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methyl 2-(3-(benzyloxy)isoxazol-5-yl)-3-methylbutanoate (39). To a $20^{\\\\circ}\\\\mathrm{C}$ mixture of methyl 2-(3-(benzyloxy)isoxazol-5-yl)acetate (38, 19.0 g, 76.9 mmol, 1.0 equiv) and 2-iodopropane (14.4 g, 84.5 mmol, 1.1 equiv) in DMF (190 mL) was added 1.0 M KOtBu in THF (99.9 mL, 99.9 mmol, 1.3 equiv). The mixture was stirred at $20^{\\\\circ}\\\\mathrm{C}$ for $12\\\\mathrm{h}$ then was diluted with EtOAc $(300\\\\times 2\\\\mathrm{mL})$ .The diluted mixture was quenched with water $(300~\\\\mathrm{mL})$ and was subsequently washed with water $(200~\\\\mathrm{mL}\\\\times 2)$ and brine $(300~\\\\mathrm{mL})$ The organic layer was dried over sodium sulfate and was concentrated under reduced pressure. The residue was purified by chromatography on silica gel (solvent gradient: $0 - 5\\\\%$ EtOAc in petroleum ether) to afford the title compound 39 $(18.3\\\\mathrm{g},82\\\\%)$ as yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $\\\\mathrm{(CDCl_3}$ $400\\\\mathrm{MHz})$ $\\\\delta$ 7.49-7.33 m5H5.94s1H5.26s2H), 3.77-3.68 m3H),3.51d $J = 8.8\\\\mathrm{Hz}$ 1H2.49-2.25m1H), 1.01 d $J = 6.4\\\\mathrm{Hz}$ 3H),0.94d $J = 6.8\\\\mathrm{Hz}$ 3H.LC-MS $(\\\\mathrm{ES + })$ .. $m/$ $z290.0[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,706,481,855]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methyl 2-(3-hydroxy-1,2-oxazol-5-yl)-3-methylbutanoate (40). A mixture of methyl 2-(3-(benzyloxy)isoxazol-5-yl)-3-methylbutanoate (39, 2.0 g, 6.91 mmol, 1.0 equiv) and titanium tetrachloride (0.99 mL, 8.99 mmol, 1.3 equiv) in DCM (20 mL) was stirred at 25 °C for 13 h then was quenched with water (10 mL). The resulting solution was extracted with EtOAc (30 mL × 3) and the combined organic layers were dried over sodium sulfate and concentrated under reduced pressure. The residue was purified by silica gel chromatography (0–15% EtOAc in petroleum ether) to afford the title compound 40 (1.30 g, 94%) as yellow oil. $^1\\\\mathrm{H}$ NMR (400 MHz, CDCl₃) δ 5.94 (s, 1H), 3.73 (s, 3H), 3.47 (d, J = 9.2 Hz, 1H), 2.43–2.30 (m, 1H), 1.00 (d, J = 6.8 Hz, 3H), 0.92 (d, J = 6.8 Hz, 3H). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,855,481,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methyl 2-(3-(2,2-diethoxyethoxy)isoxazol-5-yl)-3-methylbutanoate (41). A solution of methyl 2-(3-hydroxyisoxazol-5-yl)-3-methylbutanoate (40, 500 mg, 2.51 mmol, 1.0 equiv), 2-bromo-1,1-diethoxyethane (743 mg, 3.77 mmol, 1.5 equiv) and $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ (693 mg, 5.02 mmol, 2.0 equiv) in DMF (7 mL) was stirred at $70^{\\\\circ}\\\\mathrm{C}$ for $8\\\\mathrm{h}$ . The mixture was allowed to cool to room temperature, and the reaction was quenched by the addition of saturated aqueous $\\\\mathrm{NH}_4\\\\mathrm{Cl}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,275]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The aqueous layer was extracted with EtOAc $(100\\\\mathrm{mL}\\\\times 3)$ , and the combined organic layers were dried over anhydrous sodium sulfate and concentrated under reduced pressure. The residue was purified by prepacked C18 column (CH $_3$ CN in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3, 0$ to $80\\\\%)$ to afford the title compound 41 $(0.39\\\\mathrm{g}, 49\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 6.26 (s, 1H), 4.81 (t, $J = 5.2\\\\mathrm{Hz}$ , 1H), 4.11 (d, $J = 5.2\\\\mathrm{Hz}$ , 2H), 3.73-3.60 (m, 6H), 3.60-3.48 (m, 2H), 2.37-2.24 (m, 1H), 1.13 (t, $J = 7.0\\\\mathrm{Hz}$ , 6H), 0.94 (d, $J = 6.7\\\\mathrm{Hz}$ , 3H), 0.85 (d, $J = 6.7\\\\mathrm{Hz}$ , 3H). LC-MS (ESI): $m/z$ 316 $[\\\\mathbf{M} + \\\\mathbf{H}]^+$ . A small amount of the corresponding isoxazole $N$ -alkylation product (structure not shown) eluted ahead of compound 41 and was isolated as a yellow oil $(0.077\\\\mathrm{g}, 7\\\\%)$ . ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 5.87 (s, 1H), 4.70 (t, $J = 5.5\\\\mathrm{Hz}$ , 1H), 3.88 (d, $J = 5.5\\\\mathrm{Hz}$ , 2H), 3.66 (s, 3H), 3.62-3.51 (m, 3H), 3.41-3.39 (m, 2H), 2.34-2.21 (m, 1H), 1.12-1.04 (m, 6H), 0.95 (d, $J = 6.7\\\\mathrm{Hz}$ , 3H), 0.91 (d, $J = 6.7\\\\mathrm{Hz}$ , 3H). LC-MS $(\\\\mathrm{ES}+): m/z$ 316 $[\\\\mathbf{M} + \\\\mathbf{H}]^+$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,275,915,462]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(3-(2,2-Diethoxyethoxy)isoxazol-5-yl)-3-methylbutanoic acid (42). To a room temperature solution of methyl 2-(3-(2,2-diethoxyethoxy)isoxazol-5-yl)-3-methylbutanoate (41, 4.38 g, 12.5 mmol, 1.0 equiv) in MeOH (30 mL) and water (15 mL) was added lithium hydroxide (2.10 g, 50 mmol, 4.0 equiv). The reaction mixture was stirred at $40^{\\\\circ}\\\\mathrm{C}$ for 2 h then was cooled to room temperature. The pH was adjusted to $\\\\sim 5$ with $1.0\\\\mathrm{M}$ HCl, and the mixture was extracted with EtOAc (50 mL × 2). The combined organic layers were dried over anhydrous sodium sulfate, filtered and the filtrate was concentrated to produce the title compound 42 (4.0 g, crude) as a colorless oil. ${}^{1}\\\\mathrm{H}$ NMR (400 MHz, CDCl₃) δ 5.96 (s, 1H), 4.85 (t, J = 5.2 Hz, 1H), 4.25 (d, J = 5.2 Hz, 2H), 3.81–3.70 (m, 2H), 3.66–3.57 (m, 2H), 3.53 (d, J = 8.4 Hz, 1H), 2.48–2.28 (m, 1H), 1.24 (t, J = 6.8 Hz, 6H), 1.05 (d, J = 6.4 Hz, 3H), 0.95 (d, J = 6.8 Hz, 3H). LC-MS (ES+): m/z 302.1 [M + H]+. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,462,915,663]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methyl 3-methyl-2-[3-(1,1,2,2,3,3,4,4,4-nonafluorobutylsulfonyloxy)isoxazol-5-yl]butanoate (43). 1,1,2,2,3,3,4,4,4-Nonafluorobutane-1-sulfonyl chloride (2.81 g, 8.84 mmol, 1.1 equiv) was added dropwise to a $0^{\\\\circ}\\\\mathrm{C}$ solution of methyl 2-(3-hydroxyisoxazol-5-yl)-3-methylbutanoate (40, 1.60 g, 8.03 mmol, 1.0 equiv) and $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ (2.22 g, 16.0 mmol, 2.0 equiv) in $\\\\mathrm{CH}_3\\\\mathrm{CN}$ (20 mL). The resulting mixture was stirred at room temperature for $2\\\\mathrm{h}$ then was quenched with saturated aqueous $\\\\mathrm{NH}_4\\\\mathrm{Cl}$ and extracted with EtOAc $(100\\\\mathrm{mL} \\\\times 3)$ . The combined organic layers were dried over sodium sulfate and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (DCM: petroleum ether, 0:100 to 2:3) to afford the title compound (3.48 g, 90%) as a colorless oil. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 7.03 (s, 1H), 4.03 (d, $J = 7.9~\\\\mathrm{Hz}$ , 1H), 3.70 (s, 3H), 2.45–2.30 (m, 1H), 0.94 (d, $J = 6.7~\\\\mathrm{Hz}$ , 3H), 0.86 (d, $J = 6.7~\\\\mathrm{Hz}$ , 3H). LC-MS (ES+): $m/z$ 482 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,663,915,815]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tert-Butyl 4-(5-(1-methoxy-3-methyl-1-oxobutan-2-yl)-isoxazol-3-yl)piperazine-1-carboxylate (45). A solution of intermediate 43 $(3.20\\\\mathrm{g},6.65\\\\mathrm{mmol}$ 1.0 equiv and tert-butyl piperazine-1-carboxylate (44, $1.24\\\\mathrm{g},6.65\\\\mathrm{mmol}$ 1.0 equiv) in DMF $(32~\\\\mathrm{mL})$ was stirred at $130^{\\\\circ}\\\\mathrm{C}$ for $4\\\\mathrm{h}$ After cooling to room temperature, the reaction mixture was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ - 0 to $60\\\\%$ ) to afford the title compound $(860\\\\mathrm{mg},35\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 6.28 $\\\\left(\\\\mathrm{d},J = 1.1\\\\mathrm{Hz},1\\\\mathrm{H}\\\\right)$ 3.69- 3.58 m4H3.48-3.36m4H3.22-3.11m4H2.36-2.21 m1H),1.42 $\\\\left(\\\\mathrm{d},J = 1.2\\\\mathrm{Hz},9\\\\mathrm{H}\\\\right)$ 0.98-0.88m3H0.88-0.81m 3H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 368 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,815,915,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(3-(4-(tert-Butoxycarbonyl)piperazin-1-yl)isoxazol-5-yl)-3-methylbutanoic acid (46). To a room temperature solution of intermediate 45 $(860\\\\mathrm{mg},2.34\\\\mathrm{mmol},1.0$ equiv) in THF $(5\\\\mathrm{mL})$ was added a solution of LiOH $(112\\\\mathrm{mg},4.68\\\\mathrm{mmol})$ in $\\\\mathrm{H}_2\\\\mathrm{O}$ $(5\\\\mathrm{mL})$ . The resulting mixture was stirred at room temperature for $1\\\\textrm{h}$ then was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH_4HCO_3)}$ 0 to $50\\\\%$ ) to afford the title compound $(820\\\\mathrm{mg},99\\\\%)$ as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 6.01s,1H), 3.45-3.35 m,3H),3.22-2.99 m,6H),2.27-2.08 m,1H),1.41 s, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1290 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,70,481,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"9H), 0.92 (d, $J = 6.6\\\\\\\\mathrm{Hz}$ 3H), 0.76 (d, $J = 6.7\\\\\\\\mathrm{Hz}$ 3H). LC-MS (ES +): $m / z$ 354 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . \\\",\\\"Piperidine-4-carbaldehyde (48). A solution of tert-butyl 4-formylpiperidine-1-carboxylate (47, 500 mg, 2.34 mmol) was stirred at room temperature for $2\\\\\\\\mathrm{h}$ in a solution of HCl in 1,4-dioxane (4.0 M, 5.0 mL). The mixture was then poured into MTBE (60 mL) and the solids were collected by filtration. The filter cake was dried under reduced pressure to give the title compound (294 mg, 84%) as a white solid. ${}^{1}\\\\\\\\mathrm{H}$ NMR (400 MHz, DMSO- $\\\\\\\\tilde{d}_6$ ) $\\\\\\\\delta$ 9.59 (s, 1H), 9.09 (s, 1H), 8.86 (s, 1H), 3.29–3.13 (m, 2H), 3.00–2.79 (m, 2H), 2.69–2.58 (m, 1H), 2.09–1.95 (m, 2H), 1.72–1.60 (m, 2H). LC-MS (ES+): $m/z$ 114 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . \\\",\\\"Benzyl 4-formylpiperidine-1-carboxylate (49). To a $25^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ solution of piperidine-4-carbaldehyde (48, 250 g, 1.34 mol, 1.0 equiv) in DCM (1.75 L) was added TEA (411 mL, 2.96 mol) and benzyl chloroformate (210 mL, 1.48 mol, 1.1 equiv). The mixture was stirred at $25^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for $15\\\\\\\\mathrm{h}$ whereupon TLC analysis (petroleum ether:EtOAc = 3:1) showed that the starting material $(\\\\\\\\mathbb{R}_{\\\\\\\\mathrm{f}} = 0.0)$ was completely consumed. The reaction mixture was quenched by addition water (2 L) and was subsequently extracted with DCM $(600~\\\\\\\\mathrm{mL} \\\\\\\\times 3)$ . The combined organic layers were washed with brine $(600~\\\\\\\\mathrm{mL})$ , dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (petroleum ether:EtOAc = 50:1 to 0:1) to give the title compound 49 (440 g, 44%) as a green oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR (400 MHz, $\\\\\\\\mathrm{CDCl}_3$ ) $\\\\\\\\delta$ 9.66 (s, 1H), 7.37-7.33 (m, 3H), 7.33-7.30 (m, 2H), 5.13 (s, 2H), 4.11-4.05 (m, 2H), 3.05-3.00 (m, 2H), 2.46-2.40 (m, 1H), 1.91 (br s, 2H), 1.63-1.54 (m, 2H). \\\",\\\"Benzyl 4-(dimethoxymethyl)piperidine-1-carboxylate (50). To a $25^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ solution of benzyl 4-formylpiperidine-1-carboxylate (49, $450\\\\\\\\mathrm{g},$ $1.82\\\\\\\\mathrm{mol}$ 1.0 equiv) in trimethoxymethane $(997~\\\\\\\\mathrm{mL},$ $9.10\\\\\\\\mathrm{mol})$ was added p-TsOH $(15.7\\\\\\\\mathrm{g},$ 91 mmol, 0.50 equiv). The mixture was stirred at $25^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for $2\\\\\\\\textrm{h}$ after which TLC analysis (petroleum ether:EtOAc $= 2:1$ ) showed that the starting material $\\\\\\\\left(\\\\\\\\mathbb{R}_{\\\\\\\\mathrm{f}} = 0.40\\\\\\\\right)$ was completely consumed. The pH of the reaction mixture was adjusted to 8.0 with saturated aqueous sodium bicarbonate, and the mixture was extracted with EtOAc $(1\\\\\\\\mathrm{L}\\\\\\\\times 3)$ .The combined organic layers were washed with brine $(300~\\\\\\\\mathrm{mL})$ , dried over anhydrous sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (petroleum ether:EtOAc $= 80:1$ to 0:1) to give the title compound 50 $(330\\\\\\\\mathrm{g},63\\\\\\\\%)$ as a light yellow oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(400\\\\\\\\mathrm{MHz}$ $\\\\\\\\mathrm{CDCl}_3$ ) $\\\\\\\\delta$ 7.36-7.26 (m, 5H), 5.12 (s, 1H), 4.12-4.11 (m, 2H), 4.02-4.01 (m, 1H), 3.34 (s, 6H), 2.75 (s, 2H), 1.77-1.76 (m, 1H), 1.75-1.71 (m, 2H), 1.27-1.23 (m, 2H). \\\",\\\"4-(Dimethoxymethyl)piperidine (51). To a mixture of $\\\\\\\\mathrm{Pd / C}$ $(10\\\\\\\\mathrm{g},5\\\\\\\\%)$ in THF $(500~\\\\\\\\mathrm{mL})$ was added a solution of benzyl 4- dimethoxymethyl)piperidine-1-carboxylate (50, $95\\\\\\\\mathrm{g}$ $324\\\\\\\\mathrm{mmol}$ ) in THF $(500~\\\\\\\\mathrm{mL})$ at $25^{\\\\\\\\circ}C.$ The reaction mixture was purged with $\\\\\\\\mathrm{H}_{2}$ three times and was then stirred at $25^{\\\\\\\\circ}C$ under an $\\\\\\\\mathrm{H}_{2}$ atmosphere (45 psi) for $12\\\\\\\\mathrm{h}$ TLC analysis (petroleum ether:EtOAc $= 2:1$ showed that the starting material $(R_{\\\\\\\\mathrm{f}} = 0.50)$ was completely consumed. The reaction mixture was filtered, and the filter cake was washed with THF $(1.5\\\\\\\\mathrm{L}\\\\\\\\times 5)$ .The combined filtrate and washings were concentrated under reduced pressure to provide the title compound 51 as a brown oil. The products obtained from three additional preparations of 51 using the above method and scale were combined to give a single lot of the material $(175\\\\\\\\mathrm{g},85\\\\\\\\%)$ . ${}^{1}\\\\\\\\mathrm{H}$ NMR $(400\\\\\\\\mathrm{MHz}$ $\\\\\\\\mathrm{CDCl}_3$ 84.00-3.99 m1H3.31s6H3.07-3.04 m2H2.57-2.51m2H1.73-1.70m1H1.69-1.64m 2H),1.18-1.15m2H). \\\",\\\"Methyl 2-(3-(4-(dimethoxymethyl)piperidin-1-yl)isoxazol-5- yl)-3-methylbutanoate (52). To a $25^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ mixture of intermediate 43 $(160\\\\\\\\mathrm{g},332\\\\\\\\mathrm{mmol},1.0$ equiv) and 4-(dimethoxymethyl)piperidine (51, $79\\\\\\\\mathrm{g},499\\\\\\\\mathrm{mmol},1.5$ equiv) in DMF $(1.6~\\\\\\\\mathrm{L})$ was added DIEA $(173~\\\\\\\\mathrm{mL},997~\\\\\\\\mathrm{mmol},3.0$ equiv) in one portion. The mixture was stirred at $80^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for $12\\\\\\\\mathrm{h}$ then was cooled to $25^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ and poured into ice-water $(10\\\\\\\\mathrm{L})$ . After stirring for $15\\\\\\\\mathrm{min}$ the mixture was extracted with EtOAc $(3\\\\\\\\mathrm{L}\\\\\\\\times 5)$ . The combined organic phases were washed with brine $(1\\\\\\\\mathrm{L}\\\\\\\\times 3)$ ,dried over sodium sulfate, filtered, and were \\\"]\",\n \"page_idx\": \"29\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[512,71,915,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"concentrated in vacuum. The above procedure was repeated two additional times, and the combined crude products were dissolved in EtOAc $(200\\\\\\\\mathrm{mL})$ and filtered to remove insoluble materials. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (petroleum ether:EtOAc, 80:1 to 0:1) to give the title compound 52 $(102\\\\\\\\mathrm{g}, 26\\\\\\\\%$ yield) as a orange syrup. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(400\\\\\\\\mathrm{MHz}, \\\\\\\\mathrm{CDCl}_3)$ $\\\\\\\\delta$ 5.90 (s, 1H), 4.06-4.04 (m, 1H), 3.72-3.69 (m, 5H), 3.47-3.45 (m, 1H), 3.36 (s, 6H), 2.82-2.76 (m, 2H), 2.33-2.32 (m, 1H), 1.18-1.18 (m, 1H), 1.77-1.78 (m, 2H), 1.39-1.35 (m, 2H), 0.99-0.98 (m, 3H), 0.92-0.90 (m, 3H). \\\",\\\"2-(3-(4-(Dimethoxymethyl)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoic acid (53). A solution of intermediate 52 $(480\\\\\\\\mathrm{mg},$ $1.41\\\\\\\\mathrm{mmol}$ 1.0 equiv) and LiOH $(102\\\\\\\\mathrm{mg}$ $4.23\\\\\\\\mathrm{mmol}$ 3.0 equiv) in tetrahydrofuran $(2\\\\\\\\mathrm{mL})$ and water $(2\\\\\\\\mathrm{mL})$ was stirred at room temperature for $2\\\\\\\\mathrm{h}$ The crude reaction mixture was directly purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\%)$ $\\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ ,0 to $100\\\\\\\\%$ ) to afford the title compound $(320\\\\\\\\mathrm{mg},70\\\\\\\\%)$ as a yellow oil. ${}^{1}\\\\\\\\mathbf{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 6.13s,1H4.05 $\\\\\\\\left(\\\\\\\\mathrm{d},J = 6.7\\\\\\\\mathrm{Hz},1\\\\\\\\mathrm{H}\\\\\\\\right)$ 3.63 $\\\\\\\\left(\\\\\\\\mathrm{d},J = 12.4\\\\\\\\mathrm{Hz},2\\\\\\\\mathrm{H}\\\\\\\\right)$ 3.34 $\\\\\\\\left(\\\\\\\\mathrm{d},J = 9.0\\\\\\\\mathrm{Hz},\\\\\\\\right.$ 1H),3.25s,6H),2.76-2.62 m,2H),2.30-2.12 m,1H),1.80- 1.56 m,3H),1.32-1.14 m,2H),0.93 $\\\\\\\\left(\\\\\\\\mathrm{d},J = 6.6\\\\\\\\mathrm{Hz},3\\\\\\\\mathrm{H}\\\\\\\\right)$ 0.80 d $J$ $= 6.7~\\\\\\\\mathrm{Hz}$ 3H).LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 327 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ \\\",\\\"(2S,4R)-4-Hydroxy-1-(2-(3-hydroxyisoxazol-5-yl)-3-methylbutanoyl)-N-(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (55). A solution of intermediate 35 (248 mg, 1.24 mmol, 1.0 equiv), (2S,4R)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (54,46,54 HCl salt, 790 mg, 2.23 mmol, 1.8 equiv), HATU (710 mg, 1.87 mmol, 1.5 equiv) and DIEA (642 mg, 4.98 mmol, 4.0 equiv) in DMF (8 mL) was stirred at room temperature for 2 h. The resulting mixture was diluted with EtOAc (100 mL) and washed with water (100 mL). The organic layer was dried over sodium sulfate and was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CN_3CN}$ in water $(0.05\\\\\\\\% \\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ , 0 to $100\\\\\\\\%$ to afford (2S,4R)-4-hydroxy-1-(2-(3-methoxyisoxazol-5-yl)-3-methylbutanoyl)-N-(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (290 mg, $48\\\\\\\\%$ ) as a white solid. ${}^{1}\\\\\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\\\\\delta$ 8.99 (s, 1H), 8.64–8.31 (m, 1H), 7.45–7.29 (m, 4H), 6.16–5.97 (m, 1H), 5.12 (t, $J = 4.1~\\\\\\\\mathrm{Hz}$ , 1H), 4.57–4.19 (m, 4H), 3.90–3.64 (m, 4H), 3.57 (s, 1H), 3.45 (d, $J = 10.3~\\\\\\\\mathrm{Hz}$ , 1H), 2.45 (d, $J = 4.4~\\\\\\\\mathrm{Hz}$ , 3H), 2.30–2.16 (m, 1H), 2.12–1.98 (m, 1H), 1.98–1.81 (m, 1H), 1.00–0.55 (m, 6H). LC-MS $(\\\\\\\\mathrm{ES}+)$ : $m/z$ 499 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . A solution of this material (380 mg, 0.762 mmol) and aqueous HBr (40%, 5 mL) was stirred at $60^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for $4\\\\\\\\mathrm{h}$ . The mixture was cooled to room temperature and was directly purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\% \\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ , 0 to $100\\\\\\\\%$ to afford the title compound (210 mg, $55\\\\\\\\%$ ) as a white solid. ${}^{1}\\\\\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\\\\\delta$ 8.99 (s, 1H), 8.55–8.40 (m, 1H), 7.54–7.27 (m, 4H), 5.95–5.60 (m, 1H), 5.21–4.92 (m, 1H), 4.54–4.19 (m, 4H), 3.81–3.61 (m, 1H), 3.60–3.49 (m, 1H), 3.48–3.36 (m, 1H), 2.45 (d, $J = 4.4~\\\\\\\\mathrm{Hz}$ , 3H), 2.32–2.11 (m, 1H), 2.09–1.82 (m, 2H), 1.01–0.55 (m, 6H). LC-MS $(\\\\\\\\mathrm{ES}+)$ : $m/z$ 485 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . \\\",\\\"(2S,4R)-1-(2-(3-(2-Bromoethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)benzyl)-pyrrolidine-2-carboxamide (56). A mixture of intermediate 55 $(175\\\\\\\\mathrm{mg},0.361\\\\\\\\mathrm{mmol},1.0$ equiv), 1,2-dibromoethane $(67.8\\\\\\\\mathrm{mg},0.361$ mmol, 1.0 equiv) and $\\\\\\\\mathrm{Cs_2CO_3}$ $353~\\\\\\\\mathrm{mg}$ 1.08 mmol, 3.0 equiv) in $\\\\\\\\mathrm{CH}_3\\\\\\\\mathrm{CN}$ $(2\\\\\\\\mathrm{mL})$ was stirred at $70^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for $3\\\\\\\\mathrm{h}$ The resulting mixture was cooled to room temperature and was filtered. The filter cake was washed with $\\\\\\\\mathrm{CH}_3\\\\\\\\mathrm{CN}$ $(10~\\\\\\\\mathrm{mL})$ , and the combined filtrate and washings were concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\%)$ $\\\\\\\\mathrm{NH_4HCO_3}$ 0 to $100\\\\\\\\%$ ) to afford the title compound $(123\\\\\\\\mathrm{mg},58\\\\\\\\%)$ as a white solid. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8.98s,1H)8.49dt $J = 11.8$ $5.8~\\\\\\\\mathrm{Hz}$ 1H7.51-7.29 m4H) 6.19-6.07 m1H5.12 t $J = 3.8~\\\\\\\\mathrm{Hz}$ 1H4.71-4.19 m6H) 3.92-3.37 m5H2.44 d $J = 5.1~\\\\\\\\mathrm{Hz}$ 3H2.30-2.24 m1H) 2.07-2.01 m1H)1.98-1.83 m1H)1.05-0.50 m6H.LCMS $(\\\\\\\\mathrm{ES + })$ .. $m / z~591 / 593[\\\\\\\\mathrm{M} + \\\\\\\\mathrm{H}]^{+}$ \\\"]\",\n \"page_idx\": \"29\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1291 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,70,481,245]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-4-Hydroxy- $N\\\\cdot$ ((S)-1-(4-(4-methylthiazol-5-yl)- phenyl)ethyl)pyrrolidine-2-carboxamide (57). A solution of tert-butyl (2S,4R)-4-hydroxy-2-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)- ethyl)carbamoyl)pyrrolidine-1-carboxylate[48,55] $(2.56~\\\\mathrm{g}, 5.93~\\\\mathrm{mmol})$ and TFA $(5\\\\mathrm{mL})$ in DCM $(25~\\\\mathrm{mL})$ was stirred at room temperature overnight. The mixture was then concentrated under reduced pressure, and the residue was purified by silica gel column chromatography (MeOH:DCM, 0:100 to 1:5) to afford the title compound (TFA salt, $2.39\\\\mathrm{g}$ , $91\\\\%$ ) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) $\\\\delta$ 9.80 (br, 1H), 9.42–8.95 (m, 2H), 8.64 (s, 1H), 7.55–7.35 (m, 4H), 5.53 (s, 1H), 5.10–4.95 (m, 1H), 4.55–4.28 (m, 2H), 3.35–3.05 (m, 2H), 2.46 (s, 3H), 2.40–2.30 (m, 1H), 1.92–1.74 (m, 1H), 1.43 (d, $J = 7.0~\\\\mathrm{Hz}$ , 3H). LC-MS $(\\\\mathrm{ES+})$ : $m/z$ 332 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,245,481,607]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-4-Hydroxy-1-(2-(3-hydroxyisoxazol-5-yl)-3-methylbutanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)-pyrrolidine-2-carboxamide (58). To a room temperature solution of intermediate 57 (TFA salt, $912\\\\mathrm{mg}$ , $2.05\\\\mathrm{mmol}$ , 1.0 equiv) in DMF $(7.5\\\\mathrm{mL})$ were added intermediate 35 $(449\\\\mathrm{mg},2.25\\\\mathrm{mmol},1.1\\\\mathrm{equiv})$ and DIEA $(874\\\\mathrm{mg},6.77\\\\mathrm{mmol},3.3\\\\mathrm{equiv})$ , and HATU $(1.29\\\\mathrm{g},3.39\\\\mathrm{mmol},1.65\\\\mathrm{equiv})$ . The reaction was stirred at room temperature for $1\\\\mathrm{h}$ , then was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\\\left(\\\\mathrm{CH}_3\\\\mathrm{CN}\\\\right.$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ to afford $(2S,4R)$ -4-hydroxy-1-(2-(3-methoxyisoxazol-5-yl)-3-methylbutanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide $(865\\\\mathrm{mg},75\\\\%)$ as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 8.98 (s, 1H), 8.48–8.27 (m, 1H), 7.51–7.30 (m, 4H), 6.08 (d, $J = 1.0~\\\\mathrm{Hz}$ , 1H), 5.10 (t, $J = 3.9~\\\\mathrm{Hz}$ , 1H), 5.07–4.83 (m, 1H), 4.53–4.32 (m, 1H), 4.27 (s, 1H), 3.90–3.81 (m, 3H), 3.80–3.60 (m, 1H), 3.60–3.44 (m, 2H), 2.49–2.42 (m, 3H), 2.34–2.19 (m, 1H), 2.19–1.98 (m, 1H), 1.98–1.72 (m, 1H), 1.49–1.33 (m, 3H), 1.05–0.71 (m, 6H). LC-MS $(\\\\mathrm{ES}+)$ : $m/z$ 513 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . A solution of this material $(400\\\\mathrm{mg},0.78\\\\mathrm{mmol})$ in aqueous HBr $(40\\\\%,10\\\\mathrm{mL})$ was stirred at $60^{\\\\circ}\\\\mathrm{C}$ for $4.5\\\\mathrm{h}$ then was cooled to room temperature and directly purified by prepacked C18 column chromatography $\\\\left(\\\\mathrm{CH}_3\\\\mathrm{CN}\\\\right.$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ to afford the title compound $(380\\\\mathrm{mg},98\\\\%)$ as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 9.01–8.89 (m, 1H), 8.47–9.25 (m, 1H), 7.51–7.30 (m, 4H), 5.88–5.78 (m, 1H), 5.09 (s, 1H), 5.03–4.85 (m, 1H), 4.56–4.34 (m, 1H), 4.27 (s, 1H), 3.74–3.64 (m, 1H), 3.60–3.02 (m, 2H), 2.49–2.43 (m, 3H), 2.30–2.16 (m, 1H), 2.09–1.97 (m, 1H), 1.84–1.73 (m, 1H), 1.48–1.33 (m, 3H), 1.00–0.72 (m, 6H). LC-MS $(\\\\mathrm{ES}+)$ : $m/z$ 499 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,607,481,830]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-(2-(3-(2-Bromoethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)-ethyl)pyrrolidine-2-carboxamide (59). A mixture of intermediate 58 $(350\\\\mathrm{mg},0.702\\\\mathrm{mmol},1.0\\\\mathrm{equiv})$ , 1,2-dibromoethane $(263\\\\mathrm{mg}$ $1.40\\\\mathrm{mmol},2.0\\\\mathrm{equiv})$ and $\\\\mathrm{Cs_2CO_3}$ $(457\\\\mathrm{mg},1.41\\\\mathrm{mmol},2.0\\\\mathrm{equiv})$ in $\\\\mathrm{CH}_3\\\\mathrm{CN}$ $(3.5\\\\mathrm{mL})$ was stirred at $70^{\\\\circ}\\\\mathrm{C}$ for $2\\\\textrm{h}$ then was cooled to room temperature. The mixture was then filtered, and the filter cake was washed with $\\\\mathrm{CH}_3\\\\mathrm{CN}$ $(10~\\\\mathrm{mL})$ . The combined filtrate and washings were concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH_4HCO_3}$ 0 to $100\\\\%$ ) to afford the title compound $(160\\\\mathrm{mg},38\\\\%)$ as a light yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ DMSO $d_{6})$ $\\\\delta$ 9.02-8.88 (m, 1H), 8.47-8.25 (m, 1H), 7.52-7.28 (m, 4H), 6.19-6.08 (m, 1H), 5.09 (t, $J = 3.5~\\\\mathrm{Hz}$ 1H), 4.98-4.85 (m, 1H), 4.56-4.33 (m, 3H), 4.27 (s, 1H), 3.85-3.63 (m, 3H), 3.59-3.38 (m, 2H), 2.47-2.42 (m, 3H), 2.35-2.20 (m, 1H), 2.19-1.98 (m, 1H), 1.97-1.70 (m, 1H), 1.50-1.31 (m, 3H), 1.02-0.73 (m, 6H). LCMS $(\\\\mathrm{ES + })$ .. $m / z$ 605/607 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,830,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-(2-(3-(2,2-Diethoxyethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (60). A solution of intermediate 42 (4.80 g, 15.9 mmol, 1.01 equiv), (2S,4R)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (57, 5.78 g, 15.7 mmol, 1.0 equiv), HATU (7.29 g, 19.2 mmol, 1.2 equiv) and DIEA (6.19 g, 48.0 mmol, 3.06 equiv) in DMF (60 mL) was stirred at room temperature for 30 min. The reaction mixture was then directly purified by prepacked C18 column \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,383]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ 0 to $100\\\\%$ to afford $7.8\\\\mathrm{g}$ of a $\\\\sim 1:1$ mixture of 60 and the corresponding isopropyl epimer (structure not shown) as a yellow solid. This mixture was separated by preparative chiral SFC [column: CHIRAL ART Amylose-SA, $5\\\\times 25~\\\\mathrm{cm}^2$ $5\\\\mu \\\\mathrm{m}$ mobile phase A: $\\\\mathrm{CO}_{2}$ mobile phase B: MeOH; flow rate: $200~\\\\mathrm{mL / min}$ ; gradient: isocratic $40\\\\%$ B; column temperature $35^{\\\\circ}\\\\mathrm{C}$ back pressure: 100 bar; wavelength: 220 nm; RT1:2.61 min; RT2:3.63 min; sample solvent: MeOH $(0.1\\\\% 2\\\\mathrm{M}$ $\\\\mathrm{NH}_3$ -MeOH)] to yield $2.57\\\\mathrm{g}$ faster peak (60e, isopropyl isomer corresponding to 60, structure not shown) and $3.00\\\\mathrm{g}$ slower peak (desired isopropyl isomer, 60, $31\\\\%$ ) as yellow solids. Faster peak (undesired isomer, 60e): ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz},$ DMSO- $d_{6})$ 9.02 s, 1H),8.31 d, $J = 7.8\\\\mathrm{Hz}$ 1H),7.58-7.29 m4H),6.16s1H),5.09 $\\\\left(\\\\mathrm{d},J = 3.6\\\\mathrm{Hz},1\\\\mathrm{H}\\\\right)$ 5.05-4.71 m,2H),4.52-4.38 m,1H),4.25 s, 1H),4.19-4.04 m,2H),3.83-3.39 m,7H),2.44 d, $J = 3.4\\\\mathrm{Hz}$ 3H),2.32-1.74 m,3H),1.54-1.30 m,3H),1.23-1.09 m,6H), 1.08-0.73 m,6H).LC-MS $(\\\\mathrm{ES + })$ ..m/z 615 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ .Slower peak (desired isomer, 60): ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz},$ DMSO- $d_{6})$ 8.97 d, $J =$ $2.6\\\\mathrm{Hz},1\\\\mathrm{H})$ 8.40d $J = 7.7\\\\mathrm{Hz},1\\\\mathrm{H})$ 7.50-7.26 m,4H),6.12 s, 1H),5.08 d, $J = 3.3\\\\mathrm{Hz},1\\\\mathrm{H})$ ,4.95-4.80 m,1H),4.79 t $J = 5.2\\\\mathrm{Hz}$ 1H),4.36 t, $J = 7.8\\\\mathrm{Hz},1\\\\mathrm{H})$ ,4.26 s, 1H),4.08 d, $J = 5.2\\\\mathrm{Hz},2\\\\mathrm{H})$ 3.73-3.36 m,7H),2.44 d, $J = 1.5\\\\mathrm{Hz},3\\\\mathrm{H})$ ,2.29-1.96 m,2H), 1.80-1.65 m,1H),1.50-1.30 m,3H),1.20-1.05 m,6H),1.05- 0.90 m,3H),0.85-0.70 m,3H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 615 $[\\\\mathbf{M}+$ $\\\\mathrm{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,383,915,568]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-4-Hydroxy-1-((R)-3-methyl-2-(3-(2-oxoethoxy)-isoxazol-5-yl)butanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (61). A solution of intermediate 60 $(200\\\\mathrm{mg},0.325\\\\mathrm{mmol})$ in $1\\\\mathrm{M}\\\\mathrm{H}_2\\\\mathrm{SO}_4$ $(3\\\\mathrm{mL})$ and THF $(3\\\\mathrm{mL})$ was stirred at $50^{\\\\circ}\\\\mathrm{C}$ for $5\\\\mathrm{h}$ then was concentrated under reduced pressure. The $\\\\mathsf{pH}$ of the residue was adjusted to 7.0 with saturated aqueous $\\\\mathrm{NaHCO_3}$ solution, and the resulting mixture was extracted with EtOAc $(100~\\\\mathrm{mL}\\\\times 3)$ . The combined organic layers were washed with brine $(50~\\\\mathrm{mL})$ , dried over sodium sulfate, and were concentrated under reduced pressure to afford the crude title compound $(220\\\\mathrm{mg})$ as a yellow solid. The crude product was used in subsequent steps without further purification. LC-MS $(\\\\mathrm{ES}+)$ : $m/z$ 541 $[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ . Similar transformation of intermediate 60e afforded compound 61e (isopropyl isomer corresponding to 61, structure not shown). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,568,915,792]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(2-(2-(2-((4-Bromopyridin-2-yl)oxy)ethoxy)ethoxy)-ethoxy)ethan-1-ol (64). To a $0^{\\\\circ}\\\\mathrm{C}$ solution of 3,6,9-trioxaundecane-1,11-diol $(63,4.78\\\\mathrm{g},24.6\\\\mathrm{mmol},2.0$ equiv) in DMF $(25~\\\\mathrm{mL})$ was added NaH $(60\\\\%)$ in mineral oil, $540\\\\mathrm{mg}$ $13.5\\\\mathrm{mmol}$ 1.1 equiv). The reaction was warmed to room temperature and was stirred for 30 min whereupon 4-bromo-2-fluoropyridine $(62,2.17\\\\mathrm{g},12.3\\\\mathrm{mmol},1.0$ equiv) was added. The resulting mixture was stirred for additional $2\\\\textrm{h}$ at $75^{\\\\circ}\\\\mathrm{C}$ then was cooled to $0^{\\\\circ}\\\\mathrm{C}$ and was quenched with water (100 mL). The resulting mixture was extracted with EtOAc $(150~\\\\mathrm{mL}\\\\times 3)$ , and the combined organic layers were dried over sodium sulfate and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 100:0) to afford the title compound $(3.0\\\\mathrm{g},70\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8.07 d $J = 5.5\\\\mathrm{Hz}$ 1H7.23dd $J = 5.5$ $1.7\\\\mathrm{Hz}$ 1H 7.15d $J = 1.6\\\\mathrm{Hz}$ 1H4.58t $J = 5.4\\\\mathrm{Hz}$ 1H4.43-4.34m2H 3.78-3.68m2H3.62-3.45m10H3.45-3.36m2H.LCMS $(\\\\mathrm{ES + })$ .. $m / z$ 350 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,791,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(2-(2-(2-((4-Bromopyridin-2-yl)oxy)ethoxy)ethoxy)-ethoxy)acetic acid (65). A solution of intermediate 64 $(1.68\\\\mathrm{g},4.81$ mmol, 1.0 equiv), TEMPO $(149~\\\\mathrm{mg}$ $0.96\\\\mathrm{mmol}$ $0.20$ equiv and $\\\\mathrm{PhI(OAc)_2}$ $(4.63\\\\mathrm{g},14.4\\\\mathrm{mmol},3.0$ equiv) in DCM $(15~\\\\mathrm{mL})$ and water $(7.5~\\\\mathrm{mL})$ was stirred at room temperature for $2\\\\textrm{h}$ The resulting mixture was extracted with EtOAc $(100~\\\\mathrm{mL}\\\\times 3)$ ,and the combined organic layers were washed with water $(100~\\\\mathrm{mL})$ , dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (MeOH:DCM, 0:100 to 7:93) to afford the title compound $(810\\\\mathrm{mg},$ $46\\\\%)$ as a yellow oil. ${}^{1}\\\\mathbf{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 12.56s, 1H),8.07d $J = 5.5\\\\mathrm{Hz}$ 1H),7.23dd $J = 5.5$ $1.7\\\\mathrm{Hz}$ 1H),7.15d, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1292 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,71,481,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"$J = 1.6\\\\\\\\mathrm{Hz}$ 1H),4.43-4.34 (m,2H),4.02 (s,2H),3.78-3.69 (m, 2H),3.63-3.48 (m,8H). LC-MS $(\\\\\\\\mathrm{ES} + )$ .. $m / z$ 364 $[\\\\\\\\mathrm{M} + \\\\\\\\mathrm{H}]^{+}$ \\\",\\\"Methyl 2-(2-(2-(4-bromopyridin-2-yl)oxy)ethoxy)-ethoxy)ethoxy)acetate (66). To a $0^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ solution of intermediate 65 $(790\\\\\\\\mathrm{mg},$ 2.17 mmol, 1.0 equiv) in MeOH $(8\\\\\\\\mathrm{mL})$ was added $\\\\\\\\mathrm{SOCl}_2$ $(1.02\\\\\\\\mathrm{g},$ 8.68 mmol, 4.0 equiv). The reaction was warmed to room temperature and was stirred for $4\\\\\\\\mathrm{h}$ After quenching the reaction with aqueous $\\\\\\\\mathrm{NaHCO_3}$ solution (to adjust the $\\\\\\\\mathsf{pH}$ to $\\\\\\\\sim 8)$ the resulting mixture was extracted with DCM $(100~\\\\\\\\mathrm{mL}\\\\\\\\times 3)$ .The combined organic layers were washed with water $(100~\\\\\\\\mathrm{mL})$ ,dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure to afford the title compound $(600\\\\\\\\mathrm{mg},73\\\\\\\\%)$ as a yellow oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ ,DMSO- $d_{6})$ $\\\\\\\\delta 8.07$ d $J = 5.5\\\\\\\\mathrm{Hz}$ 1H),7.23dd $J = 5.5$ 1.7 Hz1H),7.18-7.12 m1H),4.43-4.34 m,2H),4.13s,2H),3.78-3.68m2H),3.65s,3H),3.62-3.49 m,8H).LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z378[\\\\\\\\mathrm{M} + \\\\\\\\mathrm{H}]^{+}$ \\\",\\\"tert-Butyl 8-(2-((3-oxo-2,5,8,11-tetraoxatridecan-13-yl)oxy)-pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate (68). A solution of intermediate 66 $(580\\\\\\\\mathrm{mg},1.53\\\\\\\\mathrm{mmol},1.0$ equiv), tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, $651~\\\\\\\\mathrm{mg}$ 3.07 mmol, 2.0 equiv), RuphosPd G2 (119 mg, 0.15 mmol, 0.10 equiv) and $\\\\\\\\mathrm{Cs}_2\\\\\\\\mathrm{CO}_3$ $(1.50\\\\\\\\mathrm{g},4.60\\\\\\\\mathrm{mmol},3.0$ equiv) in toluene (10 mL) was stirred at $90^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for $^{\\\\\\\\textrm{\\\\\\\\scriptsize 4h}}$ . After cooling to room temperature, the mixture was diluted with EtOAc $(100~\\\\\\\\mathrm{mL})$ and was washed with water $(100~\\\\\\\\mathrm{mL})$ . The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 90:10) to afford the title compound $(670~\\\\\\\\mathrm{mg},85\\\\\\\\%)$ as a yellow oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 7.78 d $J = 6.0~\\\\\\\\mathrm{Hz}$ 1H)6.49dd $J = 6.0$ $2.1\\\\\\\\mathrm{Hz}$ 1H) 6.15d $J = 2.0\\\\\\\\mathrm{Hz}$ 1H4.36s2H4.29t $J = 4.8~\\\\\\\\mathrm{Hz}$ 2H4.14 s,2H)3.74-3.66 m2H)3.64 s,3H)3.62-2.50(m,10H)3.07 d $J = 12.9\\\\\\\\mathrm{Hz}$ 1H)2.93d $J = 13.0\\\\\\\\mathrm{Hz}$ 1H)1.96-1.86m2H) 1.74-1.61 m,2H),1.39 s,9H.LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 510 $[\\\\\\\\mathbf{M}+$ $\\\\\\\\mathrm{H}]^{+}$ \\\",\\\"Methyl 2-(2-(2-(2-((4-(3,8-diazabicyclo[3.2.1]octan-8-yl)-pyridin-2-yl)oxy)ethoxy)ethoxy)ethoxy)ethoxy)acetate (69). A solution of intermediate 68 $(555\\\\\\\\mathrm{mg},1.09\\\\\\\\mathrm{mmol})$ in TFA $(1\\\\\\\\mathrm{mL})$ and DCM $(5\\\\\\\\mathrm{mL})$ was stirred at room temperature for $2\\\\\\\\textrm{h}$ The volatiles were removed under vacuum, and the residue was purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\% \\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ 0 to $100\\\\\\\\%$ ) to afford the title compound $(380\\\\\\\\mathrm{mg},85\\\\\\\\%)$ as a yellow oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ ,DMSO- $d_{6})$ 7.72d $J = 6.0~\\\\\\\\mathrm{Hz}$ 1H),6.40 (dd, $J = 6.0$ $2.1\\\\\\\\mathrm{Hz}$ 1H),6.01d $J = 2.1\\\\\\\\mathrm{Hz}$ 1H),4.28t $J = 4.8\\\\\\\\mathrm{Hz}$ 2H),4.16s,2H),4.14s,2H),3.73-3.66m2H),3.65s,3H), 3.62-3.51 m8H),2.84 d $J = 12.2\\\\\\\\mathrm{Hz}$ 2H),2.43d $J = 12.2\\\\\\\\mathrm{Hz}$ 2H),1.99-1.80 m,4H).LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 410 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ \\\",\\\"Methyl 2-(2-(2-(4-(3-(3-amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)ethoxy)acetate (71). A solution of intermediate 69 (460 mg, 1.12 mmol, 1.0 equiv), 4-bromo-6-chloro-pyridazin-3-amine (70, 351 mg, 1.69 mmol, 1.5 equiv) and DIEA (434 mg, 3.37 mmol, 3.0 equiv) in NMP (8 mL) was stirred at $120^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for 3 h. After cooling to room temperature, the crude mixture was purified by prepacked C18 column chromatography $\\\\\\\\left(\\\\\\\\mathrm{CH}_3\\\\\\\\mathrm{CN}\\\\\\\\right.$ in water $(0.05\\\\\\\\%)$ $\\\\\\\\mathrm{NH_4HCO_3)}$ , 0 to $100\\\\\\\\%$ ) to afford the title compound $(300~\\\\\\\\mathrm{mg},~50\\\\\\\\%)$ as a yellow oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 7.78 d $J = 6.0\\\\\\\\mathrm{Hz}$ 1H6.90s1H) 6.52dd $J = 6.1$ $2.1\\\\\\\\mathrm{Hz}$ 1H6.17d $J = 2.0\\\\\\\\mathrm{Hz}$ 1H5.84s2H) 4.47s2H4.34-4.26m2H4.13s2H3.73-3.66m2H) 3.64s3H)3.62-3.50m8H)3.18d $J = 11.6\\\\\\\\mathrm{Hz}$ 2H2.87d $J$ $= 11.6\\\\\\\\mathrm{Hz}$ 2H)2.20-2.10m2H)1.98-1.89m2H.LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 537 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ \\\",\\\"Methyl 2-(2-(2-(2-((4-(3-(3-amino-6-(2-hydroxyphenyl)- pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)- oxy)ethoxy)ethoxy)ethoxy)acetate (73). A solution of intermediate 71 $(290\\\\\\\\mathrm{mg},0.54\\\\\\\\mathrm{mmol},1.0$ equiv), 2-hydroxyphenylboronic acid $(72,223\\\\\\\\mathrm{mg},1.62\\\\\\\\mathrm{mmol},3.0$ equiv), $\\\\\\\\mathrm{K}_2\\\\\\\\mathrm{CO}_3$ $(223\\\\\\\\mathrm{mg},1.62\\\\\\\\mathrm{mmol},$ 3.0 equiv) and $\\\\\\\\mathrm{Pd(PPh_3)_4}$ $(62.3\\\\\\\\mathrm{mg},0.0538\\\\\\\\mathrm{mmol},0.10$ equiv) in 1,4- dioxane $(3\\\\\\\\mathrm{mL})$ was stirred at $90^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for $2\\\\\\\\textrm{h}$ then was cooled to room temperature. The resulting mixture was diluted with EtOAc $(100~\\\\\\\\mathrm{mL})$ and was washed with water $(100~\\\\\\\\mathrm{mL})$ .The organic layer was dried \\\"]\",\n \"page_idx\": \"31\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[512,71,915,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\% \\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ , 0 to $100\\\\\\\\%$ to afford the title compound $(120~\\\\\\\\mathrm{mg},37\\\\\\\\%)$ as a yellow solid. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(400\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.15 (s, 1H), 7.93 (dd, $J = 8.1$ $1.6\\\\\\\\mathrm{Hz}$ 1H), 7.80 (d, $J = 6.0\\\\\\\\mathrm{Hz}$ 1H), 7.51 (s, 1H), 7.27-7.18 (m, 1H), 6.91-6.81 (m, 2H), 6.55 (dd, $J = 6.1$ $2.1\\\\\\\\mathrm{Hz}$ 1H), 6.20 (d, $J = 2.1\\\\\\\\mathrm{Hz}$ 1H), 5.98 (s, 2H), 4.51 (d, $J = 4.4\\\\\\\\mathrm{Hz}$ 2H), 4.33-4.26 (m, 2H), 4.13 (s, 2H), 3.73-3.66 (m, 2H), 3.64 (s, 3H), 3.62-3.50 (m, 8H), 3.25 (d, $J = 11.3\\\\\\\\mathrm{Hz}$ ,2H), 3.03 (d, $J = 11.6\\\\\\\\mathrm{Hz}$ ,2H), 2.23-2.15 (m, 2H), 2.01-1.94 (m, 2H). LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 595 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ \\\",\\\"2-(2-(2-(4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4- yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)- ethoxy)ethoxy)acetic acid (74). A solution of intermediate 73 $(120\\\\\\\\mathrm{mg},0.20\\\\\\\\mathrm{mmol},1.0$ equiv) and LiOH $(9.7\\\\\\\\mathrm{mg},0.40\\\\\\\\mathrm{mmol},2.0$ equiv) in THF $(2\\\\\\\\mathrm{mL})$ and water $(2\\\\\\\\mathrm{mL})$ was stirred at room temperature for $^{\\\\\\\\textrm{\\\\\\\\scriptsize 1h}}$ . The crude mixture was directly purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.1\\\\\\\\%)$ TFA), 0 to $100\\\\\\\\%$ ) to afford the title compound $(110\\\\\\\\mathrm{mg},94\\\\\\\\%)$ as a yellow oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 7.93 d $J = 7.0~\\\\\\\\mathrm{Hz}$ 1H),7.63d $J = 7.4\\\\\\\\mathrm{Hz}$ 1H),7.52s,1H),7.42-7.31m1H) 7.05-6.91 m,2H),6.89-6.72 m,3H),6.55 s,1H),4.84 s,2H) 4.48-4.41 m,2H),4.01 s,2H),3.84-3.75 m,2H),3.64-3.50 m, 10H),3.23-3.12 m,2H),2.29-2.19 m,2H),2.08-1.95 m,2H). LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 581 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ \\\",\\\"(2S,4R)-1-((2S)-14-((4-(3-(3-Amino-6-(2-hydroxyphenyl)-pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)-2-(tert-butyl)-4-oxo-6,9,12-trioxa-3-azatetradecanoyl)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (11). A room temperature solution of intermediate 74 $(110\\\\\\\\mathrm{mg},0.19\\\\\\\\mathrm{mmol},1.1$ equiv), intermediate $75^{48}$ (HCl salt, 81.5 mg, 0.174 mmol, 1.0 equiv), HATU $(108\\\\\\\\mathrm{mg},0.284\\\\\\\\mathrm{mmol},1.6$ equiv) and DIEA $(164\\\\\\\\mathrm{mg},1.27\\\\\\\\mathrm{mmol},7.3$ equiv) in DMF $(3\\\\\\\\mathrm{mL})$ was stirred for $2\\\\\\\\mathrm{h}$ . The resulting mixture was diluted with EtOAc $(100\\\\\\\\mathrm{mL})$ and was washed with water $(100\\\\\\\\mathrm{mL})$ . The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by preparative HPLC [column: XBridge Prep OBD C18 column, 30 $\\\\\\\\times 150\\\\\\\\mathrm{mm}^2$ , $5\\\\\\\\mu \\\\\\\\mathrm{m}$ ; mobile phase A: water $(10\\\\\\\\mathrm{mmol / L}$ $\\\\\\\\mathrm{NH_4HCO_3})$ , mobile phase B: $\\\\\\\\mathrm{CH}_3\\\\\\\\mathrm{CN}$ ; flow rate: $60~\\\\\\\\mathrm{mL / min}$ ; gradient: $39\\\\\\\\%$ B to $56\\\\\\\\%$ B over $9\\\\\\\\mathrm{min}$ ; RT: $8.1\\\\\\\\mathrm{min}$ ] to afford the title compound $(49\\\\\\\\mathrm{mg},26\\\\\\\\%)$ as a white solid. ${}^{1}\\\\\\\\mathbf{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\\\\\delta$ 14.14 (s, 1H), 8.97 (s, 1H), 8.60 (t, $J = 6.0~\\\\\\\\mathrm{Hz}$ , 1H), 7.96-7.87 (m, 1H), 7.78 (d, $J = 5.9~\\\\\\\\mathrm{Hz}$ , 1H), 7.49 (s, 1H), 7.45-7.35 (m, 5H), 7.22 (t, $J = 7.8~\\\\\\\\mathrm{Hz}$ , 1H), 6.91-6.79 (m, 2H), 6.57-6.51 (m, 1H), 6.18 (s, 1H), 5.97 (s, 2H), 5.14 (d, $J = 3.5~\\\\\\\\mathrm{Hz}$ , 1H), 4.56 (d, $J = 9.7~\\\\\\\\mathrm{Hz}$ , 1H), 4.52-4.48 (m, 2H), 4.47-4.39 (m, 1H), 4.39-4.33 (m, 2H), 4.31-4.25 (m, 3H), 3.97 (s, 2H), 3.72-3.52 (m, 12H), 3.25 (d, $J = 11.4~\\\\\\\\mathrm{Hz}$ , 2H), 3.02 (d, $J = 11.6~\\\\\\\\mathrm{Hz}$ , 2H), 2.44 (s, 3H), 2.23-2.14 (m, 2H), 2.12-2.00 (m, 1H), 2.00-1.87 (m, 3H), 0.94 (s, 9H). LC-MS $(ES+)$ : $m/z$ 993 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . \\\",\\\"2-(2-(2-((4-Bromopyridin-2-yl)oxy)ethoxy)ethoxy)ethoxy)ethan-1-ol (81). A solution of 3,6-dioxoacetane-1,8-diol (80, 853 mg, 5.68 mmol, 2.0 equiv) and NaH (60% in mineral oil, 114 mg, 2.85 mmol, 1.05 equiv) in DMF (10 mL) was stirred at $0^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for 30 min. 4-Bromo-2-fluoro-pyridine (62, 500 mg, 2.84 mmol, 1.0 equiv) was then added and the resulting mixture was stirred at room temperature for 1 h. The reaction was quenched with saturated aqueous $\\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{Cl}$ (100 mL) and was extracted with EtOAc (100 mL × 3). The combined organic layers were dried over sodium sulfate and were concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% $\\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3$ ), 0 to 100%) to afford the title compound (600 mg, 69%) as a colorless oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 8.07 (d, J = 5.5 Hz, 1H), 7.23 (dd, J = 5.5, 1.6 Hz, 1H), 7.15 (d, J = 1.6 Hz, 1H), 4.58 (t, J = 5.4 Hz, 1H), 4.43–4.33 (m, 2H), 3.78–3.68 (m, 2H), 3.62–3.36 (m, 8H). LC-MS (ES+): m/z 306 [M + H]+. \\\",\\\"tert-Butyl 8-(2-(2-(2-(2-hydroxyethoxy)ethoxy)ethoxy)-pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate (82). A solution of tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, $3.22\\\\\\\\mathrm{g}$ , 15.1 mmol, 1.5 equiv), intermediate 81 (3.10 g, 10.1 \\\"]\",\n \"page_idx\": \"31\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,951,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1293 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,71,481,260]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"mmol, 1.0 equiv), RuPhosPd G3 (785 mg, 0.937 mmol, 0.10 equiv) and $\\\\mathrm{Cs_2CO_3}$ (9.90 g, 30.4 mmol, 3.0 equiv) in 1,4-dioxane (30 mL) was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for 2 h. The reaction was cooled to room temperature and was quenched by the addition of saturated aqueous $\\\\mathrm{NH}_4\\\\mathrm{Cl}$ (100 mL). The resulting mixture was extracted with EtOAc (100 mL × 3), and the combined organic layers were dried over sodium sulfate, filtered, and concentrated under vacuum. The residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3$ ), 0 to 100%) to afford the title compound (4.3 g, 97%) as a colorless oil. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_{6}$ ) δ 7.78 (d, $J = 5.9~\\\\mathrm{Hz}$ , 1H), 6.50 (dd, $J = 6.1$ , 2.1 Hz, 1H), 6.15 (d, $J = 2.0~\\\\mathrm{Hz}$ , 1H), 4.59 (t, $J = 5.4~\\\\mathrm{Hz}$ , 1H), 4.36 (s, 2H), 4.29 (t, $J = 4.8~\\\\mathrm{Hz}$ , 2H), 3.69 (t, $J = 4.8~\\\\mathrm{Hz}$ , 2H), 3.65–3.37 (m, 10H), 3.07 (d, $J = 12.9~\\\\mathrm{Hz}$ , 1H), 2.93 (d, $J = 13.0~\\\\mathrm{Hz}$ , 1H), 1.96–1.86 (m, 2H), 1.74–1.56 (m, 2H), 1.40 (s, 9H). LC-MS (ES+): m/z 438 [M + H]+. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,260,481,410]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(2-(2-((4-(3,8-Diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)ethoxy)ethoxy)ethan-1-ol (83). Intermediate 82 $(4.30\\\\mathrm{g},9.83$ mmol) was stirred at room temperature for $^{\\\\textrm{\\\\scriptsize 4h}}$ in a solution of HCl $(4.0\\\\mathrm{M})$ in MeOH $(50~\\\\mathrm{mL})$ . The resulting mixture was concentrated under vacuum to afford the crude title compound (HCl salt, $2.8\\\\mathrm{g}$ ) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ DMSO- $d_{6}$ 8 10.26s1H9.73 s,1H),7.98d $J = 7.2\\\\mathrm{Hz}$ 1H),6.88dd $J = 7.3$ $2.1\\\\mathrm{Hz}$ 1H),6.63 d $J = 2.2\\\\mathrm{Hz}$ 1H),4.88s,2H),4.50t $J = 4.1\\\\mathrm{Hz}$ 2H),4.13s, 1H),3.81t $J = 4.3\\\\mathrm{Hz}$ 2H),3.56-3.53m3H),3.50-3.47 m, 2H),3.45-3.37m2H),3.25d $J = 13.4\\\\mathrm{Hz}$ 1H),3.17d $J = 12.1$ Hz,2H),3.11-2.99m2H),2.30-2.20m2H),2.15-2.04m, 2H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 338 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,410,481,607]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(2-(2-((4-(3-(3-Amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)ethan-1-ol (84). A solution of intermediate 83 (HCl salt, $1.00\\\\mathrm{g}$ , $2.67\\\\mathrm{mmol}$ , $1.0$ equiv), 4-bromo-6-chloro-pyridazin-3-amine $(70,617\\\\mathrm{mg},2.96\\\\mathrm{mmol},1.1$ equiv) and DIEA $(1.15\\\\mathrm{g},8.89\\\\mathrm{mmol},3.3$ equiv) in NMP $(10\\\\mathrm{mL})$ was stirred at $120^{\\\\circ}\\\\mathrm{C}$ for $8\\\\mathrm{h}$ . After cooling to room temperature, the crude reaction mixture was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ to afford the title compound $(600\\\\mathrm{mg},44\\\\%$ over 2 steps) as a colorless oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 7.78 (d, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 6.90 (s, 1H), 6.52 (dd, $J = 6.1$ , $2.1~\\\\mathrm{Hz}$ , 1H), 6.17 (d, $J = 2.0~\\\\mathrm{Hz}$ , 1H), 5.84 (s, 2H), 4.58 (t, $J = 5.4~\\\\mathrm{Hz}$ , 1H), 4.46 (d, $J = 4.5~\\\\mathrm{Hz}$ , 2H), 4.29 (dd, $J = 5.8$ , $3.7~\\\\mathrm{Hz}$ , 2H), 3.69 (dd, $J = 5.8$ , $3.7~\\\\mathrm{Hz}$ , 2H), 3.60–3.51 (m, 4H), 3.48 (t, $J = 5.0~\\\\mathrm{Hz}$ , 2H), 3.45–3.39 (m, 2H), 3.23–3.13 (m, 2H), 2.87 (d, $J = 11.6~\\\\mathrm{Hz}$ , 2H), 2.19–2.08 (m, 2H), 1.98–1.88 (m, 2H). LC-MS $(ES+)$ : $m/z$ 465 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,607,481,867]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(2-(2-((4-(3-(3-Amino-6-(2-(methoxymethoxy)phenyl)- pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)ethan-1-ol (86). A solution of intermediate 84 $(493\\\\mathrm{mg},1.06\\\\mathrm{mmol},1.0$ equiv), (2-(methoxymethoxy)phenyl)- boronic acid $(85,289\\\\mathrm{mg},1.59\\\\mathrm{mmol},1.5$ equiv), $\\\\mathrm{Pd(PPh_3)_4}$ 122 mg, 0.11 mmol. 0.10 equiv) and $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ 438 mg, 3.18 mmol, 3.0 equiv) in 1,4-dioxane $(5\\\\mathrm{mL})$ and water $(0.5\\\\mathrm{mL})$ was stirred at $100^{\\\\circ}C$ for $4\\\\mathrm{h}$ . After cooling to room temperature, the reaction was diluted with water $(100~\\\\mathrm{mL})$ and extracted with EtOAc $(100~\\\\mathrm{mL}\\\\times$ 3). The combined organic layers were dried over sodium sulfate, filtered, and were concentrated under vacuum. The residue was purified by silica gel chromatography (MeOH:DCM, 0:100 to 13:87) to afford the title compound $(540\\\\mathrm{mg},73\\\\%)$ as a brown solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 7.77 d $J = 6.0~\\\\mathrm{Hz}$ 1H),7.58dd $J =$ 7.6,1.8 Hz,1H),7.40-7.28 m,1H),7.18-7.11 m,2H),7.11-7.03 m,1H),6.52 dd $J = 6.1$ 2.1 Hz,1H),6.18 d $J = 2.0~\\\\mathrm{Hz}$ 1H),5.73 s,2H),5.14 s,2H),4.58 t $J = 5.3~\\\\mathrm{Hz}$ 1H),4.48 s,2H),4.28 dd $J = 5.9$ 3.7 Hz,2H),3.68dd $J = 5.8$ 3.7 Hz2H),3.60-3.46 m, 6H),3.44-3.37 m,2H),3.23 s,3H),3.14 d $J = 11.3~\\\\mathrm{Hz}$ ,2H), 2.85 d $J = 11.3~\\\\mathrm{Hz}$ ,2H),2.24-2.13 m,2H),2.01-1.91 m,2H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 567 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,867,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(2-(2-((4-(3-(3-Amino-6-(2-(methoxymethoxy)phenyl)- pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)ethyl 4-methylbenzenesulfonate (87). A solution of intermediate 86 $(371\\\\mathrm{mg},0.655\\\\mathrm{mmol},1.0$ equiv), 4- methylbenzenesulfonyl chloride $(124\\\\mathrm{mg},0.651\\\\mathrm{mmol},1.0$ equiv), DMAP $(7.9\\\\mathrm{mg},0.065\\\\mathrm{mmol},0.10$ equiv) and TEA $(198\\\\mathrm{mg},1.96$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,235]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"mmol, 3.0 equiv) in DCM (3 mL) was stirred at room temperature for 10 h. The resulting mixture was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (MeOH/DCM, 0:100 to 13:87) to afford the title compound (400 mg, 85%) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_{6}$ ) $\\\\delta$ 7.81-7.73 (m, 3H), 7.58 (dd, $J = 7.6$ , 1.8 Hz, 1H), 7.45 (d, $J = 8.1\\\\mathrm{Hz}$ , 2H), 7.41-7.28 (m, 1H), 7.14 (t, $J = 4.1\\\\mathrm{Hz}$ , 2H), 7.07 (t, $J = 7.6\\\\mathrm{Hz}$ , 1H), 6.56-6.48 (m, 1H), 6.17 (d, $J = 2.0\\\\mathrm{Hz}$ , 1H), 5.74 (s, 2H), 5.14 (s, 2H), 4.48 (s, 2H), 4.27 (t, $J = 4.8\\\\mathrm{Hz}$ , 2H), 4.15-4.06 (m, 2H), 3.65 (t, $J = 4.9\\\\mathrm{Hz}$ , 2H), 3.61-3.52 (m, 2H), 3.51-3.40 (m, 4H), 3.22 (s, 3H), 3.14 (d, $J = 11.4\\\\mathrm{Hz}$ , 2H), 2.85 (d, $J = 11.4\\\\mathrm{Hz}$ , 2H), 2.39 (s, 3H), 2.24-2.10 (m, 2H), 2.03-1.87 (m, 2H). LC-MS (ES+): $m/z$ 721 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,235,915,695]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-(2-(3-(2-(2-((4-(3-(3-Amino-6-(2- (methoxymethoxy)phenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (88). A solution of intermediate 87 $(400\\\\mathrm{mg},0.55\\\\mathrm{mmol},1.0$ equiv), $(2S,4R)\\\\cdot +$ hydroxy-1-(2-(3-hydroxyisoxazol-5-yl)-3-methylbutanoyl)- $N$ -(4-(4- methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (55, 268 mg, 0.55 mmol, 1.0 equiv) and $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ $(229\\\\mathrm{mg},1.66\\\\mathrm{mmol},3.0$ equiv) in DMF $(5\\\\mathrm{mL})$ was stirred at $60^{\\\\circ}\\\\mathrm{C}$ for $4\\\\mathrm{h}$ . The mixture was allowed to cool to room temperature then was quenched with saturated aqueous $\\\\mathrm{NH_4Cl}$ $(100~\\\\mathrm{mL})$ and was extracted with EtOAc $(100~\\\\mathrm{mL}\\\\times$ 3). The combined organic layers were dried over sodium sulfate, filtered, and the filtrate was concentrated under vacuum. The residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH_4HCO_3})$ , 0 to $100\\\\%$ ) to afford the title compound ( $\\\\sim 1:1$ mixture of isopropyl group isomers, $180\\\\mathrm{mg}$ $31\\\\%$ yield) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6}$ ) $\\\\delta$ 8.98 (d, $J = 4.1~\\\\mathrm{Hz}$ 1H), 8.58-8.42 (m, 1H), 7.76 (dd, $J = 6.0$ $2.1\\\\mathrm{Hz}$ 1H), 7.58 (dd, $J =$ 7.3, 1.6 Hz, 1H), 7.48-7.27 (m, 5H), 7.18-7.10 (m, 2H), 7.06 (t, $J =$ 7.5 Hz, 1H), 6.56-6.48 (m, 1H), 6.18 (d, $J = 2.1~\\\\mathrm{Hz}$ 1H), 6.09 (d, $J$ $= 8.9~\\\\mathrm{Hz}$ , 1H), 5.73 (s, 2H), 5.28-4.95 (m, 3H), 4.48 (s, 2H), 4.43- 4.15 (m, 8H), 3.82-3.36 (m, 11H), 3.22 (d, $J = 1.5~\\\\mathrm{Hz}$ , 3H), 3.14 (d, $J =$ $11.4~\\\\mathrm{Hz}$ , 2H), 2.85 (d, $J = 11.4~\\\\mathrm{Hz}$ , 2H), 2.44 (dd, $J = 4.7$ $2.8~\\\\mathrm{Hz}$ - 3H), 2.32-2.11 (m, 3H), 2.11-1.82 (m, 4H), $0.98 - 0.55$ (m, 6H). LC-MS $(\\\\mathrm{ES}+)$ : $m / z$ 1033 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . A small amount of the corresponding isoxazole $N$ -alkylation product (structure not shown) eluted ahead of compound 88 and was isolated as a white solid (20 mg, $4\\\\%$ ). ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6}$ ) $\\\\delta$ 8.98 (d, $J = 3.9~\\\\mathrm{Hz}$ , 1H), 8.60-8.43 (m, 1H), 7.76 (d, $J = 5.9~\\\\mathrm{Hz}$ , 1H), 7.58 (dd, $J = 7.7$ , 1.8 Hz, 1H), 7.46-7.38 (m, 3H), 7.37-7.29 (m, 2H), 7.18-7.11 (m, 2H), 7.06 (td, $J = 7.5$ , 1.1 Hz, 1H), 6.52 (dd, $J = 6.1$ , 2.1 Hz, 1H), 6.17 (t, $J = 2.2~\\\\mathrm{Hz}$ , 1H), 5.78-5.67 (m, 3H), 5.20-5.00 (m, 3H), 4.47 (d, $J = 4.4~\\\\mathrm{Hz}$ , 2H), 4.45-4.19 (m, 6H), 3.97-3.86 (m, 2H), 3.75-3.41 (m, 11H), 3.22 (s, 3H), 3.14 (d, $J = 11.4~\\\\mathrm{Hz}$ , 2H), 2.85 (d, $J =$ $11.4~\\\\mathrm{Hz}$ , 2H), 2.47-2.42 (m, 3H), 2.31-2.13 (m, 3H), 2.11-1.84 (m, 4H), $1.00 - 0.60$ (m, 6H). LC-MS $(\\\\mathrm{ES}+)$ : $m / z$ $1033[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,695,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-(2-(3-(2-(2-(4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)-benzyl)pyrrolidine-2-carboxamide (89). A solution of intermediate 88 (180 mg, 0.174 mmol) in HCl (4.0 M in MeOH, 5 mL) was stirred at room temperature for 8 h. The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 100%) to afford the title compound (~1:1 mixture of isopropyl group isomers, 146 mg) as an off-white solid.¹H NMR (300 MHz, DMSO- $d_{6}$ ) δ 14.15 (s, 1H), 8.98 (d, J = 2.6 Hz, 1H), 8.48 (t, J = 6.0 Hz, 1H), 7.96–7.87 (m, 1H), 7.79 (d, J = 6.0 Hz, 1H), 7.54–7.29 (m, 5H), 7.28–7.16 (m, 1H), 6.91–6.78 (m, 2H), 6.54 (dd, J = 6.1, 2.2 Hz, 1H), 6.19 (d, J = 2.0 Hz, 1H), 6.08 (s, 1H), 5.98 (s, 2H), 5.13 (d, J = 3.6 Hz, 1H), 4.50 (s, 2H), 4.43 (t, J = 7.7 Hz, 1H), 4.37–4.16 (m, 7H), 3.80–3.63 (m, 5H), 3.62–3.43 (m, 6H), 3.24 (d, J = 11.6 Hz, 2H), 3.02 (d, J = 11.7 Hz, 2H), 2.44 (d, J = 2.2 Hz, 3H), 2.32–2.13 (m, 3H), 2.12–1.83 (m, 4H), 1.00–0.53 (m, 6H). LC-MS (ES+): m/z 989.6 [M + H]+. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[532,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1294 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,479,480]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-((2R)-2-(3-(2-(2-(4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethoxy)ethoxy)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)-benzyl)pyrrolidine-2-carboxamide (12). The mixture of isomers isolated in the previous step was separated by preparative chiral HPLC [CHIRALPAK IE, $2\\\\times 25\\\\mathrm{cm}^2$ $5\\\\mu \\\\mathrm{m}$ ; mobile phase A: 1:1 hexane:DCM (0.5% 2 M NH $_3$ -MeOH), mobile phase B: EtOH; flow rate: $20~\\\\mathrm{mL / min}$ ; gradient: isocratic 20% B; wavelength: 220/254 nm; RT1:19.7 min; RT2:34.0 min; sample solvent: EtOH; injection volume: 1 mL; number of runs: 4] to afford the title compound (slower peak, 45 mg, 26%) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 14.15 (s, 1H), 8.98 (d, $J = 3.3\\\\mathrm{Hz}$ , 1H), 8.53 (t, $J = 6.0\\\\mathrm{Hz}$ , 1H), 7.92 (dd, $J = 8.1$ , 1.6 Hz, 1H), 7.79 (dd, $J = 5.9$ , 1.9 Hz, 1H), 7.50 (s, 1H), 7.48-7.30 (m, 4H), 7.28-7.17 (m, 1H), 6.91-6.79 (m, 2H), 6.54 (dd, $J = 6.1$ , 2.1 Hz, 1H), 6.20 (d, $J = 2.0\\\\mathrm{Hz}$ , 1H), 6.11 (s, 1H), 5.98 (s, 2H), 5.12 (d, $J = 3.7\\\\mathrm{Hz}$ , 1H), 4.51 (s, 2H), 4.43-4.15 (m, 8H), 3.83-3.63 (m, 6H), 3.62-3.51 (m, 4H), 3.45 (d, $J = 10.5\\\\mathrm{Hz}$ , 1H), 3.25 (d, $J = 11.5\\\\mathrm{Hz}$ , 2H), 3.02 (d, $J = 11.6\\\\mathrm{Hz}$ , 2H), 2.44 (d, $J = 7.4\\\\mathrm{Hz}$ , 3H), 2.32-2.13 (m, 3H), 2.11-1.86 (m, 4H), 0.99-0.75 (m, 6H). LC-MS $(\\\\mathrm{ES}+)$ : m/z 989.6 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . The isomer bearing the undesired isopropyl stereocenter (12e, isopropyl isomer corresponding to 12, structure not shown) was also isolated (faster peak, $30\\\\mathrm{mg},$ $17\\\\%$ ) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 14.15 (s, 1H), 8.98 (d, $J = 2.6\\\\mathrm{Hz}$ , 1H), 8.48 (t, $J = 6.0\\\\mathrm{Hz}$ , 1H), 7.96-7.87 (m, 1H), 7.79 (d, $J = 6.0\\\\mathrm{Hz}$ , 1H), 7.54-7.29 (m, 5H), 7.28-7.16 (m, 1H), 6.91-6.78 (m, 2H), 6.54 (dd, $J = 6.1$ , 2.2 Hz, 1H), 6.19 (d, $J = 2.0\\\\mathrm{Hz}$ , 1H), 6.08 (s, 1H), 5.98 (s, 2H), 5.13 (d, $J = 3.6\\\\mathrm{Hz}$ , 1H), 4.50 (s, 2H), 4.43 (t, $J = 7.7\\\\mathrm{Hz}$ , 1H), 4.37-4.16 (m, 7H), 3.80-3.63 (m, 5H), 3.62-3.43 (m, 6H), 3.24 (d, $J = 11.6\\\\mathrm{Hz}$ , 2H), 3.02 (d, $J = 11.7\\\\mathrm{Hz}$ , 2H), 2.44 (d, $J = 2.2\\\\mathrm{Hz}$ , 3H), 2.32-2.13 (m, 3H), 2.12-1.83 (m, 4H), $1.00 - 0.53$ (m, 6H). LC-MS $(\\\\mathrm{ES}+)$ : m/z $989.6[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,480,479,728]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Benzyl 4-(2-((4-bromopyridin-2-yl)oxy)ethyl)piperazine-1-carboxylate (91). To a $0^{\\\\circ}\\\\mathrm{C}$ solution of benzyl 4-(2-hydroxyethyl)-piperazine-1-carboxylate (90, $3.00\\\\mathrm{g},$ 11.3 mmol, 1.0 equiv) in DMF $(30~\\\\mathrm{mL})$ was added NaH $(60\\\\%)$ in mineral oil, $910\\\\mathrm{mg},$ 22.7 mmol, 2.0 equiv) in portions. After stirring $10\\\\mathrm{min}$ at $0^{\\\\circ}\\\\mathrm{C},$ 4-bromo-2-fluoropyridine (62, $2.00\\\\mathrm{g},$ 11.3 mmol, 1.0 equiv) was added over 10 min at the same temperature. The resulting mixture was warmed to room temperature and was stirred for an additional $0.5\\\\mathrm{h}$ The reaction was then cooled to $0^{\\\\circ}\\\\mathrm{C}$ and was quenched with saturated aqueous $\\\\mathrm{NH_4Cl}$ $(100~\\\\mathrm{mL})$ . The resulting mixture was extracted with EtOAc $(100~\\\\mathrm{mL}\\\\times 3)$ , and the combined organic layers were washed with brine $(100~\\\\mathrm{mL})$ , dried over sodium sulfate, and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 55:45) to afford the title compound $(3.95\\\\mathrm{g},83\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz},$ DMSO- $d_{6})$ $\\\\delta$ 8.06 d $J = 5.5\\\\mathrm{Hz}$ 1H7.45- 7.26 m5H7.22dd $J = 5.5$ $1.7\\\\mathrm{Hz}$ 1H7.13d $J = 1.6\\\\mathrm{Hz}$ 1H), 5.07s2H)4.38t $J = 5.7\\\\mathrm{Hz},$ 2H)3.4-3.33m4H2.70t $J =$ $5.9\\\\mathrm{Hz},$ 2H)2.44t $J = 5.0\\\\mathrm{Hz},$ 4H.LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 420/422 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,730,479,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Benzyl 4-(2-((4-(3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2- yl)oxy)ethyl)piperazine-1-carboxylate (92). A solution of benzyl 4-(2-((4-bromopyridin-2-yl)oxy)ethyl)piperazine-1-carboxylate (91, $1.50\\\\mathrm{g},$ 3.57 mmol, 1.0 equiv), tert-butyl 3,8-diazabicyclo[3.2.1]- octane-3-carboxylate (67, $760~\\\\mathrm{mg}$ 3.57 mmol, 1.0 equiv), RuPhosPd G2 $(280~\\\\mathrm{mg},$ 0.36 mmol, 0.10 equiv), and $\\\\mathrm{Cs_2CO_3}$ 2.33 g, 7.14 mmol, 2.0 equiv) in toluene $(15~\\\\mathrm{mL})$ was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for $5\\\\mathrm{h}$ The resulting mixture was cooled to room temperature, diluted with EtOAc $(50~\\\\mathrm{mL})$ , and was quenched with saturated aqueous $\\\\mathrm{NH}_4\\\\mathrm{Cl}$ $(100~\\\\mathrm{mL})$ . The aqueous layer was extracted with EtOAc $(100~\\\\mathrm{mL}\\\\times$ 3), and the combined organic layers were dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH_4HCO_3})$ 0 to $75\\\\%$ to afford tertbutyl 8-(2-(2-(4-((benzyloxy)carbonyl)piperazin-1-yl)ethoxy)pyridin4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate $(1.1~\\\\mathrm{g},$ $56\\\\%$ as a light yellow solid. ${}^{1}\\\\mathbf{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 7.77 d $J = 6.0$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,283]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\mathrm{Hz}$ 1H),7.45-7.20 (m, 5H),6.48dd $J = 6.1$ $2.1\\\\mathrm{Hz}$ 1H),6.11d $J$ $= 2.0~\\\\mathrm{Hz}$ 1H),5.07s2H),4.35s2H),4.28t $J = 5.8\\\\mathrm{Hz}$ 2H), 3.57t $J = 16.3\\\\mathrm{Hz}$ 2H),3.45-3.34(m,4H),3.06d $J = 12.6\\\\mathrm{Hz}$ 1H),2.92d $J = 12.8\\\\mathrm{Hz}$ 1H),2.65t $J = 5.8\\\\mathrm{Hz}$ 2H),2.43t $J =$ $5.1\\\\mathrm{Hz}$ 4H),1.94-1.85m2H),1.73-1.62m2H),1.39s9H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 552 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ .A solution of this material (750 mg, 1.36 mmol) in TFA $(1.5\\\\mathrm{mL})$ and DCM $(7.5\\\\mathrm{mL})$ was stirred at room temperature for $^{\\\\textrm{\\\\scriptsize 1h}}$ The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ 0 to $100\\\\%$ ) to afford the title compound $(570\\\\mathrm{mg},93\\\\%)$ as a light yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ ,DMSO- $d_{6})$ 7.72d $J = 6.0~\\\\mathrm{Hz}$ 1H),7.44-7.26 m5H),6.39dd $J = 6.1$ $2.1\\\\mathrm{Hz}$ 1H),5.98d $J =$ $2.0\\\\mathrm{Hz}$ 1H),5.08s2H),4.28t $J = 5.8\\\\mathrm{Hz}$ 2H),4.15s2H),3.39 s,4H),3.17d $J = 3.2\\\\mathrm{Hz}$ 1H),2.89-2.78m2H),2.66t $J = 5.8$ Hz,2H),2.47-2.38m6H),1.98-1.80m4H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 452 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,283,915,470]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Benzyl 4-(2-((4-(3-(3-amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)-piperazine-1-carboxylate (93). A solution of intermediate 92 (530 mg, 1.17 mmol, 1.0 equiv), 4-bromo-6-chloropyridazin-3-amine (70, 366 mg, 1.76 mmol, 1.5 equiv), and DIEA (758 mg, 5.87 mmol, 5.0 equiv) in NMP (6 mL) was stirred at $130^{\\\\circ}\\\\mathrm{C}$ for 3 h. After cooling to room temperature, the crude mixture was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ to afford the title compound $(570\\\\mathrm{mg},84\\\\%)$ as a light yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 7.77 (d, $J = 5.9\\\\mathrm{Hz}$ , 1H), 7.43-7.25 (m, 5H), 6.89 (s, 1H), 6.50 (dd, $J = 6.1$ , 2.0 Hz, 1H), 6.13 (d, $J = 2.0\\\\mathrm{Hz}$ , 1H), 5.84 (s, 2H), 5.07 (s, 2H), 4.45 (s, 2H), 4.28 (t, $J = 5.8\\\\mathrm{Hz}$ , 2H), 3.39 (s, 4H), 3.22-3.12 (m, 2H), 2.86 (d, $J = 11.6\\\\mathrm{Hz}$ , 2H), 2.65 (t, $J = 5.8\\\\mathrm{Hz}$ , 2H), 2.43 (t, $J = 5.0\\\\mathrm{Hz}$ , 4H), 2.17-2.06 (m, 2H), 1.97-1.87 (m, 2H). LC-MS $(\\\\mathrm{ES}+)$ : $m/z$ 579 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,470,915,905]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6-(2-(Methoxymethoxy)phenyl)-4-(8-(2-(piperazin-1-yl)-ethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)-pyridazin-3-amine (94). A solution of intermediate 93 (560 mg, 0.967 mmol, 1.0 equiv), 2-(methoxymethoxy)phenylboronic acid (85, 263 mg, 1.45 mmol, 1.5 equiv), $\\\\mathrm{Pd}(\\\\mathrm{dppf})\\\\mathrm{Cl}_2\\\\bullet \\\\mathrm{CH}_2\\\\mathrm{Cl}_2$ (78.7 mg, 0.0963 mmol, 0.10 equiv) and $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ (400 mg, 2.90 mmol, 3.0 equiv) in 1,4-dioxane (6 mL) and water (1.2 mL) was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for 1.5 h. After cooling to room temperature, the crude mixture was purified by prepacked C18 column chromatography $(\\\\mathrm{CH}_3\\\\mathrm{CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ ) to afford benzyl 4-(2-((4-(3-(3-amino-6-(2-(methoxymethoxy)phenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)piperazine-1-carboxylate (475 mg, 72%) as a light brown solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 7.75 (d, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 7.56 (dd, $J = 7.6$ , 1.8 Hz, 1H), 7.41-7.23 (m, 6H), 7.16-6.99 (m, 3H), 6.55-6.45 (m, 1H), 6.13 (d, $J = 2.0~\\\\mathrm{Hz}$ , 1H), 5.72 (s, 2H), 5.12 (s, 2H), 5.05 (s, 2H), 4.45 (d, $J = 4.2~\\\\mathrm{Hz}$ , 2H), 4.26 (t, $J = 5.7~\\\\mathrm{Hz}$ , 2H), 3.37 (s, 4H), 3.20 (s, 3H), 3.12 (d, $J = 11.3~\\\\mathrm{Hz}$ , 2H), 2.83 (d, $J = 11.3~\\\\mathrm{Hz}$ , 2H), 2.64 (t, $J = 5.8~\\\\mathrm{Hz}$ , 2H), 2.41 (t, $J = 5.0~\\\\mathrm{Hz}$ , 4H), 2.23-2.11 (m, 2H), 2.03-1.85 (m, 2H). LC-MS $(\\\\mathrm{ES}+)$ : $m/z$ 681 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . A suspension of this material (465 mg, 0.68 mmol) and $10\\\\%$ Pd/C (25 mg, dry) in MeOH (20 mL) was stirred under a hydrogen atmosphere (3 atm), at room temperature for 5 h. The resulting mixture was filtered, and the filter cake was washed with MeOH (25 mL × 3). The combined filtrate and washings were concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $(\\\\mathrm{CH}_3\\\\mathrm{CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ ) to afford the title compound (220 mg, 59%) as a light yellow solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 7.75 (d, $J = 5.9~\\\\mathrm{Hz}$ , 1H), 7.57 (dd, $J = 7.6$ , 1.8 Hz, 1H), 7.37-7.27 (m, 1H), 7.16-7.09 (m, 2H), 7.05 (td, $J = 7.5$ , 1.1 Hz, 1H), 6.49 (dd, $J = 6.1$ , 2.1 Hz, 1H), 6.12 (d, $J = 2.0~\\\\mathrm{Hz}$ , 1H), 5.71 (s, 2H), 5.12 (s, 2H), 4.46 (s, 2H), 4.24 (t, $J = 5.9~\\\\mathrm{Hz}$ , 2H), 3.20 (s, 3H), 3.12 (d, $J = 11.3~\\\\mathrm{Hz}$ , 2H), 2.83 (d, $J = 11.3~\\\\mathrm{Hz}$ , 2H), 2.70-2.51 (m, 6H), 2.34 (s, 4H), 2.22-2.11 (m, 2H), 2.01-1.87 (m, 2H). LC-MS $(\\\\mathrm{ES}+)$ : $m/z$ 547 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,905,915,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-(2-(3-(2-(4-(4-(3-(3-Amino-6-(2-(methoxymethoxy)phenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)piperazin-1-yl)- \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[484,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1295 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,71,482,305]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (95). A mixture of intermediate 94 $(100\\\\mathrm{mg},0.183\\\\mathrm{mmol},1.0$ equiv) and intermediate 56 $(108\\\\mathrm{mg},0.183\\\\mathrm{mmol},1.0$ equiv), $\\\\mathrm{Cs_2CO_3}$ $(178\\\\mathrm{mg},$ $0.551\\\\mathrm{mmol},3.0$ equiv) and KI $(45.5\\\\mathrm{mg},0.274\\\\mathrm{mmol},1.5$ equiv) in $\\\\mathrm{CH}_3\\\\mathrm{CN}$ $(2\\\\mathrm{mL})$ was stirred at $70^{\\\\circ}\\\\mathrm{C}$ overnight. The reaction was cooled to room temperature, and the solids were filtered off. The filtrate was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH_4HCO_3})$ 0 to $100\\\\%$ ) to afford the title compound ( $\\\\sim 1:1$ mixture of isopropyl group isomers, $95\\\\mathrm{mg},$ $49\\\\%$ as a light yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6}$ 8 8.98 $(\\\\mathrm{d},J = 4.1~\\\\mathrm{Hz},1\\\\mathrm{H})$ $8.58 - 8.41$ m1H7.76d $J = 5.9 \\\\mathrm{Hz}$ 1H) 7.58dd $J = 7.6$ $1.8~\\\\mathrm{Hz}$ 1H7.50-7.27m5H7.17-7.02m 3H6.50dd $J = 6.3$ $2.0~\\\\mathrm{Hz}$ 1H6.17-6.03m2H5.72s2H) 5.13d $J = 1.3~\\\\mathrm{Hz}$ 3H4.45d $J = 11.6~\\\\mathrm{Hz}$ 2H4.40-4.10m 7H3.76dd $J = 9.8$ $4.9~\\\\mathrm{Hz}$ 1H3.71-3.36m2H3.25-3.08 m6H2.85d $J = 11.3~\\\\mathrm{Hz}$ 2H2.68-2.54m4H2.47-2.34 m, $10\\\\mathrm{H})$ 2.30-2.09 m4H)2.07-1.84 m4H)1.01-0.54 m, 6H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 1057 $[\\\\mathbf{M} + \\\\mathbf{H}]^+$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,305,481,585]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-(2-(3-(2-(4-(3-(3-(3-Amino-6-(2- (methoxymethoxy)phenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)piperazin-1-yl)-ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (96). A mixture of intermediate 94 (100 mg, 0.183 mmol, 1.0 equiv), intermediate 59 (149 mg, 0.246 mmol, 1.3 equiv), $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ (75.8 mg, 0.549 mmol, 3.0 equiv), and KI (45.5 mg, 0.274 mmol, 1.5 equiv) in $\\\\mathrm{CH}_3\\\\mathrm{CN}$ (2 mL) was stirred at $70^{\\\\circ}\\\\mathrm{C}$ overnight. The reaction was cooled to room temperature, and the solids were filtered off. The filtrate was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ to afford the title compound ( $\\\\sim$ 1:1 mixture of isopropyl group isomers, $134\\\\mathrm{mg}, 68\\\\%$ ) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 9.03–8.88 (m, 1H), 8.47–8.25 (m, 1H), 7.76 (dd, $J = 5.9$ , 1.2 Hz, 1H), 7.62–7.55 (m, 1H), 7.53–7.27 (m, 5H), 7.17–7.00 (m, 3H), 6.57–6.46 (m, 1H), 6.14 (t, $J = 2.2\\\\mathrm{Hz}$ , 1H), 6.08 (d, $J = 2.7\\\\mathrm{Hz}$ , 1H), 5.72 (s, 2H), 5.17–5.06 (m, 3H), 5.04–4.83 (m, 1H), 4.55–4.32 (m, 3H), 4.32–4.04 (m, 5H), 3.79–3.55 (m, 1H), 3.55–3.39 (m, 2H), 3.22 (d, $J = 1.2\\\\mathrm{Hz}$ , 3H), 3.19–3.08 (m, 3H), 2.84 (d, $J = 11.3\\\\mathrm{Hz}$ , 2H), 2.69–2.55 (m, 4H), 2.50–2.32 (m, 10H), 2.32–2.08 (m, 3H), 2.08–1.91 (m, 3H), 1.84–1.70 (m, 1H), 1.49–1.30 (m, 3H), 1.00–0.70 (m, 6H). LC–MS $(ES+): m/z$ 1071 $[M + H]^+$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,585,482,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-((2R)-2-(3-(2-(4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)piperazin-1-yl)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(4-(4-methylthiazol-5-yl)benzyl)pyrrolidine-2-carboxamide (13). A solution of intermediate 95 (95.0 mg, 0.0898 mmol) was stirred in HCl (4.0 M in MeOH, 2 mL) at room temperature overnight. The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacted C18 column chromatography (CH $_3$ CN in water (0.05% $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3$ ), 0 to 100%) to afford 60 mg of the MOM-deprotected product (~1:1 mixture of isopropyl group isomers). These compounds were separated by preparative chiral HPLC [column: CHIRALPAK ID, $2\\\\times 25~\\\\mathrm{cm}^2$ , 5 μm; mobile phase A: 1:1 hexane: DCM (0.5% 2 M $\\\\mathrm{NH}_3/\\\\mathrm{MeOH}$ ), mobile phase B: EtOH; flow rate: 20 mL/min; gradient: isocratic 30% B; wavelength: 220/254 nm; RT1:7.08 min; RT2:14.99 min; sample solvent: EtOH; injection volume: 1 mL; number of runs: 5] to afford the title compound (faster peak, 24.5 mg, 27%) as an off-white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 14.14 (s, 1H), 8.98 (s, 1H), 8.50 (t, $J = 6.1~\\\\mathrm{Hz}$ , 1H), 7.91 (d, $J = 7.9~\\\\mathrm{Hz}$ , 1H), 7.78 (d, $J = 5.9~\\\\mathrm{Hz}$ , 1H), 7.49 (s, 1H), 7.47–7.33 (m, 4H), 7.22 (t, $J = 7.6~\\\\mathrm{Hz}$ , 1H), 6.91–6.77 (m, 2H), 6.53 (d, $J = 6.4~\\\\mathrm{Hz}$ , 1H), 6.19–6.07 (m, 2H), 5.97 (s, 2H), 5.14–4.97 (m, 1H), 4.50 (s, 2H), 4.42–4.30 (m, 3H), 4.30–4.14 (m, 4H), 3.80–3.72 (m, 1H), 3.66 (d, $J = 9.6~\\\\mathrm{Hz}$ , 1H), 3.61–3.37 (m, 2H), 3.25 (d, $J = 12.1~\\\\mathrm{Hz}$ , 2H), 3.01 (d, $J = 11.7~\\\\mathrm{Hz}$ , 2H), 2.68–2.57 (m, 4H), 2.48–2.39 (m, 10H), 2.32–1.83 (m, 8H), 0.94 (d, $J = 6.5~\\\\mathrm{Hz}$ , 3H), 0.80 (d, $J = 6.7~\\\\mathrm{Hz}$ , 3H). LC-MS $(\\\\mathrm{ES}+)$ : m/z 1013 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . The isomer bearing the undesired isopropyl stereocenter (13e, isopropyl isomer corresponding to 13, structure not shown) was also isolated (slower \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,198]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"peak, $19\\\\mathrm{mg}$ $20\\\\%$ ) as an off-white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO $d_{6}$ ) $\\\\delta$ 14.14 (s, 1H), 8.98 (d, $J = 2.7\\\\mathrm{Hz}$ 1H), 8.46 (t, $J = 6.0\\\\mathrm{Hz}$ 1H), 7.91 (dd, $J = 8.0$ $1.6\\\\mathrm{Hz}$ 1H), 7.78 (d, $J = 5.9\\\\mathrm{Hz}$ 1H), 7.52-7.36 (m, 3H), 7.32 (d, $J = 8.1\\\\mathrm{Hz}$ 2H), 7.26-7.15 (m, 1H), 6.91-6.78 (m, 2H), 6.53 (dd, $J = 6.3$ $2.0\\\\mathrm{Hz}$ 1H), 6.15 (d, $J = 2.0\\\\mathrm{Hz}$ 1H), 6.06 (d, $J = 4.7\\\\mathrm{Hz}$ 1H), 5.97 (s, 2H), 5.12 (d, $J = 3.6\\\\mathrm{Hz}$ 1H), 4.52-4.38 (m, 3H), 4.37-4.20 (m, 5H), 4.20-4.11 (m, 1H), 3.76 (d, $J = 8.5\\\\mathrm{Hz}$ 1H), 3.59-3.40 (m, 2H), 3.29-3.09 (m, 3H), 3.01 (d, $J = 11.6\\\\mathrm{Hz}$ 2H), 2.69-2.53 (m, 4H), 2.47-2.33 (m, 11H), 2.31-1.83 (m, 7H), 1.00-0.53 (m, 6H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 1013 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,198,915,725]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-((2R)-2-(3-(2-(4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)piperazin-1-yl)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (14). A solution of intermediate 96 (135 mg, 0.126 mmol) in HCl (4.0 M in MeOH, 2 mL) was stirred at room temperature for 3 h. The solvent was evaporated, and the residue was purified by prepacked C18 column chromatography (MeOH in water (0.05% $\\\\mathrm{NH_4HCO_3}$ ), 0 to 100%) to afford 85 mg of the MOM-deprotected product (~1:1 mixture of isopropyl group isomers). These compounds were separated by preparative chiral HPLC [column: CHIRALPAK IK, $4.6\\\\times 150~\\\\mathrm{mm}^2$ , $5\\\\mu \\\\mathrm{m}$ ; mobile phase A: 1:1 hexane: DCM (0.5% 2 M $\\\\mathrm{NH}_3 / \\\\mathrm{MeOH}$ ), mobile phase B: EtOH; flow rate: 20 mL/min; gradient: isocratic 30% B; wavelength: 220/254 nm; RT1:10.8 min; RT2:20.4 min; sample solvent: EtOH; injection volume: 1 mL; number of runs: 5] to afford the title compound (slower peak, 19.6 mg, 15%) as an off-white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 14.14 (s, 1H), 8.98 (s, 1H), 8.41 (d, $J = 7.6~\\\\mathrm{Hz}$ , 1H), 7.96–7.87 (m, 1H), 7.79 (d, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 7.49 (s, 1H), 7.47–7.40 (m, 2H), 7.36 (d, $J = 8.1~\\\\mathrm{Hz}$ , 2H), 7.25–7.16 (m, 1H), 6.91–6.79 (m, 2H), 6.53 (dd, $J = 6.2$ , 2.0 Hz, 1H), 6.15 (d, $J = 2.0~\\\\mathrm{Hz}$ , 1H), 6.09 (s, 1H), 5.97 (s, 2H), 5.09 (d, $J = 3.7~\\\\mathrm{Hz}$ , 1H), 5.04–4.83 (m, 1H), 4.50 (s, 2H), 4.37 (t, $J = 7.9~\\\\mathrm{Hz}$ , 1H), 4.31–4.16 (m, 5H), 3.75–3.60 (m, 2H), 3.55–3.40 (m, 1H), 3.25 (d, $J = 11.5~\\\\mathrm{Hz}$ , 2H), 3.01 (d, $J = 11.6~\\\\mathrm{Hz}$ , 2H), 2.70–2.58 (m, 4H), 2.50–2.39 (m, 10H), 2.30–2.15 (m, 4H), 2.10–1.85 (m, 3H), 1.85–1.70 (m, 1H), 1.50–1.35 (m, 3H), 0.95 (d, $J = 6.4~\\\\mathrm{Hz}$ , 3H), 0.90–0.75 (m, 3H). LC-MS $(\\\\mathrm{ES}+)$ : m/z 1027 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . The isomer bearing the undesired isopropyl stereocenter (14e, isopropyl isomer corresponding to 14, structure not shown) was also isolated (faster peak, $40~\\\\mathrm{mg}$ , $31\\\\%$ ) as an off-white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 14.14 (s, 1H), 9.00–8.88 (m, 1H), 8.29 (d, $J = 7.8~\\\\mathrm{Hz}$ , 1H), 7.91 (dd, $J = 8.0$ , 1.6 Hz, 1H), 7.78 (d, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 7.48 (d, $J = 7.6~\\\\mathrm{Hz}$ , 1H), 7.46–7.36 (m, 2H), 7.31 (d, $J = 8.3~\\\\mathrm{Hz}$ , 2H), 7.25–7.16 (m, 1H), 6.91–6.78 (m, 2H), 6.53 (dd, $J = 6.1$ , 2.0 Hz, 1H), 6.19–6.11 (m, 1H), 6.08 (s, 1H), 5.97 (s, 2H), 5.10 (d, $J = 3.6~\\\\mathrm{Hz}$ , 1H), 5.06–4.81 (m, 1H), 4.50 (s, 2H), 4.42 (t, $J = 7.7~\\\\mathrm{Hz}$ , 1H), 4.33–4.14 (m, 5H), 3.74 (d, $J = 8.5~\\\\mathrm{Hz}$ , 1H), 3.60–3.38 (m, 2H), 3.33–3.19 (m, 2H), 3.01 (d, $J = 11.6~\\\\mathrm{Hz}$ , 2H), 2.70–2.58 (m, 4H), 2.49–2.39 (m, 10H), 2.34–2.11 (m, 4H), 2.10–1.91 (m, 3H), 1.84–1.70 (m, 1H), 1.50–1.30 (m, 3H), 1.00–0.71 (m, 6H). LC-MS $(\\\\mathrm{ES}+)$ : m/z $1027[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,725,915,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4-Bromo-2-(2,2-diethoxyethoxy)pyridine (97). A mixture of 2,2-diethoxyethan-1-ol $(5.71\\\\mathrm{g},42.6\\\\mathrm{mmol},1.0$ equiv) and NaH $(60\\\\%)$ in mineral oil, $1.36\\\\mathrm{g}$ $56.8~\\\\mathrm{mmol}$ 1.3 equiv) in DMF $(30~\\\\mathrm{mL})$ was stirred at $0^{\\\\circ}\\\\mathrm{C}$ for $0.5\\\\mathrm{h}$ 4-Bromo-2-fluoro-pyridine (62, $5.00\\\\mathrm{g}$ 28.4 mmol) was then added, and the mixture was stirred at room temperature for $2\\\\textrm{h}$ The reaction was quenched with saturated aqueous $\\\\mathrm{NH_4Cl}$ $(100~\\\\mathrm{mL})$ at room temperature, and the resulting mixture was extracted with EtOAc $(100~\\\\mathrm{mL}\\\\times 3)$ .The combined organic layers were washed with water $(100~\\\\mathrm{mL})$ and were dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 1:3) to afford the title compound $(6.4\\\\mathrm{g},53\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8.07 d $J = 5.5\\\\mathrm{Hz}$ 1H),7.24dd $J = 5.5$ $1.7\\\\mathrm{Hz}$ 1H), 7.15d $J = 1.7\\\\mathrm{Hz}$ 1H),4.80t $J = 5.3\\\\mathrm{Hz}$ 1H),4.24d $J = 5.3\\\\mathrm{Hz}$ 2H),3.75-3.45 m4H),1.12 t $J = 7.1\\\\mathrm{Hz}$ 6H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z290[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[484,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1296 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,479,370]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Benzyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (98). Benzyl chloroformate $(4.83\\\\mathrm{g},28.2\\\\mathrm{mmol},1.2$ equiv) was added to a $0^{\\\\circ}\\\\mathrm{C}$ solution of tert-butyl 3,8-diazabicyclo[3.2.1]octane-8-carboxylate $(5.00\\\\mathrm{g},23.5\\\\mathrm{mmol},1.0$ equiv) and TEA $(7.14\\\\mathrm{g},70.6$ mmol, 3.0 equiv) in DCM $(30~\\\\mathrm{mL})$ . The reaction was stirred at $0^{\\\\circ}\\\\mathrm{C}$ for $2\\\\textrm{h}$ then was diluted with EtOAc $(300~\\\\mathrm{mL})$ and washed with water $(200~\\\\mathrm{mL})$ . The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 30:70) to afford 3-benzyl 8-(tert-butyl) 3,8- diazabicyclo[3.2.1]octane-3,8-dicarboxylate $(5.33\\\\mathrm{g},65\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ ,DMSO- $d_{6})$ $\\\\delta$ 7.44-7.26 (m, 5H), 5.10 (d, $J$ $= 4.1\\\\mathrm{Hz},2\\\\mathrm{H})$ 4.11s2H)3.75d $J = 12.7\\\\mathrm{Hz}$ 2H)3.05d $J=$ $12.7\\\\mathrm{Hz},1\\\\mathrm{H})$ 2.94d $J = 12.7\\\\mathrm{Hz},1\\\\mathrm{H})$ 1.87-1.75 (m, 2H), 1.61- 1.48 (m, 2H), 1.41 (s, 9H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 347 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . A solution of this material $(5.23\\\\mathrm{g},15.1\\\\mathrm{mmol})$ in TFA $(10~\\\\mathrm{mL})$ and DCM $(50~\\\\mathrm{mL})$ was stirred at room temperature for $^{\\\\textrm{\\\\scriptsize 4h}}$ . The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.1\\\\%$ TFA), 0 to $100\\\\%$ ) to afford the title compound (TFA salt, $3.40\\\\mathrm{g},62\\\\%$ ) as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ ,DMSO- $d_{6})$ $\\\\delta$ 9.20s,2H)7.45-7.27m5H)5.11s,2H)4.03s,2H)3.86d $J = 13.5\\\\mathrm{Hz},2\\\\mathrm{H})$ 3.43-3.21 m,2H)1.99-1.88 m,2H)1.78-1.65 m,2H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 247 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,370,479,606]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Benzyl 8-(2-(2,2-diethoxyethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate (99). A solution of 4-bromo-2-(2,2-diethoxyethoxy)pyridine (97, $2.70\\\\mathrm{g}$ , $9.31\\\\mathrm{mmol}$ , 1.0 equiv), benzyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (98, TFA salt, $4.58\\\\mathrm{g}$ , $12.7\\\\mathrm{mmol}$ , 1.4 equiv), RuPhosPd G2 $(720\\\\mathrm{mg}, 0.927\\\\mathrm{mmol}, 0.10\\\\mathrm{equiv})$ and $\\\\mathrm{Cs_2CO_3}$ $(9.10\\\\mathrm{g}, 27.9\\\\mathrm{mmol}, 3.0\\\\mathrm{equiv})$ in toluene $(13\\\\mathrm{mL})$ was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for $4\\\\mathrm{h}$ . The resulting mixture was cooled to room temperature and was diluted with EtOAc (100 mL) and washed with water $(100\\\\mathrm{mL})$ . The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 35:65) to afford the title compound $(4.0\\\\mathrm{g}, 94\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 7.78 $(\\\\mathrm{d}, J = 5.9\\\\mathrm{Hz}, 1\\\\mathrm{H})$ , 7.43-7.27 $(\\\\mathrm{m}, 5\\\\mathrm{H})$ , 6.51 $(\\\\mathrm{dd}, J = 6.2, 2.1\\\\mathrm{Hz}, 1\\\\mathrm{H})$ , 6.16 $(\\\\mathrm{d}, J = 2.0\\\\mathrm{Hz}, 1\\\\mathrm{H})$ , 5.08 $(\\\\mathrm{d}, J = 3.9\\\\mathrm{Hz}, 2\\\\mathrm{H})$ , 4.77 $(\\\\mathrm{t}, J = 5.3\\\\mathrm{Hz}, 1\\\\mathrm{H})$ , 4.39 $(\\\\mathrm{d}, J = 10.3\\\\mathrm{Hz}, 2\\\\mathrm{H})$ , 4.15 $(\\\\mathrm{d}, J = 5.3\\\\mathrm{Hz}, 2\\\\mathrm{H})$ , 3.73-3.59 $(\\\\mathrm{m}, 4\\\\mathrm{H})$ , 3.59-3.45 $(\\\\mathrm{m}, 2\\\\mathrm{H})$ , 3.15 $(\\\\mathrm{d}, J = 12.9\\\\mathrm{Hz}, 1\\\\mathrm{H})$ , 3.03 $(\\\\mathrm{d}, J = 12.9\\\\mathrm{Hz}, 1\\\\mathrm{H})$ , 1.96-1.86 $(\\\\mathrm{m}, 2\\\\mathrm{H})$ , 1.73-1.63 $(\\\\mathrm{m}, 2\\\\mathrm{H})$ , 1.13 $(\\\\mathrm{t}, J = 7.0\\\\mathrm{Hz}, 6\\\\mathrm{H})$ . LC-MS $(ES+)$ : $m/z$ 456 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,606,479,766]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8-(2-(2,2-Diethoxyethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane (100). A solution of intermediate 99 $(4.15\\\\mathrm{g},9.11$ mmol) and $10\\\\%$ Pd/C $(484\\\\mathrm{mg})$ in EtOAc $(25~\\\\mathrm{mL})$ was stirred under a hydrogen atmosphere (3 atm) at room temperature for $12\\\\mathrm{h}$ The resulting mixture was filtered, and the filter cake was washed with EtOAc $(30~\\\\mathrm{mL}\\\\times 3)$ .The combined filtrate and washings were concentrated under reduced pressure to afford the title compound $(2.68\\\\mathrm{g},92\\\\%)$ as a black oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 7.73 $\\\\left(\\\\mathrm{d},J = 6.0\\\\mathrm{Hz},1\\\\mathrm{H}\\\\right)$ 6.41dd $J = 6.1$ 2.1 Hz1H),6.02 $\\\\left(\\\\mathrm{d},J = 2.1\\\\mathrm{Hz}\\\\right.$ 1H),4.76t $J = 5.3\\\\mathrm{Hz}$ 1H),4.20-4.11m4H),3.72-3.45m 4H),2.84d $J = 12.2\\\\mathrm{Hz}$ 2H),2.44d $J = 12.2\\\\mathrm{Hz}$ 2H),2.01-1.80 m,4H),1.13t $J = 7.1\\\\mathrm{Hz}$ 6H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 322 $[\\\\mathbf{M}+$ $\\\\mathrm{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,767,479,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(6-Amino-5-(8-(2-(2,2-diethoxyethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)pyridazin-3-yl)phenol (101). A solution of intermediate 100 $(2.60\\\\mathrm{g},8.09\\\\mathrm{mmol},1.0$ equiv), 4-bromo-6-chloro-pyridazin-3-amine (70, $2.53\\\\mathrm{g}$ 12.1 mmol, 1.5 equiv) and DIEA $(3.13\\\\mathrm{g},24.2\\\\mathrm{mmol},3.0$ equiv) in NMP $(20~\\\\mathrm{mL})$ was stirred at $120^{\\\\circ}\\\\mathrm{C}$ for $2\\\\textrm{h}$ . After cooling to room temperature, the crude was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH_4HCO_3)}$ , 0 to $100\\\\%$ ) to afford 6-chloro4-(8-(2-(2,2-diethoxyethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]-octan-3-yl)pyridazin-3-amine $(2.67\\\\mathrm{g},74\\\\%)$ as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 7.79 d $J = 6.0 \\\\mathrm{Hz}$ 1H6.89s1H) 6.53dd $J = 6.1$ $2.0\\\\mathrm{Hz}$ 1H6.17d $J = 2.0\\\\mathrm{Hz}$ 1H5.85s2H) 4.77t $J = 5.3\\\\mathrm{Hz}$ 1H4.47s2H4.15d $J = 5.2\\\\mathrm{Hz}$ 2H3.72- 3.45m4H)3.18d $J = 11.6\\\\mathrm{Hz}$ 2H)2.86d $J = 11.6\\\\mathrm{Hz}$ 2H \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,306]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.19-2.09 (m, 2H), 1.98-1.88 (m, 2H), 1.13 (t, $J = 7.0\\\\mathrm{Hz}$ 6H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z449[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ . A solution of this material (2.66 g, 5.92 mmol, 1.0 equiv), 2-hydroxyphenylboronic acid (72, 1.23 g, 8.91 mmol, 1.5 equiv), $\\\\mathrm{Pd(PPh_3)_4}$ (0.680 g, 0.589 mmol, 0.10 equiv), and $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ (2.45 g, 17.7 mmol, 3.0 equiv) in 1,4-dioxane (20 mL) and water (2 mL) was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for $2\\\\mathrm{h}$ The resulting mixture was cooled to room temperature, and was diluted with EtOAc (100 mL) and washed with water (100 mL). The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (0-100% CH3CN in water (0.05% $\\\\mathrm{NH_4HCO_3})$ , 0 to $100\\\\%$ ) to afford the title compound (2.1 g, $70\\\\%$ ) as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_{6})$ 8 14.14 s, 1H),7.92 $(\\\\mathrm{d},J = 7.8~\\\\mathrm{Hz}$ 1H),7.80 $(\\\\mathrm{d},J = 6.0~\\\\mathrm{Hz}$ 1H),7.50s1H)7.25-7.19 m, 1H),6.92-6.80 (m, 2H),6.61-6.51 (m, 1H),6.20s,1H),5.98 s,2H),4.77 t $J = 5.3\\\\mathrm{Hz}$ 1H),4.52 s,2H),4.16 d $J = 5.2\\\\mathrm{Hz}$ 2H),3.71-3.47 (m, 4H),3.26 d $J = 11.6\\\\mathrm{Hz}$ 2H),3.02 d $J = 11.5$ Hz,2H),2.25-2.15 (m, 2H), 2.03-1.90 (m, 2H), 1.13 (t, $J = 7.0\\\\mathrm{Hz}$ 6H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z507[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,307,915,527]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)acetaldehyde (102). A solution of intermediate 101 $(2.00\\\\mathrm{g}, 3.95\\\\mathrm{mmol})$ in $1\\\\mathrm{M}$ $\\\\mathrm{H}_2\\\\mathrm{SO}_4$ $(10\\\\mathrm{mL})$ and THF $(10\\\\mathrm{mL})$ was stirred at $60^{\\\\circ}\\\\mathrm{C}$ for $4\\\\mathrm{h}$ . The mixture was cooled to room temperature and was basified to $\\\\mathrm{pH}9$ with $1\\\\mathrm{M}$ NaOH solution. The resulting mixture was extracted with EtOAc $(100\\\\mathrm{mL}\\\\times 3)$ , and the combined organic layers were washed with water $(100\\\\mathrm{mL})$ , dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\left(\\\\mathrm{CH}_3\\\\mathrm{CN}\\\\right.$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ to afford the title compound $(410\\\\mathrm{mg}, 24\\\\%)$ as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 8.24–8.15 (m, 1H), 8.10 (s, 1H), 7.78 (d, $J = 7.8~\\\\mathrm{Hz}$ , 1H), 7.55 (d, $J = 5.8~\\\\mathrm{Hz}$ , 1H), 7.35–7.25 (m, 1H), 7.08 (dd, $J = 7.6$ , 2.2 Hz, 1H), 6.94–6.86 (m, 1H), 6.76 (s, 1H), 6.44 (s, 2H), 6.32 (s, 1H), 5.03–4.79 (m, 3H), 4.68–4.55 (m, 1H), 3.63–3.42 (m, 2H), 3.21–2.96 (m, 2H), 2.33–2.24 (m, 2H), 2.09–1.95 (m, 2H). LC–MS $(ES+)$ : $m/z$ 433 $[\\\\mathbf{M} + \\\\mathbf{H}]^+$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,528,915,760]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tert-Butyl (3R)-4-(2-((4-(3-(3-amino-6-(2-hydroxyphenyl)-pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)ethyl)-3-methylpiperazine-1-carboxylate (104). A solution of intermediate 102 $(200\\\\mathrm{mg},0.462\\\\mathrm{mmol},1.0$ equiv), tert-butyl (3R)-3-methyl-1-piperazinecarboxylate (103, $92.6\\\\mathrm{mg}$ $0.463\\\\mathrm{mmol}$ 1.0 equiv), and $\\\\mathrm{NaBH(OAc)_3}$ $(636\\\\mathrm{mg},3.00\\\\mathrm{mmol},6.5$ equiv) in $\\\\mathrm{CH}_3\\\\mathrm{CN}$ $(3\\\\mathrm{mL})$ was stirred at room temperature for $2\\\\mathrm{h}$ The resulting mixture was diluted with EtOAc $(100~\\\\mathrm{mL})$ washed with water $(100~\\\\mathrm{mL})$ ,and the organic layer was dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.1\\\\%$ TFA), 0 to $100\\\\%$ ) to afford the title compound $(260\\\\mathrm{mg}$ $91\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 7.93 d $J =$ $6.4\\\\mathrm{Hz}$ 1H7.61d $J = 7.4\\\\mathrm{Hz}$ 1H7.49s1H7.42-7.31 m 1H7.06-6.99m1H6.99-6.89m1H6.84s2H6.79- 6.74m1H6.40s1H4.69s2H4.60s2H3.87-3.71m 2H3.69-3.55m3H3.53-3.41m4H3.29-3.11m4H 2.24-2.12m2H)2.05-1.90m2H)1.42s9H)1.29d $J = 6.3$ Hz, 3H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 617 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,760,915,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-((2R)-2-(3-(2-(3R)-4-(2-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)-3-methylpiperazin-1-yl)ethoxy)-isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (15). A solution of intermediate 104 $(250\\\\mathrm{mg},0.406\\\\mathrm{mmol})$ in HCl $(4.0\\\\mathrm{M}$ in MeOH, $5\\\\mathrm{mL})$ was stirred at room temperature for $2\\\\mathrm{h}$ The volatiles were then removed under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ 0 to $100\\\\%$ to afford 2-(6-amino-5-(8-(2-((R)-2-methylpiperazin-1-yl)ethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)pyridazin-3-yl)phenol $(190~\\\\mathrm{mg},91\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(500\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.15s1H7.92dd $J =$ 8.0, $1.6\\\\mathrm{Hz}$ 1H),7.79d $J = 5.9\\\\mathrm{Hz}$ 1H7.50s1H7.26-7.20 m,1H),6.90-6.81m2H),6.53dd $J = 6.0$ $2.1\\\\mathrm{Hz}$ 1H),6.14d \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[532,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[484,951,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1297 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,70,481,385]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$J = 2.1\\\\mathrm{Hz},1\\\\mathrm{H})$ 5.99s,2H)4.50s,2H)4.25 $\\\\mathrm{(t,J = 6.3~Hz,2H)}$ $3.25$ d $J = 11.6\\\\mathrm{Hz}$ 2H),3.01d $J = 11.6\\\\mathrm{Hz}$ 2H)2.98-2.90m 1H),2.77-2.66 m,3H),2.64-2.53 m,2H),2.33-2.22 m,3H), 2.21-2.15 m,2H),2.01-1.92 m,2H),0.95 d $J = 5.6\\\\mathrm{Hz}$ 3H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 517 $[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ .A solution of this material (180 mg, 0.349 mmol, 1.0 equiv), intermediate 61 (188 mg, 0.348 mmol, 1.0 equiv) and $\\\\mathrm{NaBH(OAc)_3}$ 221 mg, 1.04 mmol, 3.0 equiv) in $\\\\mathrm{CH}_3\\\\mathrm{CN}$ - $4\\\\mathrm{mL}$ ) was stirred at room temperature for $12\\\\mathrm{h}$ The resulting mixture was concentrated under reduced pressure, and the residue was purified by preparative HPLC [column: XBridge Prep OBD C18 Column $19\\\\times 250\\\\mathrm{mm}^2$ $5\\\\mu \\\\mathrm{m}$ mobile phase A: water (10 mmol/L $\\\\mathrm{NH_4HCO_3}$ ), mobile phase B: $\\\\mathrm{CH}_3\\\\mathrm{CN}$ ; flow rate: $25~\\\\mathrm{mL}/$ min; gradient: $35\\\\%$ B to $55\\\\%$ B over $10\\\\mathrm{min}$ wavelength: 254/220 nmRT: $10\\\\mathrm{min}]$ to afford the title compound ( $29\\\\mathrm{mg}$ $7.9\\\\%$ yield as a white solid. ${}^{1}\\\\mathbf{H}$ NMR (300 MHz,DMSO- $d_{6}$ ) $\\\\delta$ 14.13 s,1H),8.99 s,1H),8.40d $J = 7.7\\\\mathrm{Hz}$ 1H7.92d $J = 8.0~\\\\mathrm{Hz}$ 1H7.80d $J=$ $5.9\\\\mathrm{Hz}$ 1H),7.53-7.33 m,5H),7.23 t $J = 7.8~\\\\mathrm{Hz}$ 1H),6.91-6.79 m,2H),6.53d $J = 5.9~\\\\mathrm{Hz}$ 1H),6.14s,1H),6.09s,1H),5.97s, 2H),5.09d $J = 3.7~\\\\mathrm{Hz}$ 1H),4.97-4.86 m,1H),4.50s,2H),4.38 t $J = 7.8~\\\\mathrm{Hz}$ ,1H),4.32-4.17 m,5H),3.76-3.68 m,1H),3.65 d $J = 9.8~\\\\mathrm{Hz}$ ,1H),3.51-3.41 m,1H),3.26d $J = 11.6~\\\\mathrm{Hz}$ ,2H),3.07- 2.92m3H)2.87-2.77m1H)2.75-2.59m4H)2.46s,3H), 2.43-2.33m2H)2.30-2.11m5H)2.08-1.93m3H)1.91- 1.74m2H)1.49-1.34m3H)1.02-0.91m6H)0.88-0.76 m,3H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 1042 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,385,481,620]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tert-Butyl (2S)-4-(2-((4-(3-(3-amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)-2-methylpiperazine-1-carboxylate (106). A solution of intermediate 102 $(300\\\\mathrm{mg},0.694\\\\mathrm{mmol},1.0$ equiv), tert-butyl (S)-2-methylpiperazine-1-carboxylate (105, $139~\\\\mathrm{mg}$ $0.695\\\\mathrm{mmol}$ 1.0 equiv), and $\\\\mathrm{NaBH(OAc)_3}$ $(1.47\\\\mathrm{g},6.94\\\\mathrm{mmol},10$ equiv) in $\\\\mathrm{CH}_3\\\\mathrm{CN}$ $(5\\\\mathrm{mL})$ was stirred at room temperature for $8\\\\mathrm{h}$ . The reaction was quenched with MeOH $(5\\\\mathrm{mL})$ , and the volatiles were removed under vacuum. The residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH_4HCO_3)}$ 0 to $100\\\\%$ ) to afford the title compound $(160~\\\\mathrm{mg},37\\\\%)$ as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6}$ 8 14.15s1H7.92dd $J =$ 8.0, $1.6~\\\\mathrm{Hz}$ 1H7.80d $J = 5.9~\\\\mathrm{Hz}$ 1H7.49s1H7.29-7.17 m, 1H),6.92-6.79m2H6.54dd $J = 6.1$ $2.0~\\\\mathrm{Hz}$ 1H6.16d $J = 2.0~\\\\mathrm{Hz}$ 1H),5.98s2H),4.51s2H),4.30t $J = 5.9~\\\\mathrm{Hz}$ 2H), 4.05s1H),3.65d $J = 12.8~\\\\mathrm{Hz}$ 1H),3.26d $J = 11.6~\\\\mathrm{Hz}$ 2H), 3.01-2.80m4H),2.78-2.53m3H),2.23-2.05m3H),2.01- 1.86m3H),1.38s9H),1.10d $J = 6.7~\\\\mathrm{Hz}$ 3H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 617 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,620,479,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-((2R)-2-(3-(2-(2S)-4-(2-(4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)ethyl)-2-methylpiperazin-1-yl)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (16). A solution of intermediate 106 $(160\\\\mathrm{mg},0.259\\\\mathrm{mmol})$ in HCl $(4.0\\\\mathrm{M}$ in MeOH, $5\\\\mathrm{mL})$ was stirred at room temperature for $8\\\\mathrm{h}$ The volatiles were then removed under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ 0 to $100\\\\%$ to afford 2-(6-amino-5-(8-(2-(2-((S)-3-methylpiperazin-1-yl)ethoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)pyridazin-3-yl)phenol $(120~\\\\mathrm{mg},90\\\\%)$ as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.13s1H7.92d $J =$ $8.0\\\\mathrm{Hz}$ 1H7.79d $J = 5.9\\\\mathrm{Hz}$ 1H7.50s1H7.23t $J = 7.7$ Hz1H6.92-6.80m2H6.54dd $J = 6.1$ $2.1\\\\mathrm{Hz}$ 1H6.16d $J$ $= 2.0\\\\mathrm{Hz}$ 1H),5.97s2H4.51s2H4.27t $J = 6.0~\\\\mathrm{Hz}$ 2H), 3.26d $J = 11.4~\\\\mathrm{Hz}$ 2H),3.02d $J = 11.6~\\\\mathrm{Hz}$ 2H),2.82-2.70m, 3H),2.70-2.54m4H),2.25-2.12m2H),2.02-1.86m3H), 1.60t $J = 10.1~\\\\mathrm{Hz}$ 1H),0.90d $J = 6.3~\\\\mathrm{Hz}$ 3H.LC-MS $(ES+)$ : $m / z517[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ .A solution of this material $(88.9\\\\mathrm{mg},0.172\\\\mathrm{mmol},$ 1.1 equiv), intermediate 61 $(85.0\\\\mathrm{mg},0.157\\\\mathrm{mmol},$ 1.0 equiv and $\\\\mathrm{NaBH(OAc)_3}$ 175 mg, 0.825 mmol, 5.3 equiv in $\\\\mathrm{CH}_3\\\\mathrm{CN}$ $5\\\\mathrm{mL})$ was stirred at room temperature for $10\\\\mathrm{h}$ The reaction was quenched with MeOH $(10~\\\\mathrm{mL})$ and the solvents were evaporated under vacuum.The residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH_4HCO_3})$ ,0 to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,298]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"100%) to afford $67~\\\\mathrm{mg}$ of impure product as a white solid. This material was further purified by preparative HPLC [column: XSelect CSH Fluoro Phenyl $30\\\\times 150\\\\mathrm{mm}^2$ $5\\\\mu \\\\mathrm{m}$ ; mobile phase A: water (10 mmol/L $\\\\mathrm{NH_4HCO_3}$ ), mobile phase B: $\\\\mathrm{CH}_3\\\\mathrm{CN}$ ; flow rate: $60~\\\\mathrm{mL}/$ min; gradient: $27\\\\%$ B to $50\\\\%$ B over $10\\\\mathrm{min}$ ; wavelength: 254/220 nm; RT: $8.1\\\\mathrm{min}$ ] to afford the title compound $(4.2\\\\mathrm{mg},2.5\\\\%)$ as a light yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ , DMSO- $d_{6})$ $\\\\delta$ 14.16 (s, 1H), 8.99 (s, 1H), 8.43 (d, $J = 7.6~\\\\mathrm{Hz}$ , 1H), 7.92 (dd, $J = 8.1$ , $1.6~\\\\mathrm{Hz}$ , 1H), 7.79 (dd, $J = 6.0$ , $1.8~\\\\mathrm{Hz}$ , 1H), 7.50 (s, 1H), 7.47-7.40 (m, 2H), 7.40-7.33 (m, 2H), 7.27-7.17 (m, 1H), 6.92-6.77 (m, 2H), 6.54 (dd, $J = 6.1$ , $2.1~\\\\mathrm{Hz}$ , 1H), 6.16 (d, $J = 2.0~\\\\mathrm{Hz}$ , 1H), 6.08 (s, 1H), 5.99 (s, 2H), 5.10 (d, $J = 3.7~\\\\mathrm{Hz}$ , 1H), 4.97-4.85 (m, 1H), 4.50 (s, 2H), 4.37 (t, $J = 7.8~\\\\mathrm{Hz}$ , 1H), 4.33-4.25 (m, 3H), 4.22-4.12 (m, 2H), 3.74-3.55 (m, 2H), 3.45 (dd, $J = 10.0$ , $4.9~\\\\mathrm{Hz}$ , 1H), 3.33-3.30 (m, 1H), 3.25 (d, $J = 11.5~\\\\mathrm{Hz}$ , 2H), 3.08-2.95 (m, 3H), 2.87-2.63 (m, 2H), 2.63-2.55 (m, 3H), 2.46 (s, 3H), 2.45-2.33 (m, 2H), 2.30-2.12 (m, 4H), 2.07-1.74 (m, 5H), 1.50-1.34 (m, 3H), 0.98-0.95 (m, 6H), 0.87-0.75 (m,3H). LC-MS $(ES+)$ : $m / z$ 1041.7 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,298,915,425]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"cis-3-(Benzyloxy)cyclobutan-1-ol (108). To a $0^{\\\\circ}\\\\mathrm{C}$ solution of 3-(benzyloxy)cyclobutan-1-one (107, $10.0\\\\mathrm{g}$ , 56.8 mmol, 1.0 equiv) in MeOH $(100~\\\\mathrm{mL})$ was added $\\\\mathrm{NaBH}_4$ $(2.15\\\\mathrm{g},56.9\\\\mathrm{mmol},1.0$ equiv). The resulting solution was stirred at $0^{\\\\circ}\\\\mathrm{C}$ for $1\\\\textrm{h}$ then was quenched with water $(200~\\\\mathrm{mL})$ and extracted with EtOAc $(200~\\\\mathrm{mL}\\\\times 3)$ . The organic layers were combined, dried over sodium sulfate, and were concentrated under vacuum. The residue was purified by flash chromatography on silica gel (petroleum ether:EtOAc, 80:1 to 1:1) to give the title compound $(9.85\\\\mathrm{g},97\\\\%)$ as a colorless oil. LC-MS (ES +): $m / z$ 200.9 $[\\\\mathbf{M} + \\\\mathbf{N}\\\\mathbf{a}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,425,915,665]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"trans-4-(3-(Benzyloxy)cyclobutoxy)pyridine (109). To a solution of pyridin-4-ol $(3.20\\\\mathrm{g}, 33.7\\\\mathrm{mmol}, 1.5\\\\mathrm{equiv})$ and cis-3-(benzyloxy)cyclobutan-1-ol $(108, 4.0\\\\mathrm{g}, 22.4\\\\mathrm{mmol}, 1.0\\\\mathrm{equiv})$ in THF $(200\\\\mathrm{mL})$ was added triphenylphosphine $(7.06\\\\mathrm{g}, 26.9\\\\mathrm{mmol}, 1.2\\\\mathrm{equiv})$ and DIAD $(5.45\\\\mathrm{g}, 26.9\\\\mathrm{mmol}, 1.2\\\\mathrm{equiv})$ in one portion at $10^{\\\\circ}\\\\mathrm{C}$ . The mixture was stirred at $50^{\\\\circ}\\\\mathrm{C}$ for $12\\\\mathrm{h}$ , then was cooled to room temperature and was concentrated under reduced pressure. Water $(50\\\\mathrm{mL})$ was added, and the mixture was stirred for $1\\\\mathrm{min}$ . The aqueous phase was extracted with DCM $(50\\\\mathrm{mL} \\\\times 3)$ , and the combined organic phases were washed with brine $(50\\\\mathrm{mL} \\\\times 2)$ , dried with sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (petroleum ether:THF, 20:1 to 5:1). Additional purification by reverse phase C18 column chromatography [5 to $50\\\\%$ $\\\\mathrm{CH}_3\\\\mathrm{CN}$ in water (with $0.5\\\\%$ $\\\\mathrm{NH}_4\\\\mathrm{OH}$ ] then provided the title compound $(3.2\\\\mathrm{g}, 55\\\\%)$ as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}, \\\\mathrm{CDCl}_3)$ $\\\\delta$ 8.32–8.34 (m, 2H), 7.22–7.39 (m, 5H), 6.60–6.62 (m, 2H), 4.80–4.84 (m, 1H), 4.37 (s, 2H), 4.24–4.28 (m, 1H), 2.37–2.46 (m, 4H). LC–MS $(\\\\mathrm{ES+}): m/z$ 256.0 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,665,915,765]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1-Benzyl-4-(trans-3-(benzyloxy)cyclobutoxy)pyridin-1-ium bromide (110). To a solution of intermediate 109 $(4.2\\\\mathrm{g},16.5\\\\mathrm{mmol}$ 1.0 equiv) in toluene $(65~\\\\mathrm{mL})$ was added benzyl bromide $(2.81\\\\mathrm{g},$ $16.5\\\\mathrm{mmol}$ 1.0 equiv). The mixture was stirred at $80^{\\\\circ}\\\\mathrm{C}$ for $12\\\\mathrm{h}$ then was cooled to room temperature and was concentrated under reduced pressure. The crude product was triturated with petroleum ether (80 mL) to give the title compound $(6.5\\\\mathrm{g},92\\\\%)$ as a white solid. LC-MS $(\\\\mathrm{ES + })$ .. $m / z346.0[\\\\mathrm{M}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,765,915,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"trans-1-Benzyl-4-(3-(benzyloxy)cyclobutoxy)-1,2,3,6-tetrahydropyridine (111). To a $0^{\\\\circ}\\\\mathrm{C}$ solution of intermediate 110 $(6.5\\\\mathrm{g},15.3\\\\mathrm{mmol},1.0$ equiv) in EtOH $(120~\\\\mathrm{mL})$ was added $\\\\mathrm{NaBH}_4$ $(3.46\\\\mathrm{g},91.5\\\\mathrm{mmol},6.0$ equiv). The mixture was stirred at $15^{\\\\circ}\\\\mathrm{C}$ for 4 h then was concentrated under reduced pressure. The residue was diluted with water $(25~\\\\mathrm{mL})$ and was extracted with EtOAc $(50~\\\\mathrm{mL}\\\\times$ 2). The combined organic phases were washed with brine $(40~\\\\mathrm{mL}\\\\times$ 3), dried with sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure to give the title compound (4.5 g, $84\\\\%$ ) as a colorless oil. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz},\\\\mathrm{CDCl}_3)$ $\\\\delta 7.28 - 7.38$ m, 10H), 4.57-4.58 (m, 1H), 4.42 (s, 2H), 4.36-4.38 (m, 1H), 4.13-4.28 (m, 1H), 3.59 (s, 2H), 3.01-3.02 (m, 2H), 2.60-2.62 (m, 2H), 2.36-2.38 (m, 4H), 2.06-2.35 (m, 2H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 350.1 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[484,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1298 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,70,481,195]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"trans-3-((1-Benzylpiperidin-4-yl)oxy)cyclobutan-1-ol (112). To a room temperature solution of intermediate 111 $(4.5\\\\mathrm{g},12.9$ mmol) in THF $(95~\\\\mathrm{mL})$ and EtOH $(70~\\\\mathrm{mL})$ was added $10\\\\%$ palladium on activated carbon $(0.5\\\\mathrm{g})$ . The suspension was degassed and purged with hydrogen three times then was stirred under a hydrogen atmosphere $(50~\\\\mathrm{psi})$ at $35^{\\\\circ}\\\\mathrm{C}$ for $12\\\\mathrm{h}$ . The reaction mixture was filtered, and the filtrate was concentrated. The residue was purified by silica gel chromatography (DCM:MeOH: $\\\\mathrm{NH_4OH}$ , 20:1:0 to 10:1:0.1) to give the title compound $(2.8\\\\mathrm{g},83\\\\%)$ as a colorless oil. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,196,481,370]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tert-Butyl 4-(trans-3-hydroxyclobutoxy)piperidine-1-carboxylate (113). To a room temperature solution of intermediate 112 $(1.1\\\\mathrm{g},4.21\\\\mathrm{mmol},1.0$ equiv) in MeOH $(10~\\\\mathrm{mL})$ was added $10\\\\%$ $\\\\mathrm{Pd(OH)_2}$ on activated carbon $(591\\\\mathrm{mg})$ and di-tert-butyl dicarbonate $(1.84\\\\mathrm{g},8.42\\\\mathrm{mmol},2.0$ equiv). The suspension was degassed and purged with hydrogen three times then was stirred under a hydrogen atmosphere (50 psi) at $25^{\\\\circ}\\\\mathrm{C}$ for $12\\\\mathrm{h}$ . The reaction mixture was filtered, and the filtrate was concentrated. The residue was purified by silica gel chromatography (petroleum ether:EtOAc, 20:1 to 2:1) to afford the title compound $(820\\\\mathrm{mg},71\\\\%)$ as a colorless oil. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz},\\\\mathrm{CDCl}_3)$ $\\\\delta$ 4.51s,1H),4.32-4.37m1H),3.79-3.82 m,2H),3.40-3.44m1H),2.99-3.04m2H),2.20-2.28m 4H),1.76-1.80m3H),1.60-1.62m1H),1.45-1.47m,12H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 172.0 $[\\\\mathbf{M - B o c + H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,370,481,568]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tert-Butyl 4-(trans-3-((4-bromopyridin-2-yl)oxy)-cyclobutoxy)piperidine-1-carboxylate (114). A room temperature mixture of intermediate 113 $(1.0\\\\mathrm{g},3.69\\\\mathrm{mmol},1.0$ equiv), 4-bromo-2-fluoro-pyridine (72, $778~\\\\mathrm{mg}$ $4.42\\\\mathrm{mmol}$ 1.2 equiv), and $\\\\mathrm{Cs_2CO_3}$ $(2.40\\\\mathrm{g},7.37\\\\mathrm{mmol},2.0$ equiv) in $\\\\mathrm{CH}_3\\\\mathrm{CN}$ $(10~\\\\mathrm{mL})$ was degassed and purged with nitrogen three times. The mixture was then stirred at $90^{\\\\circ}\\\\mathrm{C}$ for $12\\\\mathrm{h}$ after which it was cooled to room temperature and filtered. The filtrate was concentrated under reduced pressure, and the crude product thus obtained was purified by silica gel chromatography (petroleum ether:EtOAc, 1:0 to 10:1) to give the title compound $(1.36\\\\mathrm{g},86\\\\%)$ as colorless oil. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ $\\\\mathrm{CDCl}_3$ ) $\\\\delta$ 7.97d $J = 5.6\\\\mathrm{Hz}$ 1H)7.03-7.01m1H6.91d $J=$ $1.2\\\\mathrm{Hz}$ 1H),5.30-5.23m1H)4.43-4.31m1H)3.81d $J=$ $12.8\\\\mathrm{Hz}$ 2H),3.49-3.42m1H)3.07-3.01m2H)2.52-2.36 m,4H),1.80d $J = 8.8\\\\mathrm{Hz}$ 2H),1.55-1.47m2H)1.46s,9H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 427.1 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,568,481,828]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Benzyl 8-(2-(trans-3-((1-(tert-butoxycarbonyl)piperidin-4- yl)oxy)cyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]-octane-3-carboxylate (115). A room temperature mixture of intermediate 114 $(1.36\\\\mathrm{g},3.18\\\\mathrm{mmol}$ 1.0 equiv), benzyl 3,8- diazabicyclo[3.2.1]octane-3-carboxylate (98, $784~\\\\mathrm{mg}$ 3.18 mmol, 1.0 equiv), RuPhosPd-G2 $(148\\\\mathrm{mg},0.19\\\\mathrm{mmol},0.06$ equiv), and $\\\\mathrm{Cs_2CO_3}$ $(2.07\\\\mathrm{g},6.37\\\\mathrm{mmol},2.0$ equiv) in toluene $(27~\\\\mathrm{mL})$ was degassed and purged with nitrogen three times. The mixture was then stirred at $110^{\\\\circ}C$ for $12\\\\mathrm{h}$ after which it was cooled to room temperature. Water (30 mL) was added, and the mixture was extracted with EtOAc $(40~\\\\mathrm{mL}\\\\times$ 2). The combined organic layers were washed with brine $(30~\\\\mathrm{mL}\\\\times$ 2), dried over sodium sulfate, filtered, and the filtrate was concentrated under reduced pressure. The crude product was purified by silica gel chromatography (petroleum ether:EtOAc, 1:0 to 1:1) to give the title compound $(1.35\\\\mathrm{g},71\\\\%)$ as a colorless oil. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz},\\\\mathrm{CDCl}_3)\\\\delta 7.86$ d $J = 6.0~\\\\mathrm{Hz}$ 1H)7.40-7.29 m5H) 6.27dd $J = 6.0$ $2.4~\\\\mathrm{Hz}$ 1H5.94d $J = 2.0~\\\\mathrm{Hz}$ 1H5.29-5.24 m, 1H),5.13s,2H),4.38m1H4.22s,2H)3.86-3.68 m, 4H),3.49-3.41 m, 1H),3.33-3.18 m, 2H),3.06-3.00 m, 2H), 2.46-2.36 m, 4H),1.94-1.74 m, 4H),1.63-1.51 m, 4H),1.46 s, 9H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 593.4 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,830,481,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tert-Butyl 4-(trans-3-((4-(3,8-diazabicyclo[3.2.1]octan-8-yl)-pyridin-2-yl)oxy)cyclobutoxy)piperidine-1-carboxylate (116). To a room temperature solution of intermediate 115 $(1.35\\\\mathrm{g},2.28$ mmol) in a mixture of THF $(27~\\\\mathrm{mL})$ and EtOH $(27~\\\\mathrm{mL})$ was added $10\\\\%$ palladium hydroxide on activated carbon $(320~\\\\mathrm{mg})$ . The resulting suspension was degassed under vacuum and purged with hydrogen several times then was stirred under a hydrogen atmosphere (50 psi) at $60^{\\\\circ}\\\\mathrm{C}$ for $12\\\\mathrm{h}$ . After cooling to room temperature, the reaction mixture was filtered, and the filtrate was concentrated to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,914,95]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"provide the title compound $(932\\\\mathrm{mg},89\\\\%)$ as a brown solid. LC-MS $(\\\\mathrm{ES + })$ .. $m / z459.3[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,96,915,380]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tert-Butyl 4-(trans-3-((4-(3-(3-amino-6-chloropyridazin-4- yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidine-1-carboxylate (117). A room temperature mixture of intermediate 116 $(932\\\\mathrm{mg},2.03\\\\mathrm{mmol}$ 1.0 equiv), 4-bromo-6-chloro-pyridazin-3-amine (70, $508~\\\\mathrm{mg}$ 2.44 mmol, 1.2 equiv), and DIEA $(3.54~\\\\mathrm{mL}$ 20.3 mmol, 10 equiv) in DMSO (30 mL) was degassed and purged with nitrogen three times. The mixture was stirred at $130^{\\\\circ}C$ for $3\\\\textrm{h}$ then was cooled to room temperature. Water $(30~\\\\mathrm{mL})$ was added, and the mixture was extracted with EtOAc $(30~\\\\mathrm{mL}\\\\times 2)$ . The combined organic layers were washed with saturated aqueous sodium chloride $(30~\\\\mathrm{mL}\\\\times 2)$ , dried over sodium sulfate, and were concentrated. The residue was purified by semipreparative reverse phase HPLC [column: Phenomenex Gemini C18 $250\\\\times 50\\\\mathrm{mm}^2$ $10~\\\\mu \\\\mathrm{m}$ ; mobile phase A: water (with $0.05\\\\%$ $\\\\mathrm{NH_4OHv / v)}$ mobile phase B: $\\\\mathrm{CH}_3\\\\mathrm{CN}$ ; gradient: $45 - 70\\\\%$ B] to provide the title compound $(772\\\\mathrm{mg},64\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 7.76 d $J = 6.0~\\\\mathrm{Hz}$ 1H)6.90s1H6.50 dd $J = 6.1$ 2.1 Hz,1H)6.12d $J = 2.0~\\\\mathrm{Hz}$ 1H)5.85s2H) 5.26-5.12 m1H4.45 s2H4.31 p $J = 6.0~\\\\mathrm{Hz}$ 1H)3.66 dt $J$ $= 13.4$ $4.7\\\\mathrm{Hz}$ 2H)3.50-3.37 m1H)3.18 d $J = 11.5\\\\mathrm{Hz}$ 2H) 2.92dd $J = 35.6$ $11.5\\\\mathrm{Hz}$ 4H)2.40-2.21 m4H)2.13 d $J = 7.2$ Hz,2H),1.97-1.88 m2H)1.80-1.70 m2H)1.39 s9H) 1.33-1.20 m2H.LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 586.5 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,380,915,563]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tert-Butyl 4-(trans-3-((4-(3-(3-amino-6-(2-hydroxyphenyl)-pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)cyclobutoxy)piperidine-1-carboxylate (118). A room temperature mixture of intermediate 117 $(772\\\\mathrm{mg},$ $1.32\\\\mathrm{mmol}$ 1.0 equiv), (2-hydroxyphenyl)boronic acid (72, $218\\\\mathrm{mg}$ $1.58\\\\mathrm{mmol}$ 1.2 equiv), $\\\\mathrm{Pd(PPh_3)_4}$ $(152\\\\mathrm{mg},$ $0.13\\\\mathrm{mmol}$ 0.1 equiv), and $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ $364\\\\mathrm{mg}$ $2.63\\\\mathrm{mmol}$ 2.0 equiv) in a mixture of 1,4-dioxane $(12~\\\\mathrm{mL})$ and water $(2\\\\mathrm{mL})$ was degassed and purged with nitrogen three times. The mixture was then stirred at $90^{\\\\circ}C$ for $10\\\\mathrm{h}$ After cooling to room temperature, the reaction mixture was concentrated, and the residue was purified by semipreparative reverse phase HPLC [column: Kromasil $250\\\\times 50\\\\mathrm{mm}^2$ $10~\\\\mu \\\\mathrm{m}$ mobile phase A: water (with $0.1\\\\%$ TFA), mobile phase B: $\\\\mathrm{CH}_3\\\\mathrm{CN};$ gradient: $20 - 50\\\\%$ B] to give the title compound $(500\\\\mathrm{mg},54\\\\%)$ as a yellow solid. LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 644.4 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,563,915,710]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(6-Amino-5-(8-(2-((trans)-3-(piperidin-4-yloxy)cyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)-pyridazin-3-yl)phenol (119). To a room temperature solution of intermediate 118 $(500\\\\mathrm{mg},0.78\\\\mathrm{mmol})$ in DCM $(5\\\\mathrm{mL})$ was added HCl $(4.0\\\\mathrm{M}$ in 1,4-dioxane, $5\\\\mathrm{mL}$ ). The mixture was stirred at $20^{\\\\circ}\\\\mathrm{C}$ for $2\\\\mathrm{h}$ then was concentrated to give the crude title compound (HCl salt, $500\\\\mathrm{mg}$ ) as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz},\\\\mathrm{D}_2\\\\mathrm{O})$ $\\\\delta 7.72$ (d, $J = 7.2\\\\mathrm{Hz}$ , 1H), 7.40-7.55 (m, 3H), 6.99-7.11 (m, 2H), 6.68-6.76 (m, 1H), 6.02 (d, $J = 2.0\\\\mathrm{Hz}$ , 1H), 5.10 (dt, $J = 6.4$ , 3.2 Hz, 1H), 4.52 (m, 1H), 3.70-3.84 (m, 3H), 3.30-3.42 (m, 5H), 3.25 (br d, $J = 12.4\\\\mathrm{Hz}$ , 2H), 3.02-3.14 (m, 2H), 2.46-2.64 (m, 4H), 2.01-2.22 (m, 6H), 1.67-1.83 (m, 2H). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,710,915,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-((2R)-2-(3-(2-(4-((trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)ethoxy)-isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (17). To a solution of intermediate 119 (HCl salt, $70.0\\\\mathrm{mg}$ , 0.121 mmol, 1.0 equiv) and $\\\\mathrm{NaOAc}$ $(31.6\\\\mathrm{mg},0.385\\\\mathrm{mmol},3.2$ equiv) in MeOH $(2.1~\\\\mathrm{mL})$ and DCM $(0.7~\\\\mathrm{mL})$ was added intermediate 61 $(104\\\\mathrm{mg},0.192\\\\mathrm{mmol},1.6$ equiv) at room temperature. The reaction was stirred at room temperature for $30\\\\mathrm{min}$ after which $\\\\mathrm{NaBH}_3\\\\mathrm{CN}$ $(12.1\\\\mathrm{mg},0.192\\\\mathrm{mmol},1.6$ equiv) was addd in portions at the same temperature. The resulting mixture was stirred at room temperature for another $2\\\\mathrm{h}$ then was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH_4HCO_3})$ 0 to $100\\\\%$ to afford the title compound $(34\\\\mathrm{mg},25\\\\%)$ as an off-white solid. ${}^{1}\\\\mathbf{H}$ NMR $(400\\\\mathrm{MHz}$ DMSO- $d_{6}$ ) $\\\\delta$ 14.15 (s, 1H), 8.99 (d, $J = 1.6~\\\\mathrm{Hz}$ , 1H), 8.41 (d, $J = 7.7~\\\\mathrm{Hz}$ , 1H), 7.96-7.89 (m, 1H), 7.78 (d, $J = 5.9~\\\\mathrm{Hz}$ , 1H), 7.50 (s, 1H), 7.49-7.41 (m, 2H), 7.41-7.34 (m, 2H), 7.27-7.18 (m, 1H), 6.91-6.81 (m, 2H), 6.56-6.50 (m, 1H), 6.14 (d, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[484,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1299 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,70,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"$J = 2.0\\\\\\\\mathrm{Hz},1\\\\\\\\mathrm{H})$ 6.10s,1H)5.98s,2H),5.24-5.14m,1H)5.10 $(\\\\\\\\mathrm{d},J = 3.7\\\\\\\\mathrm{Hz},1\\\\\\\\mathrm{H}),$ 4.98-4.86m,1H)4.50d $J = 4.5\\\\\\\\mathrm{Hz},2\\\\\\\\mathrm{H})$ 4.38t $J = 7.9\\\\\\\\mathrm{Hz},1\\\\\\\\mathrm{H})$ 4.32-4.25m,2H)4.22t $J = 5.7\\\\\\\\mathrm{Hz},2\\\\\\\\mathrm{H})$ 3.75-3.61m,2H)3.50-3.41m,1H)3.31-3.22m,3H)3.02d $J = 11.6\\\\\\\\mathrm{Hz},2\\\\\\\\mathrm{H}),$ 2.80-2.71m,2H)2.69-2.61m,2H)2.46s, 3H)2.39-2.23m,5H)2.23-1.90m,7H)1.84-1.73m,3H) 1.49-1.35m,5H)0.96d $J = 6.4\\\\\\\\mathrm{Hz},3\\\\\\\\mathrm{H}),$ 0.87-0.77m,3H). LC-MS $\\\\\\\\left(\\\\\\\\mathrm{ES}+\\\\\\\\right)$ .. $m / z$ 1068.7 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ \\\",\\\"To confirm the absolute stereochemistry of intermediate 61 employed in the syntheses of 15, 16, and 17, the isopropyl epimer corresponding to 61 (61e, prepared above) was similarly transformed into the isopropyl epimer of PROTAC 17 (17e, structure not shown). To a solution of intermediate 119 (HCl salt, $150\\\\\\\\mathrm{mg}$ , $0.259\\\\\\\\mathrm{mmol}$ , 1.0 equiv) and $\\\\\\\\mathrm{NaOAc}$ (67.9 mg, 0.828 mmol, 3.2 equiv) in MeOH (2.1 mL) and DCM (0.7 mL) was added intermediate 61e (223 mg, 0.41 mmol, 1.6 equiv) at room temperature. The reaction was stirred at room temperature for 30 min after which $\\\\\\\\mathrm{NaBH}_3\\\\\\\\mathrm{CN}$ (26.0 mg, 0.414 mmol, 1.6 equiv) was added in portions at the same temperature. The resulting mixture was stirred at room temperature for another 2 h then was directly purified by prepacked C18 column chromatography $(\\\\\\\\mathrm{CH}_3\\\\\\\\mathrm{CN}$ in water $(0.05\\\\\\\\% \\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ , 0 to $100\\\\\\\\%$ to afford 17e (67 mg, $23\\\\\\\\%$ ) as an off-white solid. ${}^{1}\\\\\\\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) $\\\\\\\\delta$ 14.15 (s, 1H), 9.05–8.87 (m, 1H), 8.30 (d, $J = 7.9~\\\\\\\\mathrm{Hz}$ , 1H), 7.97–7.89 (m, 1H), 7.77 (d, $J = 5.9~\\\\\\\\mathrm{Hz}$ , 1H), 7.55–7.28 (m, 5H), 7.28–7.18 (m, 1H), 6.92–6.81 (m, 2H), 6.57–6.49 (m, 1H), 6.18–6.13 (m, 1H), 6.09 (s, 1H), 5.98 (s, 2H), 5.25–5.15 (m, 1H), 5.13–4.86 (m, 2H), 4.50 (s, 2H), 4.42 (t, $J = 7.8~\\\\\\\\mathrm{Hz}$ , 1H), 4.33–4.12 (m, 4H), 3.75 (d, $J = 8.6~\\\\\\\\mathrm{Hz}$ , 1H), 3.60–3.46 (m, 2H), 3.30–3.18 (m, 3H), 3.02 (d, $J = 11.6~\\\\\\\\mathrm{Hz}$ , 2H), 2.83–2.56 (m, 4H), 2.46 (s, 3H), 2.36–2.22 (m, 5H), 2.22–2.16 (m, 2H), 2.16–2.02 (m, 3H), 2.01–1.91 (m, 2H), 1.84–1.69 (m, 3H), 1.50–1.31 (m, 5H), 0.97 (d, $J = 6.6~\\\\\\\\mathrm{Hz}$ , 2H), 0.88–0.80 (m, 3H), 0.76 (d, $J = 6.7~\\\\\\\\mathrm{Hz}$ , 1H). LC–MS $(\\\\\\\\mathrm{ES+})$ .. $m/z$ 1068.7 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . \\\",\\\"Both 17 and 17e PROTACs were profiled in biological assessments, and the more potent diastereomer was assigned the absolute stereochemistry shown for 17 in Table 2 (cf., Table S4). This stereochemistry was consistent with that observed in the crystal structure of the BRG1-17-VBC ternary complex (Figure S8 and S9). By inference, the chiral-pure intermediate employed to generate 17 was assigned the absolute stereochemistry shown in Scheme 3 (i.e., intermediate 61). \\\",\\\"2-(6-Amino-5-(8-(2-(trans-3-((1-(2,2-diethoxyethyl)-piperidin-4-yl)oxy)cyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)pyridazin-3-yl)phenol (120). A solution of intermediate 119 $(200\\\\\\\\mathrm{mg},0.368\\\\\\\\mathrm{mmol},1.0$ equiv) and 2-bromo1,1-diethoxyethane $(145\\\\\\\\mathrm{mg},0.736\\\\\\\\mathrm{mmol},2.0$ equiv), DIEA $(143\\\\\\\\mathrm{mg},$ $1.10\\\\\\\\mathrm{mmol},3.0$ equiv), and NaI $(110\\\\\\\\mathrm{mg},0.736\\\\\\\\mathrm{mmol},2.0$ equiv) in DMF $(2\\\\\\\\mathrm{mL})$ was stirred at $70^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ overnight. The mixture was cooled to room temperature and was directly purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\% \\\\\\\\mathrm{NH_4HCO_3})$ , 0 to $100\\\\\\\\%$ ) to afford the title compound $(85\\\\\\\\mathrm{mg},35\\\\\\\\%)$ as a yellow solid. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.16s,1H)7.92dd $J = 8.0$ $1.6~\\\\\\\\mathrm{Hz}$ 1H7.77d $J = 6.0~\\\\\\\\mathrm{Hz}$ 1H7.50s,1H)7.28-7.17m, 1H)6.91-6.79m2H)6.52dd $J = 6.1$ 2.0 Hz1H)6.14d $J =$ $2.0~\\\\\\\\mathrm{Hz}$ 1H5.98s2H)5.28-5.12m1H4.58-4.45m3H) 4.27p $J = 6.1~\\\\\\\\mathrm{Hz}$ 1H)3.65-3.52m2H)3.52-3.46m2H) 3.30-3.14m3H)3.01d $J = 11.6~\\\\\\\\mathrm{Hz}$ 2H)2.80-2.65m2H) 2.37d $J = 5.2~\\\\\\\\mathrm{Hz}$ 2H)2.33-2.22m4H)2.22-2.03m4H) 2.01-1.91m2H)1.80-1.69m2H)1.46-1.29m2H)1.10t $J = 7.0~\\\\\\\\mathrm{Hz}$ 6H). LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 660 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ \\\",\\\"2-(4-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)- pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)cyclobutoxy)piperidin-1-yl)acetaldehyde (121). A solution of intermediate 120 $(100\\\\\\\\mathrm{mg},0.152\\\\\\\\mathrm{mmol})$ in $1.0\\\\\\\\mathrm{M}$ $\\\\\\\\mathrm{H}_2\\\\\\\\mathrm{SO}_4$ $(1\\\\\\\\mathrm{mL})$ and THF $(1\\\\\\\\mathrm{mL})$ was stirred at $60^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ overnight. The mixture was then cooled to room temperature and was directly purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\%)$ $\\\\\\\\mathrm{NH_4HCO_3)}$ , 0 to $30\\\\\\\\%$ ) to afford the title compound $(50\\\\\\\\mathrm{mg},66\\\\\\\\%$ purity) as an off-white solid. LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z~586[\\\\\\\\mathrm{M} + \\\\\\\\mathrm{H}]^{+}$ \\\"]\",\n \"page_idx\": \"38\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[512,71,915,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Additional purification attempts did not improve the purity, and the material was therefore used in its impure form in the next step. \\\",\\\"tert-Butyl 4-(5-((R)-1-((2S,4R)-4-hydroxy-2-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)carbamoyl)pyrrolidin-1-yl)-3-methyl-1-oxobutan-2-yl)isoxazol-3-yl)piperazine-1-carboxylate (122). To a stirred solution of intermediate 46 $(820\\\\\\\\mathrm{mg},2.32$ mmol, 1.0 equiv), (2S,4R)-4-hydroxy- $N - ((S)$ -1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (57, TFA salt, $1.02\\\\\\\\mathrm{g},2.32$ mmol, 1.0 equiv) and DIEA $(900\\\\\\\\mathrm{mg},6.96\\\\\\\\mathrm{mmol},3.0$ equiv) in DMF $(9~\\\\\\\\mathrm{mL})$ was added HATU $(1323\\\\\\\\mathrm{mg},3.48\\\\\\\\mathrm{mmol},1.5$ equiv) in portions at room temperature. The resulting mixture was stirred at room temperature for $^{\\\\\\\\textrm{\\\\\\\\scriptsize 1h}}$ then was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\% \\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ , 0 to $40 \\\\\\\\%$ to afford the coupled product $\\\\\\\\left(\\\\\\\\sim 1:1\\\\\\\\right.$ mixture of two isopropyl group isomers, $950~\\\\\\\\mathrm{mg})$ as a yellow solid. The two isomers were separated by preparative chiral HPLC [column: CHIRALPAK IF, $2\\\\\\\\times 25~\\\\\\\\mathrm{cm}^2$ $5$ $\\\\\\\\mu \\\\\\\\mathrm{m}$ ; mobile phase A: 3:1 hexane:DCM $(0.5\\\\\\\\% 2\\\\\\\\mathrm{M}\\\\\\\\mathrm{NH}_{3}\\\\\\\\cdot \\\\\\\\mathrm{MeOH})$ mobile phase B: MeOH; flow rate: $20~\\\\\\\\mathrm{mL / min}$ ; gradient: isocratic $20\\\\\\\\%$ B; wavelength: $220 / 254~\\\\\\\\mathrm{nm}$ RT1:7.39 minRT2:11.24 min sample solvent: EtOH; injection volume: $3.5~\\\\\\\\mathrm{mL}$ ; number of runs: S] to afford the title compound (slower peak, $378~\\\\\\\\mathrm{mg}$ $24\\\\\\\\%$ ) as a yellow solid. ${}^{1}\\\\\\\\mathbf{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 89.02-8.77 (m, 1H), 8.41 (d, $J = 7.7~\\\\\\\\mathrm{Hz}$ 1H),7.51-7.40 (m, 2H),7.40-7.32 (m, 2H),6.20-6.03 (m, 1H),5.09 (d, $J = 3.2~\\\\\\\\mathrm{Hz}$ 1H),4.97-4.61 (m, 1H),4.36 (t, $J = 7.8$ Hz, 1H),4.28 (s, 1H),3.71 (dd, $J = 10.6$ $4.4~\\\\\\\\mathrm{Hz}$ 1H),3.59 (d, $J = 9.8$ Hz, 1H),3.49-3.35 (m, 5H),3.20-3.05 (m, 4H),2.46 (s, 3H), 2.32-2.10 (m, 1H),2.08-1.96 (m, 1H),1.83-1.69 (m, 1H),1.49- 1.33 (m, 12H), 1.01-0.91 (m, 3H), 0.87-0.75 (m, 3H). LC-MS (ES +): m/z 667 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . The isomer bearing the undesired isopropyl stereocenter (122e, isopropyl isomer corresponding to 122, structure not shown) was also isolated (faster peak, $440~\\\\\\\\mathrm{mg}$ $28\\\\\\\\%$ ) as a yellow solid. ${}^{1}\\\\\\\\mathbf{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 89.03-8.86 (m, 1H),8.23 (d, $J = 8.0~\\\\\\\\mathrm{Hz}$ , 1H),7.54-7.26 (m, 4H),6.18 (s, 1H),5.10 (d, $J = 3.6~\\\\\\\\mathrm{Hz}$ 1H),5.05-4.82 (m, 1H),4.56-4.39 (m, 1H),4.27 (s, 1H),3.71 (d, $J$ $= 8.9~\\\\\\\\mathrm{Hz}$ , 1H),3.58-3.50 (m, 2H),3.54-3.25 (m, 4H),3.23-3.00 (m, 4H),2.46 (d, $J = 5.2~\\\\\\\\mathrm{Hz}$ , 3H),2.33-2.19 (m, 1H),2.11-1.90 (m, 1H),1.88-1.75 (m, 1H),1.50-1.31 (m, 12H), $1.00 - 0.72$ (m, 6H). LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z667[\\\\\\\\mathrm{M} + \\\\\\\\mathrm{H}]^{+}$ \\\",\\\"(2S,4R)-4-Hydroxy-1-((R)-3-methyl-2-(3-(piperazin-1-yl)-isoxazol-5-yl)butanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (123). A solution of intermediate 122 $(378\\\\\\\\mathrm{mg},0.567\\\\\\\\mathrm{mmol})$ in DCM $(5\\\\\\\\mathrm{mL})$ and TFA $(1\\\\\\\\mathrm{mL})$ was stirred at room temperature for $1\\\\\\\\textrm{h}$ then was concentrated under reduced pressure. The residue was purified by prepacted C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\%)$ $\\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ , 0 to $35\\\\\\\\%$ ) to afford the title compound $(330\\\\\\\\mathrm{mg},103\\\\\\\\%$ slightly impure) as a yellow solid. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 9.02-8.75 m1H),8.39 d $J = 7.7~\\\\\\\\mathrm{Hz}$ 1H7.51-7.40 m2H 7.37d $J = 8.5\\\\\\\\mathrm{Hz}$ 2H6.22-6.05 m1H),5.14-5.07 m1H) 5.04-4.61 m1H),4.36 t $J = 7.8~\\\\\\\\mathrm{Hz}$ 1H4.29s1H3.72dd $J$ $= 10.5$ $4.5\\\\\\\\mathrm{Hz}$ 1H),3.64-3.53 m1H),3.50-3.38 m1H),3.38- 3.15 m4H),3.10-2.93 m4H),2.49-2.43 m3H),2.31-2.11 m1H),2.09-1.88 m1H),1.83-1.69 m1H),1.52-1.30 m 3H),1.01-0.92 m3H),0.89-0.70 m3H).LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 567 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . Similar transformation of intermediate 122e afforded 123e (the isopropyl group imper corresponding to 123, structure not shown, $395\\\\\\\\mathrm{mg}$ $105\\\\\\\\%$ ,slightly impure) as a yellow solid. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 9.01-8.88 m1H),8.29 d $J = 7.7~\\\\\\\\mathrm{Hz}$ 1H),7.53-7.28 m4H),6.17 s1H),5.11 d $J = 3.6~\\\\\\\\mathrm{Hz}$ 1H) 5.05-4.79 m1H),4.56-4.38 m1H),4.27 s1H),3.70 d $J = 8.9$ Hz, 1H),3.61-3.39 m2H),3.25-3.15 m4H),2.97-2.88 m 4H),2.46 d $J = 4.2~\\\\\\\\mathrm{Hz}$ 3H),2.35-2.10 m1H),2.09-1.86 m, 1H),1.85-1.71 m, 1H),1.49-1.30 m, 3H),1.02-0.71 m, 6H). LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 567 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ \\\",\\\"(2S,4R)-1-((2R)-2-(3-(4-(2-(4-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)ethyl)piperazin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (18). A solution of intermediate 121 (25 mg, 0.043 mmol, \\\"]\",\n \"page_idx\": \"38\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"38\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"38\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"38\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"38\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1300 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"38\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"38\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,71,482,332]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.0 equiv) and intermediate 123 (25 mg, 0.044 mmol, 1.0 equiv) in MeOH (0.5 mL) and DCM (0.25 mL) was stirred at room temperature for 30 min. Then $\\\\mathrm{NaBH}_3\\\\mathrm{CN}$ (8.0 mg, 0.13 mmol, 3.0 equiv) was added, and the resulting mixture was stirred at room temperature for 24 h. The mixture was then concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 80%) to afford the title compound (4.8 mg, 10%) as a white solid. $^1\\\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) δ 14.16 (s, 1H), 9.02–8.76 (m, 1H), 8.41 (d, $J = 7.7~\\\\mathrm{Hz}$ , 1H), 7.92 (dd, $J = 8.1$ , 1.6 Hz, 1H), 7.77 (d, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 7.48 (d, $J = 9.8~\\\\mathrm{Hz}$ , 1H), 7.44 (d, $J = 8.4~\\\\mathrm{Hz}$ , 2H), 7.37 (d, $J = 8.3~\\\\mathrm{Hz}$ , 2H), 7.28–7.19 (m, 1H), 6.90–6.80 (m, 2H), 6.53 (dd, $J = 6.1$ , 2.1 Hz, 1H), 6.14 (d, $J = 2.1~\\\\mathrm{Hz}$ , 2H), 5.98 (s, 2H), 5.18 (td, $J = 6.8$ , 3.4 Hz, 1H), 5.11 (d, $J = 3.3~\\\\mathrm{Hz}$ , 1H), 4.95–4.62 (m, 1H), 4.49 (s, 2H), 4.36 (t, $J = 7.8~\\\\mathrm{Hz}$ , 1H), 4.28 (t, $J = 5.6~\\\\mathrm{Hz}$ , 2H), 3.71 (dd, $J = 10.5$ , 4.5 Hz, 1H), 3.57 (d, $J = 9.8~\\\\mathrm{Hz}$ , 1H), 3.45–3.38 (m, 2H), 3.29–3.20 (m, 3H), 3.14 (s, 4H), 3.01 (d, $J = 11.5~\\\\mathrm{Hz}$ , 2H), 2.84–2.64 (m, 2H), 2.50–2.40 (m, 11H), 2.34–2.24 (m, 3H), 2.24–2.13 (m, 4H), 2.06–1.93 (m, 4H), 1.83–1.73 (m, 3H), 1.50–1.35 (m, 5H), 0.99–0.92 (m, 3H), 0.89–0.75 (m, 3H). LC–MS (ES+): m/z 1136.6 [M + H]⁺ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,333,479,656]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To confirm the absolute stereochemistry of intermediate 123 employed in the syntheses of 18 and 20, the isopropyl epimer corresponding to 123 (123e, prepared above) was similarly transformed into the isopropyl epimer of PROTAC 18 (18e, structure not shown). A solution of intermediate 121 (25 mg, 0.043 mmol, 1.0 equiv) and intermediate 123e (25 mg, 0.044 mmol, 1.0 equiv) in MeOH (0.5 mL) and DCM (0.25 mL) was stirred at room temperature for 30 min. Then $\\\\mathrm{NaBH}_3\\\\mathrm{CN}$ (8.0 mg, 0.13 mmol, 3.0 equiv) was added, and the resulting mixture was stirred at room temperature for 24 h. The mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO), 0 to 80%) to afford 18e (6.3 mg, 13%) as a white solid. $^1\\\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) $\\\\delta$ 14.16 (s, 1H), 9.02–8.89 (m, 1H), 8.22 (d, $J = 7.8~\\\\mathrm{Hz}$ , 1H), 7.92 (dd, $J = 8.0$ , 1.6 Hz, 1H), 7.77 (d, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 7.52–7.45 (m, 2H), 7.45–7.38 (m, 2H), 7.35–7.28 (m, 1H), 7.26–7.18 (m, 1H), 6.90–6.80 (m, 2H), 6.56–6.49 (m, 1H), 6.17–6.11 (m, 2H), 5.98 (s, 2H), 5.18 (t, $J = 6.4~\\\\mathrm{Hz}$ , 1H), 5.11 (d, $J = 3.6~\\\\mathrm{Hz}$ , 1H), 5.05–4.80 (m, 1H), 4.49 (s, 2H), 4.41 (t, $J = 7.7~\\\\mathrm{Hz}$ , 1H), 4.27 (t, $J = 6.2~\\\\mathrm{Hz}$ , 2H), 3.69 (d, $J = 8.9~\\\\mathrm{Hz}$ , 1H), 3.59–3.37 (m, 2H), 3.27 (s, 1H), 3.24 (d, $J = 10.5~\\\\mathrm{Hz}$ , 3H), 3.14 (s, 1H), 3.08 (d, $J = 5.7~\\\\mathrm{Hz}$ , 3H), 3.01 (d, $J = 11.7~\\\\mathrm{Hz}$ , 2H), 2.71 (d, $J = 10.4~\\\\mathrm{Hz}$ , 2H), 2.47–2.33 (m, 9H), 2.33–2.22 (m, 5H), 2.18 (d, $J = 7.3~\\\\mathrm{Hz}$ , 2H), 2.08–1.89 (m, 6H), 1.87–1.71 (m, 3H), 1.45 (d, $J = 7.0~\\\\mathrm{Hz}$ , 1H), 1.41–1.30 (m, 4H), 0.95 (d, $J = 6.6~\\\\mathrm{Hz}$ , 2H), 0.89–0.72 (m, 4H). LC–MS (ES+): m/z 1136.5 [M + H]⁺ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,657,479,731]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Both 18 and 18e PROTACs were profiled in biological assessments, and the more potent diastereomer was assigned the absolute stereochemistry shown for 18 in Table 2 (cf., Table S4). By inference, the chiral-pure intermediates employed to generate 18 were assigned the absolute stereochemistries shown in Scheme 10 (i.e., intermediates 122 and 123). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,732,479,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tert-Butyl 4-((4-(5-((R)-1-((2S,4R)-4-hydroxy-2-(((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)carbamoyl)pyrrolidin-1-yl)-3-methyl-1-oxobutan-2-yl)isoxazol-3-yl)piperazin-1-yl)methyl)-piperidine-1-carboxylate (125). A solution of chiral-pure intermediate 123 $(100\\\\mathrm{mg},0.18\\\\mathrm{mmol},1.0$ equiv), tert-butyl 4-formylpiperidine-1-carboxylate (124, $56.5\\\\mathrm{mg}$ $0.26\\\\mathrm{mmol}$ 1.4 equiv), and NaOAc $(72.4\\\\mathrm{mg},0.88\\\\mathrm{mmol}$ 4.9 equiv) in MeOH (3 mL) and DCM $(1\\\\mathrm{mL})$ was stirred at room temperature for $30\\\\mathrm{min}$ Then $\\\\mathrm{NaBH}_3\\\\mathrm{CN}$ $(16.6\\\\mathrm{mg},0.26\\\\mathrm{mmol},1.4$ equiv) was added in portions at the same temperature and the resulting mixture was stirred for an additional $1\\\\textrm{h}$ The mixture was then concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH_4HCO_3})$ 0 to $60\\\\%$ ) to afford the title compound $(130\\\\mathrm{mg},96\\\\%)$ as a yellow solid. ${}^{1}\\\\mathbf{H}$ NMR $(500\\\\mathrm{MHz}$ ,DMSO- $d_{6})$ 8.99 $\\\\left(\\\\mathrm{d},J = 3.1\\\\mathrm{Hz},1\\\\mathrm{H}\\\\right)$ 8.40 $\\\\left(\\\\mathrm{d},J\\\\right.$ $= 7.7~\\\\mathrm{Hz}$ 1H),7.49-7.42 m2H7.37 $\\\\left(\\\\mathrm{d},J = 8.1\\\\mathrm{Hz},2\\\\mathrm{H}\\\\right)$ 6.14s, 1H),5.10 $\\\\left(\\\\mathrm{d},J = 3.6\\\\mathrm{Hz},1\\\\mathrm{H}\\\\right)$ 4.97-4.89 $\\\\left(\\\\mathrm{m},1\\\\mathrm{H}\\\\right)$ 4.37 $\\\\left(\\\\mathrm{t},J = 7.9\\\\mathrm{Hz},\\\\right.$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,145]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1H), 4.32-4.25 (m, 1H), 3.92 (d, $J = 12.7\\\\mathrm{Hz}$ 2H), 3.75-3.69 (m, 1H), 3.58 (d, $J = 9.9\\\\mathrm{Hz}$ 1H), 3.43 (d, $J = 10.9\\\\mathrm{Hz}$ 1H), 3.20-3.13 (m, 4H), 2.70 (s, 2H), 2.47-2.31 (m, 7H), 2.28-2.13 (m, 3H), 2.07-1.98 (m, 1H), 1.84-1.75 (m, 1H), 1.68 (d, $J = 12.2\\\\mathrm{Hz}$ 3H), 1.49-1.30 (m, 12H), 1.00-0.89 (m, 5H), 0.86-0.77 (m, 3H). LC-MS $(\\\\mathrm{ES}+)$ : $m/z$ 764 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,146,915,341]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$(2S,4R)$ 4-Hydroxy-1-((R)-3-methyl-2-(3-(4-(piperidin-4- ylmethyl)piperazin-1-yl)isoxazol-5-yl)butanoyl)-N-(S)-1-(4-(4- methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (126). A mixture of intermediate 125 $(130\\\\mathrm{mg},0.17\\\\mathrm{mmol})$ in DCM $(3\\\\mathrm{mL})$ and TFA $(1\\\\mathrm{mL})$ were stirred at room temperature for $^{\\\\textrm{\\\\scriptsize 1h}}$ then was concentrated under reduced pressure to afford the title compound (TFA salt, $250~\\\\mathrm{mg}$ crude) as yellow oil. The crude product was used in the next step directly without further purification. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ ,DMSO- $d_{6}$ ) $\\\\delta$ 9.78s,1H),9.01d $J = 3.2 \\\\mathrm{Hz}$ 1H),8.64s,1H),8.39d $J = 7.8 \\\\mathrm{Hz}$ 2H),7.51-7.42 m2H), 7.42-7.34 m,2H),6.30 s,1H),4.94-4.90 m,2H),4.43-4.25 m, 2H),3.85-3.68 m,3H),3.67-3.52 m,3H),3.51-3.41 m,1H), 3.36-2.99 m,8H),2.95-2.80 m,2H),2.46 s,3H),2.29-2.12 m, 2H),2.09-1.97 m,1H),1.90 d $J = 13.4 \\\\mathrm{Hz}$ 2H),1.86-1.75 m, 1H),1.50-1.29 m,5H),0.98 d $J = 6.3 \\\\mathrm{Hz}$ 3H),0.87-0.78 m, 3H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 664 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,342,915,732]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-((2R)-2-(3-(4-((1-((trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutyl)methyl)piperidin-4-yl)methyl)piperazin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)-pyrrolidine-2-carboxamide (20). A solution of intermediate 126 (TFA salt, $175\\\\mathrm{mg}$ , crude from the previous step), intermediate 138 $(170\\\\mathrm{mg},0.36\\\\mathrm{mmol})$ and NaOAc $(49.4\\\\mathrm{mg},0.60\\\\mathrm{mmol})$ in MeOH $(2.1\\\\mathrm{mL})$ and DCM $(0.7\\\\mathrm{mL})$ was stirred at room temperature for 30 min. Then $\\\\mathrm{NaBH}_3\\\\mathrm{CN}$ $(11.9\\\\mathrm{mg},0.19\\\\mathrm{mmol})$ was added in portions at the same temperature, and the resulting mixture was stirred at room temperature for an additional $1\\\\textrm{h}$ . The mixture was then concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH_4HCO_3})$ $0$ to $100\\\\%$ ) to afford the crude product $(70\\\\mathrm{mg})$ . This material was further purified by preparative HPLC [column: XBridge Prep OBD C18 Column, $30\\\\times 150\\\\mathrm{mm}^2$ $5\\\\mu \\\\mathrm{m}$ ; mobile phase A: water $(10\\\\mathrm{mmol}/$ L $\\\\mathrm{NH_4HCO_3}$ ), mobile phase B: $\\\\mathrm{CH}_3\\\\mathrm{CN}$ ; flow rate: $60~\\\\mathrm{mL / min}$ ; gradient: $28\\\\%$ to $47\\\\%$ B over $10\\\\mathrm{min}$ ; wavelength: $254 / 220\\\\mathrm{nm}$ ; RT: $10.0\\\\mathrm{min}$ ] to afford the title compound $(8.3\\\\mathrm{mg},6.1\\\\%)$ as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 14.13 (s, 1H), 8.97 (d, $J = 1.4~\\\\mathrm{Hz}$ , 1H), 8.38 (d, $J = 7.4~\\\\mathrm{Hz}$ , 1H), 7.90 (d, $J = 7.8~\\\\mathrm{Hz}$ , 1H), 7.75 (d, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 7.47 (d, $J = 6.2~\\\\mathrm{Hz}$ , 1H), 7.46-7.31 (m, 4H), 7.25-7.17 (m, 1H), 6.89-6.78 (m, 2H), 6.57-6.44 (m, 1H), 6.11 (d, $J = 5.2~\\\\mathrm{Hz}$ , 2H), 5.97 (d, $J = 11.4~\\\\mathrm{Hz}$ , 2H), 5.19-4.88 (m, 3H), 4.47 (s, 2H), 4.35 (t, $J = 7.8~\\\\mathrm{Hz}$ , 1H), 4.27 (s, 1H), 3.75-3.63 (m, 1H), 3.56 (d, $J = 9.9~\\\\mathrm{Hz}$ , 1H), 3.40 (d, $J = 10.6~\\\\mathrm{Hz}$ , 1H), 3.23 (d, $J = 11.6~\\\\mathrm{Hz}$ , 2H), 3.13 (s, 4H), 3.00 (d, $J = 11.6~\\\\mathrm{Hz}$ , 2H), 2.85-2.69 (m, 2H), 2.44 (s, 3H), 2.42-2.31 (m, 6H), 2.28-2.06 (m, 8H), 2.06-1.71 (m, 7H), 1.70-1.55 (m, 3H), 1.54-1.30 (m, 4H), 1.16-1.01 (m, 2H), 0.94 (d, $J = 6.4~\\\\mathrm{Hz}$ , 3H), 0.89-0.72 (m, 3H). LC-MS $(ES+)$ : $m/z$ $1120[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,733,915,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-((R)-2-(3-(4-(Dimethoxymethyl)piperidin-1-yl)- isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N - ((S) - 1 - (4 - (4-$ methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (127). To a room temperature solution of racemic carboxylic acid 53 $(470\\\\mathrm{mg},1.44\\\\mathrm{mmol},1.1$ equiv), chiral-pure intermediate 57 (HCl salt, $486~\\\\mathrm{mg}$ 1.32 mmol, 1.0 equiv) and DIEA $(1.86\\\\mathrm{g},14.4\\\\mathrm{mmol},$ 10.9 equiv) in DMF $(4\\\\mathrm{mL})$ was added HATU $(600\\\\mathrm{mg},1.58\\\\mathrm{mmol},$ 1.2 equiv). The reaction was stirred at room temperature for $^{\\\\textrm{\\\\scriptsize 2h}}$ then was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water containing $0.05\\\\%$ $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3$ 0 to $100\\\\%$ ) to afford a mixture of the two diastereomeric coupling products $(450\\\\mathrm{mg})$ . This mixture was separated by preparative chiral HPLC [column: CHIRALPAK IF, $2\\\\times$ $25~\\\\mathrm{cm}^2$ $5\\\\mu \\\\mathrm{m}$ ; mobile phase A: MTBE (containing $0.5\\\\%$ 2.0 M $\\\\mathrm{NH}_{3}$ in MeOH), mobile phase B: 1:1 MeOH:DCM, flow rate: $17~\\\\mathrm{mL / min}$ gradient: 0 to $30\\\\%$ B over $10.5\\\\mathrm{min}$ wavelength: $220 / 254~\\\\mathrm{nm}$ peak 1 $\\\\mathrm{RT} = 5.8\\\\mathrm{min}$ peak $2\\\\mathrm{RT} = 8.6\\\\mathrm{min}$ to afford the title compound 127 as the slower eluting entity (peak 2, $100~\\\\mathrm{mg}$ $11\\\\%$ white solid). ${}^{1}\\\\mathbf{H}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1301 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,481,306]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"NMR (300 MHz, DMSO- $d_{6}$ 89.00 d $J = 2.5\\\\mathrm{Hz}$ 1H),8.41 d $J =$ $7.7\\\\mathrm{Hz}$ 1H),7.51-7.42 m,2H),7.41-7.34 m,2H),6.13 s,1H), 5.11 d $J = 3.6\\\\mathrm{Hz}$ 1H),4.98-4.82 m,1H),4.37 t $J = 7.8\\\\mathrm{Hz}$ 1H), 4.29 s,1H),4.13-4.02 m,1H),3.77-3.51 m,4H),3.49-3.38 m, 1H),3.27 s,6H),2.79-2.63 m,2H),2.46s,3H),2.31-2.14 m, 1H),2.09-1.96 m,1H),1.86-1.70 m,2H),1.67 d $J = 13.1\\\\mathrm{Hz}$ 2H),1.50-1.34 m,3H),1.33-1.16 m,2H),1.01-0.91 m,3H), 0.86-0.76 m,3H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 640 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ .The alternate diastereomer (127e, epimeric at the isopropyl stereocenter) was also isolated as the faster eluting entity (peak 1, $120~\\\\mathrm{mg},$ $13\\\\%$ white solid): ${}^{1}\\\\mathrm{H}$ NMR (300 MHz,DMSO- $d_{6}$ )89.00 d $J = 3.9\\\\mathrm{Hz}$ 1H),8.23 d $J = 7.8\\\\mathrm{Hz}$ 1H),7.54-7.28 m,4H),6.15 d $J = 3.2$ Hz, 1H),5.11 d $J = 3.6\\\\mathrm{Hz}$ ,1H),5.08-4.81 m,1H),4.58-4.37 m, 1H),4.32-4.23 m,1H),4.11-3.97 m,1H),3.73-3.41 m,5H), 3.26 d $J = 4.3\\\\mathrm{Hz}$ 6H),2.79-2.59 m,2H),2.46 d $J = 5.6\\\\mathrm{Hz}$ 3H),2.33-2.14 m,1H),2.14-1.86 m,1H),1.86-1.58 m,4H), 1.46 d $J = 6.9\\\\mathrm{Hz}$ ,1H),1.36 d $J = 7.0\\\\mathrm{Hz},$ 2H),1.30-1.13 m, 2H),0.96 d $J = 6.6\\\\mathrm{Hz},$ 2H),0.82 d $J = 6.6\\\\mathrm{Hz},$ 3H),0.75 d $J =$ $6.6\\\\mathrm{Hz},$ 1H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 640 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,307,481,440]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-((R)-2-(3-(4-Formylpiperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (128). A solution of intermediate 127 $(50\\\\mathrm{mg},0.0780\\\\mathrm{mmol})$ in formic acid $(1.0~\\\\mathrm{mL})$ and water $(1.0~\\\\mathrm{mL})$ was stirred at $60^{\\\\circ}\\\\mathrm{C}$ for $1\\\\textrm{h}$ The mixture was cooled to room temperature and was concentrated under reduced pressure to afford the crude title compound $(46\\\\mathrm{mg})$ as an off-white solid. LCMS $(\\\\mathrm{ES + })$ .. $m / z$ 594 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . Related transformation of the alternate diastereomer (127e, epimeric at the isopropyl center) afforded 128e (the isopropyl isomer corresponding to 128, structure not shown). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,440,481,743]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$(2S,4R)$ 1-((2R)-2-(3-(4-((4-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)methyl)-piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (19). A room temperature solution of intermediate 128 $(46\\\\mathrm{mg},0.077\\\\mathrm{mmol},1.0$ equiv), intermediate 119 (Scheme 9, $75~\\\\mathrm{mg}$ $0.14\\\\mathrm{mmol}$ 1.7 equiv), and NaOAc ( $19\\\\mathrm{mg}$ $0.23\\\\mathrm{mmol}$ 3.0 equiv) in DCM $(1.0~\\\\mathrm{mL})$ and MeOH $(1.0~\\\\mathrm{mL})$ was stirred for $^{\\\\textrm{\\\\scriptsize 1h}}$ . $\\\\mathrm{NaBH}_3\\\\mathrm{CN}$ $(14\\\\mathrm{mg},0.23\\\\mathrm{mmol},3.0$ equiv) was then added, and the mixture was stirred at room temperature for an additional $^{\\\\textrm{\\\\scriptsize 1h}}$ then was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography (MeOH in water containing $0.05\\\\%$ $\\\\mathrm{NH_4HCO_3}$ 0 to $100\\\\%$ ) to yield the title compound $(30\\\\mathrm{mg},$ $34 \\\\%$ as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ ,DMSO- $d_{6})$ 8 14.15 s, 1H),8.99 d, $J = 1.5 \\\\mathrm{Hz}$ 1H),8.42 d, $J = 7.7 \\\\mathrm{Hz}$ 1H),7.96-7.88 m,1H),7.78 d, $J = 6.0 \\\\mathrm{Hz}$ 1H),7.53-7.33 m,5H),7.28-7.17 m, 1H),6.92-6.79 m,2H),6.57-6.49 m,1H),6.18-6.08 m,2H), 5.99 s,2H),5.26-5.08 m,2H),5.05-4.84 m,1H),4.50 s,2H), 4.37 t, $J = 7.8~\\\\mathrm{Hz}$ 1H),4.33-4.24 m,2H),3.77-3.67 m,1H), 3.66-3.52 m,3H),3.49-3.41 m,1H),3.30-3.21 m,3H),3.02 d, $J = 11.5~\\\\mathrm{Hz}$ 2H),2.79-2.60 m,4H),2.46 s,3H),2.39-2.14 m, 7H),2.13-1.89 m,7H),1.86-1.55 m,6H),1.50-1.34 m,5H), 1.19-1.02 m,2H),1.00-0.89 m,3H),0.87-0.76 m,3H).LCMS $(\\\\mathrm{ES + })$ .. $m / z$ 1121.8 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,745,481,866]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To confirm the absolute stereochemistry of intermediate 128 employed in the syntheses of 19, the isopropyl epimer corresponding to 128 (128e, prepared above) was similarly transformed into the isopropyl epimer of PROTAC 19 (19e, structure not shown). Both 19 and 19e PROTACs were profiled in biological assessments, and the more potent diastereomer was assigned the absolute stereochemistry shown for 19 in Table 2 (cf., Table S4). By inference, the chiral-pure intermediates employed to generate 19 was assigned the absolute stereochemistry shown in Scheme 10 (i.e., intermediates 127 and 128). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,867,481,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4-Bromo-2-(trans-3-(piperidin-4-yloxy)cyclobutoxy)-pyridine (129). A solution of intermediate 114 $(3.50\\\\mathrm{g},8.19\\\\mathrm{mmol})$ in DCM $(30~\\\\mathrm{mL})$ and TFA $(10~\\\\mathrm{mL})$ was stirred at room temperature for $^{1\\\\textrm{h}}$ . The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH_4HCO_3}$ , 0 to $80\\\\%$ ) to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,145]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"afford the title compound $(2.4\\\\mathrm{g},90\\\\%)$ as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6}$ 8.06 d, $J = 5.5~\\\\mathrm{Hz}$ 1H7.28-7.19 m, 1H),7.11 (d, $J = 1.6\\\\mathrm{Hz}$ 1H),5.31-5.17 (m, 1H),4.41-4.27 (m, 1H),3.62-3.48 (m, 1H),3.22-3.08 (m, 2H),2.97-2.83 (m, 2H), 2.46-2.26 (m, 4H), 1.99-1.85 (m, 2H), 1.67-1.49 (m, 2H). LCMS $\\\\mathrm{(ES + )}$ .. $m / z$ 327/329 $[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,146,915,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methyl 2-(3-(4-(trans-3-((4-bromopyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoate (130). A mixture of intermediate 129 $(2.00\\\\mathrm{g},6.11\\\\mathrm{mmol},1.0$ equiv), intermediate 43 $(2.94\\\\mathrm{g},6.11\\\\mathrm{mmol},1.0$ equiv) and DIEA $(2.37\\\\mathrm{g},$ $18.3\\\\mathrm{mmol},3.0$ equiv) in DMF $(25~\\\\mathrm{mL})$ was stirred at $130^{\\\\circ}\\\\mathrm{C}$ for $1\\\\textrm{h}$ The mixture was then cooled to room temperature and was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $75\\\\%$ ) to afford the title compound $(2.2\\\\mathrm{g},71\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 8.10-8.02 m, 1H), 7.27-7.18 (m, 1H), 7.11 (d, $J = 1.6~\\\\mathrm{Hz}$ 1H), 6.25 (s, 1H), 5.30-5.17 (m, 1H), 4.43-4.29 (m, 1H), 3.66 (s, 3H), 3.63-3.45 (m, 4H), 3.00-2.85 (m, 2H), 2.46-2.18 (m, 5H), 1.90-1.79 (m, 2H), 1.54- 1.36 (m, 2H), 0.93 (d, $J = 6.7~\\\\mathrm{Hz}$ , 3H), 0.84 (d, $J = 6.7~\\\\mathrm{Hz}$ , 3H). LCMS $(\\\\mathrm{ES + })$ .. $m / z~508 / s10[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,331,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methyl 2-(3-(4-(trans-3-((4-(3-(3-amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoate (131). A mixture of intermediate 130 (2.20 g, 4.33 mmol, 1.0 equiv), tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, 1.38 g, 6.49 mmol, 1.5 equiv), RuPhosPd G3 (0.36 g, 0.43 mmol, 0.10 equiv) and $\\\\mathrm{Cs_2CO_3}$ (4.23 g, 12.9 mmol, 3.0 equiv) in 1,4-dioxane (30 mL) was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for 1 h. The reaction was cooled to room temperature and was quenched with $\\\\mathrm{H}_2\\\\mathrm{O}$ (50 mL). The resulting mixture was extracted with EtOAc (100 mL × 3), and the combined organic layers were washed with brine (100 mL), dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 100%) to afford tert-butyl 8-(2-(trans-3-((1-(5-(1-methoxy-3-methyl-1-oxobutan-2-yl) isoxazol-3-yl) piperidin-4-yl) oxy)cyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate (1.2 g, 43% yield) as a brown solid. ${}^{1}\\\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) δ 7.76 (d, J = 6.0 Hz, 1H), 6.51–6.45 (m, 1H), 6.25 (s, 1H), 6.10 (d, J = 2.1 Hz, 1H), 5.25–5.15 (m, 1H), 4.39–4.28 (m, 3H), 3.68–3.40 (m, 9H), 3.07 (d, J = 13.0 Hz, 1H), 2.98–2.87 (m, 3H), 2.39–2.21 (m, 5H), 1.95–1.81 (m, 4H), 1.75–1.61 (m, 2H), 1.52–1.42 (m, 2H), 1.40 (s, 9H), 0.93 (d, J = 6.6 Hz, 3H), 0.84 (d, J = 6.7 Hz, 3H). LC−MS (ES+): m/z 640 [M + H]+. A mixture of this material (1.2 g, 1.88 mmol) in TFA (4 mL) and DCM (12 mL) was stirred at room temperature for 1 h. The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepaked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 30%) to afford methyl 2-(3-(4-(trans-3-((4-(3,8-diazabicyclo[3.2.1]-octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy) piperidin-1-yl) isoxazol-5-yl)-3-methylbutanoate (810 mg, 80%) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) δ 7.71 (d, J = 6.0 Hz, 1H), 6.42–6.35 (m, 1H), 6.25 (s, 1H), 5.98 (d, J = 2.1 Hz, 1H), 5.24–5.14 (m, 1H), 4.39–4.28 (m, 1H), 4.19–4.13 (m, 2H), 3.66 (s, 3H), 3.59 (d, J = 8.9 Hz, 1H), 3.55–3.42 (m, 3H), 3.02–2.87 (m, 2H), 2.85 (d, J = 1.8 Hz, 1H), 2.82 (d, J = 1.7 Hz, 1H), 2.48–2.40 (m, 2H), 2.39–2.21 (m, 6H), 1.98–1.80 (m, 6H), 1.52–1.38 (m, 2H), 0.93 (d, J = 6.6 Hz, 3H), 0.84 (d, J = 6.7 Hz, 3H). LC−MS (ES+): m/z 540 [M + H]+. A mixture of this intermediate (810 mg, 1.5 mmol, 1.0 equiv), 4-bromo-6-chloropyridazin-3-amine (70, 469 mg, 2.25 mmol, 1.5 equiv), and DIEA (968 mg, 7.5 mmol, 5.0 equiv) in DMSO (10 mL) was stirred at $130^{\\\\circ}\\\\mathrm{C}$ for 5 h. The reaction was cooled to room tempetature, and the mixture was directly purified by prepaked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 50%) to afford methyl 2-(3-(4-(trans-3-((4-(3-(3-amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl) oxy)cyclobutoxy) piperidin-1-yl) isoxazol-5-yl)-3-methylbutanoate (520 mg, 52%) as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) δ 7.77 (d, J = 6.0 Hz, 1H), 6.90 (s, 1H), 6.54–6.47 (m, 1H), 6.25 (s \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1302 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,479,408]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1H), 6.12 (d, $J = 2.1\\\\mathrm{Hz}$ 1H), 5.85 (s, 2H), 5.25-5.15 (m, 1H), 4.45 (s, 2H), 4.39-4.28 (m, 1H), 3.65 (s, 3H), 3.59 (d, $J = 8.9\\\\mathrm{Hz}$ 1H), 3.55-3.43 (m, 3H), 3.22-3.14 (m, 2H), 2.98-2.83 (m, 4H), 2.40-2.21 (m, 5H), 2.18-2.09 (m, 2H), 1.96-1.89 (m, 2H), 1.89-1.80 (m, 2H), 1.51-1.38 (m, 2H), 0.93 (d, $J = 6.6\\\\mathrm{Hz}$ 3H), 0.84 (d, $J = 6.7\\\\mathrm{Hz}$ 3H). LC-MS $(\\\\mathrm{ES}+)$ : $m/z$ 667 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . A mixture of this material (510 mg, 0.76 mmol, 1.0 equiv), (2-hydroxyphenyl)boronic acid (72, 158 mg, 1.15 mmol, 1.6 equiv), $\\\\mathrm{Pd(PPh_3)_4}$ (88.3 mg, 0.08 mmol, 0.10 equiv) and $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ (317 mg, 2.29 mmol, 3.0 equiv) in 1,4-dioxane (15 mL) and water (1.5 mL) was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for $1\\\\mathrm{h}$ . The reaction was cooled to room temperature and was diluted with water (50 mL). The mixture was extracted with EtOAc (100 mL × 3) and the combined organic layers were washed with brine (100 mL), dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ - 0 to $70\\\\%$ ) to afford the title compound (375 mg, $68\\\\%$ ) as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) $\\\\delta$ 14.16 (s, 1H), 7.96-7.89 (m, 1H), 7.78 (d, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 7.51 (s, 1H), 7.27-7.18 (m, 1H), 6.91-6.81 (m, 2H), 6.57-6.50 (m, 1H), 6.25 (s, 1H), 6.15 (d, $J = 2.1$ Hz, 1H), 5.98 (s, 2H), 5.25-5.15 (m, 1H), 4.50 (d, $J = 4.2~\\\\mathrm{Hz}$ , 2H), 4.39-4.28 (m, 1H), 3.65 (s, 3H), 3.59 (d, $J = 8.9~\\\\mathrm{Hz}$ , 1H), 3.55-3.42 (m, 3H), 3.25 (d, $J = 11.4~\\\\mathrm{Hz}$ , 2H), 3.02 (d, $J = 11.6~\\\\mathrm{Hz}$ , 2H), 2.98-2.87 (m, 2H), 2.40-2.22 (m, 5H), 2.18 (d, $J = 7.2~\\\\mathrm{Hz}$ , 2H), 2.00-1.93 (m, 2H), 1.89-1.80 (m, 2H), 1.51-1.38 (m, 2H), 0.93 (d, $J =$ $6.6~\\\\mathrm{Hz}$ ,3H),0.84 $(\\\\mathrm{d},J = 6.8~\\\\mathrm{Hz}$ ,3H). LC-MS $(\\\\mathrm{ES}+)$ : $m/z$ 725 $[\\\\mathbf{M}+$ $\\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,410,479,620]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(3-(4-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)- pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoic acid (132). A solution of intermediate 131 $(365\\\\mathrm{mg},0.503$ mmol, 1.0 equiv) and LiOH $(24.2\\\\mathrm{mg},1.01\\\\mathrm{mmol},2.0$ equiv) in water $(6\\\\mathrm{mL})$ and THF $(6\\\\mathrm{mL})$ was stirred at room temperature for $1\\\\textrm{h}$ The resulting mixture was concentrated under reduced pressure to afford the crude title compound as a yellow solid. This material was used in the next step without further purification. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 7.95-7.86 (m, 1H), 7.76 (d, $J = 5.9~\\\\mathrm{Hz}$ , 1H), 7.48 (s, 1H), 7.27-7.15 (m, 1H), 6.90-6.78 (m, 2H), 6.55-6.47 (m, 1H), 6.16-6.04 (m, 2H), 5.95 (s, 2H), 5.18 (t, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 4.48 (s, 2H), 4.36-4.26 (m, 1H), 3.53-3.42 (m, 3H), 3.28-3.18 (m, 3H), 3.00 (d, $J = 11.6~\\\\mathrm{Hz}$ , 2H), 2.88 (t, $J = 10.7~\\\\mathrm{Hz}$ , 2H), 2.38-2.25 (m, 4H), 2.25-2.12 (m, 3H), 1.95 (s, 2H), 1.82 (d, $J = 12.4~\\\\mathrm{Hz}$ , 2H), 1.52-1.33 (m, 2H), 0.92 (d, $J = 6.6~\\\\mathrm{Hz}$ , 3H), 0.78 (d, $J = 6.7~\\\\mathrm{Hz}$ , 3H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 711 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,620,479,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(25,4R)-1-((2R)-2-(3-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $(S)$ -1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (21). To a room temperature solution of intermediate 132 (290 mg, 0.41 mmol, 1.0 equiv), intermediate 57 (203 mg, 0.61 mmol, 1.5 equiv) and DIEA (264 mg, 2.04 mmol, 5.0 equiv) in DMF (5 mL) was added HATU (186 mg, 0.489 mmol, 1.2 equiv) in portions. The resulting mixture was stirred at room temperature for 1 h. The reaction mixture was directly purified by prepacked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 55%) to afford 100 mg of the coupled product as a ~1:1 mixture of isopropyl group isomers. This material was further purified by preparative chiral HPLC [column: CHIRALPAK IA, 2 × 25 cm², 5 μm; mobile phase A: 1:1 hexane:DCM (0.5% 2 M NH₃-MeOH), mobile phase B: EtOH; flow rate: 20 mL/min; gradient: isocratic 40% B; wavelength: 220/254 nm; RT1:6.30 min; RT2:9.16 min; sample solvent: EtOH; injection volume: 0.40 mL; number of runs: 12] to afford the title compound (slower peak, 16 mg, 3.9%) as a yellow solid. $^1\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 14.13 (s, 1H), 8.97 (s, 1H), 8.38 (d, J = 7.7 Hz, 1H), 7.96–7.87 (m, 1H), 7.76 (d, J = 5.9 Hz, 1H), 7.52–7.39 (m, 3H), 7.35 (d, J = 8.2 Hz, 2H), 7.27–7.15 (m, 1H), 6.90–6.79 (m, 2H), 6.58–6.46 (m, 1H), 6.16–6.06 (m, 2H), 5.97 (d, J = 6.7 Hz, 2H), 5.25–5.14 (m, 1H), 5.08 (d, J = 3.7 Hz, 1H), 5.00–4.83 (m, 1H), 4.48 (s, 2H), 4.40–4.21 (m, 3H), 3.76–3.64 (m, 1H), 3.55 (d, J \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,308]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$= 9.8\\\\mathrm{Hz}$ 1H),3.53-3.36 (m,4H),3.24 (d, $J = 11.5\\\\mathrm{Hz}$ 2H),3.00 (d, $J = 11.6\\\\mathrm{Hz}$ 2H),2.96-2.80 (m,2H),2.44s,3H),2.39-2.25 (m, 4H),2.25-2.10 (m,3H),2.06-1.90 (m,3H),1.90-1.70 (m,3H), 1.54-1.40 (m,2H),1.36 (d, $J = 7.0~\\\\mathrm{Hz}$ 3H),0.93 (d, $J = 6.4~\\\\mathrm{Hz}$ 3H),0.86-0.69 (m,3H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 1024 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . The isomer bearing the undesired isopropyl stereocenter (21e, isopropyl isomer corresponding to 21, structure not shown) was also isolated faster peak, $25.5\\\\mathrm{mg},6.1\\\\%$ as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.13 s,1H),9.00-8.85 m,1H),8.25-7.86 m,2H), 7.76 d, $J = 6.0\\\\mathrm{Hz}$ 1H),7.53-7.35 (m,4H),7.30 d, $J = 8.2\\\\mathrm{Hz}$ 1H),7.26-7.15 (m,1H),6.89-6.78 (m,2H),6.57-6.48 (m,1H), 6.13 d, $J = 2.0\\\\mathrm{Hz}$ ,2H),5.96s,2H),5.19d $J = 6.1\\\\mathrm{Hz}$ ,1H),5.13- 4.80 (m,2H),4.48s,2H),4.41t $J = 7.6\\\\mathrm{Hz}$ ,1H),4.36-4.18 (m, 2H),3.67d $J = 8.9\\\\mathrm{Hz}$ ,1H),3.60-3.35 (m,5H),3.24d $J = 11.2$ Hz,2H),3.00d $J = 11.7\\\\mathrm{Hz}$ ,2H),2.94-2.74 (m,2H),2.44d $J =$ $6.6\\\\mathrm{Hz}$ ,3H),2.29s,5H),2.17d $J = 7.3\\\\mathrm{Hz}$ ,2H),2.07-1.89 (m, 3H),1.89-1.72 (m,3H),1.53-1.38 (m,3H),1.34d $J = 7.0~\\\\mathrm{Hz}$ 2H),0.94d $J = 6.6~\\\\mathrm{Hz}$ ,2H),0.87-0.70 (m,4H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 1024 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,308,915,518]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methyl trans-3-(4-bromopyridin-2-yl)oxy)cyclobutane-1-carboxylate (134). To a stirred mixture of cis-methyl 3-hydroxycyclobutanecarboxylate (133, $2.00\\\\mathrm{g}$ , $15.3\\\\mathrm{mmol}$ , 1.0 equiv), 4-bromopyridin-2-ol $(2.67\\\\mathrm{g}, 15.3\\\\mathrm{mmol}, 1.0\\\\mathrm{equiv})$ , and $\\\\mathrm{PPh}_3$ (6.04 g, $23.0\\\\mathrm{mmol}$ , 1.5 equiv) in THF $(25\\\\mathrm{mL})$ was added DIAD $(4.66\\\\mathrm{g}, 23.0\\\\mathrm{mmol}, 1.5\\\\mathrm{equiv})$ dropwise at $0^{\\\\circ}\\\\mathrm{C}$ . The resulting mixture was stirred for $1\\\\mathrm{h}$ at room temperature then was diluted with water (75 mL) and extracted with EtOAc $(100\\\\mathrm{mL} \\\\times 3)$ . The combined organic layers were washed with brine $(100\\\\mathrm{mL})$ and were dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\left(\\\\mathrm{CH}_3\\\\mathrm{CN}\\\\right.$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ to afford the title compound $(3.0\\\\mathrm{g}, 68\\\\%)$ as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 8.06 (d, $J = 5.5\\\\mathrm{Hz}$ , 1H), 7.26-7.19 (m, 1H), 7.13-7.07 (m, 1H), 5.34-5.22 (m, 1H), 3.66 (s, 3H), 3.22-3.10 (m, 1H), 2.68-2.57 (m, 2H), 2.44-2.31 (m, 2H). LC-MS (ES +): $m/z$ 286/288 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,518,915,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methyl trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)-pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)cyclobutane-1-carboxylate (135). A mixture of intermediate 134 $(3.00\\\\mathrm{g},10.4\\\\mathrm{mmol},1.0$ equiv), tert-butyl 3,8-diazabicyclo[3.2.1]-octane-3-carboxylate (67, $3.34\\\\mathrm{g}$ 15.7 mmol, 1.5 equiv), RuPhosPd G3 $(880\\\\mathrm{mg},1.05\\\\mathrm{mmol},0.10$ equiv) and $\\\\mathrm{Cs_2CO_3}$ $(10.2\\\\mathrm{g},31.4\\\\mathrm{mmol},$ 3.0 equiv) in 1,4-dioxane $(30~\\\\mathrm{mL})$ was stirred at $90^{\\\\circ}C$ for $1\\\\textrm{h}$ The resulting mixture was cooled to room temperature and was diluted with water $(75~\\\\mathrm{mL})$ . The mixture was then extracted with EtOAc $(100~\\\\mathrm{mL}\\\\times 3)$ , and the combined organic layers were washed with brine $(100~\\\\mathrm{mL})$ , dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 30:70) to afford tert-butyl 8-(2-(trans-3-(methoxycarbonyl)cyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate $(3.5\\\\mathrm{g},80\\\\%)$ as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ DMSO- $d_{6})$ 7.76 d, $J = 6.0\\\\mathrm{Hz}$ 1H),6.52-6.45 m1H6.11d $J = 2.1\\\\mathrm{Hz}$ 1H) 5.31-5.19 m, 1H),4.35 s,2H),3.65 s,3H),3.62-3.50 m,2H), 3.19-3.03 m,2H),2.92 d $J = 12.9\\\\mathrm{Hz}$ 1H),2.63-2.53 m,2H), 2.38-2.26 m,2H),1.95-1.87 m,2H),1.75-1.62 m,2H),1.40 s, 9H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 418 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ .A solution of this material $(3.50\\\\mathrm{g},8.38\\\\mathrm{mmol})$ in DCM $(30~\\\\mathrm{mL})$ and TFA $(10~\\\\mathrm{mL})$ was stirred at room temperature for $^{\\\\textrm{\\\\scriptsize 1h}}$ . The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ 0 to $100\\\\%$ ) to afford methyl trans-3-((4-(3,8-diazabicyclo[3.2.1]- octan-8-yl)pyridin-2-yl)oxy)cyclobutane-1-carboxylate $(2.1\\\\mathrm{g},79\\\\%)$ as a yellow solid. $^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 7.83 d $J = 6.0\\\\mathrm{Hz}$ 1H),6.57-6.49 m, 1H),6.18 d $J = 2.0~\\\\mathrm{Hz}$ 1H),5.35-5.19 m, 1H),4.45 s,2H),3.66 s,3H),3.21-3.07 m, 1H),3.07-2.92 m, 4H),2.66-2.52 m,2H),2.41-2.25 m,2H),2.11-1.96 m,4H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 318 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ .A solution of this material (2.10 g, 6.62 mmol, 1.0 equiv), 4-bromo-6-chloro-pyridazin-3-amine (70, $1.38\\\\mathrm{g},6.62\\\\mathrm{mmol},1.0$ equiv) and DIEA $(2.57\\\\mathrm{g},19.8\\\\mathrm{mmol},3.0$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[484,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1303 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,71,482,421]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"equiv) in DMSO $(20~\\\\mathrm{mL})$ was stirred at $130^{\\\\circ}\\\\mathrm{C}$ for $1\\\\textrm{h}$ . After cooling to room temperature, the mixture was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH_4HCO_3)}$ 0 to $100\\\\%$ ) to afford methyl trans-3-((4-(3-(3-amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutane-1-carboxylate $(1.9\\\\mathrm{g},65\\\\%)$ as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ ,DMSO- $d_{6}$ 7.76 (d, $J = 6.0~\\\\mathrm{Hz}$ 1H),6.90s1H) $6.55 - 6.47$ m1H)6.12d $J = 2.0\\\\mathrm{Hz}$ 1H)5.84s2H)5.33-5.18 m1H)4.45s2H)3.65s3H)3.23-3.05m3H)2.87d $J =$ $11.6\\\\mathrm{Hz}$ 2H)2.65-2.51m2H)2.40-2.24m2H)2.20-2.02 m2H)1.97-1.88m2H.LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 445 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ .A mixture of this material $(1.90\\\\mathrm{g},$ 4.27 mmol, 1.0 equiv), 2-hydroxyphenylboronic acid (72, 883 mg, 6.41 mmol, 1.5 equiv), $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ 1.77 g, 12.8 mmol, 3.0 equiv and $\\\\mathrm{Pd(PPh_3)_4}$ 493 mg, 0.426 mmol, 0.10 equiv) in 1,4-dioxane $(30~\\\\mathrm{mL})$ was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for 2 h. The resulting mixture was cooled to room temperature then was diluted with EtOAc $(100~\\\\mathrm{mL})$ . The mixture was washed with brine $(100~\\\\mathrm{mL})$ , and the organic layer was dried over sodium sulfate and filtered. The filtrate was concentrated under vacuum, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 3:1) to afford the title compound (1.2 g, $56 \\\\%$ ) as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz,DMSO- $d_{6}$ 8 14.15 s, 1H)7.97-7.88 m1H)7.78d $J = 6.0\\\\mathrm{Hz}$ 1H7.50s1H7.29-7.17m1H) 6.92-6.79m2H6.58-6.50m1H6.15d $J = 2.0~\\\\mathrm{Hz}$ 1H) 5.98s2H)5.34-5.18m1H)4.50s2H)3.65s3H)3.25d $J =$ $11.5\\\\mathrm{Hz}$ 2H)3.20-3.05m1H)3.02d $J =$ $11.6\\\\mathrm{Hz}$ 2H) 2.65-2.51m2H)2.41-2.25m2H)2.23-2.10m2H)2.02- 1.85m2H.LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 503 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,421,481,595]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4- yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutane-1-carboxylic acid (136). A mixture of intermediate 135 $(890\\\\mathrm{mg},$ $1.77\\\\mathrm{mmol}$ , 1.0 equiv) and LiOH $(85.0\\\\mathrm{mg},$ $3.54\\\\mathrm{mmol}$ 2.0 equiv) in THF $(5\\\\mathrm{mL})$ and water $(5\\\\mathrm{mL})$ was stirred at room temperature for $1\\\\textrm{h}$ . The resulting mixture was concentrated under vacuum to afford the crude title compound as a yellow solid. The crude product was used in the next step without further purification. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ DMSO- $d_{6})$ 7.97 $\\\\left(\\\\mathrm{d},J = 7.2\\\\mathrm{Hz},1\\\\mathrm{H}\\\\right)$ 7.56dd, $J = 7.9$ $1.7~\\\\mathrm{Hz}$ 1H),7.52s,1H),7.45-7.37m1H)7.15-6.92m 4H),6.92-6.82 m,1H),6.27 d $J = 2.2\\\\mathrm{Hz}$ 1H),5.27-5.15 m, 1H),4.88 s,2H),3.66 d $J = 12.2\\\\mathrm{Hz}$ 2H),3.25-3.09 m,3H), 2.85-2.72 m,2H),2.47-2.35 m,2H),2.29-2.16 m,2H),2.01 d, $J = 9.6\\\\mathrm{Hz}$ 2H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 489 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,595,482,805]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4- yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)-N-methoxy-N-methylcyclobutane-1-carboxamide (137). A mixture of intermediate 136 $(880\\\\mathrm{mg},$ $1.80\\\\mathrm{mmol}$ 1.0 equiv), N,O-dimethylhydroxylamine hydrochloride $(263~\\\\mathrm{mg},$ $2.68~\\\\mathrm{mmol}$ 2.0 equiv), DIEA $(1.16\\\\mathrm{g},$ $9.01\\\\mathrm{mmol}$ 5.0 equiv), and HATU $(1.02\\\\mathrm{g},$ $2.68\\\\mathrm{mmol}$ 2.0 equiv) in DMF $(15~\\\\mathrm{mL})$ was stirred at room temperature for $1\\\\textrm{h}$ The reaction mixture was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ to afford the title compound $(320\\\\mathrm{mg},$ $33\\\\%$ as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.15 s,1H)7.99-7.87 m,1H) 7.77 d, $J = 5.9\\\\mathrm{Hz}$ 1H7.51s1H7.28-7.15m1H6.94-6.79 m,2H)6.59-6.49 m,1H)6.16d $J = 2.0\\\\mathrm{Hz}$ 1H5.98s,2H) 5.25-5.13 m,1H)4.50 s,2H)3.62 s,3H)3.45 s,1H)3.25 d, $J = 11.4\\\\mathrm{Hz}$ 2H)3.12 s,3H)3.02 d, $J = 11.6\\\\mathrm{Hz}$ 2H)2.62-2.53 s,2H)2.36-2.24 m,2H)2.24-2.10 m,2H)2.05-1.90 m,2H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 532 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,805,482,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4- yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutane-1-carbaldehyde (138). To a $0^{\\\\circ}\\\\mathrm{C}$ solution of intermediate 137 $(300\\\\mathrm{mg},0.564\\\\mathrm{mmol},1.0$ equiv) in THF (15 mL) was added $\\\\mathrm{LiAlH_4}$ $(1.0\\\\mathrm{M}$ in THF, $0.85~\\\\mathrm{mL}$ $0.85\\\\mathrm{mmol}$ 1.5 equiv). The resulting mixture was stirred at room temperature for $1\\\\textrm{h}$ then was cooled to $0^{\\\\circ}\\\\mathrm{C}$ and quenched with solid $\\\\mathrm{Na}_2\\\\mathrm{SO}_4\\\\cdot 10\\\\mathrm{H}_2\\\\mathrm{O}$ $(200\\\\mathrm{mg})$ . The resulting mixture was filtered, and the filter cake was washed with MeOH $(30~\\\\mathrm{mL})$ . The filtrate and washings were concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,172]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\mathrm{NH_4HCO_3)}$ 0 to $100\\\\%$ ) to afford the title compound $(110\\\\mathrm{mg},41\\\\%)$ as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.16 (s, 1H), $9.86 - 9.61(\\\\mathrm{m},1\\\\mathrm{H})$ 7.97-7.88 (m, 1H), 7.82-7.70 (m, 1H), 7.50 (s, 1H), 7.29-7.17 (m, 1H), 6.97-6.77 (m, 2H), 6.60-6.42 (s, 1H), 6.19-6.09 (m, 1H), 5.98 (s, 2H), 5.20-5.04 (m, 1H), 4.50 (s, 2H), 3.55-3.40 (m, 1H),3.25 (d, $J = 11.6~\\\\mathrm{Hz}$ ,2H),3.02 (d, $J = 11.7~\\\\mathrm{Hz}$ $2\\\\mathrm{H})$ ,2.60-2.53 (m, 2H), 2.34-2.06 (m, 4H), 2.03-1.80 (m, 2H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 473 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,172,915,492]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-((2R)-2-(3-(4-((trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutyl)methyl)piperazin-1-yl)-isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (22). A solution of intermediate 138 (50 mg, 0.106 mmol, 1.0 equiv), chiral-pure intermediate 123 (60 mg, 0.106 mmol, 1.0 equiv), and NaOAc (43 mg, 0.529 mmol, 5.0 equiv) in MeOH (2.1 mL) and DCM (0.7 mL) was stirred at room temperature for 30 min. Then $\\\\mathrm{NaBH}_3\\\\mathrm{CN}$ (8.6 mg, 0.14 mmol, 1.3 equiv) was added in portions at the same temperature. The resulting mixture was stirred at room temperature for 1 h then was concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH_4HCO_3})$ 0 to $100\\\\%$ ) to afford the title compound (6.6 mg, $6.1\\\\%$ ) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (500 MHz, DMSO- $d_6$ ) $\\\\delta$ 14.15 (s, 1H), 8.99 (d, $J = 2.4~\\\\mathrm{Hz}$ , 1H), 8.41 (d, $J = 7.7~\\\\mathrm{Hz}$ , 1H), 7.92 (d, $J = 7.9~\\\\mathrm{Hz}$ , 1H), 7.77 (d, $J = 5.9~\\\\mathrm{Hz}$ , 1H), 7.50 (d, $J = 1.9~\\\\mathrm{Hz}$ , 1H), 7.49-7.42 (m, 2H), 7.37 (d, $J = 8.0~\\\\mathrm{Hz}$ , 2H), 7.26-7.19 (m, 1H), 6.90-6.82 (m, 2H), 6.55-6.50 (m, 1H), 6.17-6.10 (m, 2H), 5.99 (s, 2H), 5.24-5.09 (m, 1H), 5.04-4.87 (m, 2H), 4.50 (s, 2H), 4.36 (t, $J = 7.8~\\\\mathrm{Hz}$ , 1H), 4.29 (t, $J = 4.2~\\\\mathrm{Hz}$ , 1H), 3.75-3.68 (m, 1H), 3.58 (d, $J = 10.0~\\\\mathrm{Hz}$ , 1H), 3.43 (d, $J = 10.9~\\\\mathrm{Hz}$ , 1H), 3.30-3.11 (m, 6H), 3.02 (d, $J = 11.7~\\\\mathrm{Hz}$ , 2H), 2.54-2.40 (m, 10H), 2.28-2.10 (m, 6H), 2.06-1.90 (m, 3H), 1.83-1.74 (m, 1H), 1.69 (s, 1H), 1.48-1.35 (m, 3H), 0.95 (d, $J = 6.6~\\\\mathrm{Hz}$ , 3H), $0.85 - 0.77$ (m, 3H). LC-MS $(\\\\mathrm{ES + })$ : m/z 1024 $[\\\\mathbf{M} + \\\\mathbf{H}]^+$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,492,915,755]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-(2-(3-(4-(Dimethoxymethyl)piperidin-1-yl)- isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -((S)-1-(4-(4- methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (139). A solution of intermediate 53 $(280~\\\\mathrm{mg}$ $0.860~\\\\mathrm{mmol}$ 1.0 equiv), intermediate 57 (free base, $284~\\\\mathrm{mg}$ $0.860~\\\\mathrm{mmol}$ 1.0 equiv), DIEA $(332~\\\\mathrm{mg}$ $2.57~\\\\mathrm{mmol}$ 3.0 equiv), and HATU $(489~\\\\mathrm{mg}$ 1.29 mmol, 1.5 equiv) in DMF $(3\\\\mathrm{mL})$ was stirred at room temperature for $2\\\\mathrm{h}$ The resulting mixture was diluted with EtOAc $(100~\\\\mathrm{mL})$ washed with water $(100~\\\\mathrm{mL})$ ,and the organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ 0 to $100\\\\%$ to afford the title compound ( $\\\\sim 1:1$ mixture of diastereomers, $220~\\\\mathrm{mg}$ $40\\\\%$ ) as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 8.99s,1H) 8.41d $J = 7.8 \\\\mathrm{Hz}$ 1H7.53-7.28m4H6.18-6.09m1H) 5.11d $J = 3.6 \\\\mathrm{Hz}$ 1H5.05-4.83m1H4.48-4.32m1H) 4.28s1H4.12-3.98m1H3.77-3.48m5H3.26d $J = 4.3$ Hz,6H2.78-2.60m3H2.48-2.44m3H2.31-2.10m 1H2.10-1.87m1H1.85-1.52m3H1.50-1.08m5H) 0.96dd $J = 6.7$ $2.5\\\\mathrm{Hz}$ 3H0.86-0.71m3H.LC-MS $(ES+)$ .. $m / z640[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,755,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-(2-(3-(4-Formylpiperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $(N$ -(S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (140). A solution of intermediate 139 $(220\\\\mathrm{mg},0.343\\\\mathrm{mmol})$ in aqueous $\\\\mathrm{H}_2\\\\mathrm{SO}_4$ $(1.0\\\\mathrm{M},2\\\\mathrm{mL})$ and THF $(2\\\\mathrm{mL})$ was stirred at $60^{\\\\circ}\\\\mathrm{C}$ for $2\\\\mathrm{h}$ . The mixture was then cooled to room temperature and was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3)$ , 0 to $100\\\\%$ ) to afford the title compound $(150\\\\mathrm{mg},74\\\\%)$ as a yellow solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 9.60 $(d,J = 7.9\\\\mathrm{Hz},1\\\\mathrm{H})$ , 9.03-8.88 $(m,1\\\\mathrm{H})$ , 8.47-8.18 $(m,1\\\\mathrm{H})$ , 7.53-7.28 $(m,4\\\\mathrm{H})$ , 6.21-6.13 $(m,1\\\\mathrm{H})$ , 5.11 $(s,1\\\\mathrm{H})$ , 5.03-4.82 $(m,1\\\\mathrm{H})$ , 4.60-4.33 $(m,1\\\\mathrm{H})$ , 4.28 $(s,1\\\\mathrm{H})$ , 3.76-3.65 $(m,1\\\\mathrm{H})$ , 3.65-3.48 $(m,3\\\\mathrm{H})$ , 3.48-3.35 $(m,1\\\\mathrm{H})$ , 3.25-3.13 $(m,1\\\\mathrm{H})$ , 2.95-2.75 $(m,2\\\\mathrm{H})$ , 2.48-2.41 $(m,3\\\\mathrm{H})$ , 2.33-2.10 $(m,1\\\\mathrm{H})$ , 2.10-1.69 $(m,4\\\\mathrm{H})$ , 1.55-1.31 $(m,5\\\\mathrm{H})$ , 1.00-0.71 $(m,6\\\\mathrm{H})$ . LC-MS $(ES+)$ : $m/z$ 594 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1304 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"42\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,71,481,295]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"43\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tert-Butyl 4-((4-bromopyridin-2-yl)oxy)piperidine-1-carboxylate (142). A suspension of tert-butyl 4-hydroxypiperidine-1-carboxylate (141, $2.00\\\\mathrm{g}$ , $9.94\\\\mathrm{mmol}$ , 1.0 equiv) and $\\\\mathrm{NaH}$ ( $60\\\\%$ in mineral oil, $0.480\\\\mathrm{g}$ , $12.0\\\\mathrm{mmol}$ , 1.2 equiv) in DMF ( $20\\\\mathrm{mL}$ ) was stirred at $0^{\\\\circ}\\\\mathrm{C}$ for $1\\\\mathrm{h}$ . 4-Bromo-2-fluoro-pyridine ( $62$ , $2.62\\\\mathrm{g}$ , $14.9\\\\mathrm{mmol}$ , 1.5 equiv) was then added, and the mixture was warmed to room temperature and stirred for $1\\\\mathrm{h}$ . After quenching at room temperature with saturated aqueous $\\\\mathrm{NH}_4\\\\mathrm{Cl}$ , the mixture was extracted with EtOAc ( $100\\\\mathrm{mL} \\\\times 3$ ). The combined organic layers were washed with water ( $100\\\\mathrm{mL}$ ), dried over sodium sulfate, and were filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography ((EtOAc: petroleum ether, 0:100 to 66:44) to afford the title compound ( $2.70\\\\mathrm{g}$ , $76\\\\%$ ) as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR ( $300\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 8.07 (d, $J = 5.5\\\\mathrm{Hz}$ , 1H), 7.22 (dd, $J = 5.5$ , $1.7\\\\mathrm{Hz}$ , 1H), 7.11 (d, $J = 1.6\\\\mathrm{Hz}$ , 1H), 5.22–5.10 (m, 1H), 3.75–3.60 (m, 2H), 3.17 (t, $J = 11.2\\\\mathrm{Hz}$ , 2H), 1.99–1.87 (m, 2H), 1.62–1.46 (m, 2H), 1.41 (s, 9H). LC-MS (ES+): $m/z$ 357 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,295,481,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"43\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tert-Butyl 4-((4-(3-(3-amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)-piperidine-1-carboxylate (143). A solution of intermediate 142 $(2.65\\\\mathrm{g},7.42\\\\mathrm{mmol},1.0$ equiv), benzyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (98, TFA salt, $3.65\\\\mathrm{g}$ $10.1\\\\mathrm{mmol}$ , 1.4 equiv), $\\\\mathrm{Cs_2CO_3}$ $(7.25\\\\mathrm{g},22.3\\\\mathrm{mmol},3.0$ equiv), and RuPhosPd G2 $(0.580\\\\mathrm{g},0.746$ mmol, 0.10 equiv) in toluene $(20~\\\\mathrm{mL})$ was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for $2\\\\textrm{h}$ The reaction mixture was cooled to room temperature and was diluted with EtOAc $(100~\\\\mathrm{mL})$ . The resulting mixture was washed with water $(100~\\\\mathrm{mL})$ , and the organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 1:1) to afford benzyl 8-(2-((1- tert-butoxycarbonyl)piperidin-4-yl)oxy)pyridin-4-yl)-3,8- diazabicyclo[3.2.1]octane-3-carboxylate $(1.95\\\\mathrm{g},50\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ $\\\\mathrm{DMSO - d_6})$ 7.78 $(d,J = 6.0\\\\mathrm{Hz}$ 1H),7.52- 7.11 (m, 5H), 6.48 (dd, $J = 6.0$ $2.1\\\\mathrm{Hz}$ 1H), 6.11 (d, $J = 2.0\\\\mathrm{Hz}$ 1H), 5.17-5.01 (m, 3H), 4.38 (d, $J = 10.0\\\\mathrm{Hz}$ 2H), 3.80-3.58 (m, 4H), 3.21-2.95 (m, 4H), 1.95-1.80 (m, 4H), 1.72-1.59 (m, 2H), 1.55- 1.43 (m, 2H), 1.41 (s, 9H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z523[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ . This material $(1.90\\\\mathrm{g},3.64\\\\mathrm{mmol})$ was combined with $10\\\\%$ Pd/C (300 mg) in EtOAc $(20~\\\\mathrm{mL})$ , and the resulting suspension was stirred at room temperature for $^{\\\\textrm{\\\\scriptsize 4h}}$ under hydrogen (3 atm). The mixture was then filtered, and the filter cake was washed with EtOAc $(20~\\\\mathrm{mL}\\\\times 2)$ The combined filtrate and washings were concentrated under reduced pressure, and the residue was purified by prepacted C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH_4HCO_3})$ , 0 to $100 \\\\%$ ) to afford tert-butyl 4-((4-(3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2- yl)oxy)piperidine-1-carboxylate $(900~\\\\mathrm{mg}$ $64 \\\\%$ ) as a white solid. $^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 7.72 (d, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 6.38 (dd, $J =$ $6.0$ $2.0~\\\\mathrm{Hz}$ , 1H), 5.97 (d, $J = 2.1~\\\\mathrm{Hz}$ , 1H), 5.16-5.04 (m, 1H), 4.14 (s, 2H), 3.78-3.60 (m, 2H), 3.12 (t, $J = 11.2~\\\\mathrm{Hz}$ , 2H), 2.83 (d, $J =$ $12.2~\\\\mathrm{Hz}$ , 2H), 2.42 (d, $J = 12.2~\\\\mathrm{Hz}$ , 2H), 1.97-1.80 (m, 6H), 1.56- 1.45 (m, 2H), 1.41 (s, 9H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z389[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ . A solution of this material $(880~\\\\mathrm{mg}$ $2.27~\\\\mathrm{mmol}$ , 1.0 equiv), 4-bromo-6-chloro-pyridazin-3-amine (70, $708~\\\\mathrm{mg}$ $3.40~\\\\mathrm{mmol}$ , 1.5 equiv) and DIEA $(877~\\\\mathrm{mg},6.80~\\\\mathrm{mmol}$ , 3.0 equiv) in NMP $(10~\\\\mathrm{mL})$ was stirred at $120^{\\\\circ}\\\\mathrm{C}$ for $^{\\\\textrm{\\\\scriptsize 2h}}$ After cooling to room temperature, the mixture was directly purified by prepacted C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH_4HCO_3})$ , 0 to $100 \\\\%$ ) to afford tert-butyl 4-(4-(3-(3-amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)- pyridin-2-yl)oxy)piperidine-1-carboxylate $(1.06~\\\\mathrm{g},91\\\\%)$ as a yellow solid. $^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ $7.78$ d, $J = 5.6~\\\\mathrm{Hz}$ , 1H), 6.91 (d, $J = 1.7~\\\\mathrm{Hz}$ , 1H), 6.51 (d, $J = 5.9~\\\\mathrm{Hz}$ , 1H), 6.13 (s, 1H), 5.84 (s, 2H), 5.11 (s, 1H), 4.46 (s, 2H), 3.71 (d, $J = 13.1~\\\\mathrm{Hz}$ , 2H), 3.25- $3.05(\\\\mathfrak{m},4\\\\mathsf{H})$ , 2.87 (d, $J = 11.7~\\\\mathrm{Hz}$ , 2H), 2.17-2.05 (m, 2H), 1.97- $1.82(\\\\mathfrak{m},4\\\\mathsf{H})$ , 1.60-1.45 (m, 2H), 1.41 (d, $J = 1.8~\\\\mathrm{Hz}$ , 9H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z516[\\\\mathrm{M} + \\\\mathrm{H}]^{+}$ . A solution of this material $(1.00~\\\\mathrm{g},$ 1.94 mmol, 1.0 equiv), 2-hydroxyphenylboronic acid (72, $401~\\\\mathrm{mg}$ , 2.91 mmol, 1.5 equiv), $\\\\mathbb { K } _ { 2 } \\\\mathbb { C } \\\\mathbb { O } _ { 3 }$ $(802~\\\\mathrm{mg},$ $5.81~\\\\mathrm{mmol}$ .3.O equiv and Pd(PPh<sub>3</sub>)<sub>4</sub> $(224~\\\\mathrm{mg},$ $0.190~\\\\mathrm{mmol},$ $0.10~\\\\mathrm{equiv})$ in I,4-dioxane $(10~\\\\mathrm{mL})$ and water $(1~\\\\mathrm{mL})$ was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for $^{\\\\textrm{\\\\scriptsize}2\\\\textrm{h}}$ . The reaction was then \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,235]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"43\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"cooled to room temperature and was diluted with EtOAc $(100~\\\\mathrm{mL})$ The resulting mixture was washed with water $(100~\\\\mathrm{mL})$ ,and the organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 100:0) to afford the title compound $(600\\\\mathrm{mg},54\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 14.15s1H7.93d $J = 7.7\\\\mathrm{Hz}$ 1H),7.79d $J = 5.9\\\\mathrm{Hz}$ 1H),7.51s1H),7.24t $J = 7.4\\\\mathrm{Hz}$ 1H), 6.96-6.80 m2H),6.58-6.49 m1H),6.15 s1H),5.98 s2H), 5.18-5.04 m1H),4.50 s2H),3.78-3.62 m2H),3.26 d $J =$ $11.7\\\\mathrm{Hz}$ 2H),3.20-3.08 m2H),3.02 d $J = 11.5\\\\mathrm{Hz}$ 2H),2.18 d $J = 7.3\\\\mathrm{Hz}$ 2H),2.04-1.85 m4H),1.59-1.45m2H),1.41 s, 9H). LC-MS $\\\\left(\\\\mathrm{ES + }\\\\right)$ .. $m / z$ 574 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,235,915,396]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"43\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(6-Amino-5-(8-(2-(piperidin-4-yloxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)pyridazin-3-yl)phenol (144). A solution of intermediate 143 $(550\\\\mathrm{mg},0.960\\\\mathrm{mmol})$ and TFA (1 mL) in dichloromethane $(5\\\\mathrm{mL})$ was stirred at room temperature for $4\\\\mathrm{h}$ . The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.1\\\\%$ TFA), 0 to $100\\\\%$ ) to afford the title compound (TFA salt, $410\\\\mathrm{mg},73\\\\%$ yield) as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6}$ 8.73s2H7.95d $J = 6.7~\\\\mathrm{Hz}$ 1H7.58 $(\\\\mathrm{d},J = 7.8\\\\mathrm{Hz}$ 1H7.50s1H7.39t $J = 7.6\\\\mathrm{Hz}$ 1H7.08-6.91 m4H6.82d $J = 6.9\\\\mathrm{Hz}$ 1H6.50s1H5.14s1H4.79 s, 2H),3.62d $J = 12.1\\\\mathrm{Hz}$ 2H),3.33-3.05m6H2.25-2.06m 4H),2.05-1.81m4H.LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 474 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,396,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"43\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-((2R)-2-(3-(4-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)piperidin-1-yl)methyl)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (23). A solution of intermediate 144 (130 mg, 0.275 mmol, 1.0 equiv), intermediate 140 (163 mg, 0.275 mmol, 1.0 equiv), and $\\\\mathrm{NaBH(OAc)_3}$ (175 mg, 0.825 mmol, 3.0 equiv) in $\\\\mathrm{CH}_3\\\\mathrm{CN}$ (4 mL) was stirred at room temperature for 4 h. The resulting mixture was diluted with EtOAc (100 mL) and was washed with water (100 mL). The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by preparative HPLC [column: XBridge Shield RP18 OBD Column, $30\\\\times 150~\\\\mathrm{mm}^2$ $5\\\\mu \\\\mathrm{m}$ ; mobile phase A: Water (10 mmol/L $\\\\mathrm{NH_4HCO_3}$ ), mobile phase B: $\\\\mathrm{CH}_3\\\\mathrm{CN}$ ; flow rate: 60 mL/min; gradient: 40 to 63% B over 10 min; wavelength: 254/220 nm; RT: 8.83 min] to afford a $\\\\sim 1:1$ mixture of the title compound and the corresponding isopropyl group epimer (38 mg). This mixture was subsequently separated by preparative chiral HPLC [column: CHIRAL ART Amylose-SA, $5\\\\times 25~\\\\mathrm{cm}^2$ $5\\\\mu \\\\mathrm{m}$ ; mobile phase A: 3:1 hexane:DCM (0.5% 2 M $\\\\mathrm{NH}_3$ -MeOH), mobile phase B: EtOH; flow rate: 20 mL/min; gradient: isocratic 50% B; wavelength: 220/254 nm; RT1:13.23 min; RT2:29.80 min; sample solvent: EtOH] to afford the title compound (slower peak, 6.2 mg, 2.1%) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 14.14 (s, 1H), 8.99 (s, 1H), 8.40 (d, $J = 7.7~\\\\mathrm{Hz}$ , 1H), 7.97–7.89 (m, 1H), 7.79 (d, $J = 5.9~\\\\mathrm{Hz}$ , 1H), 7.49 (d, $J = 8.5~\\\\mathrm{Hz}$ , 1H), 7.45 (d, $J = 8.0~\\\\mathrm{Hz}$ , 2H), 7.37 (d, $J = 8.2~\\\\mathrm{Hz}$ , 2H), 7.29–7.17 (m, 1H), 6.92–6.80 (m, 2H), 6.51 (dd, $J = 6.2$ , 2.0 Hz, 1H), 6.16–6.08 (m, 2H), 5.98 (d, $J = 5.0~\\\\mathrm{Hz}$ , 2H), 5.10 (d, $J = 3.6~\\\\mathrm{Hz}$ , 1H), 5.04–4.87 (m, 2H), 4.51 (d, $J = 4.5~\\\\mathrm{Hz}$ , 2H), 4.37 (t, $J = 7.8~\\\\mathrm{Hz}$ , 1H), 4.29 (s, 1H), 3.78–3.49 (m, 4H), 3.42 (d, $J = 10.2~\\\\mathrm{Hz}$ , 1H), 3.31–3.24 (m, 2H), 3.02 (d, $J = 11.5~\\\\mathrm{Hz}$ , 2H), 2.81–2.66 (m, 4H), 2.50–2.42 (m, 3H), 2.30–1.87 (m, 12H), 1.87–1.51 (m, 6H), 1.50–1.30 (m, 3H), 1.21–1.07 (m, 2H), 0.96 (t, $J = 5.8~\\\\mathrm{Hz}$ , 3H), 0.89–0.76 (m, 3H). LC-MS $(\\\\mathrm{ES + })$ : m/z 1051.6 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . The compound bearing the undesired isopropyl stereocenter $(23e,$ isopropyl isomer corresponding to 23, structure not shown) was also isolated (faster peak, $6.2~\\\\mathrm{mg}$ , $2.1\\\\%$ ) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(300~\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\delta$ 14.14 (s, 1H), 9.0–8.87 (m, 1H), 8.20 (d, $J = 7.8~\\\\mathrm{Hz}$ , 1H), 7.97–7.88 (m, 1H), 7.79 (d, $J = 5.9~\\\\mathrm{Hz}$ , 1H), 7.56–7.28 (m, 5H), 7.23 (t, $J = 7.7~\\\\mathrm{Hz}$ , 1H), 6.92–6.80 (m, 2H), 6.59–6.47 (m, 1H), 6.13 (d, $J = 2.0~\\\\mathrm{Hz}$ , 2H), 5.97 (s, 2H), 5.10 (d, $J = 3.6~\\\\mathrm{Hz}$ , 1H), 5.07–4.84 (m, 2H), 4.50 (s, 2H), 4.43 (t, $J = 7.6~\\\\mathrm{Hz}$ , 1H), 4.33–4.22 (m, 1H), 3.77–3.40 (m, 5H), 3.26 (d, $J = 11.7~\\\\mathrm{Hz}$ , 2H), \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"43\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[532,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"43\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"43\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[484,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"43\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1305 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"43\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"43\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,70,482,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"3.02 (d, $J = 11.5\\\\\\\\mathrm{Hz}$ 2H), 2.82-2.60 (m, 4H), 2.50-2.42 (m, 3H), 2.32-2.05 (m, 8H), 2.00-1.88 (m, 4H), 1.88-1.50 (m, 6H), 1.47 (d, $J = 6.9\\\\\\\\mathrm{Hz}$ 1H), 1.36 (d, $J = 6.9\\\\\\\\mathrm{Hz}$ 2H), 1.19-1.00 (m, 2H), 0.98-0.67 (m, 6H). LC-MS $(\\\\\\\\mathrm{ES}+)$ : $m / z$ 1051.5 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . \\\",\\\"(2S,4R)-4-Hydroxy-1-(3-methyl-2-(3-(prop-2-yn-1-xyloxy)- isoxazol-5-yl)butanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)- phenyl)ethyl)pyrrolidine-2-carboxamide (145). A solution of intermediate 58 $(250\\\\\\\\mathrm{mg},0.501\\\\\\\\mathrm{mmol},1.0$ equiv), propargyl bromide $(59.5\\\\\\\\mathrm{mg},0.500\\\\\\\\mathrm{mmol},1.0$ equiv), and $\\\\\\\\mathrm{K}_2\\\\\\\\mathrm{CO}_3$ $208\\\\\\\\mathrm{mg}$ $1.50\\\\\\\\mathrm{mmol}$ 3.0 equiv) in DMF $(4\\\\\\\\mathrm{mL})$ was stirred at room temperature for $2\\\\\\\\mathrm{h}$ The reaction was diluted with EtOAc $(100~\\\\\\\\mathrm{mL})$ , and the resulting mixture was washed with water $(100~\\\\\\\\mathrm{mL})$ . The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\%)$ $\\\\\\\\mathrm{NH_4HCO_3)}$ 0 to $100\\\\\\\\%$ ) to afford the title compound $(120\\\\\\\\mathrm{mg},45\\\\\\\\%)$ as a yellow oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6}$ 89.01-8.88 m, 1H),8.50-8.32 m, 1H),7.56-7.21 m, 4H),6.22-6.10 m, 1H), 5.10 s, 1H),5.03-4.81 m, 3H),4.57-4.31 m, 1H),4.26 s, 1H), 3.81-3.59 m, 2H),3.57-3.34 m, 2H),2.45 d, $J = 2.6~\\\\\\\\mathrm{Hz}$ 3H), 2.35-2.14 m, 1H),2.14-1.86 m, 1H),1.86-1.64 m, 1H),1.49- 1.27 m, 3H),1.01-0.71 m, 6H). LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 537 $[\\\\\\\\mathbf{M}+$ $\\\\\\\\mathrm{H}]^{+}$ . A considerable amount of the corresponding isoxazole Nalkylation product eluted from the column ahead of the desired compound and was also isolated $(90\\\\\\\\mathrm{mg},33\\\\\\\\%)$ as a yellow oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6}$ 89.02-8.94 m, 1H),8.50-8.32 m, 1H),7.52-7.29 m, 4H),5.79 s, 1H),5.11 d, $J = 3.7~\\\\\\\\mathrm{Hz}$ 1H), 5.08-4.85 m, 1H),4.58 d, $J = 2.6~\\\\\\\\mathrm{Hz}$ 2H),4.48-4.35 m, 1H), 4.27 s, 1H),3.72-3.39 m, 4H),2.45 d, $J = 2.8~\\\\\\\\mathrm{Hz}$ , 3H),2.35-2.12 m, 1H),2.12-1.98(m, 1H),1.85-1.62 m, 1H),1.48-1.31 m, 3H),1.02-0.66 m, 6H). LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 537 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ \\\",\\\"2-trans-3-(Benzyloxy)cyclobutoxy)-4-bromopyridine (146). A suspension of 3-benzyloxycyclobutanol $(108,2.95\\\\\\\\mathrm{g},16.6\\\\\\\\mathrm{mmol},$ 1.0 equiv) and NaH $60\\\\\\\\%$ in mineral oil, $0.790\\\\\\\\mathrm{g}$ 19.7 mmol, 1.2 equiv) in DMF $(20.0~\\\\\\\\mathrm{mL})$ was stirred at $0^{\\\\\\\\circ}C$ for $0.5\\\\\\\\mathrm{h}$ 4-Bromo-2fluoro-pyridine $(4.37\\\\\\\\mathrm{g},24.8\\\\\\\\mathrm{mmol},1.5$ equiv) was then added, and the reaction was warmed to room temperature and was stirred for $1\\\\\\\\textrm{h}$ The mixture was quenched at room temperature with saturated aqueous $\\\\\\\\mathrm{NH_4Cl}$ and was subsequently extracted with EtOAc $(100~\\\\\\\\mathrm{mL}$ $\\\\\\\\times 3)$ .The combined organic layers were washed with water $(100~\\\\\\\\mathrm{mL})$ and were dried over magnesium sulfate. After filtration, the filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 65:35) to afford the title compound $(4.00\\\\\\\\mathrm{g},72\\\\\\\\%)$ as a colorless oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8.02 d $J = 5.5\\\\\\\\mathrm{Hz}$ 1H),7.37-7.23 m, 5H),7.19dd $J = 5.5$ $1.7\\\\\\\\mathrm{Hz}$ 1H),7.08d $J = 1.6\\\\\\\\mathrm{Hz}$ 1H4.77p $J = 7.1\\\\\\\\mathrm{Hz}$ 1H),4.37s2H),3.78p $J = 6.9\\\\\\\\mathrm{Hz}$ 1H2.86-2.72m, 2H),2.05-1.87m2H.LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 334 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ \\\",\\\"tert-Butyl 8-(2-(trans-3-hydroxycyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octane-3-carboxylate (147). A solution of intermediate 146 $(3.90\\\\\\\\mathrm{g},11.7\\\\\\\\mathrm{mmol},1.0$ equiv), tert-butyl 3,8-diazabicyclo[3.2.1]octane-3-carboxylate (67, $4.95\\\\\\\\mathrm{g}$ 23.3 mmol, 2.0 equiv), $\\\\\\\\mathrm{Cs_2CO_3}$ $(11.4\\\\\\\\mathrm{g},35.0\\\\\\\\mathrm{mmol},3.0$ equiv) and RuPhosPd G2 $(0.910\\\\\\\\mathrm{g},1.17\\\\\\\\mathrm{mmol},0.10$ equiv) in toluene $(35~\\\\\\\\mathrm{mL})$ was stirred at 90 $^\\\\\\\\circ \\\\\\\\mathrm{C}$ for $^{\\\\\\\\textrm{\\\\\\\\scriptsize 2h}}$ The reaction was cooled to room temperature and was diluted with EtOAc $(100~\\\\\\\\mathrm{mL})$ . The resulting mixture was washed with water $(100~\\\\\\\\mathrm{mL})$ , and the organic layer was dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc:petroleum ether, 0:100 to 65:35) to afford tert-butyl 8-(2- (trans-3-(benzyloxy)cyclobutoxy)pyridin-4-yl)-3,8-diazabicyclo[3.2.1]-octane-3-carboxylate $(4.27\\\\\\\\mathrm{g},79\\\\\\\\%)$ as a yellow oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6}$ ) $\\\\\\\\delta$ 7.81-7.69 m, 1H), 7.47-7.08 m, 5H), 6.45dd $J = 6.1$ $2.1\\\\\\\\mathrm{Hz}$ 1H),6.09d $J = 2.0\\\\\\\\mathrm{Hz}$ 1H),4.74p $J =$ $7.2\\\\\\\\mathrm{Hz}$ 1H),4.37s2H),4.32s2H),3.76p $J = 6.9~\\\\\\\\mathrm{Hz}$ 1H), 3.65-3.42 m, 2H),3.12-2.82 m, 2H),2.80-2.66 m, 2H),1.98- 1.80m4H)1.72-1.58m2H)1.37s9H.LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ $466[\\\\\\\\mathrm{M} + \\\\\\\\mathrm{H}]^{+}$ . This material $(4.20\\\\\\\\mathrm{g},9.02\\\\\\\\mathrm{mmol})$ was dissolved in MeOH $(100~\\\\\\\\mathrm{mL})$ and $10\\\\\\\\%$ Pd/C $(2.50\\\\\\\\mathrm{g})$ was added in portions. The resulting suspension was stirred at room temperature for $^{12\\\\\\\\mathrm{h}}$ under a \\\"]\",\n \"page_idx\": \"44\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[512,71,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"hydrogen atmosphere then was filtered. The filter cake was washed with $\\\\\\\\mathrm{MeOH}$ $(20\\\\\\\\mathrm{mL}\\\\\\\\times 3)$ , and the combined filtrate and washings were concentrated under reduced pressure. The residue was purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\%)$ $\\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ 0 to $70\\\\\\\\%$ ) to afford the title compound $(1.90\\\\\\\\mathrm{g},56\\\\\\\\%)$ as a yellow oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 7.73 (d, $J = 6.0~\\\\\\\\mathrm{Hz}$ 1H),6.45dd, $J = 6.0$ 2.1 Hz1H),6.07d $J = 2.0\\\\\\\\mathrm{Hz}$ 1H),5.09 d, $J = 6.5\\\\\\\\mathrm{Hz}$ 1H),4.62p, $J = 7.2\\\\\\\\mathrm{Hz}$ 1H),4.33s,2H),3.88-3.71 m, 1H),3.67-3.45 m,2H),3.04d $J = 13.1\\\\\\\\mathrm{Hz}$ 1H),2.90d $J = 13.0$ $\\\\\\\\mathrm{Hz}$ 1H),2.77-2.62m2H),1.97-1.75m4H),1.71-1.56m, 2H),1.37s9H.LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 376 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ \\\",\\\"trans-3-((4-(3-(3-Amino-6-(2-(methoxymethoxy)phenyl)-pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)cyclobutan-1-ol (148). A solution of intermediate 147 $(1.88\\\\\\\\mathrm{g},$ 5.01 mmol) in TFA $(4\\\\\\\\mathrm{mL})$ and DCM $(20~\\\\\\\\mathrm{mL})$ was stirred at room temperature for $4\\\\\\\\mathrm{h}$ The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in Water $(0.1\\\\\\\\%$ TFA), 0 to $50\\\\\\\\%$ to afford trans-3-((4-(3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)-oxy)cyclobutan-1-ol (TFA salt, $1.20\\\\\\\\mathrm{g},$ $62\\\\\\\\%$ ) as a yellow oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ ,DMSO- $d_{6}$ ) $\\\\\\\\delta$ 9.66 (s, 1H), 9.28 (s, 1H), 7.97 (d, $J = 7.1$ Hz, 1H), 6.81 (dd, $J = 7.1$ $2.1\\\\\\\\mathrm{Hz}$ , 1H), 6.30 (d, $J = 2.2\\\\\\\\mathrm{Hz}$ , 1H), 4.80 (s, 2H), 4.66 (p, $J = 7.0\\\\\\\\mathrm{Hz}$ , 1H), 3.82 (p, $J = 7.1\\\\\\\\mathrm{Hz}$ , 1H), 3.28-3.01 (m, 4H), 2.98-2.80 (m, 2H), 2.10 (s, 4H), 2.03-1.87 (m, 2H). LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 276 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . A solution of this material $(1.19\\\\\\\\mathrm{g},$ 3.05 mmol, 1.0 equiv), 4-bromo-6-chloro-pyridazin-3-amine (70, 1.35 g, 6.48 mmol, 2.1 equiv) and DIEA $(1.67\\\\\\\\mathrm{g},$ 13.0 mmol, 4.3 equiv) in NMP $(15~\\\\\\\\mathrm{mL})$ was stirred at $120^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for $2\\\\\\\\textrm{h}$ After cooling to room temperature, the reaction mixture was directly purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\%$ $\\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ - 0 to $50\\\\\\\\%$ to afford trans-3-((4-(3-(3-amino-6-chloropyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutan-1-ol $(800~\\\\\\\\mathrm{mg},$ $65\\\\\\\\%$ ) as a yellow oil. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ ,DMSO- $d_{6}$ ) $\\\\\\\\delta$ 7.75 (d, $J = 6.0~\\\\\\\\mathrm{Hz}$ , 1H), 6.90 (s, 1H), 6.49 (dd, $J = 6.0$ $2.1~\\\\\\\\mathrm{Hz}$ , 1H), 6.11 (d, $J = 2.0~\\\\\\\\mathrm{Hz}$ , 1H), 5.84 (s, 2H), 5.12 (d, $J = 6.5~\\\\\\\\mathrm{Hz}$ , 1H), 4.65 (p, $J = 7.3~\\\\\\\\mathrm{Hz}$ , 1H), 4.45 (s, 2H), 3.81 (q, $J = 7.0~\\\\\\\\mathrm{Hz}$ , 1H), 3.22-3.13 (m, 2H), 2.87 (d, $J = 11.6~\\\\\\\\mathrm{Hz}$ , 2H), 2.76-2.61 (m, 2H), 2.13 (d, $J =$ $7.2~\\\\\\\\mathrm{Hz}$ , 2H), 1.98-1.75 (m, 4H). LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 403 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . A solution of this material $(790~\\\\\\\\mathrm{mg},$ $1.96~\\\\\\\\mathrm{mmol}$ , 1.0 equiv), $(2-$ methoxymethoxy)phenyl)boronic acid (85, $535~\\\\\\\\mathrm{mg}$ , 2.94 mmol, 1.5 equiv), $\\\\\\\\mathrm{K}_2\\\\\\\\mathrm{CO}_3$ (812 mg, $5.88~\\\\\\\\mathrm{mmol}$ , 3.0 equiv) and $\\\\\\\\mathrm{Pd(PPh_3)_4}$ (226 mg, 0.196 mmol, 0.10 equiv) in water $(1~\\\\\\\\mathrm{mL})$ and 1,4-dioxane $(10~\\\\\\\\mathrm{mL})$ was stirred at $90^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for $2\\\\\\\\textrm{h}$ . The resulting mixture was cooled to room temperature and was extracted with EtOAc $(75~\\\\\\\\mathrm{mL} \\\\\\\\times 3)$ . The combined organic layers were washed with water $(100~\\\\\\\\mathrm{mL})$ and were dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\%$ $\\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ - O to $50\\\\\\\\%$ to afford the title compound $(590~\\\\\\\\mathrm{mg},$ $60\\\\\\\\%$ ) as a yellow solid. $^{1}\\\\\\\\mathrm{H}$ NMR $(300~\\\\\\\\mathrm{MHz}$ ,DMSO- $d_{6}$ ) $\\\\\\\\delta$ 7.74 (d, $J = 6.0~\\\\\\\\mathrm{Hz}$ , 1H), 7.59 (dd, $J = 7.6$ $1.8~\\\\\\\\mathrm{Hz}$ , 1H), 7.34 (ddd, $J = 8.8$ $7.2$ $1.8~\\\\\\\\mathrm{Hz}$ , 1H), 7.19-7.01 (m, 3H), 6.50 (dd, $J = 6.0$ $2.1~\\\\\\\\mathrm{Hz}$ , 1H), 6.12 (d, $J = 2.0$ Hz, 1H), 5.72 (s, 2H), $5.13(s,2H)$ ,5.08 (d, $J = 6.3~\\\\\\\\mathrm{Hz}$ , 1H),4.64 (p, $J = 7.3~\\\\\\\\mathrm{Hz}$ , 1H),4.47 (s, 2H),3.79 (p, $J = 7.1~\\\\\\\\mathrm{Hz}$ , 1H),3.22 (s, 3H), $3.20 - 3.09$ (m, 2H),2.86 (d, $J = 11.4~\\\\\\\\mathrm{Hz}$ , 2H),2.78-2.62 (m, 2H), $2.29 - 2.11$ (m, 2H), $2.02 - 1.75$ (m,4H). LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 505 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . \\\",\\\"4-(8-(2-((trans-3-((6-lodopyridin-3-yl)oxy)cyclobutoxy)-pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)-6-(2-(methoxymethoxy)phenyl)pyridazin-3-amine (149). To a $0^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ solution of $\\\\\\\\mathrm{PPh}_3$ 264 mg, 1.00 mmol, 4.8 equiv) in THF (5 mL) was added DIAD (202 mg, 1.00 mmol, 4.8 equiv). The mixture was stirred for 5 min at $0^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ , then 6-iodopyridin-3-ol (221 mg, 1.00 mmol, 4.8 equiv) was added followed by intermediate 148 (105 mg, 0.208 mmol). The resulting mixture was warmed to room temperature and was stirred for a additional 12 h. The reaction was then diluted with EtOAc (100 mL) and the mixture was washed with water (100 mL). The organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in \\\"]\",\n \"page_idx\": \"44\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"44\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"44\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"44\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"44\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1306 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"44\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"44\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,481,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"water $(0.05\\\\\\\\% \\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ 0 to $60\\\\\\\\%$ ) to afford the title compound $(85\\\\\\\\mathrm{mg},58\\\\\\\\%)$ as a yellow solid. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8.06 (d, $J = 3.2~\\\\\\\\mathrm{Hz}$ 1H),7.75(d, $J = 6.0~\\\\\\\\mathrm{Hz}$ 1H),7.69 (d, $J = 8.7~\\\\\\\\mathrm{Hz}$ 1H),7.59dd, $J = 7.6$ $1.8\\\\\\\\mathrm{Hz}$ 1H),7.35td $J = 7.3$ $1.8\\\\\\\\mathrm{Hz}$ 1H), 7.19-7.02 (m, 4H),6.53dd, $J = 6.1$ $2.0\\\\\\\\mathrm{Hz}$ 1H),6.17d $J = 2.0$ $\\\\\\\\mathrm{Hz},1\\\\\\\\mathrm{H})$ ,5.74s,2H),5.29q, $J = 5.7\\\\\\\\mathrm{Hz}$ 1H),5.15s,2H),4.97t, $J = 5.5\\\\\\\\mathrm{Hz}$ 1H),4.49s,2H),3.23s,3H),3.16d $J = 10.7\\\\\\\\mathrm{Hz}$ 2H), 2.86 d, $J = 11.4\\\\\\\\mathrm{Hz}$ 2H),2.58-2.50 m,4H),2.20 d, $J = 7.1~\\\\\\\\mathrm{Hz}$ 2H),2.01-1.92 (m, 2H). LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 708 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ \\\",\\\"(2S,4R)-1-((2R)-2-(3-((3-5-(trans-3-((4-3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)pyridin-2-yl)prop-2-yn-1-yl)oxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (24). A solution of intermediate 149 (75.0 mg, 0.106 mmol, 1.0 equiv), intermediate 145 (56.9 mg, 0.106 mmol, 1.0 equiv), CuI (2.0 mg, 0.011 mmol, 0.10 equiv), TEA (32.1 mg, 0.320 mmol, 3.0 equiv), and $\\\\\\\\mathrm{Pd}(\\\\\\\\mathrm{PPh}_3)_2\\\\\\\\mathrm{Cl}_2$ (7.4 mg, 0.010 mmol, 0.10 equiv) in DMF (3 mL) was stirred at $65^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for $3\\\\\\\\mathrm{~h}$ . The reaction was cooled to room temperature and was diluted with EtOAc (75 mL). The resulting mixture was washed with water (75 mL) and was dried over sodium sulfate and filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\% \\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ , 0 to $100\\\\\\\\%$ to afford (2S,4R)-1-(2-(3-((3-(5-(trans-3-((4-(3-(3-amino-6-(2-methoxymethoxy)phenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]-octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)pyridin-2-yl)prop-2-yn-1-yl)oxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide ( $\\\\\\\\sim$ 1:1 mixture of isopropyl group isomers, 90.0 mg, $76\\\\\\\\%$ ) as a white solid. $^{1}\\\\\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\\\\\delta$ 9.03–8.89 (m, 1H), 8.45–8.25 (m, 1H), 8.22 (t, $J = 3.3\\\\\\\\mathrm{~Hz}$ , 1H), 7.81–7.52 (m, 4H), 7.52–7.22 (m, 6H), 7.22–7.05 (m, 2H), 6.54 (dd, $J = 6.0$ , 2.0 Hz, 1H), 6.28–6.12 (m, 2H), 5.92–5.75 (m, 4H), 5.36–4.83 (m, 6H), 4.56–4.35 (m, 2H), 4.32–4.21 (m, 1H), 3.84–3.57 (m, 2H), 3.57–3.30 (m, 6H), 3.28–3.15 (m, 3H), 2.98–2.85 (m, 1H), 2.58–2.50 (m, 3H), 2.48–2.41 (m, 3H), 2.35–2.15 (m, 3H), 2.08–1.89 (m, 3H), 1.87–1.73 (m, 1H), 1.49–1.31 (m, 3H), 1.01–0.74 (m, 6H). LC-MS $(\\\\\\\\mathrm{ES}+)$ : $m/z$ 1116 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . A solution of this material (80.0 mg, 0.0717 mmol) in HCl (4.0 M in MeOH, 2 mL) was stirred at room temperature for $4\\\\\\\\mathrm{~h}$ . The resulting mixture was concentrated under reduced pressure, and the residue was purified by preparative HPLC [column: XBridge Prep OBD C18 Column, $30\\\\\\\\times 150\\\\\\\\mathrm{~mm}^2$ , $5\\\\\\\\mu\\\\\\\\mathrm{m}$ ; mobile phase A: water (10 mmol/L $\\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3$ ), mobile phase B: $\\\\\\\\mathrm{CH}_3\\\\\\\\mathrm{CN}$ ; flow rate: $60\\\\\\\\mathrm{~mL/min}$ ; gradient: 21 to $41\\\\\\\\%$ B over $10\\\\\\\\mathrm{~min}$ ; wavelength: $254/220\\\\\\\\mathrm{~nm}$ ; RT: $9.3\\\\\\\\mathrm{~min}$ ] to afford $16\\\\\\\\mathrm{mg}$ of the MOM-deprotected product as a $\\\\\\\\sim$ 1:1 mixture of the two isopropyl group isomers. These compounds were subsequently separated by preparative chiral HPLC [column: CHIRALPAK IA $2\\\\\\\\times 25\\\\\\\\mathrm{~cm}^2$ , $5\\\\\\\\mu\\\\\\\\mathrm{m}$ ; mobile phase A: MTBE (0.1% FA), mobile phase B: 1:1 MeOH:DCM; flow rate: $18\\\\\\\\mathrm{~mL/min}$ ; gradient: isocratic $40\\\\\\\\%$ B; RT:1:57 min; RT:2:20 min; sample solvent: EtOH; injection volume: $1.0\\\\\\\\mathrm{~mL}$ ; number of runs: 2] to afford the title compound (slower peak, $2.2\\\\\\\\mathrm{mg}$ , $2.9\\\\\\\\%$ ) as a white solid. $^{1}\\\\\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\\\\\delta$ 14.15 (s, 1H), 8.99 (s, 1H), 8.42 (d, $J = 7.6\\\\\\\\mathrm{~Hz}$ , 1H), 8.23 (d, $J = 2.8\\\\\\\\mathrm{~Hz}$ , 1H), 7.93 (d, $J = 7.9\\\\\\\\mathrm{~Hz}$ , 1H), 7.79 (d, $J = 5.9\\\\\\\\mathrm{~Hz}$ , 1H), 7.51 (t, $J = 4.3\\\\\\\\mathrm{~Hz}$ , 2H), 7.50–7.26 (m, 5H), 7.26–7.18 (m, 1H), 6.90–6.82 (m, 2H), 6.56 (dd, $J = 6.2$ , $1.8\\\\\\\\mathrm{~Hz}$ , 1H), 6.24–6.15 (m, 2H), 5.98 (s, 2H), 5.38–5.28 (m, 1H), 5.16 (s, 2H), 5.04 (t, $J = 5.4\\\\\\\\mathrm{~Hz}$ , 1H), 4.92 (t, $J = 7.2\\\\\\\\mathrm{~Hz}$ , 1H), 4.52 (s, 2H), 4.39 (t, $J = 7.8\\\\\\\\mathrm{~Hz}$ , 1H), 4.29 (s, 1H), 3.71 (d, $J = 9.6\\\\\\\\mathrm{~Hz}$ , 1H), 3.70–3.45 (m, 3H), 3.30–3.22 (m, 3H), 3.03 (d, $J = 11.6\\\\\\\\mathrm{~Hz}$ , 2H), 2.61–2.54 (m, 3H), 2.46 (s, 3H), 2.31–2.12 (m, 3H), 2.09–1.90 (m, 3H), 1.85–1.71(m, 1H), 1.51–1.31 (m, 3H), 1.02–0.75 (m, 6H). LC-MS $(\\\\\\\\mathrm{ES}+)$ : $m/z$ $1072[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . The isomer bearing the undesired isopropyl stereocenter $(24e,$ isopropyl isomer corresponding to $^{24}$ structure not shown) was also isolated (faster peak, $3.3\\\\\\\\mathrm{mg},$ $4.3\\\\\\\\%$ ) as a white solid. $^{1}\\\\\\\\mathrm{H}$ NMR $(300\\\\\\\\mathrm{MHz},$ DMSO- $d_6$ ) $\\\\\\\\delta$ $14\\\\\\\\.13$ (s, $1\\\\\\\\mathrm{~Hz}$ ), $8\\\\\\\\.98$ (d, $J =$ $9\\\\\\\\.8\\\\\\\\mathrm{~Hz}$ , $1\\\\\\\\mathrm{~Hz}$ ), $8\\\\\\\\.43 -8\\\\\\\\.8$ (m, $1\\\\\\\\mathrm{~Hz}$ ), $8\\\\\\\\.22$ (t, $J =$ $9\\\\\\\\.1\\\\\\\\mathrm{~Hz}$ , $1\\\\\\\\mathrm{~Hz}$ ), $7\\\\\\\\.92$ (d, $J =$ $7\\\\\\\\.9\\\\\\\\mathrm{~Hz}$ , $1\\\\\\\\mathrm{~Hz}$ ), $7\\\\\\\\.78$ (d, $J =$ $5\\\\\\\\.9\\\\\\\\mathrm{~Hz}$ , $1\\\\\\\\mathrm{~Hz}$ ), $7\\\\\\\\.54 -7\\\\\\\\.38$ (m, $4\\\\\\\\mathrm{~Hz}$ ), $7\\\\\\\\.37 -7\\\\\\\\.17$ \\\"]\",\n \"page_idx\": \"45\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[514,70,915,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"$(\\\\\\\\mathrm{m},4\\\\\\\\mathrm{H})$ 6.86dd $J = 10.2$ $7.8~\\\\\\\\mathrm{Hz}$ 2H),6.56dd $J = 6.0$ $2.0~\\\\\\\\mathrm{Hz}$ 1H),6.28-6.15 $\\\\\\\\mathrm{(m,2H)}$ 5.98s,2H),5.32 $\\\\\\\\mathrm{(t,J = 6.0Hz,1H)}$ ,5.15 $\\\\\\\\mathrm{(d,J = 11.4Hz,2H)}$ 5.03 $\\\\\\\\mathrm{(d,J = 7.1Hz,1H)}$ 4.90 $\\\\\\\\mathrm{(t,J = 7.2Hz}$ 1H),4.52s,2H),4.44 $\\\\\\\\mathrm{(t,J = 7.7Hz,1H)}$ 4.27s,1H),3.80 $\\\\\\\\mathrm{(d,J =}$ $8.5\\\\\\\\mathrm{Hz}$ 1H),3.61-3.45 $\\\\\\\\mathrm{(m,3H)}$ 3.29-3.20 $\\\\\\\\mathrm{(m,3H)}$ 3.03 $\\\\\\\\mathrm{(d,J =}$ $11.6\\\\\\\\mathrm{Hz},2\\\\\\\\mathrm{H})$ 2.62-2.52 $\\\\\\\\mathrm{(m,3H)}$ 2.50-2.40 $\\\\\\\\mathrm{(m,3H)}$ 2.36-2.10 $\\\\\\\\mathrm{(m,3H)}$ 2.03-1.92 $\\\\\\\\mathrm{(m,3H)}$ 1.84-1.70 $\\\\\\\\mathrm{(m,1H)}$ 1.47 $\\\\\\\\mathrm{(d,J = 7.0Hz}$ 1H),1.35 $\\\\\\\\mathrm{(d,J = 7.0Hz,2H)}$ 0.98 $\\\\\\\\mathrm{(d,J = 6.6Hz,2H)}$ 0.90-0.69 $\\\\\\\\mathrm{(m,4H)}$ .LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z$ 1072 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ \\\",\\\"(2S,4S)-1-((R)-2-(3-(2,2-Diethoxyethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (150).DIAD $(263\\\\\\\\mathrm{mg},$ $1.30\\\\\\\\mathrm{mmol}$ 1.6 equiv) was added to a $0^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ solution of $\\\\\\\\mathrm{PPh}_3$ $(340\\\\\\\\mathrm{mg},$ $1.29\\\\\\\\mathrm{mmol}$ 1.6 equiv) in THF $(15\\\\\\\\mathrm{mL})$ . The reaction was stirred at $0^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for $1\\\\\\\\textrm{h}$ then intermediate 60 $(500\\\\\\\\mathrm{mg},0.814\\\\\\\\mathrm{mmol},1.0$ equiv) and AcOH $(80.8\\\\\\\\mathrm{mg},1.3\\\\\\\\mathrm{mmol},1.6$ equiv) were added sequentially. The reaction was stirred at $0^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for $1\\\\\\\\textrm{h}$ then was maintained at room temperature for an additional $2\\\\\\\\textrm{h}$ . The volatiles were removed under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\\\\\% \\\\\\\\mathrm{NH}_4\\\\\\\\mathrm{HCO}_3)$ , 0 to $55\\\\\\\\%$ ) to afford (3S,5S)-1-((R)-2-(3-(2,2-diethoxyethoxy)isoxazol-5- yl)-3-methylbutanoyl)-5-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)- ethyl)carbamoyl)pyrrolidin-3-yl acetate $(170~\\\\\\\\mathrm{mg},32\\\\\\\\%)$ as a white solid. ${}^{1}\\\\\\\\mathrm{H}$ NMR (400 MHz, DMSO- $d_{6}$ 8.99 (s, 1H), 8.53-8.13 (m, 1H), 7.71-7.31 (m, 4H), 6.17 (s, 1H), 5.16-5.06 (m, 1H), 5.00- 4.88 (m, 1H), 4.84-4.71 (m, 1H), 4.49-4.41 (m, 1H), 4.12-4.06 (m, 2H), 3.90-3.77 (m, 1H), 3.77-3.48 (m, 6H), 2.48-2.39 (m, 4H),2.33-2.22 (m, 1H), 2.02-1.93 (m, 1H), 1.80-1.60 (m, 3H), $1.48 - 1.36$ m, 3H), 1.13 t $J = 7.0~\\\\\\\\mathrm{Hz}$ 6H), $1.02 - 0.91$ m, 3H), $0.80$ d $J = 6.5~\\\\\\\\mathrm{Hz}$ ,3H.LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z~657[\\\\\\\\mathrm{M} + \\\\\\\\mathrm{H}]^{+}$ .This material $(160~\\\\\\\\mathrm{mg},$ $0.244\\\\\\\\mathrm{mmol})$ was dissolved in MeOH $(1\\\\\\\\mathrm{mL})$ at room temperature and $\\\\\\\\mathrm{NH}_3$ $(7.0\\\\\\\\mathrm{M}$ in MeOH, $5\\\\\\\\mathrm{mL})$ was added. The reaction was stirred at room temperature for $2\\\\\\\\textrm{h}$ then the volatiles were removed under reduced pressure. The residue was diluted with DCM $(30~\\\\\\\\mathrm{mL})$ , and the resulting mixture was washed with brine (20 mL). The organic layer was dried over sodium sulfate and was filtered. Concentration of the filtrate under reduced pressure afforded the title compound $(120\\\\\\\\mathrm{mg},80\\\\\\\\%$ yield) as a white solid. $^{1}\\\\\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_{6}$ ) $\\\\\\\\delta$ 8.99 (s, 1H), 8.46 (d, $J = 7.7~\\\\\\\\mathrm{Hz}$ , 1H), $7.51 - 7.32$ (m, 4H),6.17 s, 1H),5.39-5.19 (m, 1H),5.01-4.86 (m, 1H),4.86- 4.73 (m, 1H),4.40-4.27 (m, 1H),4.27-4.15 (m, 1H),4.15-3.97 (m, 2H), $3.85 - 3.60$ (m, 4H), $3.60 - 3.46$ (m, 3H),2.46 (s, 3H), $2.41 - 2.18$ m, 2H), $1.71 - 1.58$ (m, 1H), $1.50 - 1.32$ (m, 3H), $1.13$ t $J = 7.1~\\\\\\\\mathrm{Hz}$ ,6H),0.96d $J = 6.7~\\\\\\\\mathrm{Hz}$ ,3H),0.81d $J = 6.6~\\\\\\\\mathrm{Hz}$ ,3H). LC-MS $(\\\\\\\\mathrm{ES + })$ .. $m / z~615[\\\\\\\\mathrm{M} + \\\\\\\\mathrm{H}]^{+}$ \\\",\\\"(2S,4S)-4-Hydroxy-1-((R)-3-methyl-2-(3-(2-oxoethoxy)-isoxazol-5-yl)butanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (151). A solution of intermediate 150 $(115\\\\\\\\mathrm{mg},0.187\\\\\\\\mathrm{mmol})$ in formic acid $(2\\\\\\\\mathrm{mL})$ and water $(2\\\\\\\\mathrm{mL})$ was stirred at $60^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ for $2\\\\\\\\mathrm{h}$ . After cooling to room temperature, the solvent was removed under reduced pressure to afford the crude title compound $(105\\\\\\\\mathrm{mg})$ as a white solid. This material was used in the next step without further purification. ${}^{1}\\\\\\\\mathrm{H}$ NMR $(400\\\\\\\\mathrm{MHz}$ , DMSO- $d_6$ ) $\\\\\\\\delta$ 9.61 (s, 1H), 8.99 (s, 1H), 8.50-8.43 (m, 1H), 7.50-7.33 (m, 4H), 6.28-6.08 (m, 1H), 5.33 (s, 1H), 4.95 (d, $J = 9.7\\\\\\\\mathrm{Hz}$ , 2H), 4.38-4.16 (m, 2H), 4.07-3.93 (m, 1H), 3.81-3.64 (m, 2H), 3.57-3.46 (m, 1H), 2.46 (d, $J = 5.7\\\\\\\\mathrm{Hz}$ , 3H), 2.38-2.17 (m, 2H), 1.70-1.60 (m, 1H), 1.45-1.30 (m, 3H), 1.03-0.89 (m, 3H), 0.89-0.75 (m, 3H). LC-MS $(\\\\\\\\mathrm{ES + })$ : $m / z$ 541 $[\\\\\\\\mathbf{M} + \\\\\\\\mathbf{H}]^{+}$ . \\\",\\\"(2S,4S)-1-((2R)-2-(3-(2-(4-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)ethoxy)-isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (25). A solution of intermediate 151 $(95.0\\\\\\\\mathrm{mg}$ $0.176\\\\\\\\mathrm{mmol}$ 1.0 equiv), intermediate 119 (HCl salt, $111\\\\\\\\mathrm{mg}$ $0.191\\\\\\\\mathrm{mmol}$ 1.1 equiv), and NaOAc $(43.0\\\\\\\\mathrm{mg}$ $0.524\\\\\\\\mathrm{mmol}$ 3.0 equiv) in DCM $(0.7\\\\\\\\mathrm{mL})$ and MeOH $(2.1\\\\\\\\mathrm{mL})$ was stirred at room temperature for $^{\\\\\\\\textrm{\\\\\\\\scriptsize 1h}}$ . $\\\\\\\\mathrm{NaBH}_3\\\\\\\\mathrm{CN}$ $(16.5\\\\\\\\mathrm{mg},0.263\\\\\\\\mathrm{mmol}$ 1.5 equiv) was the added and the mixture was stirred at room temperature overnight. The volatiles were removed under reduced pressure, and the residue was purified by preparative \\\"]\",\n \"page_idx\": \"45\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"45\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"45\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"45\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"45\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1307 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"45\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"45\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,71,479,283]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"46\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HPLC [column: XBridge Prep OBD C18 Column, $30 \\\\times 150 \\\\mathrm{~mm}^2$ , $5 \\\\mu \\\\mathrm{m}$ ; mobile phase A: water(10 mmol/L $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3$ ), mobile phase B: $\\\\mathrm{CH}_3\\\\mathrm{CN}$ ; flow rate: $60 \\\\mathrm{~mL} / \\\\mathrm{min}$ ; gradient: 52 to $69\\\\%$ B over $10 \\\\mathrm{~min}$ ; wavelength: $254 / 220 \\\\mathrm{~nm}$ ; RT: $9.3 \\\\mathrm{~min}$ ] to afford the title compound (61 mg, $33\\\\%$ ) as a pink solid. ${}^{1}\\\\mathrm{H}$ NMR (400 MHz, DMSO- $d_6$ ) $\\\\delta$ 14.15 (s, 1H), 8.99 (s, 1H), 8.44 (d, $J = 7.7 \\\\mathrm{~Hz}$ , 1H), 8.00-7.88 (m, 1H), 7.77 (d, $J = 5.9 \\\\mathrm{~Hz}$ , 1H), 7.50 (s, 1H), 7.49-7.43 (m, 2H), 7.43-7.35 (m, 2H), 7.27-7.19 (m, 1H), 6.91-6.80 (m, 2H), 6.57-6.50 (m, 1H), 6.20-6.09 (m, 2H), 5.97 (s, 2H), 5.33 (d, $J = 7.2 \\\\mathrm{~Hz}$ , 1H), 5.26-5.15 (m, 1H), 4.99-4.88 (m, 1H), 4.49 (d, $J = 4.5 \\\\mathrm{~Hz}$ , 2H), 4.35-4.25 (m, 2H), 4.25-4.15 (m, 3H), 3.80-3.65 (m, 2H), 3.58-3.48 (m, 1H), 3.31-3.18 (m, 3H), 3.02 (d, $J = 11.6 \\\\mathrm{~Hz}$ , 2H), 2.74 (d, $J = 11.1 \\\\mathrm{~Hz}$ , 2H), 2.64 (t, $J = 5.6 \\\\mathrm{~Hz}$ , 2H), 2.46 (s, 3H), 2.38-2.25 (m, 6H), 2.22-2.09 (m, 4H), 2.01-1.92 (m, 2H), 1.77 (d, $J = 12.3 \\\\mathrm{~Hz}$ , 2H), 1.69-1.60 (m, 1H), 1.47-1.37 (m, 5H), 1.01-0.91 (m, 3H), 0.82 (t, $J = 7.5 \\\\mathrm{~Hz}$ , 3H). LC-MS ( $\\\\mathrm{ES+}$ ): $m/z$ 1068 [M + H]+ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,285,479,720]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"46\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6-Phenyl-4-(8-(2-(trans-3-(piperidin-4-yloxy)cyclobutoxy)-pyridin-4-yl)-3,8-diazabicyclo[3.2.1]octan-3-yl)pyridazin-3-amine (152). A solution of intermediate 117 (200 mg, 0.340 mmol, 1.0 equiv), phenylboronic acid (83 mg, 0.680 mmol, 2.0 equiv), $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ (141 mg, 1.02 mmol, 3.0 equiv) and $\\\\mathrm{Pd(PPh_3)_4}$ (39 mg, 0.0341 mmol, 0.10 equiv) in 1,4-dioxane (5 mL) and water (0.5 mL) was stirred at $90^{\\\\circ}\\\\mathrm{C}$ for 3 h. The reaction mixture was cooled to room temperature and was diluted with EtOAc (100 mL). The resulting solution was washed with water (100 mL), and the organic layer was dried over sodium sulfate and was filtered. The filtrate was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% $\\\\mathrm{NH_4HCO_3}$ ), 0 to 80%) to afford tert-butyl 4-(trans-3-((4-(3-(3-amino-6-phenylpyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)-pyridin-2-yl)oxy)cyclobutoxy)-piperidine-1-carboxylate (130 mg, 61%) as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 8.02–7.93 (m, 2H), 7.76 (d, $J = 5.9~\\\\mathrm{Hz}$ , 1H), 7.47–7.32 (m, 3H), 7.27 (s, 1H), 6.52 (d, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 6.13 (s, 1H), 5.74 (s, 2H), 5.25–5.10 (m, 1H), 4.49 (s, 2H), 4.36–4.26 (m, 1H), 3.75–3.56 (m, 2H), 3.49–3.39 (m, 1H), 3.20 (d, $J = 11.5~\\\\mathrm{Hz}$ , 2H), 3.08–2.85 (m, 4H), 2.40–2.21 (m, 4H), 2.18 (d, $J = 7.1~\\\\mathrm{Hz}$ , 2H), 2.03–1.87 (m, 2H), 1.83–1.66 (m, 2H), 1.39 (s, 9H), 1.33–1.21 (m, 2H). LC-MS (ES+): m/z 628 [M + H]+. A solution of this material (120 mg, 0.191 mmol) in HCl (4.0 M in MeOH, 4 mL) was stirred at room temperature for 2 h. The resulting mixture was concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% NH₄HCO₃), 0 to 100%) to afford the title compound (95 mg, 94%) as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 8.02–7.92 (m, 2H), 7.76 (d, $J = 6.0~\\\\mathrm{Hz}$ , 1H), 7.50–7.31 (m, 3H), 7.27 (s, 1H), 6.52 (dd, $J = 6.1$ , 2.0 Hz, 1H), 6.13 (d, $J = 2.1~\\\\mathrm{Hz}$ , 1H), 5.74 (s, 2H), 5.26–5.13 (m, 1H), 4.48 (s, 2H), 4.33–4.24 (m, 1H), 3.45–3.33 (m, 1H), 3.20 (d, $J = 11.4~\\\\mathrm{Hz}$ , 2H), 3.04–2.90 (m, 4H), 2.66–2.54 (m, 2H), 2.37–2.23 (m, 4H), 2.22–2.13 (m, 2H), 1.99–1.92 (m, 2H), 1.86–1.77 (m, 2H), 1.46–1.30 (m, 2H). LC-MS $(\\\\mathrm{ES+})$ : m/z 528 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,720,479,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"46\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-((2R)-2-(3-(2-(4-(trans-3-((4-(3-(3-Amino-6-phenylpyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (26). A solution of intermediate 152 $(30.0\\\\mathrm{mg},0.0568\\\\mathrm{mmol}$ 1.0 equiv), intermediate 61 $(30.7\\\\mathrm{mg},0.0568\\\\mathrm{mmol}$ 1.0 equiv), and NaOAc $(14.0\\\\mathrm{mg},0.170$ mmol, 3.0 equiv) in MeOH $(3\\\\mathrm{mL})$ was stirred at room temperature for $^{\\\\textrm{\\\\scriptsize 1h}}$ . $\\\\mathrm{NaBH}_3\\\\mathrm{CN}$ $(5.3\\\\mathrm{mg},0.084\\\\mathrm{mmol}$ 1.5 equiv) was then added, and the reaction was stirred at room temperature for $^{\\\\textrm{\\\\scriptsize 1h}}$ After quenching at room temperature with water $(2\\\\mathrm{mL})$ ,the volatiles were removed under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\%$ $\\\\mathrm{NH_4HCO_3)}$ 0 to $100\\\\%$ ) to afford $33~\\\\mathrm{mg}$ of impure product. This material was further purified by preparative HPLC [column: XBridge Prep OBD C18 Column, $30\\\\times 150\\\\mathrm{mm}^2$ $5\\\\mu \\\\mathrm{m};$ mobile phase A: water $(10\\\\mathrm{mmol / L}$ $\\\\mathrm{NH_4HCO_3})$ , mobile phase B: $\\\\mathrm{CH}_3\\\\mathrm{CN}$ flow rate: 60 mL/min; gradient: 18 to $42\\\\%$ B over $10\\\\mathrm{min}$ wavelength: 254/220 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,71,914,208]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"46\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"nm; RT: $9.6\\\\mathrm{min}$ to afford the title compound $(6.7\\\\mathrm{mg},11\\\\%$ yield) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 8.97 (d, $J = 1.1~\\\\mathrm{Hz}$ 1H), 8.39 (d, $J = 7.6~\\\\mathrm{Hz}$ 1H), 8.00-7.91 (m, 2H), 7.75 (d, $J = 5.9$ Hz, 1H), 7.49-7.30 (m, 7H), 7.25 (s, 1H), 6.50 (dd, $J = 6.1$ $2.0\\\\mathrm{Hz}$ 1H), 6.15-6.05 (m, 2H), 5.71 (s, 2H), 5.25-5.11 (m, 1H), 5.08 (d, $J$ $= 3.7\\\\mathrm{Hz}$ , 1H), 4.96-4.82 (m, 1H), 4.47 (s, 2H), 4.41-4.15 (m, 5H), 3.74-3.58 (m, 2H), 3.43 (d, $J = 10.8~\\\\mathrm{Hz}$ , 1H), 3.28-3.13 (m, 3H), 2.94 (d, $J = 11.4~\\\\mathrm{Hz}$ , 2H), 2.79-2.67 (m, 2H), 2.63 (t, $J = 5.6~\\\\mathrm{Hz}$ - 2H), 2.44 (s, 3H), 2.36-2.05 (m, 9H), 2.05-1.84 (m, 3H), 1.83- 1.68 (m, 3H), 1.49-1.29 (m, 5H), 0.94 (d, $J = 6.3~\\\\mathrm{Hz}$ , 3H), 0.85- 0.71 (m, 3H). LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 1053 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,208,914,700]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"46\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4S)-1-((R)-2-(3-(4-(Dimethoxymethyl)piperidin-1-yl)-isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (153). To a solution of intermediate 127 (300 mg, 0.469 mmol, 1.0 equiv) and HOAc (56.1 mg, 0.935 mmol, 2.0 equiv) and $\\\\mathrm{PPh}_3$ (246 mg, 0.935 mmol, 2.0 equiv) in THF (2 mL) was added a solution of DIAD (189 mg, 0.935 mmol, 2.0 equiv) in THF (1 mL) at $0^{\\\\circ}\\\\mathrm{C}$ . The reaction was warmed to room temperature and was stirred at that temperature for 1 h. The volatiles were then removed under reduced pressure, and the residue was purified by silica gel chromatography (EtOAc: petroleum ether, 0:100 to 3:1) to afford (3S,SS)-1-((R)-2-(3-(4-(dimethoxymethyl)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-5-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)carbamoyl)-pyrrolidin-3-yl acetate (301 mg, 94% yield) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 8.97 (s, 1H), 8.10 (d, $J = 7.8~\\\\mathrm{Hz}$ , 1H), 7.46-7.27 (m, 4H), 6.14 (s, 1H), 5.16-5.03 (m, 1H), 5.01-4.86 (m, 1H), 4.43 (dd, $J = 9.3$ , 3.4 Hz, 1H), 4.04 (dd, $J = 10.5$ , 6.7 Hz, 1H), 3.82 (dd, $J = 11.3$ , 5.7 Hz, 1H), 3.76-3.54 (m, 4H), 3.25 (d, $J = 2.0~\\\\mathrm{Hz}$ , 6H), 2.76-2.62 (m, 2H), 2.47-2.36 (m, 4H), 2.31-2.13 (m, 1H), 2.03-1.91 (m, 1H), 1.83-1.68 (m, 4H), 1.64 (d, $J = 13.5~\\\\mathrm{Hz}$ , 2H), 1.40 (dd, $J = 10.7$ , 7.0 Hz, 3H), 1.32-1.15 (m, 2H), 0.99-0.87 (m, 3H), 0.83-0.74 (m, 3H). LC-MS $(\\\\mathrm{ES+})$ : $m/z$ 682 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . To a solution of this material (300 mg, 0.440 mmol) in MeOH (4 mL) was added $\\\\mathrm{NH}_3$ (7.0 M in MeOH, 5 mL) at room temperature. The reaction mixture was stirred at room temperature for $2.5\\\\mathrm{h}$ then was concentrated under reduced pressure. The residue was adjusted to pH 7 with aqueous $1\\\\mathrm{M}$ HCl (50 mL), and the resulting solution was extracted with EtOAc $(100~\\\\mathrm{mL} \\\\times 3)$ . The combined organic layers were dried over sodium sulfate, filtered, and the filtrate was concentrated under vacuum. The residue was purified by silica gel chromatography (MeOH:DCM, 0:100 to 4:96) to afford the title compound (195 mg, 69%) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) $\\\\delta$ 8.98 (s, 1H), 8.41 (d, $J = 7.7~\\\\mathrm{Hz}$ , 1H), 7.48-7.30 (m, 4H), 6.13 (s, 1H), 5.36-5.22 (m, 1H), 4.99-4.85 (m, 1H), 4.29 (dd, $J = 8.9$ , 5.2 Hz, 1H), 4.23-4.13 (m, 1H), 4.05 (d, $J = 6.8~\\\\mathrm{Hz}$ , 1H), 3.74-3.55(m, 4H), 3.51 (dd, $J = 10.1$ , 4.7 Hz, 1H), 3.22 (d, $J = 3.8~\\\\mathrm{Hz}$ , 6H), 2.76-2.60 (m, 2H), 2.45 (s, 3H), 2.38-2.14 (m, 2H), 1.77-1.57 (m, 4H), 1.39-1.34 (m, 3H), 1.27-1.19 (m, 2H), 0.98-0.91 (m, 3H), 0.82-0.75 (m, 3H). LC-MS $(\\\\mathrm{ES+})$ : $m/z$ 640 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,700,914,882]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"46\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4S)-1-((R)-2-(3-(4-Formylpiperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N-((S)-1-(4-(4-methylthiazol-5-yl)-phenyl)ethyl)pyrrolidine-2-carboxamide (154). A solution of intermediate 153 $(30\\\\mathrm{mg},0.0469\\\\mathrm{mmol})$ in formic acid $(0.5\\\\mathrm{mL})$ and water $(0.5\\\\mathrm{mL})$ was stirred at $60^{\\\\circ}\\\\mathrm{C}$ for $1\\\\textrm{h}$ The reaction mixture was then cooled to room temperature and was concentrated under reduced pressure to afford the crude title compound $(32\\\\mathrm{mg})$ as an off-white solid. ${}^{1}\\\\mathrm{H}$ NMR $(300\\\\mathrm{MHz}$ DMSO- $d_{6})$ 89.62s1H8.99 s,1H),8.43d $J = 7.7~\\\\mathrm{Hz}$ 1H),7.56-7.26 m4H6.17s1H), 5.30 d $J = 7.0~\\\\mathrm{Hz}$ 1H),5.00-4.87 m,1H),4.30dd $J = 8.8$ 5.2 Hz,1H),4.26-4.14 m,1H),3.76-3.62 m,2H),3.62-3.47 m, 3H),2.96-2.59 m,2H),2.46 s,3H),2.39-2.16 m,2H),2.03- 1.82 m,2H),1.76-1.58 m,2H),1.58-1.42 m,2H),1.40 d $J =$ $7.0~\\\\mathrm{Hz}$ 3H),1.04-0.88 m,3H),0.88-0.74 m,3H).LC-MS (ES +): $m / z$ 594 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[518,883,914,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"46\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4S)-1-((2R)-2-(3-(4-((4-(trans-3-((4-(3-(3-Amino-6-(2-hydroxyphenyl)pyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)methyl)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy-N((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-car \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"46\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[532,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"46\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"46\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[484,952,512,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"46\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1308 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[716,953,912,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"46\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[764,962,912,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"46\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,71,482,345]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"47\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"boxamide (27). A solution of intermediate 154 $(32\\\\mathrm{mg},0.054\\\\mathrm{mmol}$ 1.0 equiv), intermediate 119 (HCl salt, $30~\\\\mathrm{mg}$ $0.052\\\\mathrm{mmol}$ 1.0 equiv) and NaOAc $(12.0\\\\mathrm{mg}$ $0.146\\\\mathrm{mmol}$ 2.7 equiv) in DCM (0.2 mL) and MeOH $(0.6~\\\\mathrm{mL})$ was stirred at room temperature for $1\\\\textrm{h}$ $\\\\mathrm{NaBH}_3\\\\mathrm{CN}$ $(6.0\\\\mathrm{mg}$ $0.095\\\\mathrm{mmol}$ 1.7 equiv) was then added, and the reaction was stirred at room temperature overnight. The mixture was then concentrated under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN)}$ in water $(0.05\\\\%)$ $\\\\mathrm{NH_4HCO_3}$ 0 to $100\\\\%$ ) to afford the title compound $(24\\\\mathrm{mg},43\\\\%)$ as a white solid. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ DMSO- $d_{6})$ $\\\\delta$ 14.15s,1H8.99s,1H8.42d $J = 7.7~\\\\mathrm{Hz}$ 1H7.92dd $J = 8.0$ $1.6\\\\mathrm{Hz},1\\\\mathrm{H})$ 7.77d $J = 5.9~\\\\mathrm{Hz},$ 1H7.50s,1H7.48-7.42m, 2H7.42-7.32m2H7.27-7.18m1H6.90-6.80m2H 6.56-6.50m1H6.14d $J = 1.9~\\\\mathrm{Hz},$ 2H5.98s2H5.33d $J$ $= 7.2\\\\mathrm{Hz},$ 1H),5.24-5.15m1H),5.01-4.89m1H),4.49s2H) 4.29dd $J = 8.9$ $5.0~\\\\mathrm{Hz},$ 2H),4.19q $J = 5.6~\\\\mathrm{Hz},$ 1H3.77-3.56 m4H),3.52dd $J = 10.4$ $4.8~\\\\mathrm{Hz},$ 1H),3.28-3.19m3H3.01d $J = 11.6~\\\\mathrm{Hz},$ 2H),2.82-2.60m4H),2.46s3H),2.32-2.13m, 9H),2.11s,1H),2.04-1.92m4H),1.83-1.75m2H),1.75- 1.59m4H),1.49-1.35m5H),1.18-1.02m2H),0.95d $J =$ $6.6~\\\\mathrm{Hz},$ 3H),0.85-0.76m3H).LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 1122 $[\\\\mathbf{M}+$ $\\\\mathrm{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,346,482,755]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"47\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-1-((2R)-2-(3-(4-((4-(trans-3-((4-(3-(3-Amino-6-phenylpyridazin-4-yl)-3,8-diazabicyclo[3.2.1]octan-8-yl)pyridin-2-yl)oxy)cyclobutoxy)piperidin-1-yl)methyl)piperidin-1-yl)isoxazol-5-yl)-3-methylbutanoyl)-4-hydroxy- $N$ -(S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (28). A solution of intermediate 128 (40 mg, 0.067 mmol, 1.0 equiv), and intermediate 152 (57 mg, 0.108 mmol, 1.6 equiv) and NaOAc (16.5 mg, 0.201 mmol, 3.0 equiv) in DCM (0.2 mL) and MeOH (0.6 mL) was stirred at room temperature for 0.5 h. $\\\\mathrm{NaBH}_3\\\\mathrm{CN}$ (8.4 mg, 0.13 mmol, 1.9 equiv) was then added, and the reaction was stirred at room temperature for 1 h. After quenching by the addition of water (10 mL), the resulting mixture was extracted with EtOAc (20 mL × 3). The combined organic layers were dried over sodium sulfate, filtered, and the filtrate was concentrated under vacuum. The residue was purified by prepacked C18 column chromatography (CH₃CN in water (0.05% $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3$ ), 0 to 100%) to afford 32 mg of impure product as a white solid. This material was further purified by preparative HPLC [column: XSelect CSH Fluoro Phenyl $30 \\\\times 150$ mm², 5 μm; mobile phase A: water (10 mmol/L $\\\\mathrm{NH}_4\\\\mathrm{HCO}_3$ ), mobile phase B: CH₃CN; flow rate: 60 mL/min; gradient: 58 to 75% B over 11 min; wavelength: 254 nm; RT: 8.47 min] to afford the title compound (3.2 mg, 6.1% over two steps) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 8.97 (d, $J = 1.4$ Hz, 1H), 8.39 (d, $J = 7.7$ Hz, 1H), 8.00–7.91 (m, 2H), 7.74 (d, $J = 5.9$ Hz, 1H), 7.49–7.32 (m, 6H), 7.34 (s, 1H), 7.25 (s, 1H), 6.54–6.46 (m, 1H), 6.14–6.06 (m, 2H), 5.71 (s, 2H), 5.22–5.13 (m, 1H), 5.09 (d, $J = 3.7$ Hz, 1H), 4.90 (t, $J = 7.2$ Hz, 1H), 4.47 (s, 2H), 4.34 (t, $J = 7.8$ Hz, 1H), 4.27 (s, 2H), 3.69 (d, $J = 7.2$ Hz, 1H), 3.65–3.46 (m, 3H), 3.40 (d, $J = 10.6$ Hz, 1H), 3.27–3.13 (m, 3H), 2.93 (d, $J = 11.4$ Hz, 2H), 2.80–2.59 (m, 4H), 2.44 (s, 3H), 2.35–2.22 (m, 4H), 2.21–2.02 (m, 5H), 2.01–1.87 (m, 5H), 1.80–1.51 (m, 6H), 1.48–1.32 (m, 5H), 1.16–0.99(m, 2H), 0.93 (d, $J = 6.4$ Hz, 3H), 0.87–0.73 (m, 3H). LC–MS $(\\\\mathrm{ES}+)$ : m/z 1106 $[\\\\mathbf{M} + \\\\mathbf{H}]^+$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,755,482,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"47\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methyl 2-(2-(2-methoxyethoxy)ethyl)-3-oxo-2,3-dihydroisoxazol-5-yl)-3-methylbutanoate (157). A solution of racemic intermediate 40 $(500\\\\mathrm{mg},2.51\\\\mathrm{mmol},1.0$ equiv), 1-bromo-2-(2-methoxyethoxy)ethane $(459\\\\mathrm{mg},2.51\\\\mathrm{mmol},1.0$ equiv), and $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ $(1.04\\\\mathrm{g},7.53\\\\mathrm{mmol},3.0$ equiv) in DMF $(6\\\\mathrm{mL})$ was stirred at $60^{\\\\circ}\\\\mathrm{C}$ for $1\\\\textrm{h}$ The mixture was cooled to room temperature, and the solids were filtered off. The filtrate was directly purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.05\\\\% \\\\mathrm{NH_4HCO_3})$ 0 to $100\\\\%$ ) to afford the title compound $(612\\\\mathrm{mg},81\\\\%)$ as a yellow oil. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ DMSO- $d_{6})$ 6.23s1H4.29-4.23m 2H3.75-3.68m3H3.67s3H3.60-3.53m2H3.48- 3.41m2H)3.24s3H)2.37-2.23m1H)0.94d $J = 6.7~\\\\mathrm{Hz}$ 3H)0.85d $J = 6.7~\\\\mathrm{Hz}$ 3H.LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 302 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ .A small amount of the corresponding isoxazole $N$ -alkylation product (structure not shown) eluted ahead of compound 157 and was \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,71,915,135]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"47\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"isolated as a yellow oil (105 mg, 14%). ${}^{1}\\\\mathrm{H}$ NMR (400 MHz, DMSO- $d_{6}$ ) $\\\\delta$ 5.84 (s, 1H), 3.95 (t, $J = 5.4\\\\mathrm{~Hz}$ , 2H), 3.69 (s, 3H), 3.65-3.55 (m, 3H), 3.48 (dd, $J = 5.9$ , 3.7 Hz, 2H), 3.38 (dd, $J = 5.9$ , 3.6 Hz, 2H), 3.22 (s, 3H), 2.34-2.21 (m, 1H), 0.95 (d, $J = 6.7\\\\mathrm{~Hz}$ , 3H), 0.91 (d, $J = 6.8\\\\mathrm{~Hz}$ , 3H). LC-MS (ES+): $m/z$ 302 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,133,915,281]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"47\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2-(3-(2-(2-Methoxyethoxy)ethoxy)isoxazol-5-yl)-3-methylbutanoic acid (158). A solution of intermediate 157 $(300\\\\mathrm{mg},0.997$ mmol, 1.0 equiv) and LiOH $(47.7\\\\mathrm{mg},1.99\\\\mathrm{mmol},2.0$ equiv) in THF $(2.5~\\\\mathrm{mL})$ and water $(2.5~\\\\mathrm{mL})$ was stirred at room temperature for $2\\\\mathrm{h}$ The volatiles were then removed under reduced pressure, and the residue was purified by prepacked C18 column chromatography $\\\\mathrm{(CH_3CN}$ in water $(0.1\\\\%$ FA), 0 to $100\\\\%$ ) to afford the title compound $(251\\\\mathrm{mg},88\\\\%)$ as a colorless oil. ${}^{1}\\\\mathrm{H}$ NMR $(400\\\\mathrm{MHz}$ DMSO- $d_{6})$ 8 12.96s,1H)6.17s1H4.29-4.23m2H3.75- 3.69m2H)3.63-3.53m2H)3.50d $J = 8.6 \\\\mathrm{Hz}$ 1H)3.48- 3.42m2H)3.24s3H)2.34-2.21m1H)0.96d $J = 6.7 \\\\mathrm{Hz}$ 3H),0.85d $J = 6.7 \\\\mathrm{Hz}$ 3H.LC-MS $(\\\\mathrm{ES + })$ .. $m / z$ 288 $[\\\\mathbf{M} + \\\\mathbf{H}]^{+}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,281,915,712]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"47\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2S,4R)-4-Hydroxy-1-((R)-2-(3-(2-(2-methoxyethoxy)-ethoxy)isoxazol-5-yl)-3-methylbutanoyl)-N-((S)-1-(4-(4-methylthiazol-5-yl)phenyl)ethyl)pyrrolidine-2-carboxamide (155). A solution of intermediate 158 (200 mg, 0.696 mmol, 1.0 equiv), intermediate 57 (HCl salt, 256 mg, 0.695 mmol, 1.0 equiv), DIEA (449 mg, 3.48 mmol, 5.0 equiv), and HATU (397 mg, 1.04 mmol, 1.5 equiv) in DMF (5 mL) was stirred at room temperature for 1 h. The crude mixture was directly purified by prepacked C18 column chromatography (CH $_3$ CN in water (0.05% NH $_4$ HCO $_3$ ), 0 to 100%) to afford 227 mg of a ~1:1 mixture of 155 and 156. This mixture was subsequently separated by preparative chiral HPLC [column: CHIRALPAK IA, $2 \\\\times 25~\\\\mathrm{cm}^2$ , 5 μm; mobile phase A: 3:1 hexane:DCM (0.5% 2 M NH $_3$ -MeOH), mobile phase B: EtOH; flow rate: 20 mL/min; gradient: isocratic 10% B; wavelength: 220/254 nm; RT1:5.65 min; RT2:9.19 min; sample solvent: EtOH; injection volume: 1.0 mL; number of runs: 6] to afford the title compound (slower peak, 86 mg, 21%) as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 9.00 (d, J = 2.4 Hz, 1H), 8.43 (d, J = 7.6 Hz, 1H), 7.45 (d, J = 8.3 Hz, 2H), 7.37 (d, J = 8.3 Hz, 2H), 6.11 (s, 1H), 5.10 (d, J = 3.7 Hz, 1H), 5.06–4.86 (m, 1H), 4.38 (t, J = 7.9 Hz, 1H), 4.32–4.19 (m, 3H), 3.76–3.61 (m, 4H), 3.57 (dd, J = 5.9, 3.5 Hz, 2H), 3.49–3.40 (m, 3H), 3.25 (s, 3H), 2.47 (d, J = 1.6 Hz, 3H), 2.27–2.16 (m, 1H), 2.09–1.88 (m, 1H), 1.85–1.70 (m, 1H), 1.50–1.31 (m, 3H), 0.96 (d, J = 6.3 Hz, 3H), 0.80 (d, J = 6.7 Hz, 3H). LC-MS (ES+): m/z 601 [M + H]+. The configuration of the isopropyl group was assigned based on the crystal structure shown in Figure S15. Compound 156 (faster peak, 52 mg, 13%) was also isolated as a white solid. ${}^{1}\\\\mathrm{H}$ NMR (300 MHz, DMSO- $d_6$ ) δ 9.03–8.88 (m, 1H), 8.33 (d, J = 7.8 Hz, 1H), 7.47–7.26 (m, 4H), 6.13 (d, J = 15.8 Hz, 1H), 5.11 (d, J = 3.6 Hz, 1H), 5.07–4.85 (m, 1H), 4.55–4.37 (m, 1H), 4.30–4.18 (m, 3H), 3.76 (d, J = 8.7 Hz, 1H), 3.72–3.64 (m, 2H), 3.60–3.38 (m, 6H), 3.23 (d, J = 5.0 Hz, 3H), 2.47 (d, J = 3.4 Hz, 3H), 2.35–2.20 (m, 1H), 2.19–1.97 (m, 1H), 1.97–1.70 (m, 1H), 1.46 (d, J = 6.9 Hz, 1H), 1.36 (d, J = 7.0 Hz, 2H), 1.00–0.69 (m, 6H). LC-MS (ES+): m/z 601 [M + H]+.\\\\n\\\\n \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,723,721,737]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"47\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ASSOCIATED CONTENT \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,741,708,755]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"47\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Supporting Information \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,756,915,785]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"47\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jmedchem.3c01781. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[551,788,915,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"47\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"BRM/BRG1 and VHL Alpha-LISA binding assay details, determination of BRM-10 crystal structure, cell-based assay descriptions, in vitro and in vivo DMPK assay protocols, SPR assay details, crystal structure determination of BRG1-VBC-17 ternary complex, descriptions of in vivo PK/PD and efficacy experiments, BRM $\\\\mathrm{DC}_{50}$ and $D_{\\\\mathrm{max}}$ values of more and less potent PROTAC diastereomers (separated via chiral methods), VHL crystal structure of compound 155, depictions of ${}^{1}\\\\mathrm{H}$ NMR and LC-MS characterization data for new compounds listed in Table 2 (PDF) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"47\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": 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\"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1309 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"47\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"47\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[118,75,481,103]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Molecular formula strings for new compounds listed in Table 2 (CSV) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,125,293,140]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"AUTHOR INFORMATION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,145,245,160]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Corresponding Authors \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[98,161,471,257]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Michael Berlin - Arvinas LLC, New Haven, Connecticut 06511, United States; Phone: 203-535-1456; Email: michael.berlin@arvinas.com \\\",\\\"Peter S. Dragovich - Genentech Inc., South San Francisco, California 94080, United States; $\\\\\\\\odot$ orcid.org/0000-0001-7372-2862; Phone: 650-467-6854; Email: dragovich.peter@gene.com \\\"]\",\n \"page_idx\": \"48\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[80,266,138,280]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Authors \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[98,282,479,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Jennifer Cantley - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Mark Bookbinder - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Elizabeth Bortolon - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Fabio Broccatelli - Genentech Inc., South San Francisco, California 94080, United States \\\",\\\"Greg Cadelina - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Emily W. Chan - Genentech Inc., South San Francisco, California 94080, United States \\\",\\\"Huifen Chen - Genentech Inc., South San Francisco, California 94080, United States; $\\\\\\\\odot$ orcid.org/0000-0001-8273-9295 \\\",\\\"Xin Chen - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Yunxing Cheng - Pharmaron Beijing, Co. Ltd., Beijing 100176, P. R. China \\\",\\\"Tommy K. Cheung - Genentech Inc., South San Francisco, California 94080, United States \\\",\\\"Kim Davenport - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Dean DiNicola - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Debbie Gordon - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Brian D. Hamman - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Alicia Harbin - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Roy Haskell - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Mingtao He - Pharmaron Beijing, Co. Ltd., Beijing 100176, P.R.China \\\",\\\"Alison J. Hole - Evotec (U.K.) Ltd., Abingdon, Oxfordshire OX14 4RY, U.K. \\\",\\\"Thomas Januario - Genentech Inc., South San Francisco, California 94080, United States \\\",\\\"Philip S. Kerry - Evotec (U.K.) Ltd., Abingdon, Oxfordshire OX14 4RY, U.K. \\\",\\\"Stefan G. Koenig - Genentech Inc., South San Francisco, California 94080, United States; orcid.org/0000-0002-1878-614X \\\",\\\"Limei Li - Pharmaron Beijing, Co. Ltd., Beijing 100176, P. R. China \\\",\\\"Mark Merchant - Genentech Inc., South San Francisco, California 94080, United States \\\"]\",\n \"page_idx\": \"48\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[532,71,914,525]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Inmaculada Pérez-Dorado - Evotec (U.K.) Ltd., Abingdon, Oxfordshire OX14 4RY, U.K. \\\",\\\"Jennifer Pizzano - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Connor Quinn - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Christopher M. Rose - Genentech Inc., South San Francisco, California 94080, United States; $\\\\\\\\text{©}$ orcid.org/0000-0002-7502-3368 \\\",\\\"Emma Rousseau - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Leofal Soto - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Leanna R. Staben - Genentech Inc., South San Francisco, California 94080, United States \\\",\\\"Hongming Sun - Pharmaron Beijing, Co. Ltd., Beijing 100176, P. R. China \\\",\\\"Qingping Tian - Genentech Inc., South San Francisco, California 94080, United States \\\",\\\"Jing Wang - Arvinas LLC, New Haven, Connecticut 06511, United States \\\",\\\"Weifeng Wang - Pharmaron Beijing, Co. Ltd., Beijing 100176, P. R. China \\\",\\\"Crystal S. Ye - Genentech Inc., South San Francisco, California 94080, United States \\\",\\\"Xiaofen Ye - Genentech Inc., South San Francisco, California 94080, United States \\\",\\\"Penghong Zhang - Pharmaron Beijing, Co. Ltd., Beijing 100176, P. R. China \\\",\\\"Yuhui Zhou - Genentech Inc., South San Francisco, California 94080, United States \\\",\\\"Robert Yauch - Genentech Inc., South San Francisco, California 94080, United States \\\"]\",\n \"page_idx\": \"48\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[514,530,856,560]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Complete contact information is available at: https://pubs.acs.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,571,558,583]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Notes \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,586,853,600]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The authors declare no competing financial interest. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,613,711,627]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ACKNOWLEDGMENTS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,633,915,703]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The authors acknowledge the use of the Diamond Light Source and the Swiss Light Source for structural data collection and thank the staff for their support. They also thank Drs. James Kiefer and Yoana Dimitrova for many helpful discussions regarding the manuscript. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,715,716,730]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABBREVIATIONS USED \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,735,915,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"AcOH, acetic acid; Alpha-LISA, amplified luminescent proximity homogeneous assay-linked immunosorbent assay; Boc, tert-butyloxycarbonyl; BRM, Brahma homologue; BRG1, Brahma-related gene 1; Cbz, benzyloxycarbonyl; DCM, dichloromethane; DIAD, diisopropyl azodicarboxylate; DIEA, N,N-diisopropylethylamine; DMA, N,N-dimethylacetamide; DMAP, 4-dimethylaminopyridine; DME, dimethoxyethane; DMF, N,N-dimethylformamide; DMSO, dimethyl sulfoxide; EEDQ, N-ethoxycarbonyl-2-ethoxy-1,2-dihydroquinoline; EtOAc, ethyl acetate; EtOH, ethanol; FA, formic acid; HATU, 1-[bis(dimethylamino)methylene]-1H-1,2,3-triazolo[4,5-b]pyridinium 3-oxide hexafluorophosphate; HP-beta-CD, 2-hydroxypropyl- $\\\\beta$ -cyclodextrin; HPLC, high-performance liquid chromatography; IP, intraperitoneal; IV, intravenous; LC-MS, liquid chromatography-mass spectrometry; LDA, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,46,311,61]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Medicinal Chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[530,48,632,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pubs.acs.org/jmc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[864,48,904,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[482,952,512,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1310 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,952,914,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1021/acs.jmedchem.3c01781 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[762,962,914,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"48\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Med.Chem.2024,67,1262-1313 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[77,71,482,293]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"49\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"lithium diisopropylamide; MeOH, methanol; MOM, methoxymethyl; MTBE, methyl tert-butyl ether; NMP, $N$ -methyl-2-pyrrolidone; PEG, polyethylene glycol; PK/PD, pharmacokinetic-pharmacodynamic; PROTAC, proteolysis targeting chimera (PROTAC is a registered trademark of Arvinas Operations, Inc.); rt, room temperature; SFC, supercritical fluid chromatography; SMARCA2, SWI/SNF-related, matrix-associated, actin-dependent regulator of chromatin subfamily A member 2; SMARCA4, SWI/SNF-related, matrix-associated, actin-dependent regulator of chromatin subfamily A member 4; SPR, surface plasmon resonance; T3P, propanephosphonic acid anhydride; TEA, triethylamine; TEMPO, 2,2,6,6-tetramethylpiperidine-1-oxyl radical; TFA, trifluoroacetic acid; THF, tetrahydrofuran; TLC, thin-layer chromatography; VBC, VHL, elongin B, and elongin C complex; VHL, Von Hippel-Lindau tumor suppressor \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,307,207,322]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"49\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"REFERENCES \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,327,481,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(1) Wanior, M.; Kramer, A.; Knapp, S.; Joerger, A. C. Exploiting vulnerabilities of SWI/SNF chromatin remodelling complexes for cancer therapy. Oncogene 2021, 40, 3637-3654. \\\",\\\"(2) St. Pierre, R.; Kadoch, C. Mammalian SWI/SNF complexes in cancer: emerging therapeutic opportunities. Curr. Opin. Genet. Dev. 2017, 42, 56-67. \\\",\\\"(3) Mashtalir, N.; Dao, H. T.; Sankar, A.; Liu, H.; Corin, A. J.; Bagert, J. D.; Ge, E. J.; D'Avino, A. R.; Filipovski, M.; Michel, B. C.; Dann, G. P.; Muir, T. W.; Kadoch, C. Chromatin landscape signals differentially dictate the activities of mSWI/SNF family complexes. Science 2021, 373, 306-315. \\\",\\\"(4) Sahu, R. K.; Singh, S.; Tomar, R. S. The mechanisms of action of chromatin remodelers and implications in development and disease. Biochem. Pharmacol. 2020, 180, 114200. \\\",\\\"(5) Jancewicz, I.; Siedlecki, J. A.; Sarnowski, T. J.; Sarnowska, E. BRM: the core ATPase subunit of SWI/SNF chromatin-remodelling complex - a tumour suppressor or tumour-promoting factor? Epigenetics Chromatin 2019, 12, 68. \\\",\\\"(6) Schick, S.; Rendeiro, A. F.; Runggatscher, K.; Ringler, A.; Boidol, B.; Hinkel, M.; Majek, P.; Vulliard, L.; Penz, T.; Parapatics, K.; Schmidl, C.; Menche, J.; Boehmelt, G.; Petronczki, M.; Müller, A. C.; Bock, C.; Kubicek, S. Systematic characterization of BAF mutations provides insights into intracomplex synthetic lethalities in human cancers. Nat. Genet. 2019, 51, 1399-1410. \\\",\\\"(7) Hoffman, G. R.; Rahal, R.; Buxton, F.; Xiang, K.; McAllister, G.; Frias, E.; Bagdasarian, L.; Huber, J.; Lindeman, A.; Chen, D.; Romero, R.; Ramadan, N.; Phadke, T.; Haas, K.; Jaskelioff, M.; Wilson, B. G.; Meyer, M. J.; Saenz-Vash, V.; Zhai, H.; Myer, V. E.; Porter, J. A.; Keen, N.; McLaughlin, M. E.; Mickanin, C.; Roberts, C. W. M.; Stegmeier, F.; Jagani, Z. Functional epigenetics approach identifies BRM/SMARCA2 as a critical synthetic lethal target in BRG1-deficient cancers. Proc. Natl. Acad. Sci. 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S.; Schramm, M.; Becher, I.; Steidel, M.; Noh, K.-M.; Bergamini, G.; Beck, M.; Bantscheff, M.; Savitski, M. M. Systematic analysis of protein turnover in primary cells. Nat. Commun. 2018, 9, 689. \\\",\\\"(51) Dragovich, P. S.; Pillow, T. H.; Blake, R. A.; Sadowsky, J. D.; Adaligil, E.; Adhikari, P.; Bhakta, S.; Blaquiere, N.; Chen, J.; dela Cruz-Chuh, J.; Gascoigne, K. E.; Hartman, S. J.; He, M.; Kaufman, S.; Kleinheinz, T.; Kozak, K. R.; Liu, L.; Liu, L.; Liu, Q.; Lu, Y.; Meng, F.; Mulvihill, M. M.; O'Donohue, A.; Rowntree, R. K.; Staben, L. R.; Staben, S. T.; Wai, J.; Wang, J.; Wei, B.; Wilson, C.; Xin, J.; Xu, Z.; Yao, H.; Zhang, D.; Zhang, H.; Zhou, H.; Zhu, X. Antibody-mediated delivery of chimeric BRD4 degraders. Part 1: Exploration of antibody linker, payload loading, and payload molecular properties. J. Med. Chem. 2021, 64, 2534-2575. \\\",\\\"(52) Roy, M.; Winkler, S.; Hughes, S. J.; Whitworth, C.; Galant, M.; Farnaby, W.; Rumpel, K.; Ciulli, A. 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ACS Chem. Biol. 2019, 14, 361-368. \\\",\\\"(53) Rago, F.; DiMare, M. T.; Elliott, G.; Ruddy, D. A.; Sovath, S.; Kerr, G.; Bhang, H.-e. C.; Jagani, Z. Degron mediated BRM/SMARCA2 depletion uncovers novel combination partners for treatment of BRG1/SMARCA4-mutant cancers. Biochem. Biophys. Res. Commun. 2019, 508, 109-116. \\\",\\\"(54) Wang, X.-R.; Wang, S.; Mu, H.-X.; Xu, K.-Y.; Wang, X.-T.; Shi, J.-T.; Cui, Q.-H.; Zhang, L.-W.; Chen, S.-W. Discovery of novel VEGFR-2-PROTAC degraders based on the localization of lysine residues via recruiting VHL for the treatment of gastric cancer. Eur. J. Med. Chem. 2022, 244, 114821. \\\",\\\"(55) Wang, C.; Zheng, C.; Wang, H.; Shui, S.; Jin, H.; Liu, G.; Xu, F.; Liu, Z.; Zhang, L.; Sun, D.; Xu, P. Dual degradation mechanism of GPX4 degrader in induction of ferroptosis exerting anti-resistant tumor effect. Eur. J. Med. Chem. 2023, 247, 115072. \\\",\\\"(56) de Nooy, A. E. J.; Besemer, A. C.; van Bekkum, H. On the use of stable organic nitroxyl radicals for the oxidation of primary and seconday alcohols. Synthesis 1996, 1153-1174. \\\",\\\"(57) Ruiz-Castillo, P.; Buchwald, S. L. Applications of palladium-catalyzed C-N cross-coupling reactions. Chem. Rev. 2016, 116, 12564-12649. \\\",\\\"(58) Miyaura, N.; Suzuki, A. Palladium-catalyzed cross-coupling reactions of organoboron compounds. Chem. Rev. 1995, 95, 2457-2483. \\\",\\\"(59) Franck, D.; Kniess, T.; Steinbach, J.; Zitzmann-Kolbe, S.; Friebe, M.; Dinkelborg, L. M.; Graham, K. Investigations into the synthesis, radiofluorination and conjugation of a new $\\\\\\\\left[{ }^{18} \\\\\\\\mathrm{~F}\\\\\\\\right]$ -fluorocyclobutyl prosthetic group and its in vitro stability using a tyrosine model system. Bioorg. Med. Chem. 2013, 21, 643-652. \\\",\\\"(60) Swamy, K. C. K.; Kumar, N. N. B.; Balaraman, E.; Kumar, K. V. P. P. Mitsunobu and related reactions: Advances and applications. Chem. 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Azevedo, Guilherme|Barros, Nathan|Mendonça, Raquel|Sobek, Sebastian"},"content_list":{"kind":"list like","value":[{"bbox":"[68,174,898,218]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Comparing methane ebullition variability across space and time in a Brazilian reservoir ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,232,916,268]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Annika Linkhorst $^{1*}$ Carolin Hiller, $^{1,\\dagger}$ Tonya DelSontro $^{2}$ Guilherme M. Azevedo, $^{3}$ Nathan Barros, $^{3}$ Raquel Mendonça, $^{3}$ Sebastian Sobek $^{1}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,269,898,325]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"$^{1}$ Limnology, Department of Ecology and Genetics, Uppsala University, Uppsala, Sweden \",\"$^{2}$ Aquatic Physics Group, Faculty of Science, Department F.-A. Forel for Environmental and Aquatic Sciences, University of Geneva, Geneva, Switzerland \",\"$^{3}$ Department of Biology, Institute of Biological Sciences, Federal University of Juiz de Fora, Juiz de Fora, Brazil \"]","page_idx":"0","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[129,335,200,350]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[125,355,897,583]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The potent greenhouse gas methane $\\left(\\mathrm{CH}_4\\right)$ is readily emitted from tropical reservoirs, often via ebullition (bubbles). This highly stochastic emission pathway varies in space and time, however, hampering efforts to accurately assess total $\\mathrm{CH}_4$ emissions from water bodies. We systematically studied both the spatial and temporal scales of ebullition variability in a river inflow bay of a tropical Brazilian reservoir. We conducted multiple highly resolved spatial surveys of $\\mathrm{CH}_4$ ebullition using a hydroacoustic approach supplemented with bubble traps over a 12-month and a 2-week timescale to evaluate which scale of variation was more important. To quantify the spatial and temporal variability of $\\mathrm{CH}_4$ ebullition, we used the quartile coefficients of dispersion at each point in space and time and compared their frequency distributions across the various temporal and spatial scales. We found that $\\mathrm{CH}_4$ ebullition varied more temporally than spatially and that the intra-annual variability was stronger than daily variability within 2 weeks. We also found that $\\mathrm{CH}_4$ ebullition was positively related to water temperature increase and pressure decrease, but no consistent relationship with water column depth or sediment characteristics was found, further highlighting that temporal drivers of emissions were stronger than spatial drivers. Annual estimates of $\\mathrm{CH}_4$ ebullition from our study area may vary by $75 - 174\\%$ if ebullition is not resolved in time and space, but at a minimum we recommend conducting spatially resolved measurements at least once during each major hydrologic season in tropical regions (i.e., in dry and rainy season when water levels are falling and rising, respectively). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,608,501,779]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Inland waters have been recognized as relevant carbon sources to the atmosphere (Cole et al. 2007; Tranvik et al. 2009; DelSontro et al. 2018; Drake et al. 2018) and integrated into the greenhouse gas budget of the Intergovernmental Panel on Climate Change (IPCC 2013) report. It has been suggested that the impoundment of rivers may increase emission due to flooding of terrestrial organic matter, and additionally through accumulation of sediment containing degradable organic material (St. Louis et al. 2000; Prairie et al. 2018). Tropical reservoirs, in particular, have been indicated as strong sources of the powerful greenhouse gas methane $\\mathrm{(CH_4}$ ; Barros et al. 2011) because these warmer ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[521,608,955,851]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"regions of the earth are rich in biomass (St. Louis et al. 2000). As greenhouse gas emission from reservoirs can be highly variable across space and time (Abril et al. 2005; DelSontro et al. 2011; Maeck et al. 2013; Maeck et al. 2014; Musenze et al. 2014; Paranaíba et al. 2018), it is difficult to upscale from single measurements at discrete sampling occasions or locations to a whole-system flux estimate. Ebullition (bubbling), often, although not always, the dominant $\\mathrm{CH}_4$ emission pathway from reservoirs (Deemer et al. 2016), has been described as stochastic with high variability in space and time (DelSontro et al. 2011, 2015) and is especially difficult to representatively measure for system-wide estimates. Consequently, ebullition has often been excluded from $\\mathrm{CH}_4$ emission studies (Deemer et al. 2016) not only leading to underestimation of $\\mathrm{CH}_4$ emissions from reservoirs, but also to a substantial lack of knowledge regarding the spatiotemporal variability of $\\mathrm{CH}_4$ ebullition in reservoirs. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[521,851,955,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Previous studies have shown that lake or reservoir $\\mathrm{CH}_4$ ebullition can peak at certain points in space (\"hot spots\") or time (\"hot moments\"). Hot spots were predominantly found in shallow areas (Ostrovsky 2003; Grinham et al. 2011; Zheng et al. 2011; Deshmukh et al. 2014; Natchimuthu et al. 2016; ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[911,8,991,69]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Check for updates ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[70,79,352,145]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"LIMNOLOGY and OCEANOGRAPHY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[792,78,954,120]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ASLO ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[790,126,954,136]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Limnol.Oceanogr.9999,2020,1-12 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[550,135,954,144]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"© 2020 The Authors. Limnology and Oceanography published by Wiley Periodicals, Inc. on ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[624,144,954,153]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"behalf of Association for the Sciences of Limnology and Oceanography. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[843,153,954,162]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"doi:10.1002/lno.11410 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[68,801,321,813]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"*Correspondence: liannika@alumni.ethz.ch ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[68,822,501,860]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[68,869,501,894]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Additional Supporting Information may be found in the online version of this article. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[68,902,500,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"†Present address: Department of Hydrology, Bayreuth Center of Ecology and Environmental Sciences, University of Bayreuth, Bayreuth, Germany ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[508,946,517,956]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[44,110,470,502]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"de Mello et al. 2018), in areas close to tributary river inflows (DelSontro et al. 2011; Zhao et al. 2013; Musenze et al. 2014; Beaulieu et al. 2016; Descloux et al. 2017; Harrison et al. 2017; Tušer et al. 2017; de Mello et al. 2018; Hilgert et al. 2019), and in areas with high sediment accumulation (Sobek et al. 2012; Maeck et al. 2013; Hilgert et al. 2019), high organic carbon content (Grinham et al. 2018; Hilgert et al. 2019), or high organic matter reactivity (Sobek et al. 2012). Hot moments of ebullition tend to correlate positively with air temperature (Delsontro et al. 2010; Maeck et al. 2013; Wik et al. 2013; Peixoto et al. 2015; Wilkinson et al. 2015; Natchimuthu et al. 2016), bottom water temperature (Deshmukh et al. 2014), sediment temperature (Tušer et al. 2017), low hydrostatic pressure (Ostrovsky 2003; Varadharajan and Hemond 2012; Wik et al. 2013; Deshmukh et al. 2014; Harrison et al. 2017; Grinham et al. 2018), and low air pressure (Mattson and Likens 1990; Deshmukh et al. 2014; Grinham et al. 2018; Marcon et al. 2019). Interestingly, some authors have mentioned a shift in spatial variability of $\\mathrm{CH}_4$ ebullition over time. For example, high-flux zones can shift seasonally from shallower to deeper regions in subarctic lakes (Wik et al. 2013) or temperate reservoirs (Tušer et al. 2017), presumably as a result of seasonal changes in sediment temperature (Tušer et al. 2017). Similarly, it has also been suggested that $\\mathrm{CH}_4$ emission from shallower lakes responds stronger to temperature than that from deeper lakes (Natchimuthu et al. 2016). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[44,505,470,836]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"While there are a number of studies that measured $\\mathrm{CH}_4$ ebullition in reservoirs at low latitudes, both in the tropics (Keller and Stallard 1994; Abril et al. 2005; Ramos et al. 2006; DelSontro et al. 2011; de Mello et al. 2018) and subtropics (Grinham et al. 2011; Deshmukh et al. 2014; Beaulieu et al. 2016; Guérin et al. 2016; Grinham et al. 2018; Yang et al. 2018; Hilgert et al. 2019; Marcon et al. 2019), only a few of them (Keller and Stallard 1994; Deshmukh et al. 2014; Yang et al. 2018; Marcon et al. 2019) have studied temporal trends of ebullition in enough detail to identify seasonal trends. None of these studies have systematically compared the magnitude of the variability of $\\mathrm{CH}_4$ ebullition over scales of both space and time. Furthermore, very few studies have measured ebullitive emission from reservoirs at a high spatial resolution using an echosounder (Delsontro et al. 2010; DelSontro et al. 2011; Maeck et al. 2013; Maeck and Lorke 2014; Tušer et al. 2017), and only one of those studies was on a tropical reservoir (DelSontro et al. 2011). Hence, our understanding of $\\mathrm{CH}_4$ ebullition in low-latitude reservoirs is limited by a lack of quantitative information on its spatiotemporal variability, despite indications that $\\mathrm{CH}_4$ emissions from reservoirs of these regions are some of the highest worldwide (St. Louis et al. 2000; Barros et al. 2011; Deemer et al. 2016). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[44,837,470,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Here, we present results from a large bay with a river inflow in the oligotrophic water supply reservoir Chapéu d'Uvas (CDU) in the Atlantic Forest biome of Southeastern Brazil, situated at the threshold of the tropical and subtropical climate zone. We performed measurements of $\\mathrm{CH}_4$ ebullition at high spatial resolution using a hydroacoustic echosounder and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,110,924,291]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bubble traps at (1) an intra-annual scale, with one survey per month over 1 year and (2) an intra-monthly scale with one survey every 2–3 d over 3 weeks (2 weeks with hydroacoustics). We also include results from (3) a diel study with continuous measurements at 3-h time intervals over $24\\mathrm{h}$ (A. Linkhorst et al., unpubl.). For further understanding of variability, we studied the drivers of $\\mathrm{CH}_4$ ebullition at each timescale. Thus, we quantify the magnitude and variability of $\\mathrm{CH}_4$ ebullition over different timescales (from diel to seasonal) at a high spatial resolution along with its main drivers in a low-latitude reservoir. The overall aim was to determine the best way to representatively measure $\\mathrm{CH}_4$ ebullition with minimum sampling effort. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,313,566,327]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[496,334,727,348]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sampling site and general setup ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[496,350,924,589]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The studied bay of CDU reservoir in Brazil (see Table S1 for its characteristics) is roughly $2\\mathrm{km}$ long, with an area of $0.326\\mathrm{km}^2$ and a maximum depth of $15\\mathrm{m}$ , and it is characterized by a river inflow in its northern end with a catchment area of $20\\mathrm{km}^2$ covered by grass land and forest patches. We measured $\\mathrm{CH}_4$ ebullition with high spatial resolution using bubble traps and a hydroacoustic echosounder at three temporal scales: once a month between August 2015 and August 2016 (intra-annual scale), every 2–3 d over a period of $22\\mathrm{d}$ in November to December 2016 (intra-monthly scale), and continuously over $24\\mathrm{h}$ with the data binned in 3-h intervals on 09–10 May 2016 (diel study; A. Linkhorst et al., unpubl.). We also measured $\\mathrm{CH}_4$ concentrations in sediment pore water before and after the intra-monthly study on 18 November 2016 and 16 December 2016, and further analyzed sediment and preflooding soil properties from cores taken on 29 March 2018. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,611,602,624]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\mathrm{CH}_4$ ebullition ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[496,626,924,881]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We measured $\\mathrm{CH}_4$ ebullition using bubble traps combined with a spatial hydroacoustic echosounder survey at each sampling occasion. For the intra-annual scale, we covered the whole bay, and for the intra-monthly scale, we covered only the northern part of the bay closest to the river inflow, which was expected to be a hot spot of $\\mathrm{CH}_4$ ebullition (DelSontro et al. 2011; Maeck et al. 2013). The sampling scheme is illustrated in Fig. S1. For the intra-annual scale, we sampled on 18 August 2016, 19 September 2016, 24 October 2016, 09 March 2017, 31 March 2017, 21 April 2017, 25 May 2017, 03 July 2017, and 03 August 2017. For the intra-monthly scale, we sampled on 25 November 2016, 28 November 2016, 30 November 2016, 02 December 2016, 05 December 2016, 07 December 2016, 09 December 2016, 12 December 2016, 14 December 2016, and 16 December 2016. November is often the beginning of the rainy season, which was expected to result in changes of system properties and potentially ebullition fluxes. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,884,924,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For hydroacoustic measurements, we used a Simrad EY60 portable scientific echosounder (Kongsberg Maritime AC, Norway) with a $120\\mathrm{-kHz}$ split-beam transducer (downward facing, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[42,68,140,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Linkhorst et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[691,68,926,81]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$CH_4$ ebullition across space and time ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[478,946,488,956]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[73,108,500,411]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$7^{\\circ}$ beam angle, ping rate: $5\\mathrm{~s}^{-1}$ ) mounted downward facing to our boat while traversing across and along the bay (Fig. S1b,c). Hydroacoustic data were analyzed with Sonar5 Pro (Lindem Acquisition, Norway), which enables distinction between bubbles and fish/plankton based on their travel path, velocity and signal intensity (Ostrovsky et al. 2008; DelSontro et al. 2011). Each hydroacoustic file was divided into segments of $300 \\pm 5$ pings, which equates to distances of $\\sim 24\\mathrm{~m}$ for the intra-annual scale and $\\sim 10\\mathrm{~m}$ for the intra-monthly scale. Bubble density was determined per water volume covered by the echosounder beam and converted into bubble gas flux following DelSontro et al. (2011, 2015) and accounting for bubble dissolution during rise using the model described in McGinnis et al. (2006), assuming an average $\\mathrm{CH}_4$ content of $70\\%$ in the bubbles (discussed in Text S1). We used only the $3\\mathrm{~m}$ closest to the sediment for further data analysis and excluded any hydroacoustic measurement in the near-field zone of the transducer ( $\\sim 1.5\\mathrm{~m}$ ). During the intramonthly study, echosounder measurements were conducted only over $15\\mathrm{~d}$ of the 22-day study period (02-16 December 2016) due to an instrument failure. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[73,413,500,806]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For the ebullition measurements with the bubble traps, we used custom-built conical plastic frames (50 cm in diameter, 43 cm tall) covered with impermeable tarp and equipped with 220-mL glass bottles screwed into threads at the narrow ends of the funnels. For the intra-annual scale, we distributed four to seven bubble traps along the northern part of the bay. For the intra-monthly scale, we distributed 14 bubble traps along a longitudinal transect in the northern part of the bay, alternatingly close to the shore and in the middle (Fig. S1b,c). Each bubble trap was attached to a buoy in 1.5-m distance, which was anchored, so that it could move around the buoy in a radius of $1.5\\mathrm{m}$ . The bubble traps were completely submerged in water, and the bottles were filled with water and screwed on top of the traps at the beginning of each trap deployment. Gas in the glass bottles was sampled after 3-5 h with a syringe, and $\\mathrm{CH}_4$ concentrations were determined by injection into an ultraportable greenhouse gas analyzer (UGGA, Los Gatos Research) within the same day (see Paranaíba et al. 2018, for details on manual gas injection of discrete samples into the UGGA). We injected 3-7 mL as we found that at our concentrations, we need at least 3 mL of gas for robust $\\mathrm{CH}_4$ concentration measurements. The volume of the captured gas was determined by measuring the water volume in the glass bottle after deployment and subtracting this volume from its maximum capacity of $220\\pm 2\\mathrm{mL}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[73,808,500,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Hydroacoustic measurements can cover space but are limited in temporal coverage. Bubble traps are fixed in space and cover a very small area, but integrate over the duration of deployment. In shallow water depths $(0 - 3\\mathrm{m})$ , hydroacoustics cannot be used at all, whereas bubble traps as ours $(50~\\mathrm{cm}$ height) can be deployed at depths of less than $1\\textrm{m}$ . Therefore, the results gained from these two methods cannot be directly compared to each other. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[527,108,952,260]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The data sets for the intra-annual scale and the intramonthly scale are presented as independent data sets, as the methodological approach slightly differed; whereas we covered the whole bay with hydroacoustic surveys for the intra-annual scale, we covered only the northern part of the bay for the intra-monthly scale. Although at both intra-annual and intra-monthly study we had bubble traps distributed only in the northern part of the bay, they were differently distributed, and twice as abundant for the intra-monthly than for the intra-annual study. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[527,277,929,291]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sediment properties and $\\mathrm{CH_4}$ pore-water concentrations ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[527,293,952,532]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sediment cores for determination of sediment characteristics were taken using a UWITEC gravity corer equipped with a hammer device on 29 March 2018, directly at the spots where bubble traps had been deployed during the intra-monthly sampling (Fig. S1c). Each core was separated into post-flooding sediment and pre-flooding soil by visual distinction in color and texture, and each of the layers was homogenized separately. We analyzed each homogenized layer of each core for grain size distribution, total organic carbon (TOC) content and total nitrogen (TN) content (methods are described in Text S2), and calculated the molar carbon to nitrogen $(\\mathrm{C / N})$ ratio. Sediment cores for $\\mathrm{CH_4}$ pore-water content were taken at spots as illustrated in Fig. S1c once before and once after the intramonthly sampling, on 18 November 2016 and 16 December 2016. $\\mathrm{CH_4}$ concentrations were analyzed for each $2\\mathrm{-cm}$ layer down each of the cores, as further described in Text S3. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[527,550,705,563]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Environmental variables ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[527,565,952,867]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A 24-h average of air temperature and barometric pressure was taken from the nearest weather station in Juiz de Fora (INMET, Brazilian National Institute of Meteorology) for each sampling day. During each survey, we measured water temperature (YSI 6600 V2 for intra-annual scale; HOBO Water Temperature Pro v2 for intra-monthly scale) every $1\\mathrm{m}$ depth in the water column at one location with a mean depth of $\\sim 12\\mathrm{m}$ $(10 - 17\\mathrm{m})$ for the intra-annual scale and $\\sim 8\\mathrm{m}$ $(7.7 - 8.7\\mathrm{m})$ for the intra-monthly scale (see Fig. S1b,c for the profile locations). Temperature depth profiles were assumed to apply to the entire bay area. The range in maximum depth at the locations for the water temperature profiles varied mostly with variations in water level, but also because of minor variations in location of the profile. Total pressure change at the sediment-water interface per sampling day was calculated from the difference in water level (measured daily and provided by the dam operator CESAMA) between the previous day and the actual sampling day, where we assumed a pressure of $100\\mathrm{mbar}$ per $1\\mathrm{m}$ water column height, plus the difference in atmospheric pressure (as averaged over $24\\mathrm{h}$ ) between the previous day and the actual sampling day. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[527,869,952,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Bathymetry was extracted from the data points of all hydroacoustic surveys, which yielded a total number of 3869 depth measurements, where each depth measure represents an area of about $7 - 17\\mathrm{m}^2$ (segments of 10 and $24\\mathrm{m}$ for intra-annual ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[71,68,169,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Linkhorst et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[720,68,954,81]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$CH_4$ ebullition across space and time ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[508,946,517,956]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[39,108,470,170]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and intra-monthly study, respectively, multiplied by a mean beam width of $0.7\\mathrm{m}$ at a mean depth of $6\\mathrm{m}$ ). The total coverage for the bathymetry and hydroacoustic flux measurements is shown in Fig. S2. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[40,189,233,203]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Calculations and statistics ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[39,205,473,356]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The $\\mathrm{CH}_4$ ebullition from each hydroacoustic survey was interpolated with Inverse Distance Weighting (ArcGIS version 10.6.1) across the whole bay for the intra-annual scale, and across the northern part of the bay for the intra-monthly scale. It was then gridded to cells of $0.0006^{\\circ} \\times 0.0006^{\\circ}$ (decimal degrees, dd; see Text S4 for optimal cell size determination), which is equivalent to $66.43 \\times 66.17 \\mathrm{~m}$ at $21^{\\circ}$ latitude. For each sampling day, we extracted the mean $\\mathrm{CH}_4$ ebullition of each grid cell, which is the mean of all values produced by the interpolation within each grid cell. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[39,356,473,569]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For each grid cell, we then averaged the means from all sampling days, which we hereafter refer to as the \"temporally resolved mean\" for each grid cell. For our \"spatiotemporally resolved\" total $\\mathrm{CH}_4$ ebullition estimate for the whole bay, we then averaged all temporally resolved means from the intraannual scale, and multiplied them by the total area of grid cells. In addition to these calculations, we interpolated the temporally resolved means of all grid cells, separately for the intra-annual and the intra-monthly scale, to create maps of temporally resolved $\\mathrm{CH}_4$ flux for each temporal scale study. For each grid cell, we also calculated the coefficient of variance (CV) between the means of the different sampling occasions as an expression of temporal variability, which was then interpolated for mapping purposes for the two temporal scale studies. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[39,570,472,645]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For comparing the variability of ebullition at different temporal and spatial scales, we used the frequency distribution of the quartile coefficient of dispersion (QCD), which is a measure of variability suitable for comparisons of data sets with non-normally distributed residuals (Bonett 2006), ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[197,659,472,691]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathrm {Q C D} = \\frac {Q 3 - Q 1}{Q 3 + Q 1}, \\tag {1}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[39,703,470,779]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where Q1 and Q3 are the first and third quartile of a data set, respectively. The QCD can have values between 0 and 1, where a high value indicates high variability. The methods behind these frequency distribution plots for spatiotemporal comparisons are explained in further detail in Text S5 and Fig. S3. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[39,779,472,826]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Calculations were done in R version 3.5.2 and Matlab version R2018a, spatial analyses in ArcGIS version 10.6.1 and all other graphics in R. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[40,848,101,862]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[40,869,303,883]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Spatial variability of $\\mathrm{CH}_4$ ebullition ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[39,883,473,930]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We found that high $\\mathrm{CH_4}$ ebullition (up to $1572\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1}$ annual mean in one grid cell) can occur at multiple depths and locations along the bay, from the shallow northern part of the bay ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[491,108,926,336]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"close to the river inflow $(0 - 5\\mathrm{m})$ to the deeper part further south $(10 - 15\\mathrm{m};$ Fig. 1a). In the intra-annual data, which cover the entire bay, we observed areas of high annual mean $\\mathrm{CH}_4$ ebullition closest to the river inflow, but also in the middle and in the southern end of the bay (Fig. 1b). The intra-monthly data, which cover the northern part of the bay only, also reveal highest mean $\\mathrm{CH}_4$ ebullition closest to the river inflow as well as patches of high ebullition further downstream (Fig. 1d). The mean spatiotemporally resolved $\\mathrm{CH}_4$ ebullition at the intra-monthly scale (Fig. 1d, $270\\mathrm{mgCm}^{-2}$ $\\mathrm{d}^{-1}$ ) was similar to the mean temporally and spatially resolved $\\mathrm{CH}_4$ ebullition at the intra-annual scale (Fig. 1b, $281\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1}$ ), but the spatial variability of mean $\\mathrm{CH}_4$ ebullition between grid cells was much larger at the intra-annual scale (Fig. 1b, range: $38 - 1572\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1}$ ) compared to at the intra-monthly scale (Fig. 1d, range: $64 - 704\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1}$ ). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[491,337,928,611]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"There was no apparent relationship between water depth and $\\mathrm{CH_4}$ ebullition. Binning all hydroacoustic $\\mathrm{CH_4}$ ebullition flux data (intra-annual + intra-monthly scale) into categories of 1.5–3, 3–5, 5–10, and $10 - 15\\mathrm{m}$ (Fig. 2a) and all bubble trap data into categories of 0.9–3, 3–5, and $5 - 8\\mathrm{m}$ (Fig. 2b) revealed a similar magnitude and variability of $\\mathrm{CH_4}$ ebullition flux for all depth categories. Mean fluxes in the shallowest depth categories from the hydroacoustic and bubble trap data sets were similar (1.5– $3\\mathrm{m}:256\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1}$ vs. $0.9 - 3\\mathrm{m}:230\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1}$ ). Interestingly though, highest fluxes observed in the bubble trap data were in this shallow zone, whereas $\\mathrm{CH_4}$ ebullition was highest in the deepest bins of the hydroacoustic data set (10–15 m, $569\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1}$ ). Ultimately, $\\mathrm{CH_4}$ ebullition estimated via the hydroacoustic approach varied over four to five orders of magnitude within each depth category, presumably due to the much higher spatial resolution achieved at all depths with the echosounder surveys (Fig. 2a) compared to that achieved with bubble trap deployments (Fig. 2b). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[493,626,777,640]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Temporal variability of $\\mathrm{CH}_4$ ebullition ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[491,641,926,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The variability of $\\mathrm{CH_4}$ ebullition over time was calculated for each grid cell as the CV, which was highest in the northern part of the bay (Fig. 1c) in close proximity to the river inflow (Fig. 1e), indicating more temporal variability in the northern part compared to the southern part of the bay. At an intra-annual timescale, both bubble trap data and hydroacoustic data showed that $\\mathrm{CH_4}$ ebullition was highest on 9 March during falling water level, and lowest on 03 July during rising water level (Figs. 3a, S4, S5a; Table S4). However, the range in mean fluxes across the year (i.e., mean flux from all grid cells for each sampling day) using the hydroacoustic approach was $581 - 1271\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1}$ , which is roughly twice as high as those from the bubble traps $(44 - 527\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1})$ , likely illustrating the difference in spatial coverage resolution between the two approaches (discussed below). At an intra-monthly timescale, bubble trap data showed highest mean flux occurring on 07 December and the lowest flux 2 days later on 09 December (Fig. 3b, Table S4), which was the date that the hydroacoustic data recorded its highest flux of the intra-monthly survey (lowest was 16 December; Fig. S5b). Again, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[42,67,142,81]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Linkhorst et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[689,67,926,82]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$CH_4$ ebullition across space and time ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[478,946,491,958]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[80,148,467,551]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0156/f439cdf7190a68268e299d163c3556fc355ad3164a901c5f0e0c59811af86f4c.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[468,110,944,391]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0193/7a02526d8f1275f0b0bd12681fa436432d0ff0647e9f64597a1d4069c3863f05.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[468,403,944,612]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 1 Maps of the studied bay in CDU reservoir: (a) map of bathymetry as extracted from all segments of the hydroacoustic analysis and categorized into depth categories as further used in this study. The arrow marks the river inflow, and the bracket marks the area studied at the intra-monthly scale; (b) map of the mean ebulitive $\\\\mathrm{CH}_4$ emission at the intra-annual timescale, based on eight hydroacoustic surveys over 1 year, interpolated over the whole bay; (c) map of the CV at the intra-annual timescale; (d) map of the mean ebulitive $\\\\mathrm{CH}_4$ emission at the intra-monthly timescale, based on six hydroacoustic surveys over 2 weeks, interpolated over the northern part of the bay, (e) map of the CV at the intra-monthly timescale. \"]","image_footnote":"[]","img_path":"images/0436/c47574268620a0322356e38d2276bda03b2b657609faa0930ff5ddeeeaa7cfec.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[68,716,501,853]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"hydroacoustic data were the most variable during the month with mean fluxes of $5 - 470\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1}$ compared to $5 - 293\\mathrm{mg}$ $\\mathrm{Cm}^{-2}\\mathrm{d}^{-1}$ for the bubble trap data (Table S4). Ultimately, a higher degree of $\\mathrm{CH}_4$ ebullition variability was found over the entire year (hydroacoustics: $581 - 1271\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1}$ , bubble traps: $44 - 527\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1}$ ; Table S3) than over a single month that was characterized by intermediate fluxes (hydroacoustics: $5 - 470\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1}$ , bubble traps: $5 - 293\\mathrm{mgCm}^{-2}\\mathrm{d}^{-1}$ ; Table S4). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,868,467,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Comparison of spatial and temporal variability of $\\mathrm{CH}_4$ ebullition ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,900,501,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As the greatest spatial and temporal coverage was acquired by the hydroacoustic surveys, we primarily use this data set to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[521,716,954,898]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"investigate both the spatial and temporal variability of $\\mathrm{CH}_4$ ebullition. At the intra-annual timescale, the spatial variability of $\\mathrm{CH}_4$ ebullition was comparable to the temporal variability on about half of the sampling occasions, visible via the overlap in QCD distributions in Fig. 4a. On the other half of the sampling occasions, however, $\\mathrm{CH}_4$ ebullition was less variable in space than in time as indicated by the smaller QCD values for the intra-annual spatial data set. $\\mathrm{CH}_4$ ebullition varied strongly in both space and time in the intra-monthly data, but the temporal variability was greater than the spatial variability (i.e., higher QCD range for intra-monthly temporal variability in Fig. 4a). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[522,900,954,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Comparing the QCD distributions of both temporal scales (Fig. 4a), we find that $\\mathrm{CH}_4$ ebullition varied more at the intra ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[71,67,171,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Linkhorst et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[718,67,954,82]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$CH_4$ ebullition across space and time ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[508,946,517,956]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[210,111,480,305]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0993/53b6bc71d618f0d87a48a96e7fd8d8b02a6825bf544e3b592b300f5af74bddb1.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[488,111,756,305]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 2 Ebullitive $\\\\mathrm{CH}_4$ flux both at the intra-annual and intra-monthly timescale, measured with (a) hydroacoustics, sorted into depth categories of $1.5 - 3\\\\mathrm{m}$ $(n = 625)$ , $3 - 5\\\\mathrm{m}$ $(n = 1889)$ , $5 - 10\\\\mathrm{m}$ $(n = 1538)$ , and $10 - 15\\\\mathrm{m}$ $(n = 177)$ and (b) bubble traps, sorted into depth categories of $0.9 - 3\\\\mathrm{m}$ $(n = 67)$ , $3 - 5\\\\mathrm{m}$ $(n = 86)$ , and $5 - 8\\\\mathrm{m}$ $(n = 43)$ . The horizontal lines show the median flux, the whiskers show the upper and lower quartiles of the data, and the blue stars indicate the mean flux for each depth category. Ebullition is plotted at a log scale for improvement of visibility. \"]","image_footnote":"[]","img_path":"images/0340/6d5d7c6eef1a9cc9c2008b08c912db02a3459306e77cdce702176c4a95379509.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[86,389,477,625]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/1010/79b0f482e739dcc533199050e6e7be264585fa15f98ec6a860c83031b2a201a0.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[488,388,880,625]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 3 $\\\\mathrm{CH}_4$ ebullition from the bubble traps in the northern part of the bay, at (a) the intra-annual timescale with monthly sampling over 1 year from August 2016 to August 2017 and (b) the intra-monthly timescale with bi- to tri-daily sampling over 1 month in November–December 2016. The points represent measured fluxes for each bubble trap with their respective water column depth indicated by color. The boxes show the distribution patterns over time, where each box represents all single bubble trap fluxes for each sampling day; the horizontal lines show the medians, and the whiskers show the upper and lower quartile of the data. \"]","image_footnote":"[]","img_path":"images/0533/5b84dc1d05455d4ed86ef6966d98f784e3d3b2bb3ef8b18ccc74ba0aa50813c4.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[39,716,473,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"annual timescale than at the intra-monthly timescale. Similarly, the spatial variability of $\\mathrm{CH}_4$ ebullition was more pronounced throughout the intra-annual study than during the intra-monthly study (i.e., intra-annual QCD distribution range was higher in Fig. 4a). We also investigated the temporal variability in $\\mathrm{CH}_4$ ebullition at fixed locations over multiple timescales using bubble trap data (Fig. 4b). For this comparison, we added measurements of $\\mathrm{CH}_4$ ebullition over one diel cycle at one location at the northernmost area of the same bay (A. Linkhorst et al., unpubl.) to the bubble trap measurements we present here. Ultimately, the temporal variability in $\\mathrm{CH}_4$ ebullition was similarly high at diel, intra-monthly and intra-annual timescales, but a larger range in variability was observed at the longer timescales (Fig. 4b). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[493,716,901,746]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Characteristics and $\\mathrm{CH}_4$ pore-water content of sediment and pre-flooding soil ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[493,746,928,930]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The thickness of postflooding sediment varied between 0 and $32\\mathrm{cm}$ . TOC and TN content, as well as the C/N ratio, were higher in the post-flooding sediment than in the pre-flooding soil (Table S5). There was no systematic difference in the median particle size between sediment and pre-flooding soil (Table S5). Multivariate analyses (principal components analysis and partial least squares regression; not shown) showed no significant relationships between $\\mathrm{CH}_4$ ebullition and sediment thickness or characteristics of adjacent cores. Mean $\\mathrm{CH}_4$ porewater concentration at the five cores sampled for $\\mathrm{CH}_4$ porewater profiles was $323 - 1245\\mu \\mathrm{M}$ on 18 November 2016 and $1426 - 4024\\mu \\mathrm{M}$ on 16 December 2016 (Table S2; Fig. S6). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[42,67,140,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Linkhorst et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[689,67,926,82]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$CH_4$ ebullition across space and time ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[478,946,488,958]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[184,110,514,305]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0199/7150590961077e1ad8393ddeac223d3b23e35b3d0b65c3a298346c0f82125c45.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[521,111,839,305]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 4 Frequency distributions of the QCD for comparison of the spatiotemporal variability of $\\\\mathrm{CH}_4$ ebullition, shown with Gaussian smoothing, measured by (a) hydroacoustics and (b) bubble traps. Spatial variability is the QCD between all grid cells of the northern part of the bay (Plot a, green shading, $n = 37$ ), comparing all sampling campaigns of the respective data set. Temporal variability is the QCD for each grid cell of the northern part of the bay between the sampling campaigns of the respective data set (Plot a, intra-annual, dark purple shading, $n = 8$ ; intra-monthly, light purple shading, $n = 6$ ; Plot b, intra-annual red shading, $n = 9$ , intra-monthly, yellow shading, $n = 11$ ; diel, blue shading, $n = 8$ ). Overlapping peaks suggest that variability is similar, whereas a peak with higher QCD suggests higher variability than whichever other variability with which we are comparing. Fig. S3 aims to visualize the methods behind this figure, and the methods are described in detail in text S5. The diel variability data in plot b is from one 24-h cycle at one location in the study area (A. Linkhorst et al., unpubl.). \"]","image_footnote":"[]","img_path":"images/0152/22eb4f0e169a58efaf3e65c108ce4beb3a355e36c9c336a1df291288983d505e.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[70,443,253,456]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Environmental variables ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,459,503,656]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The water level fluctuated $4.9\\mathrm{m}$ over the intra-annual study with four samplings during falling water and five samplings during rising water (Fig. S4). During the intra-monthly study, water level fluctuated only by $0.2\\mathrm{m}$ without a clear overall rising or falling trend. Daily mean air temperature $(24\\mathrm{h}$ average) was on average $18.2^{\\circ}\\mathrm{C}$ (range: $13.4 - 21.6^{\\circ}\\mathrm{C})$ during the intra-annual study and $19.9^{\\circ}\\mathrm{C}$ (range: $15.2 - 22.6^{\\circ}\\mathrm{C})$ during the intra-monthly study. Mean surface water temperature during sampling was $24.1^{\\circ}\\mathrm{C}$ (range: $19.6 - 29.0^{\\circ}\\mathrm{C})$ and $27.3^{\\circ}\\mathrm{C}$ (range: $25.4 - 29.5^{\\circ}\\mathrm{C})$ and mean bottom water temperature during sampling was $23.4^{\\circ}\\mathrm{C}$ (range $19.7 - 28.3^{\\circ}\\mathrm{C})$ and $25.1^{\\circ}\\mathrm{C}$ (range: $24.4 - 25.9^{\\circ}\\mathrm{C})$ for the intra-annual and intra-monthly studies, respectively (see Tables S3, S4 for more details). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,681,158,696]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Discussion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,701,496,716]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Variability of $\\mathrm{CH}_4$ ebullition at temporal and spatial scales ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,717,500,837]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"While many previous studies have pointed out the importance of spatial variability in low-latitude reservoir $\\mathrm{CH}_4$ ebullition (Grinham et al. 2011; DelSontro et al. 2015; Hilgert et al. 2019), and some others have found seasonal patterns (Deshmukh et al. 2014; Yang et al. 2018; Marcon et al. 2019), this is, to our knowledge, the first study to systematically compare the variability of $\\mathrm{CH}_4$ ebullition both spatially and over different scales of time. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,837,501,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We found that $\\mathrm{CH}_4$ ebullition varied strongly in both space and time, but that the temporal variability of $\\mathrm{CH}_4$ ebullition was in general more pronounced than its spatial variability, at both the intra-annual and at the intra-monthly scale (Fig. 4a). We conclude that measurements of $\\mathrm{CH}_4$ ebullition made seasonally are likely to capture the most pronounced variability ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[521,443,957,775]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"in emission from our study system. The variability of $\\mathrm{CH}_4$ ebullition as measured from the bubble traps over $24\\mathrm{h}$ at one site was similar in magnitude as the variability at intramonthly (at 14 sites) and intra-annual timescales (at 4-7 sites). However, the total range in variability was smaller for our diel study than for at the intra-monthly and intra-annual timescales. In two studies with measuring automated bubble traps over 5 months in a temperate reservoir (Maeck et al. 2014) and over 1 year in a subtropical reservoir in Brazil (Marcon et al. 2019), ebullition rates also varied strongly over different timescales from minutes to days. Differences between seasons were suggested to be due to seasonal temperature differences (Maeck et al. 2013, 2014) or stratification and mixing dynamics (Marcon et al. 2019). With respect to variability on shorter time scales, no diel variability was observed during monitoring of $\\mathrm{CH}_4$ ebullition in the subtropical Brazilian reservoir (Marcon et al. 2019). Eddy covariance studies (Eugster et al. 2011; Deshmukh et al. 2014; Podgrajsek et al. 2016) achieve high temporal resolution over different scales but since they cannot distinguish between diffusive and ebullitive emission, their findings of temporal variability at different scales are not directly comparable to our results. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[521,778,957,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Our analysis also shows that the spatial variability in $\\mathrm{CH}_4$ ebullition can be high (Fig. 4a), even in relatively small areas such as our study bay $(0.326\\mathrm{km}^2)$ . It is possible that increasing the survey area will result in greater overall spatial variability of ebullitive emission, because other areas will have different depth, and possibly different sediment characteristics and deposition rate, as well as bottom water properties. To attain representative measurements of system-wide $\\mathrm{CH}_4$ ebullition, it is crucial that measurements are distributed in space as well as in time. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[71,67,171,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Linkhorst et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[718,67,954,82]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$CH_4$ ebullition across space and time ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[506,946,519,956]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[40,110,264,124]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Drivers of temporal variability ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[39,125,473,427]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The temporal variability of $\\mathrm{CH_4}$ ebullition measured via both the hydroacoustic and bubble trap approaches was related to water level, pressure changes on the sediment, as well as surface and bottom water temperature (Fig. 5; Tables S3, S4). The highest fluxes occurred at low water level (see Fig. S4 for a hydrograph) for both timescales of the hydroacoustic data (Fig. 5a,e), but patterns were less evident for bubble trap data, which admittedly cover a much smaller surface area. Low water level translates into lower hydrostatic pressure on the sediment, which eases the release of bubbles from the sediment, a phenomenon that has been observed in temperate reservoirs (Maeck et al. 2014; Harrison et al. 2017). Accordingly, $\\mathrm{CH_4}$ ebullition was higher during periods of decreasing pressure on the sediment than during periods of increasing pressure on the sediment (Fig. 5b,f), in agreement with previous studies (Mattson and Likens 1990; Ostrovsky 2003; Harrison et al. 2017). However, temperature variability between dry rainy season may also likely have played a role, and without experimental work, it is difficult to disaggregate the physical from the biological drivers. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[40,429,472,474]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Temperature has a strong positive effect on $\\mathrm{CH}_4$ production rates (Yvon-Durocher et al. 2014) and $\\mathrm{CH}_4$ ebullition (Aben et al. 2017). Both bottom and surface water temperature were ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[493,108,926,216]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"related to mean ebullitive $\\mathrm{CH}_4$ flux across the study areas (Fig. 5c,d,g,h). Surface water temperature was a good predictor of $\\mathrm{CH}_4$ ebullition for both timescales, albeit less so at the intramonthly timescale when temperature varied less (Fig. 5c,g). Bottom water temperature from the temperature profile locations was positively related to $\\mathrm{CH}_4$ ebullition measured via both approaches at the intra-annual timescale (Fig. 5d). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[493,232,702,246]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Drivers of spatial variability ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[493,246,928,474]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Some previous studies have found significant relationships between $\\mathrm{CH}_4$ ebullition and depth in reservoirs (Keller and Stallard 1994; Deshmukh et al. 2014), whereas others have not (DelSontro et al. 2011, 2015; Hilgert et al. 2019). We did not find a consistent trend of $\\mathrm{CH}_4$ ebullition variability over water depth in our study area (Fig. 5), and even though the bathymetric information is based on high-resolution measurements (Fig. S2), we cannot exclude that averaging both water depth and ebullition flux per grid cell may hide smaller-scale patterns. Furthermore, spatial variability in $\\mathrm{CH}_4$ ebullition appears not to be related to distance from the shore as high fluxes were found throughout the bay (Fig. 1b), contrary to what has been reported for a tropical floodplain lake (Peixoto et al. 2015). High ebullitive fluxes were observed in the shallow area $(1 - 5\\mathrm{m})$ closest to the river inflow but also in the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[40,507,931,870]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 5 Mean eullutive $\\\\mathrm{CH}_4$ flux per sampling day as measured with hydroacoustics (circles) and bubble traps (triangles) during the intra-annual (a-d; blue) and intra-monthly (e-h; red) study, plotted against water level (a, e); total pressure change, that is, the difference of pressure on the sediment between the previous day and the sampling day (b, f); surface water temperature (c, g); and bottom water temperature (d, h). Linear regressions with a significant slope are marked with a star. Detailed regression statistics can be found in Tables S7 (hydroacoustics) and S8 (bubble traps). \"]","image_footnote":"[]","img_path":"images/0621/f7b308140c5dc20a693619add5348ff0fdba033dee816283a1a58a86f181af62.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[40,67,140,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Linkhorst et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[689,67,926,82]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$CH_4$ ebullition across space and time ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[478,946,490,956]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[73,110,500,549]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"deepest area (10–15 m) at the southern end of the bay (Figs. 1a,b, 2), contrasting some studies that did not observe ebullition deeper than 10 m (Abril et al. 2005). Interestingly, the high-flux area closest to the river inflow was characterized by high temporal variability in ebullition, while the high-flux area in the southern end of the bay did not vary as much over the year (Fig. 1c). The lack of direct relationship between $\\mathrm{CH}_4$ ebullition and water depth may be related to the heterogeneity of sediment deposition and bottom morphometry of reservoirs (Mendonça et al. 2014), particularly near a river inflow; however, in contrast to other studies (Sobek et al. 2012; Wilkinson et al. 2015; Grinham et al. 2018; Hilgert et al. 2019), our own data do not indicate any relationship between sediment characteristics (i.e., OC content, N content, C/N ratio, grain size, thickness of the sediment layer; Table S5) and $\\mathrm{CH}_4$ ebullition (not shown). This may be due to the lower water level in the dry seasons such as during the extreme drought in 2014 (Kosten et al. 2018), during which we observed that the shallowest areas closest to the river inflow (0–5 m) had dried out and were covered with grass. This fresh input of organic matter likely stimulated high $\\mathrm{CH}_4$ production rates upon inundation prior to our study (Prairie et al. 2018), and may blur relationships with sediment characteristics. Also, we lack core sampling sites in the southernmost part of the bay, an area with high $\\mathrm{CH}_4$ ebullition. We included information on sediment accumulation from three additional sediment cores from the southern part of the bay (Table S6), which, however, did not show higher sediment deposition rates than in the shallower northern part of the bay. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[71,565,410,594]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\mathrm{CH_4}$ pore-water concentration in sediment and preflooding soil ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[73,596,500,760]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We measured $\\mathrm{CH}_4$ concentrations in the pore water of sediment and preflooding soil before and after the intra-monthly study to see if we can explain total $\\mathrm{CH}_4$ ebullition by an equivalent loss in $\\mathrm{CH}_4$ from the sediment. However, $\\mathrm{CH}_4$ concentrations in the pore water were higher at the end of the intra-monthly sampling campaign than at its start, indicating that $\\mathrm{CH}_4$ concentrations fluctuate over shorter timescales than 1 month. Nevertheless, 7 of 10 pore-water profiles contained at least one depth layer where $\\mathrm{CH}_4$ was oversaturated (Fig. S6), indicating that the sediment is prone to form and release bubbles, in congruence with the measured ebullitive $\\mathrm{CH}_4$ fluxes. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[73,763,500,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Interestingly, in 5 of 10 profiles, we observed supersaturated $\\mathrm{CH}_4$ layers in preflooding soils (Fig. S6; Table S2). However, the sampled spots were shallow enough ( $<9\\mathrm{m}$ ) to be exposed to air at least for 1-month long periods during previous extreme dry seasons (see historical water level in Fig. S7). Therefore, even though we observed ebullition coming from deep layers that we determined as preflooded soils, it might be that those layers were fed by fresh terrestrial organic material when roots of terrestrial plants have entered deeper bottom layers during exposure to the atmosphere. As fresh land plant material can rapidly be degraded to $\\mathrm{CH}_4$ at anoxic conditions (Grasset et al. 2018), ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[527,110,952,275]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"this fresh input of organic matter likely stimulated high $\\mathrm{CH_4}$ production rates upon inundation prior to our study (Prairie et al. 2018). The water level fluctuated over a total range of $15\\mathrm{m}$ between 2003 and 2016, with a water level fluctuation between dry and rainy season of $6 - 13\\mathrm{m}$ (Fig. S7). Essentially, this means that large areas of the reservoir bottom have at some point been exposed to the atmosphere and may contain rather fresh organic material in their deep bottom layers. Because of the supply of fresh organic material, these parts of the reservoir bottom can emit $\\mathrm{CH_4}$ even 22 years after dam construction and initial flooding of the land. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[527,292,844,306]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Comparison of different upscaling scenarios ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[527,307,952,427]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We upscaled $\\mathrm{CH}_4$ ebullition for the entire study area using different temporal and spatial resolutions to investigate the effect of measurement variability on upscaled estimates. The upscaling scenarios as shown in Fig. S8 and Table 1 are compared to our spatiotemporally resolved best estimate (33 t C yr $^{-1}$ ; Fig. 1b), which is based on the interpolation of spatially resolved hydroacoustic $\\mathrm{CH}_4$ ebullition measurements at a monthly resolution over 1 year. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[527,429,952,594]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The first scenario extrapolates from a single, yet spatially resolved, measurement occasion to an annual flux, similar to DelSontro et al. (2011). Extrapolation from the lowest and highest mean fluxes that we observed during our annual survey (09 March and 03 July) to the whole year led to $\\mathrm{CH}_4$ emission of 8 and $81\\mathrm{tCyr}^{-1}$ from our study area, respectively. Extrapolation from the months of lowest and highest flux during the year thus differed by $76\\%$ and $145\\%$ from our best estimate (Fig. S8b,c; Table 1), illustrating the significance of seasonally resolved measurements of $\\mathrm{CH}_4$ ebullition for calculating whole-system estimates. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[527,596,952,837]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The second scenario extrapolates total flux from measurements at only a few locations but over several sampling occasions, similar to Dos Santos et al. (2006). Performing extrapolations using only data from areas with the highest ebullitive fluxes (as derived from interpolation of our measured fluxes, spots marked in Fig. S8d) would overestimate total $\\mathrm{CH}_4$ ebullition by $174\\%$ ( $92\\mathrm{tCyr}^{-1}$ ) compared to our spatiotemporally resolved best estimate ( $33\\mathrm{tCyr}^{-1}$ ). If, on the other hand, we extrapolated using only data from the areas with lowest ebullition (spots marked in Fig. S8e), we would underestimate the total flux by $79\\%$ ( $7\\mathrm{tCyr}^{-1}$ ; Table 1). Although these are worst-case scenarios, we can conclude that disregarding spatial variability also risks introducing large errors in whole-system estimates of $\\mathrm{CH}_4$ ebullition. Ultimately, spatially resolved measurements at seasonal temporal resolution are required for robust quantification of $\\mathrm{CH}_4$ ebullition. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[527,837,952,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The third scenario extrapolates total flux from measurements of the bubble traps, which compared to hydroacoustic surveys have low spatial resolution but integrate over longer temporal scales at fixed sites. Upscaling from the temporally resolved bubble trap measurements of the inter-annual study (4-7 traps in the northern part of the bay; Fig. S8f) to the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[71,68,169,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Linkhorst et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[718,68,954,81]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$CH_4$ ebullition across space and time ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[508,946,517,956]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"9 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[40,170,928,355]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0740/87d3cac735e13cfd99dbbf7f0c1397b7a4adb66c1f667360db7fa8052d975c65.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":"<table><tr><td>Scenario</td><td>Time</td><td>Data set</td><td>Mean flux (mg C m-2d-1)</td><td>Median flux (mg C m-2d-1)</td><td>Total flux (t C yr-1)</td></tr><tr><td>*</td><td>Whole year</td><td>Hydroacoustics, intra-annual</td><td>281</td><td>195</td><td>33</td></tr><tr><td rowspan=\"2\">1</td><td>09 Mar. 2017 (survey with highest flux)</td><td>Hydroacoustics, intra-annual</td><td>681</td><td>385</td><td>81</td></tr><tr><td>03 Jul. 2017 (survey with lowest flux)</td><td>Hydroacoustics, intra-annual</td><td>71</td><td>4</td><td>8</td></tr><tr><td rowspan=\"2\">2</td><td>Whole year</td><td>Hydroacoustics, intra-annual, 20 grid cells of highest flux</td><td>769</td><td>640</td><td>92</td></tr><tr><td>Whole year</td><td>Hydroacoustics, intra-annual, 20 grid cells of lowest flux</td><td>62</td><td>62</td><td>7</td></tr><tr><td>3</td><td>Whole year</td><td>Bubble traps, intra-annual, upscaled according to bathymetry</td><td>173</td><td>128</td><td>21</td></tr></table>","table_caption":"[\"Table 1. Mean, median and total ebullitive $\\\\mathrm{CH}_4$ emission for different upscaling scenarios. The total flux was calculated from the product of the mean flux and total bay area (0.326 km²). The star marks our best estimate, based on spatiotemporally resolved hydroacoustic measurements, using the mean from all grid cells from all sampling campaigns over the year (Fig. 1b). The other upscaling scenarios are illustrated in Fig. S7. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[39,373,470,434]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"entire bay area by means of bathymetry (i.e., applying the $\\mathrm{CH}_4$ ebullition means of the depth categories in Fig. 2) results in a total ebullitive $\\mathrm{CH}_4$ flux of $21\\mathrm{tCyr}^{-1}$ , underestimating our spatiotemporally resolved best estimate by $36\\%$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[37,434,473,630]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This result illustrates the potential effect of low spatial resolution when sampling, but also the fact that bubble traps were only deployed at depths of $0.9 - 8\\mathrm{m}$ in the northern part of the bay, thereby missing high ebullition areas in the south of the bay that were only recorded by the hydroacoustic surveys. This difference in spatial resolution and total areal coverage most likely led to the large discrepancy in daily mean $\\mathrm{CH}_4$ ebullition between hydroacoustic surveys (581-1271 mg C $\\mathrm{m}^{-2}\\mathrm{d}^{-1}$ ; Fig. S5a) and bubble trap deployments (44-527 mg C $\\mathrm{m}^{-2}\\mathrm{d}^{-1}$ ; Fig. 3a). The overall lower mean fluxes measured by bubble trap deployments compared to hydroacoustics indicate that a better temporal resolution of $\\mathrm{CH}_4$ ebullition does not necessarily compensate for lower spatial resolution. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[40,656,138,670]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Implications ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[39,670,470,851]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Our study shows that to derive a robust estimate of $\\mathrm{CH_4}$ ebullition from a tropical reservoir, measurements must be conducted during different seasons of the year, at least once during falling and once during rising water level, and that these measurements should be spatially well resolved as well. Hydroacoustics is currently the most well-suited method for accomplishing seasonally distributed samplings at high spatial coverage. Time is the biggest constraint for using an echosounder to sufficiently resolve ebullition variability over time and space. For example, each individual hydroacoustic survey of our studied bay took about $2.3\\mathrm{h}$ , but we only covered $3\\%$ (i.e., $0.326\\mathrm{km}^2$ ) of this relatively small reservoir ( $12\\mathrm{km}^2$ ). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[39,853,473,932]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"While our study indicates that a few seasonally distributed measurement campaigns are required to capture the most pronounced temporal variability in $\\mathrm{CH}_4$ ebullition, a challenge for future studies is how to select sampling locations within individual systems for representative measurements of the variability of system-wide $\\mathrm{CH}_4$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[493,373,926,510]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ebullition, especially in large waterbodies in which even massive sampling efforts will only be able to cover a minute fraction of the total area. Unfortunately, we cannot offer a concrete advice regarding the spatial resolution necessary for accurate system-wide estimates of $\\mathrm{CH}_4$ ebullition, but we do suggest measuring flux in river inflow bays as well as regions not influenced by such external inputs. It cannot be overstated either that the hydroacoustic approach better resolved the spatial variability in ebullitive flux in all regions than a dozen randomly placed bubble traps did. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,545,581,559]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[495,564,926,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Aben, R. C. H., et al. 2017. Cross continental increase in methane ebullition under climate change. Nat. Commun. 8: 1-8. doi:10.1038/s41467-017-01535-y \",\"Abril, G., and others. 2005. Carbon dioxide and methane emissions and the carbon budget of a 10-year old tropical reservoir (Petit Saut, French Guiana). Global Biogeochem. Cycles 19: 1-16. doi:10.1029/2005GB002457 \",\"Barros, N., J. J. Cole, L. Tranvik, Y. T. Prairie, D. Bastviken, V. L. M. Huszar, P. del Giorgio, and F. Roland. 2011. Carbon emission from hydroelectric reservoirs linked to reservoir age and latitude. Nat. Geosci. 4: 593-596. doi:10.1038/ngeo1211 \",\"Beaulieu, J. J., M. G. McManus, and C. T. Nietch. 2016. Estimates of reservoir methane emissions based on a spatially balanced probabilistic-survey. Limnol. Oceanogr. 61: S27-S40. doi:10.1002/lno.10284 \",\"Bonett, D. G. 2006. Confidence interval for a coefficient of quartile variation. Comput. Stat. Data Anal. 50: 2953-2957. doi:10.1016/j.csd.a.2005.05.007 \",\"Cole, J. J., and others. 2007. Plumbing the global carbon cycle: Integrating inland waters into the terrestrial carbon budget. Ecosystems 10: 171-184. doi:10.1007/s10021-006-9013-8 \",\"Deemer, B. R., and others. 2016. Greenhouse gas emissions from reservoir water surfaces: A new global synthesis. Bioscience 66: 949-964. doi:10.1093/biosci/biw117 \"]","page_idx":"9","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[42,67,140,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Linkhorst et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[689,67,926,82]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$CH_4$ ebullition across space and time ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[475,946,495,956]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[71,108,501,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"DelSontro, T., J. J. Beaulieu, and J. A. Downing. 2018. Greenhouse gas emissions from lakes and impoundments: Upscaling in the face of global change. Limnol. Oceanogr. Lett. 3: 64-75. doi:10.1002/lol2.10073 \",\"DelSontro, T., D. F. McGinnis, S. Sobek, I. Ostrovsky, and B. Wehrli. 2010. Extreme methane emissions from a Swiss hydropower reservoir: Contribution from bubbling sediments. Environ. Sci. Technol. 44: 2419-2425. doi:10.1021/es9031369 \",\"DelSontro, T., M. J. Kunz, T. Kempter, A. Wiest, B. Wehrli, and D. B. Senn. 2011. Spatial heterogeneity of methane ebullition in a large tropical reservoir. Environ. Sci. Technol. 45: 9866-9873. doi:10.1021/es2005545 \",\"DelSontro, T., D. F. McGinnis, B. Wehrli, and I. Ostrovsky. 2015. Size does matter: Importance of large bubbles and small-scale hot spots for methane transport. Environ. Sci. Technol. 49: 1268-1276. doi:10.1021/es5054286 \",\"de Mello, N. A. S. T., L. S. Brighenti, F. A. R. Barbosa, P. A. Staehr, and J. F. Bezerra Neto. 2018. Spatial variability of methane $(\\\\mathrm{CH}_4)$ ebullition in a tropical hypereutrophic reservoir: Silted areas as a bubble hot spot. Lake Reserv. Manag. 34: 105-114. doi:10.1080/10402381.2017.1390018 \",\"Descloux, S., V. Chanudet, D. Serca, and F. Guérin. 2017. Methane and nitrous oxide annual emissions from an old eutrophic temperate reservoir. Sci. Total Environ. 598: 959-972. doi:10.1016/j.scitotenv.2017.04.066 \",\"Deshmukh, C., and others. 2014. Physical controls on CH4 emissions from a newly flooded subtropical freshwater hydroelectric reservoir: Nam Theun 2. Biogeosciences 11: 4251-4269. doi:10.5194/bg-11-4251-2014 \",\"dos Santos, M. A., L. P. Rosa, B. Sikar, E. Sikar, and E. O. dos Santos. 2006. Gross greenhouse gas fluxes from hydropower reservoir compared to thermo-power plants. Energy Policy 34: 481-488. doi:10.1016/j.enpol.2004.06.015 \",\"Drake, T. W., P. A. Raymond, and R. G. M. Spencer. 2018. Terrestrial carbon inputs to inland waters: A current synthesis of estimates and uncertainty. Limnol. Oceanogr. Lett. 3: 132-142. doi:10.1002/lol2.10055 \",\"Eugster, W., T. Delsontro, and S. Sobek. 2011. Eddy covariance flux measurements confirm extreme $\\\\mathrm{CH}_4$ emissions from a Swiss hydropower reservoir and resolve their short-term variability. Biogeosciences 8: 2815-2831. doi:10.5194/bg-8-2815-2011 \",\"Grasset, C., R. Mendonça, G. Villamor Saucedo, D. Bastviken, F. Roland, and S. Sobek. 2018. Large but variable methane production in anoxic freshwater sediment upon addition of allochthonous and autochthonous organic matter. Limnol. Oceanogr. 63: 1488-1501. doi:10.1002/lno.10786 \",\"Grinham, A., S. Albert, N. Deering, M. Dunbabin, D. Bastviken, B. Sherman, C. E. Lovelock, and C. D. Evans. 2018. The importance of small artificial water bodies as sources of methane emissions in Queensland. Australia. Hydrol. Earth Syst. Sci. 22: 5281-5298. doi:10.5194/hess-22-5281-2018 \",\"Grinham, A., M. Dunbabin, D. Gale, and J. Udy. 2011. Quantification of ebullitive and diffusive methane release to \"]","page_idx":"10","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[526,110,954,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"atmosphere from a water storage. Atmos. Environ. 45: 7166-7173. doi:10.1016/j.atmosenv.2011.09.011 \",\"Guérin, F., and others. 2016. Effect of sporadic destratification, seasonal overturn, and artificial mixing on $\\\\mathrm{CH}_4$ emissions from a subtropical hydroelectric reservoir. Biogeosciences 13: 3647-3663. doi:10.5194/bg-13-3647-2016 \",\"Harrison, J. A., B. R. Deemer, M. K. Birchfield, and M. T. O'Malley. 2017. Reservoir water-level drawdowns accelerate and amplify methane emission. Environ. Sci. Technol. 51: 1267-1277. doi:10.1021/acs.est.6b03185 \",\"Hilgert, S., C. V. Scapulatempo Fernandes, and S. 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","text_format":null,"text_level":null,"type":"header"},{"bbox":"[718,67,954,82]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$CH_4$ ebullition across space and time ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[504,946,522,956]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"11 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[42,110,473,898]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Musenze, R. S., A. Grinham, U. Werner, D. Gale, K. Sturm, J. Udy, and Z. Yuan. 2014. Assessing the spatial and temporal variability of diffusive methane and nitrous oxide emissions from subtropical freshwater reservoirs. Environ. Sci. Technol. 48: 14499-14507. doi:10.1021/es505324h \",\"Natchimuthu, S., I. Sundgren, M. Gålfalk, L. Klemedtsson, P. Crill, Å. Danielsson, and D. Bastviken. 2016. Spatiotemporal variability of lake $\\\\mathrm{CH}_4$ fluxes and its influence on annual whole lake emission estimates. Limnol. Oceanogr. 61: S13-S26. doi:10.1002/lno.10222 \",\"Ostrovsky, I. 2003. Methane bubbles in Lake Kinneret: Quantification and temporal and spatial heterogeneity. Limnol. Oceanogr. 48: 1030-1036. doi:10.4319/lo.2003.48.3.1030 \",\"Ostrovsky, I., D. F. McGinnis, L. Lapidus, and W. Eckert. 2008. Quantifying gas ebullition with echosounder: The role of methane transport by bubbles in a medium-sized lake. Limnol. Oceanogr. Methods 6: 105-118. doi:10.4319/lom.2008.6.105 \",\"Paranaíba, J. R., N. Barros, R. Mendonça, A. Linkhorst, A. Isidorova, F. Roland, R. M. Almeida, and S. Sobek. 2018. Spatially resolved measurements of $\\\\mathrm{CO}_{2}$ and $\\\\mathrm{CH}_4$ concentration and gas-exchange velocity highly influence carbon-emission estimates of reservoirs. Environ. Sci. Technol. 52: 607-615. doi:10.1021/acs.est.7b05138 \",\"Peixoto, R. B., F. Machado-Silva, H. Marotta, A. Enrich-Prast, and D. Bastviken. 2015. Spatial versus day-to-day within-lake variability in tropical floodplain lake $\\\\mathrm{CH}_4$ emissions—Developing optimized approaches to representative flux measurements. PLoS One 10: e0123319. doi:10.1371/journal.pone.0123319 \",\"Podgrajsek, E., E. Sahlee, D. Bastviken, S. Natchimuthu, N. Kljun, H. E. Chmiel, L. Klemedtsson, and A. Rutgersson. 2016. Methane fluxes from a small boreal lake measured with the eddy covariance method. Limnol. Oceanogr. 61: S41-S50. doi:10.1002/lno.10245 \",\"Prairie, Y. T., and others. 2018. Greenhouse gas emissions from freshwater reservoirs: What does the atmosphere see? Ecosystems 21: 1058-1071. doi:10.1007/s10021-017-0198-9 \",\"Ramos, F. M., I. B. T. Lima, R. R. Rosa, E. A. Mazzi, J. C. Carvalho, M. F. F. L. Rasera, J. P. H. B. Ometto, A. T. Assireu, and J. L. Stech. 2006. Extreme event dynamics in methane ebullition fluxes from tropical reservoirs. Geophys. Res. Lett. 33: 1-4. doi:10.1029/2006GL027943 \",\"Sobek, S., T. DelSontro, N. Wongfun, and B. Wehrli. 2012. Extreme organic carbon burial fuels intense methane bubbling in a temperate reservoir. Geophys. Res. Lett. 39: 1-4. doi:10.1029/2011GL050144 \",\"St. Louis, V. L., C. A. Kelly, É. Duchemin, J. W. M. Rudd, and D. M. Rosenberg. 2000. Reservoir surfaces as sources of greenhouse gases to the atmosphere: A global estimate. Bioscience 50: 766-775. \",\"Tranvik, L., and others. 2009. Lakes and reservoirs as regulators of carbon cycling and climate. Limnol. 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Biogeo. 118: 1307-1321. doi:10.1002/jgrg.20103 \",\"Wilkinson, J., A. Maeck, Z. Alshboul, and A. Lorke. 2015. Continuous seasonal river ebullition measurements linked to sediment methane formation. Environ. Sci. Technol. 49: 13121-13129. doi:10.1021/acs.est.5b01525 \",\"Yang, L., H. Li, C. Yue, and J. Wang. 2018. Seasonal and spatial variability of methane emissions from a subtropical reservoir in Eastern China. Biogeosciences Discuss.: 1-37. doi: 10.5194/bg-2018-195 \",\"Yvon-Durocher, G., A. P. Allen, D. Bastviken, R. Conrad, C. Gudasz, A. St-Pierre, N. Thanh-Duc, and P. a del Giorgio. 2014. Methane fluxes show consistent temperature dependence across microbial to ecosystem scales. Nature 507: 488-491. doi:10.1038/nature13164 \",\"Zhao, Y., B. F. Wu, and Y. Zeng. 2013. Spatial and temporal patterns of greenhouse gas emissions from three gorges reservoir of China. Biogeosciences 10: 1219-1230. doi:10.5194/bg-10-1219-2013 \",\"Zheng, H., X. Zhao, T. Zhao, F. Chen, W. Xu, X. Duan, X. Wang, and Z. Ouyang. 2011. Spatial-temporal variations of methane emissions from the Ertan hydroelectric reservoir in Southwest China. Hydrol. Process. 25: 1391-1396. doi:10.1002/hyp.7903 \"]","page_idx":"11","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[496,621,633,635]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgments ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[495,637,926,751]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We are grateful to Carlos Henrique Estrada for his help with the daily and monthly surveys, and Icaro Barbosa and Carlos Henrique Estrada for sediment sampling. The research leading to these results has been funded by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement $n^{\\circ}$ 336642. S.S. received additional support by the program Pesquisador Visitante Especial, Ciencia sem Fronteiras, No. 401384/2014-4, and N. B. received additional support by Fundação de Amparo à Pesquisa do Estado de Minas Gerais/FAPEMIG (CRA APQ 03045/16). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[495,784,635,798]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conflict of Interest ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,800,620,813]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"None declared. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[787,831,924,845]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Submitted 08 July 2019 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[769,846,924,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Revised 15 November 2019 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[774,862,924,875]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Accepted 03 January 2020 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[733,884,924,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Associate editor: Kelly Benoit-Bird ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[42,67,140,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Linkhorst et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[689,67,926,82]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$CH_4$ ebullition across space and time ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[475,946,493,956]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"12 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[68,174,898,218]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Comparing methane ebullition variability across space and time in a Brazilian reservoir \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,232,916,268]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Annika Linkhorst $^{1*}$ Carolin Hiller, $^{1,\\\\dagger}$ Tonya DelSontro $^{2}$ Guilherme M. Azevedo, $^{3}$ Nathan Barros, $^{3}$ Raquel Mendonça, $^{3}$ Sebastian Sobek $^{1}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,269,898,325]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"$^{1}$ Limnology, Department of Ecology and Genetics, Uppsala University, Uppsala, Sweden \\\",\\\"$^{2}$ Aquatic Physics Group, Faculty of Science, Department F.-A. Forel for Environmental and Aquatic Sciences, University of Geneva, Geneva, Switzerland \\\",\\\"$^{3}$ Department of Biology, Institute of Biological Sciences, Federal University of Juiz de Fora, Juiz de Fora, Brazil \\\"]\",\n \"page_idx\": \"0\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[129,335,200,350]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[125,355,897,583]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The potent greenhouse gas methane $\\\\left(\\\\mathrm{CH}_4\\\\right)$ is readily emitted from tropical reservoirs, often via ebullition (bubbles). This highly stochastic emission pathway varies in space and time, however, hampering efforts to accurately assess total $\\\\mathrm{CH}_4$ emissions from water bodies. We systematically studied both the spatial and temporal scales of ebullition variability in a river inflow bay of a tropical Brazilian reservoir. We conducted multiple highly resolved spatial surveys of $\\\\mathrm{CH}_4$ ebullition using a hydroacoustic approach supplemented with bubble traps over a 12-month and a 2-week timescale to evaluate which scale of variation was more important. To quantify the spatial and temporal variability of $\\\\mathrm{CH}_4$ ebullition, we used the quartile coefficients of dispersion at each point in space and time and compared their frequency distributions across the various temporal and spatial scales. We found that $\\\\mathrm{CH}_4$ ebullition varied more temporally than spatially and that the intra-annual variability was stronger than daily variability within 2 weeks. We also found that $\\\\mathrm{CH}_4$ ebullition was positively related to water temperature increase and pressure decrease, but no consistent relationship with water column depth or sediment characteristics was found, further highlighting that temporal drivers of emissions were stronger than spatial drivers. Annual estimates of $\\\\mathrm{CH}_4$ ebullition from our study area may vary by $75 - 174\\\\%$ if ebullition is not resolved in time and space, but at a minimum we recommend conducting spatially resolved measurements at least once during each major hydrologic season in tropical regions (i.e., in dry and rainy season when water levels are falling and rising, respectively). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,608,501,779]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Inland waters have been recognized as relevant carbon sources to the atmosphere (Cole et al. 2007; Tranvik et al. 2009; DelSontro et al. 2018; Drake et al. 2018) and integrated into the greenhouse gas budget of the Intergovernmental Panel on Climate Change (IPCC 2013) report. It has been suggested that the impoundment of rivers may increase emission due to flooding of terrestrial organic matter, and additionally through accumulation of sediment containing degradable organic material (St. Louis et al. 2000; Prairie et al. 2018). Tropical reservoirs, in particular, have been indicated as strong sources of the powerful greenhouse gas methane $\\\\mathrm{(CH_4}$ ; Barros et al. 2011) because these warmer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[521,608,955,851]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"regions of the earth are rich in biomass (St. Louis et al. 2000). As greenhouse gas emission from reservoirs can be highly variable across space and time (Abril et al. 2005; DelSontro et al. 2011; Maeck et al. 2013; Maeck et al. 2014; Musenze et al. 2014; Paranaíba et al. 2018), it is difficult to upscale from single measurements at discrete sampling occasions or locations to a whole-system flux estimate. Ebullition (bubbling), often, although not always, the dominant $\\\\mathrm{CH}_4$ emission pathway from reservoirs (Deemer et al. 2016), has been described as stochastic with high variability in space and time (DelSontro et al. 2011, 2015) and is especially difficult to representatively measure for system-wide estimates. Consequently, ebullition has often been excluded from $\\\\mathrm{CH}_4$ emission studies (Deemer et al. 2016) not only leading to underestimation of $\\\\mathrm{CH}_4$ emissions from reservoirs, but also to a substantial lack of knowledge regarding the spatiotemporal variability of $\\\\mathrm{CH}_4$ ebullition in reservoirs. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[521,851,955,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Previous studies have shown that lake or reservoir $\\\\mathrm{CH}_4$ ebullition can peak at certain points in space (\\\"hot spots\\\") or time (\\\"hot moments\\\"). Hot spots were predominantly found in shallow areas (Ostrovsky 2003; Grinham et al. 2011; Zheng et al. 2011; Deshmukh et al. 2014; Natchimuthu et al. 2016; \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[911,8,991,69]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Check for updates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[70,79,352,145]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"LIMNOLOGY and OCEANOGRAPHY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[792,78,954,120]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ASLO \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[790,126,954,136]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Limnol.Oceanogr.9999,2020,1-12 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[550,135,954,144]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"© 2020 The Authors. Limnology and Oceanography published by Wiley Periodicals, Inc. on \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[624,144,954,153]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"behalf of Association for the Sciences of Limnology and Oceanography. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[843,153,954,162]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"doi:10.1002/lno.11410 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[68,801,321,813]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"*Correspondence: liannika@alumni.ethz.ch \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[68,822,501,860]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[68,869,501,894]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Additional Supporting Information may be found in the online version of this article. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[68,902,500,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"†Present address: Department of Hydrology, Bayreuth Center of Ecology and Environmental Sciences, University of Bayreuth, Bayreuth, Germany \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[508,946,517,956]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[44,110,470,502]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"de Mello et al. 2018), in areas close to tributary river inflows (DelSontro et al. 2011; Zhao et al. 2013; Musenze et al. 2014; Beaulieu et al. 2016; Descloux et al. 2017; Harrison et al. 2017; Tušer et al. 2017; de Mello et al. 2018; Hilgert et al. 2019), and in areas with high sediment accumulation (Sobek et al. 2012; Maeck et al. 2013; Hilgert et al. 2019), high organic carbon content (Grinham et al. 2018; Hilgert et al. 2019), or high organic matter reactivity (Sobek et al. 2012). Hot moments of ebullition tend to correlate positively with air temperature (Delsontro et al. 2010; Maeck et al. 2013; Wik et al. 2013; Peixoto et al. 2015; Wilkinson et al. 2015; Natchimuthu et al. 2016), bottom water temperature (Deshmukh et al. 2014), sediment temperature (Tušer et al. 2017), low hydrostatic pressure (Ostrovsky 2003; Varadharajan and Hemond 2012; Wik et al. 2013; Deshmukh et al. 2014; Harrison et al. 2017; Grinham et al. 2018), and low air pressure (Mattson and Likens 1990; Deshmukh et al. 2014; Grinham et al. 2018; Marcon et al. 2019). Interestingly, some authors have mentioned a shift in spatial variability of $\\\\mathrm{CH}_4$ ebullition over time. For example, high-flux zones can shift seasonally from shallower to deeper regions in subarctic lakes (Wik et al. 2013) or temperate reservoirs (Tušer et al. 2017), presumably as a result of seasonal changes in sediment temperature (Tušer et al. 2017). Similarly, it has also been suggested that $\\\\mathrm{CH}_4$ emission from shallower lakes responds stronger to temperature than that from deeper lakes (Natchimuthu et al. 2016). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[44,505,470,836]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"While there are a number of studies that measured $\\\\mathrm{CH}_4$ ebullition in reservoirs at low latitudes, both in the tropics (Keller and Stallard 1994; Abril et al. 2005; Ramos et al. 2006; DelSontro et al. 2011; de Mello et al. 2018) and subtropics (Grinham et al. 2011; Deshmukh et al. 2014; Beaulieu et al. 2016; Guérin et al. 2016; Grinham et al. 2018; Yang et al. 2018; Hilgert et al. 2019; Marcon et al. 2019), only a few of them (Keller and Stallard 1994; Deshmukh et al. 2014; Yang et al. 2018; Marcon et al. 2019) have studied temporal trends of ebullition in enough detail to identify seasonal trends. None of these studies have systematically compared the magnitude of the variability of $\\\\mathrm{CH}_4$ ebullition over scales of both space and time. Furthermore, very few studies have measured ebullitive emission from reservoirs at a high spatial resolution using an echosounder (Delsontro et al. 2010; DelSontro et al. 2011; Maeck et al. 2013; Maeck and Lorke 2014; Tušer et al. 2017), and only one of those studies was on a tropical reservoir (DelSontro et al. 2011). Hence, our understanding of $\\\\mathrm{CH}_4$ ebullition in low-latitude reservoirs is limited by a lack of quantitative information on its spatiotemporal variability, despite indications that $\\\\mathrm{CH}_4$ emissions from reservoirs of these regions are some of the highest worldwide (St. Louis et al. 2000; Barros et al. 2011; Deemer et al. 2016). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[44,837,470,927]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Here, we present results from a large bay with a river inflow in the oligotrophic water supply reservoir Chapéu d'Uvas (CDU) in the Atlantic Forest biome of Southeastern Brazil, situated at the threshold of the tropical and subtropical climate zone. We performed measurements of $\\\\mathrm{CH}_4$ ebullition at high spatial resolution using a hydroacoustic echosounder and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,110,924,291]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bubble traps at (1) an intra-annual scale, with one survey per month over 1 year and (2) an intra-monthly scale with one survey every 2–3 d over 3 weeks (2 weeks with hydroacoustics). We also include results from (3) a diel study with continuous measurements at 3-h time intervals over $24\\\\mathrm{h}$ (A. Linkhorst et al., unpubl.). For further understanding of variability, we studied the drivers of $\\\\mathrm{CH}_4$ ebullition at each timescale. Thus, we quantify the magnitude and variability of $\\\\mathrm{CH}_4$ ebullition over different timescales (from diel to seasonal) at a high spatial resolution along with its main drivers in a low-latitude reservoir. The overall aim was to determine the best way to representatively measure $\\\\mathrm{CH}_4$ ebullition with minimum sampling effort. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,313,566,327]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,334,727,348]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sampling site and general setup \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,350,924,589]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The studied bay of CDU reservoir in Brazil (see Table S1 for its characteristics) is roughly $2\\\\mathrm{km}$ long, with an area of $0.326\\\\mathrm{km}^2$ and a maximum depth of $15\\\\mathrm{m}$ , and it is characterized by a river inflow in its northern end with a catchment area of $20\\\\mathrm{km}^2$ covered by grass land and forest patches. We measured $\\\\mathrm{CH}_4$ ebullition with high spatial resolution using bubble traps and a hydroacoustic echosounder at three temporal scales: once a month between August 2015 and August 2016 (intra-annual scale), every 2–3 d over a period of $22\\\\mathrm{d}$ in November to December 2016 (intra-monthly scale), and continuously over $24\\\\mathrm{h}$ with the data binned in 3-h intervals on 09–10 May 2016 (diel study; A. Linkhorst et al., unpubl.). We also measured $\\\\mathrm{CH}_4$ concentrations in sediment pore water before and after the intra-monthly study on 18 November 2016 and 16 December 2016, and further analyzed sediment and preflooding soil properties from cores taken on 29 March 2018. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,611,602,624]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\mathrm{CH}_4$ ebullition \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,626,924,881]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We measured $\\\\mathrm{CH}_4$ ebullition using bubble traps combined with a spatial hydroacoustic echosounder survey at each sampling occasion. For the intra-annual scale, we covered the whole bay, and for the intra-monthly scale, we covered only the northern part of the bay closest to the river inflow, which was expected to be a hot spot of $\\\\mathrm{CH}_4$ ebullition (DelSontro et al. 2011; Maeck et al. 2013). The sampling scheme is illustrated in Fig. S1. For the intra-annual scale, we sampled on 18 August 2016, 19 September 2016, 24 October 2016, 09 March 2017, 31 March 2017, 21 April 2017, 25 May 2017, 03 July 2017, and 03 August 2017. For the intra-monthly scale, we sampled on 25 November 2016, 28 November 2016, 30 November 2016, 02 December 2016, 05 December 2016, 07 December 2016, 09 December 2016, 12 December 2016, 14 December 2016, and 16 December 2016. November is often the beginning of the rainy season, which was expected to result in changes of system properties and potentially ebullition fluxes. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,884,924,927]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For hydroacoustic measurements, we used a Simrad EY60 portable scientific echosounder (Kongsberg Maritime AC, Norway) with a $120\\\\mathrm{-kHz}$ split-beam transducer (downward facing, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[42,68,140,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Linkhorst et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[691,68,926,81]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$CH_4$ ebullition across space and time \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[478,946,488,956]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[73,108,500,411]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$7^{\\\\circ}$ beam angle, ping rate: $5\\\\mathrm{~s}^{-1}$ ) mounted downward facing to our boat while traversing across and along the bay (Fig. S1b,c). Hydroacoustic data were analyzed with Sonar5 Pro (Lindem Acquisition, Norway), which enables distinction between bubbles and fish/plankton based on their travel path, velocity and signal intensity (Ostrovsky et al. 2008; DelSontro et al. 2011). Each hydroacoustic file was divided into segments of $300 \\\\pm 5$ pings, which equates to distances of $\\\\sim 24\\\\mathrm{~m}$ for the intra-annual scale and $\\\\sim 10\\\\mathrm{~m}$ for the intra-monthly scale. Bubble density was determined per water volume covered by the echosounder beam and converted into bubble gas flux following DelSontro et al. (2011, 2015) and accounting for bubble dissolution during rise using the model described in McGinnis et al. (2006), assuming an average $\\\\mathrm{CH}_4$ content of $70\\\\%$ in the bubbles (discussed in Text S1). We used only the $3\\\\mathrm{~m}$ closest to the sediment for further data analysis and excluded any hydroacoustic measurement in the near-field zone of the transducer ( $\\\\sim 1.5\\\\mathrm{~m}$ ). During the intramonthly study, echosounder measurements were conducted only over $15\\\\mathrm{~d}$ of the 22-day study period (02-16 December 2016) due to an instrument failure. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[73,413,500,806]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For the ebullition measurements with the bubble traps, we used custom-built conical plastic frames (50 cm in diameter, 43 cm tall) covered with impermeable tarp and equipped with 220-mL glass bottles screwed into threads at the narrow ends of the funnels. For the intra-annual scale, we distributed four to seven bubble traps along the northern part of the bay. For the intra-monthly scale, we distributed 14 bubble traps along a longitudinal transect in the northern part of the bay, alternatingly close to the shore and in the middle (Fig. S1b,c). Each bubble trap was attached to a buoy in 1.5-m distance, which was anchored, so that it could move around the buoy in a radius of $1.5\\\\mathrm{m}$ . The bubble traps were completely submerged in water, and the bottles were filled with water and screwed on top of the traps at the beginning of each trap deployment. Gas in the glass bottles was sampled after 3-5 h with a syringe, and $\\\\mathrm{CH}_4$ concentrations were determined by injection into an ultraportable greenhouse gas analyzer (UGGA, Los Gatos Research) within the same day (see Paranaíba et al. 2018, for details on manual gas injection of discrete samples into the UGGA). We injected 3-7 mL as we found that at our concentrations, we need at least 3 mL of gas for robust $\\\\mathrm{CH}_4$ concentration measurements. The volume of the captured gas was determined by measuring the water volume in the glass bottle after deployment and subtracting this volume from its maximum capacity of $220\\\\pm 2\\\\mathrm{mL}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[73,808,500,927]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Hydroacoustic measurements can cover space but are limited in temporal coverage. Bubble traps are fixed in space and cover a very small area, but integrate over the duration of deployment. In shallow water depths $(0 - 3\\\\mathrm{m})$ , hydroacoustics cannot be used at all, whereas bubble traps as ours $(50~\\\\mathrm{cm}$ height) can be deployed at depths of less than $1\\\\textrm{m}$ . Therefore, the results gained from these two methods cannot be directly compared to each other. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,108,952,260]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The data sets for the intra-annual scale and the intramonthly scale are presented as independent data sets, as the methodological approach slightly differed; whereas we covered the whole bay with hydroacoustic surveys for the intra-annual scale, we covered only the northern part of the bay for the intra-monthly scale. Although at both intra-annual and intra-monthly study we had bubble traps distributed only in the northern part of the bay, they were differently distributed, and twice as abundant for the intra-monthly than for the intra-annual study. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,277,929,291]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sediment properties and $\\\\mathrm{CH_4}$ pore-water concentrations \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,293,952,532]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sediment cores for determination of sediment characteristics were taken using a UWITEC gravity corer equipped with a hammer device on 29 March 2018, directly at the spots where bubble traps had been deployed during the intra-monthly sampling (Fig. S1c). Each core was separated into post-flooding sediment and pre-flooding soil by visual distinction in color and texture, and each of the layers was homogenized separately. We analyzed each homogenized layer of each core for grain size distribution, total organic carbon (TOC) content and total nitrogen (TN) content (methods are described in Text S2), and calculated the molar carbon to nitrogen $(\\\\mathrm{C / N})$ ratio. Sediment cores for $\\\\mathrm{CH_4}$ pore-water content were taken at spots as illustrated in Fig. S1c once before and once after the intramonthly sampling, on 18 November 2016 and 16 December 2016. $\\\\mathrm{CH_4}$ concentrations were analyzed for each $2\\\\mathrm{-cm}$ layer down each of the cores, as further described in Text S3. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,550,705,563]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Environmental variables \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,565,952,867]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A 24-h average of air temperature and barometric pressure was taken from the nearest weather station in Juiz de Fora (INMET, Brazilian National Institute of Meteorology) for each sampling day. During each survey, we measured water temperature (YSI 6600 V2 for intra-annual scale; HOBO Water Temperature Pro v2 for intra-monthly scale) every $1\\\\mathrm{m}$ depth in the water column at one location with a mean depth of $\\\\sim 12\\\\mathrm{m}$ $(10 - 17\\\\mathrm{m})$ for the intra-annual scale and $\\\\sim 8\\\\mathrm{m}$ $(7.7 - 8.7\\\\mathrm{m})$ for the intra-monthly scale (see Fig. S1b,c for the profile locations). Temperature depth profiles were assumed to apply to the entire bay area. The range in maximum depth at the locations for the water temperature profiles varied mostly with variations in water level, but also because of minor variations in location of the profile. Total pressure change at the sediment-water interface per sampling day was calculated from the difference in water level (measured daily and provided by the dam operator CESAMA) between the previous day and the actual sampling day, where we assumed a pressure of $100\\\\mathrm{mbar}$ per $1\\\\mathrm{m}$ water column height, plus the difference in atmospheric pressure (as averaged over $24\\\\mathrm{h}$ ) between the previous day and the actual sampling day. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,869,952,927]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Bathymetry was extracted from the data points of all hydroacoustic surveys, which yielded a total number of 3869 depth measurements, where each depth measure represents an area of about $7 - 17\\\\mathrm{m}^2$ (segments of 10 and $24\\\\mathrm{m}$ for intra-annual \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[71,68,169,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Linkhorst et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[720,68,954,81]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$CH_4$ ebullition across space and time \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[508,946,517,956]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[39,108,470,170]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and intra-monthly study, respectively, multiplied by a mean beam width of $0.7\\\\mathrm{m}$ at a mean depth of $6\\\\mathrm{m}$ ). The total coverage for the bathymetry and hydroacoustic flux measurements is shown in Fig. S2. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[40,189,233,203]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Calculations and statistics \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[39,205,473,356]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The $\\\\mathrm{CH}_4$ ebullition from each hydroacoustic survey was interpolated with Inverse Distance Weighting (ArcGIS version 10.6.1) across the whole bay for the intra-annual scale, and across the northern part of the bay for the intra-monthly scale. It was then gridded to cells of $0.0006^{\\\\circ} \\\\times 0.0006^{\\\\circ}$ (decimal degrees, dd; see Text S4 for optimal cell size determination), which is equivalent to $66.43 \\\\times 66.17 \\\\mathrm{~m}$ at $21^{\\\\circ}$ latitude. For each sampling day, we extracted the mean $\\\\mathrm{CH}_4$ ebullition of each grid cell, which is the mean of all values produced by the interpolation within each grid cell. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[39,356,473,569]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For each grid cell, we then averaged the means from all sampling days, which we hereafter refer to as the \\\"temporally resolved mean\\\" for each grid cell. For our \\\"spatiotemporally resolved\\\" total $\\\\mathrm{CH}_4$ ebullition estimate for the whole bay, we then averaged all temporally resolved means from the intraannual scale, and multiplied them by the total area of grid cells. In addition to these calculations, we interpolated the temporally resolved means of all grid cells, separately for the intra-annual and the intra-monthly scale, to create maps of temporally resolved $\\\\mathrm{CH}_4$ flux for each temporal scale study. For each grid cell, we also calculated the coefficient of variance (CV) between the means of the different sampling occasions as an expression of temporal variability, which was then interpolated for mapping purposes for the two temporal scale studies. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[39,570,472,645]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For comparing the variability of ebullition at different temporal and spatial scales, we used the frequency distribution of the quartile coefficient of dispersion (QCD), which is a measure of variability suitable for comparisons of data sets with non-normally distributed residuals (Bonett 2006), \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[197,659,472,691]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathrm {Q C D} = \\\\frac {Q 3 - Q 1}{Q 3 + Q 1}, \\\\tag {1}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[39,703,470,779]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where Q1 and Q3 are the first and third quartile of a data set, respectively. The QCD can have values between 0 and 1, where a high value indicates high variability. The methods behind these frequency distribution plots for spatiotemporal comparisons are explained in further detail in Text S5 and Fig. S3. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[39,779,472,826]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Calculations were done in R version 3.5.2 and Matlab version R2018a, spatial analyses in ArcGIS version 10.6.1 and all other graphics in R. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[40,848,101,862]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[40,869,303,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Spatial variability of $\\\\mathrm{CH}_4$ ebullition \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[39,883,473,930]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We found that high $\\\\mathrm{CH_4}$ ebullition (up to $1572\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1}$ annual mean in one grid cell) can occur at multiple depths and locations along the bay, from the shallow northern part of the bay \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[491,108,926,336]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"close to the river inflow $(0 - 5\\\\mathrm{m})$ to the deeper part further south $(10 - 15\\\\mathrm{m};$ Fig. 1a). In the intra-annual data, which cover the entire bay, we observed areas of high annual mean $\\\\mathrm{CH}_4$ ebullition closest to the river inflow, but also in the middle and in the southern end of the bay (Fig. 1b). The intra-monthly data, which cover the northern part of the bay only, also reveal highest mean $\\\\mathrm{CH}_4$ ebullition closest to the river inflow as well as patches of high ebullition further downstream (Fig. 1d). The mean spatiotemporally resolved $\\\\mathrm{CH}_4$ ebullition at the intra-monthly scale (Fig. 1d, $270\\\\mathrm{mgCm}^{-2}$ $\\\\mathrm{d}^{-1}$ ) was similar to the mean temporally and spatially resolved $\\\\mathrm{CH}_4$ ebullition at the intra-annual scale (Fig. 1b, $281\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1}$ ), but the spatial variability of mean $\\\\mathrm{CH}_4$ ebullition between grid cells was much larger at the intra-annual scale (Fig. 1b, range: $38 - 1572\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1}$ ) compared to at the intra-monthly scale (Fig. 1d, range: $64 - 704\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1}$ ). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[491,337,928,611]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"There was no apparent relationship between water depth and $\\\\mathrm{CH_4}$ ebullition. Binning all hydroacoustic $\\\\mathrm{CH_4}$ ebullition flux data (intra-annual + intra-monthly scale) into categories of 1.5–3, 3–5, 5–10, and $10 - 15\\\\mathrm{m}$ (Fig. 2a) and all bubble trap data into categories of 0.9–3, 3–5, and $5 - 8\\\\mathrm{m}$ (Fig. 2b) revealed a similar magnitude and variability of $\\\\mathrm{CH_4}$ ebullition flux for all depth categories. Mean fluxes in the shallowest depth categories from the hydroacoustic and bubble trap data sets were similar (1.5– $3\\\\mathrm{m}:256\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1}$ vs. $0.9 - 3\\\\mathrm{m}:230\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1}$ ). Interestingly though, highest fluxes observed in the bubble trap data were in this shallow zone, whereas $\\\\mathrm{CH_4}$ ebullition was highest in the deepest bins of the hydroacoustic data set (10–15 m, $569\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1}$ ). Ultimately, $\\\\mathrm{CH_4}$ ebullition estimated via the hydroacoustic approach varied over four to five orders of magnitude within each depth category, presumably due to the much higher spatial resolution achieved at all depths with the echosounder surveys (Fig. 2a) compared to that achieved with bubble trap deployments (Fig. 2b). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[493,626,777,640]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Temporal variability of $\\\\mathrm{CH}_4$ ebullition \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[491,641,926,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The variability of $\\\\mathrm{CH_4}$ ebullition over time was calculated for each grid cell as the CV, which was highest in the northern part of the bay (Fig. 1c) in close proximity to the river inflow (Fig. 1e), indicating more temporal variability in the northern part compared to the southern part of the bay. At an intra-annual timescale, both bubble trap data and hydroacoustic data showed that $\\\\mathrm{CH_4}$ ebullition was highest on 9 March during falling water level, and lowest on 03 July during rising water level (Figs. 3a, S4, S5a; Table S4). However, the range in mean fluxes across the year (i.e., mean flux from all grid cells for each sampling day) using the hydroacoustic approach was $581 - 1271\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1}$ , which is roughly twice as high as those from the bubble traps $(44 - 527\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1})$ , likely illustrating the difference in spatial coverage resolution between the two approaches (discussed below). At an intra-monthly timescale, bubble trap data showed highest mean flux occurring on 07 December and the lowest flux 2 days later on 09 December (Fig. 3b, Table S4), which was the date that the hydroacoustic data recorded its highest flux of the intra-monthly survey (lowest was 16 December; Fig. S5b). Again, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[42,67,142,81]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Linkhorst et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[689,67,926,82]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$CH_4$ ebullition across space and time \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[478,946,491,958]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[80,148,467,551]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0156/f439cdf7190a68268e299d163c3556fc355ad3164a901c5f0e0c59811af86f4c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[468,110,944,391]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0193/7a02526d8f1275f0b0bd12681fa436432d0ff0647e9f64597a1d4069c3863f05.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[468,403,944,612]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 1 Maps of the studied bay in CDU reservoir: (a) map of bathymetry as extracted from all segments of the hydroacoustic analysis and categorized into depth categories as further used in this study. The arrow marks the river inflow, and the bracket marks the area studied at the intra-monthly scale; (b) map of the mean ebulitive $\\\\\\\\mathrm{CH}_4$ emission at the intra-annual timescale, based on eight hydroacoustic surveys over 1 year, interpolated over the whole bay; (c) map of the CV at the intra-annual timescale; (d) map of the mean ebulitive $\\\\\\\\mathrm{CH}_4$ emission at the intra-monthly timescale, based on six hydroacoustic surveys over 2 weeks, interpolated over the northern part of the bay, (e) map of the CV at the intra-monthly timescale. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0436/c47574268620a0322356e38d2276bda03b2b657609faa0930ff5ddeeeaa7cfec.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[68,716,501,853]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"hydroacoustic data were the most variable during the month with mean fluxes of $5 - 470\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1}$ compared to $5 - 293\\\\mathrm{mg}$ $\\\\mathrm{Cm}^{-2}\\\\mathrm{d}^{-1}$ for the bubble trap data (Table S4). Ultimately, a higher degree of $\\\\mathrm{CH}_4$ ebullition variability was found over the entire year (hydroacoustics: $581 - 1271\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1}$ , bubble traps: $44 - 527\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1}$ ; Table S3) than over a single month that was characterized by intermediate fluxes (hydroacoustics: $5 - 470\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1}$ , bubble traps: $5 - 293\\\\mathrm{mgCm}^{-2}\\\\mathrm{d}^{-1}$ ; Table S4). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,868,467,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Comparison of spatial and temporal variability of $\\\\mathrm{CH}_4$ ebullition \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,900,501,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As the greatest spatial and temporal coverage was acquired by the hydroacoustic surveys, we primarily use this data set to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[521,716,954,898]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"investigate both the spatial and temporal variability of $\\\\mathrm{CH}_4$ ebullition. At the intra-annual timescale, the spatial variability of $\\\\mathrm{CH}_4$ ebullition was comparable to the temporal variability on about half of the sampling occasions, visible via the overlap in QCD distributions in Fig. 4a. On the other half of the sampling occasions, however, $\\\\mathrm{CH}_4$ ebullition was less variable in space than in time as indicated by the smaller QCD values for the intra-annual spatial data set. $\\\\mathrm{CH}_4$ ebullition varied strongly in both space and time in the intra-monthly data, but the temporal variability was greater than the spatial variability (i.e., higher QCD range for intra-monthly temporal variability in Fig. 4a). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[522,900,954,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Comparing the QCD distributions of both temporal scales (Fig. 4a), we find that $\\\\mathrm{CH}_4$ ebullition varied more at the intra \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[71,67,171,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Linkhorst et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[718,67,954,82]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$CH_4$ ebullition across space and time \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[508,946,517,956]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[210,111,480,305]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0993/53b6bc71d618f0d87a48a96e7fd8d8b02a6825bf544e3b592b300f5af74bddb1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[488,111,756,305]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 2 Ebullitive $\\\\\\\\mathrm{CH}_4$ flux both at the intra-annual and intra-monthly timescale, measured with (a) hydroacoustics, sorted into depth categories of $1.5 - 3\\\\\\\\mathrm{m}$ $(n = 625)$ , $3 - 5\\\\\\\\mathrm{m}$ $(n = 1889)$ , $5 - 10\\\\\\\\mathrm{m}$ $(n = 1538)$ , and $10 - 15\\\\\\\\mathrm{m}$ $(n = 177)$ and (b) bubble traps, sorted into depth categories of $0.9 - 3\\\\\\\\mathrm{m}$ $(n = 67)$ , $3 - 5\\\\\\\\mathrm{m}$ $(n = 86)$ , and $5 - 8\\\\\\\\mathrm{m}$ $(n = 43)$ . The horizontal lines show the median flux, the whiskers show the upper and lower quartiles of the data, and the blue stars indicate the mean flux for each depth category. Ebullition is plotted at a log scale for improvement of visibility. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0340/6d5d7c6eef1a9cc9c2008b08c912db02a3459306e77cdce702176c4a95379509.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[86,389,477,625]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/1010/79b0f482e739dcc533199050e6e7be264585fa15f98ec6a860c83031b2a201a0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[488,388,880,625]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 3 $\\\\\\\\mathrm{CH}_4$ ebullition from the bubble traps in the northern part of the bay, at (a) the intra-annual timescale with monthly sampling over 1 year from August 2016 to August 2017 and (b) the intra-monthly timescale with bi- to tri-daily sampling over 1 month in November–December 2016. The points represent measured fluxes for each bubble trap with their respective water column depth indicated by color. The boxes show the distribution patterns over time, where each box represents all single bubble trap fluxes for each sampling day; the horizontal lines show the medians, and the whiskers show the upper and lower quartile of the data. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0533/5b84dc1d05455d4ed86ef6966d98f784e3d3b2bb3ef8b18ccc74ba0aa50813c4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[39,716,473,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"annual timescale than at the intra-monthly timescale. Similarly, the spatial variability of $\\\\mathrm{CH}_4$ ebullition was more pronounced throughout the intra-annual study than during the intra-monthly study (i.e., intra-annual QCD distribution range was higher in Fig. 4a). We also investigated the temporal variability in $\\\\mathrm{CH}_4$ ebullition at fixed locations over multiple timescales using bubble trap data (Fig. 4b). For this comparison, we added measurements of $\\\\mathrm{CH}_4$ ebullition over one diel cycle at one location at the northernmost area of the same bay (A. Linkhorst et al., unpubl.) to the bubble trap measurements we present here. Ultimately, the temporal variability in $\\\\mathrm{CH}_4$ ebullition was similarly high at diel, intra-monthly and intra-annual timescales, but a larger range in variability was observed at the longer timescales (Fig. 4b). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[493,716,901,746]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Characteristics and $\\\\mathrm{CH}_4$ pore-water content of sediment and pre-flooding soil \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[493,746,928,930]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The thickness of postflooding sediment varied between 0 and $32\\\\mathrm{cm}$ . TOC and TN content, as well as the C/N ratio, were higher in the post-flooding sediment than in the pre-flooding soil (Table S5). There was no systematic difference in the median particle size between sediment and pre-flooding soil (Table S5). Multivariate analyses (principal components analysis and partial least squares regression; not shown) showed no significant relationships between $\\\\mathrm{CH}_4$ ebullition and sediment thickness or characteristics of adjacent cores. Mean $\\\\mathrm{CH}_4$ porewater concentration at the five cores sampled for $\\\\mathrm{CH}_4$ porewater profiles was $323 - 1245\\\\mu \\\\mathrm{M}$ on 18 November 2016 and $1426 - 4024\\\\mu \\\\mathrm{M}$ on 16 December 2016 (Table S2; Fig. S6). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[42,67,140,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Linkhorst et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[689,67,926,82]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$CH_4$ ebullition across space and time \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[478,946,488,958]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[184,110,514,305]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0199/7150590961077e1ad8393ddeac223d3b23e35b3d0b65c3a298346c0f82125c45.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[521,111,839,305]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 4 Frequency distributions of the QCD for comparison of the spatiotemporal variability of $\\\\\\\\mathrm{CH}_4$ ebullition, shown with Gaussian smoothing, measured by (a) hydroacoustics and (b) bubble traps. Spatial variability is the QCD between all grid cells of the northern part of the bay (Plot a, green shading, $n = 37$ ), comparing all sampling campaigns of the respective data set. Temporal variability is the QCD for each grid cell of the northern part of the bay between the sampling campaigns of the respective data set (Plot a, intra-annual, dark purple shading, $n = 8$ ; intra-monthly, light purple shading, $n = 6$ ; Plot b, intra-annual red shading, $n = 9$ , intra-monthly, yellow shading, $n = 11$ ; diel, blue shading, $n = 8$ ). Overlapping peaks suggest that variability is similar, whereas a peak with higher QCD suggests higher variability than whichever other variability with which we are comparing. Fig. S3 aims to visualize the methods behind this figure, and the methods are described in detail in text S5. The diel variability data in plot b is from one 24-h cycle at one location in the study area (A. Linkhorst et al., unpubl.). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0152/22eb4f0e169a58efaf3e65c108ce4beb3a355e36c9c336a1df291288983d505e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[70,443,253,456]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Environmental variables \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,459,503,656]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The water level fluctuated $4.9\\\\mathrm{m}$ over the intra-annual study with four samplings during falling water and five samplings during rising water (Fig. S4). During the intra-monthly study, water level fluctuated only by $0.2\\\\mathrm{m}$ without a clear overall rising or falling trend. Daily mean air temperature $(24\\\\mathrm{h}$ average) was on average $18.2^{\\\\circ}\\\\mathrm{C}$ (range: $13.4 - 21.6^{\\\\circ}\\\\mathrm{C})$ during the intra-annual study and $19.9^{\\\\circ}\\\\mathrm{C}$ (range: $15.2 - 22.6^{\\\\circ}\\\\mathrm{C})$ during the intra-monthly study. Mean surface water temperature during sampling was $24.1^{\\\\circ}\\\\mathrm{C}$ (range: $19.6 - 29.0^{\\\\circ}\\\\mathrm{C})$ and $27.3^{\\\\circ}\\\\mathrm{C}$ (range: $25.4 - 29.5^{\\\\circ}\\\\mathrm{C})$ and mean bottom water temperature during sampling was $23.4^{\\\\circ}\\\\mathrm{C}$ (range $19.7 - 28.3^{\\\\circ}\\\\mathrm{C})$ and $25.1^{\\\\circ}\\\\mathrm{C}$ (range: $24.4 - 25.9^{\\\\circ}\\\\mathrm{C})$ for the intra-annual and intra-monthly studies, respectively (see Tables S3, S4 for more details). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,681,158,696]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,701,496,716]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Variability of $\\\\mathrm{CH}_4$ ebullition at temporal and spatial scales \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,717,500,837]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"While many previous studies have pointed out the importance of spatial variability in low-latitude reservoir $\\\\mathrm{CH}_4$ ebullition (Grinham et al. 2011; DelSontro et al. 2015; Hilgert et al. 2019), and some others have found seasonal patterns (Deshmukh et al. 2014; Yang et al. 2018; Marcon et al. 2019), this is, to our knowledge, the first study to systematically compare the variability of $\\\\mathrm{CH}_4$ ebullition both spatially and over different scales of time. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,837,501,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We found that $\\\\mathrm{CH}_4$ ebullition varied strongly in both space and time, but that the temporal variability of $\\\\mathrm{CH}_4$ ebullition was in general more pronounced than its spatial variability, at both the intra-annual and at the intra-monthly scale (Fig. 4a). We conclude that measurements of $\\\\mathrm{CH}_4$ ebullition made seasonally are likely to capture the most pronounced variability \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[521,443,957,775]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"in emission from our study system. The variability of $\\\\mathrm{CH}_4$ ebullition as measured from the bubble traps over $24\\\\mathrm{h}$ at one site was similar in magnitude as the variability at intramonthly (at 14 sites) and intra-annual timescales (at 4-7 sites). However, the total range in variability was smaller for our diel study than for at the intra-monthly and intra-annual timescales. In two studies with measuring automated bubble traps over 5 months in a temperate reservoir (Maeck et al. 2014) and over 1 year in a subtropical reservoir in Brazil (Marcon et al. 2019), ebullition rates also varied strongly over different timescales from minutes to days. Differences between seasons were suggested to be due to seasonal temperature differences (Maeck et al. 2013, 2014) or stratification and mixing dynamics (Marcon et al. 2019). With respect to variability on shorter time scales, no diel variability was observed during monitoring of $\\\\mathrm{CH}_4$ ebullition in the subtropical Brazilian reservoir (Marcon et al. 2019). Eddy covariance studies (Eugster et al. 2011; Deshmukh et al. 2014; Podgrajsek et al. 2016) achieve high temporal resolution over different scales but since they cannot distinguish between diffusive and ebullitive emission, their findings of temporal variability at different scales are not directly comparable to our results. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[521,778,957,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Our analysis also shows that the spatial variability in $\\\\mathrm{CH}_4$ ebullition can be high (Fig. 4a), even in relatively small areas such as our study bay $(0.326\\\\mathrm{km}^2)$ . It is possible that increasing the survey area will result in greater overall spatial variability of ebullitive emission, because other areas will have different depth, and possibly different sediment characteristics and deposition rate, as well as bottom water properties. To attain representative measurements of system-wide $\\\\mathrm{CH}_4$ ebullition, it is crucial that measurements are distributed in space as well as in time. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[71,67,171,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Linkhorst et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[718,67,954,82]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$CH_4$ ebullition across space and time \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[506,946,519,956]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[40,110,264,124]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Drivers of temporal variability \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[39,125,473,427]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The temporal variability of $\\\\mathrm{CH_4}$ ebullition measured via both the hydroacoustic and bubble trap approaches was related to water level, pressure changes on the sediment, as well as surface and bottom water temperature (Fig. 5; Tables S3, S4). The highest fluxes occurred at low water level (see Fig. S4 for a hydrograph) for both timescales of the hydroacoustic data (Fig. 5a,e), but patterns were less evident for bubble trap data, which admittedly cover a much smaller surface area. Low water level translates into lower hydrostatic pressure on the sediment, which eases the release of bubbles from the sediment, a phenomenon that has been observed in temperate reservoirs (Maeck et al. 2014; Harrison et al. 2017). Accordingly, $\\\\mathrm{CH_4}$ ebullition was higher during periods of decreasing pressure on the sediment than during periods of increasing pressure on the sediment (Fig. 5b,f), in agreement with previous studies (Mattson and Likens 1990; Ostrovsky 2003; Harrison et al. 2017). However, temperature variability between dry rainy season may also likely have played a role, and without experimental work, it is difficult to disaggregate the physical from the biological drivers. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[40,429,472,474]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Temperature has a strong positive effect on $\\\\mathrm{CH}_4$ production rates (Yvon-Durocher et al. 2014) and $\\\\mathrm{CH}_4$ ebullition (Aben et al. 2017). Both bottom and surface water temperature were \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[493,108,926,216]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"related to mean ebullitive $\\\\mathrm{CH}_4$ flux across the study areas (Fig. 5c,d,g,h). Surface water temperature was a good predictor of $\\\\mathrm{CH}_4$ ebullition for both timescales, albeit less so at the intramonthly timescale when temperature varied less (Fig. 5c,g). Bottom water temperature from the temperature profile locations was positively related to $\\\\mathrm{CH}_4$ ebullition measured via both approaches at the intra-annual timescale (Fig. 5d). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[493,232,702,246]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Drivers of spatial variability \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[493,246,928,474]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Some previous studies have found significant relationships between $\\\\mathrm{CH}_4$ ebullition and depth in reservoirs (Keller and Stallard 1994; Deshmukh et al. 2014), whereas others have not (DelSontro et al. 2011, 2015; Hilgert et al. 2019). We did not find a consistent trend of $\\\\mathrm{CH}_4$ ebullition variability over water depth in our study area (Fig. 5), and even though the bathymetric information is based on high-resolution measurements (Fig. S2), we cannot exclude that averaging both water depth and ebullition flux per grid cell may hide smaller-scale patterns. Furthermore, spatial variability in $\\\\mathrm{CH}_4$ ebullition appears not to be related to distance from the shore as high fluxes were found throughout the bay (Fig. 1b), contrary to what has been reported for a tropical floodplain lake (Peixoto et al. 2015). High ebullitive fluxes were observed in the shallow area $(1 - 5\\\\mathrm{m})$ closest to the river inflow but also in the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[40,507,931,870]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 5 Mean eullutive $\\\\\\\\mathrm{CH}_4$ flux per sampling day as measured with hydroacoustics (circles) and bubble traps (triangles) during the intra-annual (a-d; blue) and intra-monthly (e-h; red) study, plotted against water level (a, e); total pressure change, that is, the difference of pressure on the sediment between the previous day and the sampling day (b, f); surface water temperature (c, g); and bottom water temperature (d, h). Linear regressions with a significant slope are marked with a star. Detailed regression statistics can be found in Tables S7 (hydroacoustics) and S8 (bubble traps). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0621/f7b308140c5dc20a693619add5348ff0fdba033dee816283a1a58a86f181af62.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[40,67,140,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Linkhorst et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[689,67,926,82]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$CH_4$ ebullition across space and time \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[478,946,490,956]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[73,110,500,549]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"deepest area (10–15 m) at the southern end of the bay (Figs. 1a,b, 2), contrasting some studies that did not observe ebullition deeper than 10 m (Abril et al. 2005). Interestingly, the high-flux area closest to the river inflow was characterized by high temporal variability in ebullition, while the high-flux area in the southern end of the bay did not vary as much over the year (Fig. 1c). The lack of direct relationship between $\\\\mathrm{CH}_4$ ebullition and water depth may be related to the heterogeneity of sediment deposition and bottom morphometry of reservoirs (Mendonça et al. 2014), particularly near a river inflow; however, in contrast to other studies (Sobek et al. 2012; Wilkinson et al. 2015; Grinham et al. 2018; Hilgert et al. 2019), our own data do not indicate any relationship between sediment characteristics (i.e., OC content, N content, C/N ratio, grain size, thickness of the sediment layer; Table S5) and $\\\\mathrm{CH}_4$ ebullition (not shown). This may be due to the lower water level in the dry seasons such as during the extreme drought in 2014 (Kosten et al. 2018), during which we observed that the shallowest areas closest to the river inflow (0–5 m) had dried out and were covered with grass. This fresh input of organic matter likely stimulated high $\\\\mathrm{CH}_4$ production rates upon inundation prior to our study (Prairie et al. 2018), and may blur relationships with sediment characteristics. Also, we lack core sampling sites in the southernmost part of the bay, an area with high $\\\\mathrm{CH}_4$ ebullition. We included information on sediment accumulation from three additional sediment cores from the southern part of the bay (Table S6), which, however, did not show higher sediment deposition rates than in the shallower northern part of the bay. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[71,565,410,594]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\mathrm{CH_4}$ pore-water concentration in sediment and preflooding soil \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[73,596,500,760]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We measured $\\\\mathrm{CH}_4$ concentrations in the pore water of sediment and preflooding soil before and after the intra-monthly study to see if we can explain total $\\\\mathrm{CH}_4$ ebullition by an equivalent loss in $\\\\mathrm{CH}_4$ from the sediment. However, $\\\\mathrm{CH}_4$ concentrations in the pore water were higher at the end of the intra-monthly sampling campaign than at its start, indicating that $\\\\mathrm{CH}_4$ concentrations fluctuate over shorter timescales than 1 month. Nevertheless, 7 of 10 pore-water profiles contained at least one depth layer where $\\\\mathrm{CH}_4$ was oversaturated (Fig. S6), indicating that the sediment is prone to form and release bubbles, in congruence with the measured ebullitive $\\\\mathrm{CH}_4$ fluxes. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[73,763,500,927]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Interestingly, in 5 of 10 profiles, we observed supersaturated $\\\\mathrm{CH}_4$ layers in preflooding soils (Fig. S6; Table S2). However, the sampled spots were shallow enough ( $<9\\\\mathrm{m}$ ) to be exposed to air at least for 1-month long periods during previous extreme dry seasons (see historical water level in Fig. S7). Therefore, even though we observed ebullition coming from deep layers that we determined as preflooded soils, it might be that those layers were fed by fresh terrestrial organic material when roots of terrestrial plants have entered deeper bottom layers during exposure to the atmosphere. As fresh land plant material can rapidly be degraded to $\\\\mathrm{CH}_4$ at anoxic conditions (Grasset et al. 2018), \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,110,952,275]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"this fresh input of organic matter likely stimulated high $\\\\mathrm{CH_4}$ production rates upon inundation prior to our study (Prairie et al. 2018). The water level fluctuated over a total range of $15\\\\mathrm{m}$ between 2003 and 2016, with a water level fluctuation between dry and rainy season of $6 - 13\\\\mathrm{m}$ (Fig. S7). Essentially, this means that large areas of the reservoir bottom have at some point been exposed to the atmosphere and may contain rather fresh organic material in their deep bottom layers. Because of the supply of fresh organic material, these parts of the reservoir bottom can emit $\\\\mathrm{CH_4}$ even 22 years after dam construction and initial flooding of the land. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,292,844,306]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Comparison of different upscaling scenarios \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,307,952,427]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We upscaled $\\\\mathrm{CH}_4$ ebullition for the entire study area using different temporal and spatial resolutions to investigate the effect of measurement variability on upscaled estimates. The upscaling scenarios as shown in Fig. S8 and Table 1 are compared to our spatiotemporally resolved best estimate (33 t C yr $^{-1}$ ; Fig. 1b), which is based on the interpolation of spatially resolved hydroacoustic $\\\\mathrm{CH}_4$ ebullition measurements at a monthly resolution over 1 year. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,429,952,594]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The first scenario extrapolates from a single, yet spatially resolved, measurement occasion to an annual flux, similar to DelSontro et al. (2011). Extrapolation from the lowest and highest mean fluxes that we observed during our annual survey (09 March and 03 July) to the whole year led to $\\\\mathrm{CH}_4$ emission of 8 and $81\\\\mathrm{tCyr}^{-1}$ from our study area, respectively. Extrapolation from the months of lowest and highest flux during the year thus differed by $76\\\\%$ and $145\\\\%$ from our best estimate (Fig. S8b,c; Table 1), illustrating the significance of seasonally resolved measurements of $\\\\mathrm{CH}_4$ ebullition for calculating whole-system estimates. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,596,952,837]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The second scenario extrapolates total flux from measurements at only a few locations but over several sampling occasions, similar to Dos Santos et al. (2006). Performing extrapolations using only data from areas with the highest ebullitive fluxes (as derived from interpolation of our measured fluxes, spots marked in Fig. S8d) would overestimate total $\\\\mathrm{CH}_4$ ebullition by $174\\\\%$ ( $92\\\\mathrm{tCyr}^{-1}$ ) compared to our spatiotemporally resolved best estimate ( $33\\\\mathrm{tCyr}^{-1}$ ). If, on the other hand, we extrapolated using only data from the areas with lowest ebullition (spots marked in Fig. S8e), we would underestimate the total flux by $79\\\\%$ ( $7\\\\mathrm{tCyr}^{-1}$ ; Table 1). Although these are worst-case scenarios, we can conclude that disregarding spatial variability also risks introducing large errors in whole-system estimates of $\\\\mathrm{CH}_4$ ebullition. Ultimately, spatially resolved measurements at seasonal temporal resolution are required for robust quantification of $\\\\mathrm{CH}_4$ ebullition. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,837,952,927]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The third scenario extrapolates total flux from measurements of the bubble traps, which compared to hydroacoustic surveys have low spatial resolution but integrate over longer temporal scales at fixed sites. Upscaling from the temporally resolved bubble trap measurements of the inter-annual study (4-7 traps in the northern part of the bay; Fig. S8f) to the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[71,68,169,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Linkhorst et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[718,68,954,81]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$CH_4$ ebullition across space and time \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[508,946,517,956]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"9 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[40,170,928,355]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0740/87d3cac735e13cfd99dbbf7f0c1397b7a4adb66c1f667360db7fa8052d975c65.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Scenario</td><td>Time</td><td>Data set</td><td>Mean flux (mg C m-2d-1)</td><td>Median flux (mg C m-2d-1)</td><td>Total flux (t C yr-1)</td></tr><tr><td>*</td><td>Whole year</td><td>Hydroacoustics, intra-annual</td><td>281</td><td>195</td><td>33</td></tr><tr><td rowspan=\\\"2\\\">1</td><td>09 Mar. 2017 (survey with highest flux)</td><td>Hydroacoustics, intra-annual</td><td>681</td><td>385</td><td>81</td></tr><tr><td>03 Jul. 2017 (survey with lowest flux)</td><td>Hydroacoustics, intra-annual</td><td>71</td><td>4</td><td>8</td></tr><tr><td rowspan=\\\"2\\\">2</td><td>Whole year</td><td>Hydroacoustics, intra-annual, 20 grid cells of highest flux</td><td>769</td><td>640</td><td>92</td></tr><tr><td>Whole year</td><td>Hydroacoustics, intra-annual, 20 grid cells of lowest flux</td><td>62</td><td>62</td><td>7</td></tr><tr><td>3</td><td>Whole year</td><td>Bubble traps, intra-annual, upscaled according to bathymetry</td><td>173</td><td>128</td><td>21</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. Mean, median and total ebullitive $\\\\\\\\mathrm{CH}_4$ emission for different upscaling scenarios. The total flux was calculated from the product of the mean flux and total bay area (0.326 km²). The star marks our best estimate, based on spatiotemporally resolved hydroacoustic measurements, using the mean from all grid cells from all sampling campaigns over the year (Fig. 1b). The other upscaling scenarios are illustrated in Fig. S7. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[39,373,470,434]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"entire bay area by means of bathymetry (i.e., applying the $\\\\mathrm{CH}_4$ ebullition means of the depth categories in Fig. 2) results in a total ebullitive $\\\\mathrm{CH}_4$ flux of $21\\\\mathrm{tCyr}^{-1}$ , underestimating our spatiotemporally resolved best estimate by $36\\\\%$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[37,434,473,630]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This result illustrates the potential effect of low spatial resolution when sampling, but also the fact that bubble traps were only deployed at depths of $0.9 - 8\\\\mathrm{m}$ in the northern part of the bay, thereby missing high ebullition areas in the south of the bay that were only recorded by the hydroacoustic surveys. This difference in spatial resolution and total areal coverage most likely led to the large discrepancy in daily mean $\\\\mathrm{CH}_4$ ebullition between hydroacoustic surveys (581-1271 mg C $\\\\mathrm{m}^{-2}\\\\mathrm{d}^{-1}$ ; Fig. S5a) and bubble trap deployments (44-527 mg C $\\\\mathrm{m}^{-2}\\\\mathrm{d}^{-1}$ ; Fig. 3a). The overall lower mean fluxes measured by bubble trap deployments compared to hydroacoustics indicate that a better temporal resolution of $\\\\mathrm{CH}_4$ ebullition does not necessarily compensate for lower spatial resolution. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[40,656,138,670]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Implications \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[39,670,470,851]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Our study shows that to derive a robust estimate of $\\\\mathrm{CH_4}$ ebullition from a tropical reservoir, measurements must be conducted during different seasons of the year, at least once during falling and once during rising water level, and that these measurements should be spatially well resolved as well. Hydroacoustics is currently the most well-suited method for accomplishing seasonally distributed samplings at high spatial coverage. Time is the biggest constraint for using an echosounder to sufficiently resolve ebullition variability over time and space. For example, each individual hydroacoustic survey of our studied bay took about $2.3\\\\mathrm{h}$ , but we only covered $3\\\\%$ (i.e., $0.326\\\\mathrm{km}^2$ ) of this relatively small reservoir ( $12\\\\mathrm{km}^2$ ). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[39,853,473,932]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"While our study indicates that a few seasonally distributed measurement campaigns are required to capture the most pronounced temporal variability in $\\\\mathrm{CH}_4$ ebullition, a challenge for future studies is how to select sampling locations within individual systems for representative measurements of the variability of system-wide $\\\\mathrm{CH}_4$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[493,373,926,510]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ebullition, especially in large waterbodies in which even massive sampling efforts will only be able to cover a minute fraction of the total area. Unfortunately, we cannot offer a concrete advice regarding the spatial resolution necessary for accurate system-wide estimates of $\\\\mathrm{CH}_4$ ebullition, but we do suggest measuring flux in river inflow bays as well as regions not influenced by such external inputs. It cannot be overstated either that the hydroacoustic approach better resolved the spatial variability in ebullitive flux in all regions than a dozen randomly placed bubble traps did. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,545,581,559]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[495,564,926,927]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Aben, R. C. H., et al. 2017. Cross continental increase in methane ebullition under climate change. Nat. 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Lakes and reservoirs as regulators of carbon cycling and climate. Limnol. Oceanogr. 54: 2298-2314. doi:10.4319/lo.2009.54.6_part_2.2298 \\\"]\",\n \"page_idx\": \"11\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[496,110,924,610]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Tušer, M., T. Picek, Z. Sajdlova, T. Júza, M. Muška, and J. Frouzová. 2017. Seasonal and spatial dynamics of gas ebullition in a temperate water-storage reservoir. Water Resour. Res. 53: 8266-8276. doi:10.1002/2017WR020694 \\\",\\\"Varadharajan, C., and H. F. Hemond. 2012. Time-series analysis of high-resolution ebullition fluxes from a stratified, freshwater lake. J. Geophys. Res. 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Zeng. 2013. Spatial and temporal patterns of greenhouse gas emissions from three gorges reservoir of China. Biogeosciences 10: 1219-1230. doi:10.5194/bg-10-1219-2013 \\\",\\\"Zheng, H., X. Zhao, T. Zhao, F. Chen, W. Xu, X. Duan, X. Wang, and Z. Ouyang. 2011. Spatial-temporal variations of methane emissions from the Ertan hydroelectric reservoir in Southwest China. Hydrol. Process. 25: 1391-1396. doi:10.1002/hyp.7903 \\\"]\",\n \"page_idx\": \"11\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[496,621,633,635]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgments \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[495,637,926,751]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We are grateful to Carlos Henrique Estrada for his help with the daily and monthly surveys, and Icaro Barbosa and Carlos Henrique Estrada for sediment sampling. The research leading to these results has been funded by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement $n^{\\\\circ}$ 336642. S.S. received additional support by the program Pesquisador Visitante Especial, Ciencia sem Fronteiras, No. 401384/2014-4, and N. B. received additional support by Fundação de Amparo à Pesquisa do Estado de Minas Gerais/FAPEMIG (CRA APQ 03045/16). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[495,784,635,798]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conflict of Interest \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,800,620,813]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"None declared. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[787,831,924,845]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Submitted 08 July 2019 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[769,846,924,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Revised 15 November 2019 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[774,862,924,875]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Accepted 03 January 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[733,884,924,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Associate editor: Kelly Benoit-Bird \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[42,67,140,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Linkhorst et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[689,67,926,82]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$CH_4$ ebullition across space and time \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[475,946,493,956]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"12 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1002/lno.11410"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Earth and Atmospheric Sciences"},"sha256":{"kind":"string","value":"bd1a83c9a01252a822c9fd8b2e6a52b5541224af003633458a8724b859581866"},"title":{"kind":"string","value":"Comparing methane ebullition variability across space and time in a Brazilian reservoir"}}},{"rowIdx":240,"cells":{"abstract":{"kind":"string","value":""},"author":{"kind":"string","value":"Kong Mun Lo|Edward R.T. Tiekink|See Mun Lee"},"content_list":{"kind":"list like","value":[{"bbox":"[82,79,539,97]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"See Mun Lee, Kong Mun Lo and Edward R.T. Tiekink\\* ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,102,852,199]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Crystal structure of dichloridodimethylbis(tri-4- tolylphosphane oxide-κO)-tin(IV), C44H48Cl2O2P2Sn ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[80,234,480,436]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0787/564a6494761ddec77555cee9a3d3ffb854e5e9492eb8aba918f1b78d81782e1d.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[82,455,433,495]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1515/ncrs-2020-0378 Received July 21, 2020; accepted August 18, 2020; available online August 27, 2020 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,513,144,525]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[82,529,482,592]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\mathrm { C } _ { 4 4 } \\mathrm { H } _ { 4 8 } \\mathrm { C l } _ { 2 } \\mathrm { O } _ { 2 } \\mathrm { P } _ { 2 } \\mathrm { S n } .$ , orthorhombic, Pbca (no. 61), $a = 1 7 . 8 3 1 2 ( 1 ) \\textrm { \\AA }$ , $b = 1 2 . 0 2 9 1 ( 1 ) \\mathrm { ~ \\AA ~ }$ , $c = 1 8 . 5 8 9 5 ( 1 ) \\mathrm { ~ \\AA ~ }$ , $V = 3 9 8 7 . 3 2 ( 5 ) \\mathrm { ~ \\AA ~ } ^ { 3 }$ , $Z = 4$ , $R _ { \\mathrm { g t } } ( F ) = 0 . 0 1 9 6$ , $w R _ { \\mathrm { r e f } } ( F ^ { 2 } ) = 0 . 0 5 6 4 ;$ ， $T = 1 0 0 ( 2 ) \\textrm { K }$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,602,208,616]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CCDC no.: 2023888 ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[84,626,480,691]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The molecular structure is shown in the figure. Table 1 contains crystallographic data and Table 2 contains the list of the atoms including atomic coordinates and displacement parameters. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,706,213,720]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Source of material ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[84,723,480,770]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Tri(4-tolyl)phosphine oxide was prepared by the oxidation of tri(4-tolyl)phosphine (Merck) with $3 0 \\%$ hydrogen peroxide (Merck) in ethanol. Dimethyltin dichloride (Merck, $_ { 0 . 2 2 \\ \\mathrm { g } }$ , ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[497,261,897,422]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0193/48e5c7cdb7fb77b3834c6353e113b98e832959154ab33398126ad8fce661571d.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":"<table><tr><td>Crystal:</td><td>Colourless prism</td></tr><tr><td>Size: Wavelength:</td><td>0.11×0.09×0.05 mm Cu Kα radiation (1.54184 A)</td></tr><tr><td></td><td></td></tr><tr><td>μ:</td><td>7.37 mm-1</td></tr><tr><td>Diffractometer,scan mode:</td><td>XtaLAB Synergy,W</td></tr><tr><td>0max,completeness:</td><td>67.1°,>99%</td></tr><tr><td>N(hkl measured,N(hkl)unique, Rint:</td><td>47255,3553,0.024</td></tr><tr><td>Criterion for lobs,N(hkl)gt:</td><td>lobs>2o(obs),3391</td></tr><tr><td>N(param)refined:</td><td>235</td></tr><tr><td>Programs:</td><td>CrysAlisPRO [1], SHELX [2,3], WinGX/ORTEP [4]</td></tr></table>","table_caption":"[\"Table 1: Data collection and handling. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[495,490,897,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/1002/a5dd70bbd51b8c44d5f9a88d4518ea58393598803b83b2ea99565ebb89d07cbd.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":"<table><tr><td>Atom</td><td>X</td><td>y</td><td>Z</td><td>Uiso*/Ueq</td></tr><tr><td>Sn1</td><td>0.5</td><td>0.5</td><td>0.5</td><td>0.01216(7)</td></tr><tr><td>Cl1</td><td>0.55361(2)</td><td>0.67812(3)</td><td>0.55689(2)</td><td>0.02163(10)</td></tr><tr><td>P1</td><td>0.65744(2)</td><td>0.54160(3)</td><td>0.38148(2)</td><td>0.01201(9)</td></tr><tr><td>01</td><td>0.59770(6)</td><td>0.48389(9)</td><td>0.42508(6)</td><td>0.0160(2)</td></tr><tr><td>C1</td><td>0.68095(8)</td><td>0.45559(12)</td><td>0.30549(8)</td><td>0.0138(3)</td></tr><tr><td>C2</td><td>0.74054(10)</td><td>0.48362(14)</td><td>0.26046(9)</td><td>0.0186(3)</td></tr><tr><td>H2</td><td>0.768419</td><td>0.549541</td><td>0.269227</td><td>0.022*</td></tr><tr><td>C3</td><td>0.75929(9)</td><td>0.41574(14)</td><td>0.20297(8)</td><td>0.0188(3)</td></tr><tr><td>H3</td><td>0.799884</td><td>0.435761</td><td>0.172513</td><td>0.023*</td></tr><tr><td>C4</td><td>0.71925(9)</td><td>0.31833(13)</td><td>0.18929(8)</td><td>0.0172(3)</td></tr><tr><td>C5</td><td>0.65885(9)</td><td>0.29248(13)</td><td>0.23361(9)</td><td>0.0187(3)</td></tr><tr><td>H5</td><td>0.630181</td><td>0.227541</td><td>0.224138</td><td>0.022*</td></tr><tr><td>C6</td><td>0.63961(9)</td><td>0.35998(13)</td><td>0.29159(8)</td><td>0.0163(3)</td></tr><tr><td>H6</td><td>0.598414</td><td>0.340793</td><td>0.321517</td><td>0.020*</td></tr><tr><td>C7</td><td>0.74249(10)</td><td>0.24351(14)</td><td>0.12839(9)</td><td>0.0227(4)</td></tr><tr><td>H7A</td><td>0.725930</td><td>0.167381</td><td>0.138384</td><td>0.034*</td></tr><tr><td>H7B</td><td>0.797212</td><td>0.244893</td><td>0.123538</td><td>0.034*</td></tr><tr><td>H7C</td><td>0.719477</td><td>0.269520</td><td>0.083571</td><td>0.034*</td></tr><tr><td>C8</td><td>0.74137(8)</td><td>0.56116(13)</td><td>0.43352(8)</td><td>0.0139(3)</td></tr><tr><td>C9</td><td>0.79463(9)</td><td>0.64230(13)</td><td>0.41671(8)</td><td>0.0157(3)</td></tr><tr><td>H9</td><td>0.785775</td><td>0.692252</td><td>0.378048</td><td>0.019*</td></tr><tr><td>C10</td><td>0.86057(9)</td><td>0.65024(13)</td><td>0.45636(8)</td><td>0.0167(3)</td></tr><tr><td>H10</td><td>0.896634</td><td>0.705307</td><td>0.444298</td><td>0.020*</td></tr><tr><td>C11</td><td>0.87430(9)</td><td>0.57810(14)</td><td>0.51372(9)</td><td>0.0175(3)</td></tr><tr><td>C12</td><td>0.82115(10)</td><td>0.49717(13)</td><td>0.52984(9)</td><td>0.0192(4)</td></tr><tr><td>H12</td><td>0.830105</td><td>0.447167</td><td>0.568449</td><td>0.023*</td></tr><tr><td>C13</td><td>0.75509(12)</td><td>0.48820(14)</td><td>0.49040(9)</td><td>0.0179(4)</td></tr><tr><td>H13</td><td>0.719386</td><td>0.432482</td><td>0.502176</td><td>0.021*</td></tr><tr><td>C14</td><td>0.94453(9)</td><td>0.58833(15)</td><td>0.55813(9)</td><td>0.0232(4)</td></tr><tr><td>H14A</td><td>0.932651</td><td>0.624533</td><td>0.603959</td><td>0.035*</td></tr><tr><td>H14B</td><td>0.981554</td><td>0.632972</td><td>0.531980</td><td>0.035*</td></tr><tr><td>H14C</td><td>0.965122</td><td>0.514157</td><td>0.567357</td><td>0.035*</td></tr><tr><td>C15</td><td>0.63062(8)</td><td>0.67447(12)</td><td>0.34630(8)</td><td>0.0141(3)</td></tr><tr><td>C16</td><td>0.60132(9)</td><td>0.68328(13)</td><td>0.27686(8)</td><td>0.0168(3)</td></tr><tr><td>H16</td><td>0.600004</td><td>0.619885</td><td>0.246405</td><td>0.020*</td></tr><tr><td>C17</td><td>0.57412(9)</td><td>0.78443(14)</td><td>0.25226(9)</td><td>0.0197(3)</td></tr><tr><td>H17</td><td>0.553345</td><td>0.789359</td><td>0.205312</td><td>0.024*</td></tr><tr><td>C18</td><td>0.57689(9)</td><td>0.87852(13)</td><td>0.29541(9)</td><td>0.0186(3)</td></tr><tr><td>C19</td><td>0.60768(9)</td><td>0.86981(13)</td><td>0.36417(9)</td><td>0.0172(3)</td></tr><tr><td>H19</td><td>0.610976</td><td>0.934087</td><td>0.393697</td><td>0.021*</td></tr><tr><td>C20</td><td>0.63349(8)</td><td>0.76888(13)</td><td>0.39001(8)</td><td>0.0158(3)</td></tr><tr><td>H20</td><td>0.653141</td><td>0.763812</td><td>0.437398</td><td>0.019*</td></tr><tr><td>C21</td><td>0.54820(11)</td><td>0.98855(14)</td><td>0.26854(11)</td><td>0.0274(4)</td></tr><tr><td>H21Aa</td><td>0.554656</td><td>1.044997</td><td>0.306052</td><td>0.041*</td></tr><tr><td>H21Ba</td><td>0.576363</td><td>1.010491</td><td>0.225559</td><td>0.041*</td></tr><tr><td>H21Ca</td><td>0.494876</td><td>0.981855</td><td>0.256517</td><td>0.041*</td></tr><tr><td>H21Da</td><td>0.529274</td><td>0.979899</td><td>0.219367</td><td>0.041*</td></tr><tr><td>H21Ea</td><td>0.507567</td><td>1.014404</td><td>0.299859</td><td>0.041*</td></tr><tr><td>H21Fa</td><td>0.589054</td><td>1.043040</td><td>0.268902</td><td>0.041*</td></tr><tr><td>C22</td><td>0.44035(9)</td><td>0.59927(14)</td><td>0.42539(9)</td><td>0.0186(3)</td></tr><tr><td>H22A</td><td>0.403899</td><td>0.553064</td><td>0.399644</td><td>0.028*</td></tr><tr><td>H22B</td><td>0.475561</td><td>0.632011</td><td>0.390908</td><td>0.028*</td></tr><tr><td>H22C</td><td>0.413961</td><td>0.658687</td><td>0.451089</td><td>0.028*</td></tr></table>","table_caption":"[\"Table 2: Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters $( \\\\mathring { \\\\mathsf { A } } ^ { 2 } )$ . \"]","table_footnote":"[\"aOccupancy: 0.5. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[82,41,176,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"DE GRUYTER ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[84,805,477,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"\\*Corresponding author: Edward R.T. Tiekink, Research Centre for Crystalline Materials, School of Science and Technology, Sunway University, Bandar Sunway 47500 , Selangor Darul Ehsan, Malaysia, e-mail: edwardt@sunway.edu.my. https://orcid.org/0000-0003- 1401-1520 See Mun Lee and Kong Mun Lo: Research Centre for Crystalline Materials, School of Science and Technology, Sunway University, Bandar Sunway 47500, Selangor Darul Ehsan, Malaysia ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[82,925,433,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Open Access. © 2020 See Mun Lee et al., published by De Gruyter. International License. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[638,41,915,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Z. Kristallogr. NCS 2020; 235(6): 1527–1529 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[917,41,937,63]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"a ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[435,925,512,938]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"BY ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[100,105,500,467]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":"[\"\"]","table_footnote":"[\"\"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[102,495,500,674]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$1 . 0 \\ \\mathrm { m m o l } ,$ ) and tri $\\lceil p$ -tolyl)phosphine oxide $\\left( 0 . 6 4 \\ \\mathbf { g } , 2 . 0 \\ \\mathrm { m m o l } \\right)$ were heated in $9 5 \\%$ ethanol $\\mathrm { 3 0 ~ m L } )$ for 1 h and filtered. After filtration, the filtrate was evaporated slowly until a white crystalline compound was obtained. Yield: $0 . 5 2 \\mathrm { ~ g ~ } ( 3 0 . 2 \\% )$ . M. pt. (Stuart SMP30 digital melting point apparatus; uncorrected): 460–462 K. IR (Bruker Vertex 70v FTIR Spectrometer; $\\mathrm { c m } ^ { - 1 }$ ): 1598 $\\mathrm { ( m ) }$ $\\mathsf { v } ( \\mathsf { C } \\mathrm { = C } )$ , 1496 (m) $\\mathsf { v } ( \\mathsf { C } \\mathrm { = C } )$ , 1140 (s) $\\mathsf { v } ( \\mathsf { P = } 0 )$ , 1083 (s) ν(P-Ar). ${ \\bf \\delta _ { 1 } } _ { \\bf H }$ NMR (Bruker Ascend $4 0 0 ~ \\mathrm { M H z }$ NMR spectrometer; $\\mathrm { C D C l } _ { 3 }$ ; ppm relative to $\\mathbf { M e } _ { 4 } \\mathbf { S i }$ ): δ 2.21 (s, 6H, $\\mathrm { C H } _ { 3 }$ ), 2.40 (s, 18H, $\\mathrm { C H } _ { 3 } .$ ), 6.88–7.54 (m, 24H, Ph-H). ${ } ^ { 1 3 } { \\bf C } \\{ { \\bf H } \\}$ NMR (as for $^ 1 \\mathrm { H }$ NMR): 21.6 $\\left( \\mathrm { C H } _ { 3 } \\right)$ , 48.5 $\\mathrm { ( C H } _ { 3 } )$ ), 116.9, 129.2, 142.6, 149.9 (Ph—C). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[102,689,247,703]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Experimental details ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[102,707,500,788]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The C-bound H atoms were geometrically placed $\\left( \\mathrm { C - H } = 0 . 9 5 – 0 . 9 8 \\mathrm { \\ : \\mathring { A } } \\right)$ ) and refined as riding with $U _ { \\mathrm { i s o } } ( \\mathrm { H } ) { = } 1 . 2 \\mathrm { - }$ $1 . 5 U _ { \\mathrm { e q } } ( \\mathrm { C } )$ . The $\\mathrm { H }$ atoms of the C21-methyl group were found to be statistically disordered over two positions with one orientation rotated $6 0 ^ { \\circ }$ with respect to the other. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[102,803,171,817]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Comment ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[102,820,500,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The title compound, $\\mathrm { M e } _ { 2 } \\mathrm { S n C l } _ { 2 } \\mathrm { [ O = P ( 4 \\mathrm { - } t o l y l ) _ { 3 } ] } _ { 2 }$ , (I), was investigated in connection with recent structural studies of bis(sulphoxide) [5], bis(triorganophosphane) [6] and bis (triorganoarsane) [7] adducts of ${ \\mathrm { R } } _ { 2 } { \\mathrm { S n C l } } _ { 2 }$ . The common feature of the crystallographically determined structures of molecules of the general formula $\\mathrm { R } _ { 2 } \\mathrm { S n C l } _ { 2 } [ 0 { = } \\mathrm { P R } ^ { \\prime } { } _ { 3 } ] _ { 2 }$ is the adoption of an all-trans $\\mathrm { C } _ { 2 } \\mathrm { C l } _ { 2 } \\mathrm { O } _ { 2 }$ coordination geometry for Sn; see ref. [6] for a review. This is also true for the structure of (I), for which the crystal and molecular structures are described herein. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,81,914,145]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,148,915,292]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The molecular structure of (I) is shown in the figure $7 0 \\%$ displacement ellipsoids; unlabelled atoms are related by the symmetry operation (i) $1 - x , \\ 1 - y , \\ 1 - z )$ . The Sn atom is located on a centre of inversion and is coordinated by symmetry-related pairs of methyl-C [2.1168(15) Å], Cl [2.5735(4) Å] and oxide-O [2.2387(11) $\\mathring \\mathrm { A } ]$ atoms. The resulting $\\mathrm { C } _ { 2 } \\mathrm { C l } _ { 2 } \\mathrm { O } _ { 2 }$ donor set is based on an octahedron with all likeatoms being mutually trans, in accord with expectation [6]. The Sn—O1—P1 angle is bent, at $1 4 7 . 6 0 ( 7 ) ^ { \\circ }$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,296,915,441]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Very recently, the closely related structure formulated as $( 4 { \\cdot } \\mathrm { C l } \\mathrm C _ { 6 } \\mathrm H _ { 4 } ) _ { 2 } \\mathrm { S n C l } _ { 2 } [ 0 { = } \\mathrm { P } ( 4 { \\cdot } \\mathrm { t o l y l } ) _ { 3 } ] _ { 2 }$ was described [6]. As for (I), the Sn atom is situated on a centre on inversion. Reflecting the presence of the electron-withdrawing tin-bound 4-chlorophenyl substituents, the Sn—C [2.1441(15) Å], Sn—Cl [2.5333(4) Å] and Sn—O [2.1746(11) $\\mathring \\mathrm { A } ]$ bond lengths have elongated, contracted and contracted, respectively, compared with (I), with, relatively electropositive tin-bound methyl groups. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,443,915,654]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the crystal, tolyl- $\\mathrm { { C - H \\cdot \\cdot \\cdot C l } }$ $\\mathrm { [ C 1 7 - H 1 7 \\cdot \\cdot \\cdot C l 1 ^ { i i } }$ : $\\mathrm { H 1 7 \\cdot \\cdot \\cdot C l 1 ^ { i i } } = 2 . 7 9 \\mathrm { ~ \\AA ~ }$ , $\\mathrm { C 1 7 \\cdot \\cdot \\cdot C l 1 ^ { i i } } = 3 . 6 7 7 9 ( 1 7 ) ~ .$ Å with angle at $\\mathrm { H } 1 7 = 1 5 7 ^ { \\circ }$ for (ii) $x , ~ 3 / 2 - y , ~ - 1 / 2 + z ]$ interactions connect molecules into a supramolecular layer in the bc-plane as each molecule participates in four such interactions, i.e. two donor and two acceptor interactions per molecule. The connections between layers to consolidate the three-dimensional architecture are of the type tolyl-methyl- $\\mathrm { C - H } { \\cdot } \\cdot \\cdot \\pi ( \\mathrm { t o l y l } )$ $\\scriptstyle [ \\mathbf { C 7 - H 7 c \\cdot \\cdot \\cdot C g } ( \\mathbf { C 8 - C 1 } 3 ) ^ { \\mathrm { i i i } }$ : $\\mathrm { H 7 c } \\cdot \\cdot \\cdot \\mathrm { C g ( C 8 - C 1 3 ) ^ { i i i } } = 2 . 8 6 \\mathrm { \\normalfont ~ \\AA }$ with angle at $\\mathrm { H } 7 \\mathbf { c } = 1 5 4 ^ { \\circ }$ for (iii) $3 / 2 - x , \\ 1 - y , \\ - 1 / 2 + z ]$ and tolyl-phenyl- $\\operatorname { C - H } ( \\cdot \\cdot \\cdot \\pi ( \\operatorname { t o l y l } ) \\ [ \\operatorname { C 1 9 - H 1 9 } \\cdot \\cdot \\cdot \\operatorname { C g } ( \\operatorname { C 8 - C 1 3 } ) ^ { \\operatorname { i v } }$ : $\\mathrm { H 1 9 \\cdot \\cdot \\cdot C g ( C 8 - C 1 3 ) ^ { i v } } = 2 . 6 4$ Å with angle at ${ \\mathrm { H } } 1 9 = 1 5 0 ^ { \\circ }$ for (iv) $3 / 2 - x , 1 / 2 + y , z ]$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,656,914,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Following standard practices [8] and the program Crystal Explorer 17 [9], the molecular packing in the crystal of (I) was further analysed by calculating the Hirshfeld surface as well as the full and delineated two-dimensional fingerprint plots; there were no significant differences between the disorder models. The main contribution to the surface is due to $\\mathrm { H } \\cdot \\cdot \\cdot \\mathrm { H }$ contacts which account for $6 8 . 5 \\%$ of all contacts with the next most significant contribution being from $\\mathrm { H } { \\cdots } { \\bf C } / { \\bf C } { \\cdots } { \\bf H }$ contacts, at $1 9 . 8 \\%$ . After this, $\\mathrm { H } { \\cdot } \\cdot \\cdot \\mathrm { C l } / \\mathrm { C l } { \\cdot } \\cdot \\cdot \\mathrm { H }$ contacts account for $8 . 6 \\%$ and $\\mathrm { C } { \\cdot } \\cdot \\cdot \\mathrm { C }$ contacts amount to $2 . 9 \\%$ . These contributions may be compared with those calculated for $( 4 \\mathrm { - C l C _ { 6 } H _ { 4 } } ) _ { 2 } \\mathrm { S n C l _ { 2 } } [ \\mathrm { O = P } ( 4 \\cdot$ $\\operatorname { t o l y l } ) _ { 3 } ] _ { 2 }$ [6], i.e. $\\mathrm { H } \\cdot \\cdot \\cdot \\mathrm { H }$ $\\left[ 5 9 . 6 \\% \\right]$ , $\\mathrm { H } { \\cdots } { \\bf C } / { \\bf C } { \\cdots } { \\bf H }$ $[ 2 2 . 4 \\% ]$ and $\\mathrm { H } { \\cdot } \\cdot \\cdot \\mathrm { C l } / \\mathrm { C l } { \\cdot } \\cdot \\cdot \\mathrm { H }$ $[ 1 5 . 6 \\% ]$ , with the differences correlating with the presence of additional chloride substituents in the latter molecule. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[821,41,914,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"DE GRUYTER ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[104,41,349,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1528 | Lee et al.: C44H48Cl2O2P2Sn ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[84,83,480,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgements: Sunway University Sdn Bhd is thanked for financial support of this work through Grant No. STR-RCTR-RCCM-001-2019. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,166,163,179]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[84,194,478,332]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Rigaku Oxford Diffraction: CrysAlisPRO. Rigaku Corporation, Oxford, UK (2018). \n2. Sheldrick, G. M.: A short history of SHELX. Acta Crystallogr. A64 (2008) 112–122. \n3. Sheldrick, G. M.: Crystal structure refinement with SHELXL. Acta Crystallogr. C71 (2015) 3–8. \n4. Farrugia, L. J.: WinGX and ORTEP for Windows: an update. J. Appl. Cryst. 45 (2012) 849–854. \n5. Amin, N. A. B. M.; Hussen, R. S. D.; Lee, S. M.; Halcovitch, N. R.; Jotani, M. M.; Tiekink, E. R. T.: trans-Dichloridobis(dimethyl sulfoxide- $\\kappa O \\mathrm { , }$ )bis(4-fluorobenzyl- $\\mathsf { \\kappa } C ^ { 1 }$ )tin(IV): crystal structure and Hirshfeld surface analysis. Acta Crystallogr. E73 (2017) \n667–672. \n6. Lee, S. M.; Lo, K. M.; Tiekink, E. R. T.: Crystal structure of dichloridobis(tri-4-tolylphosphane oxide- $\\boldsymbol { \\kappa } O$ )-di(4-chlorophenylκC)tin(IV), $\\mathsf { C } _ { 5 4 } \\mathsf { H } _ { 5 0 } \\mathsf { C l } _ { 4 } 0 _ { 2 } \\mathsf { P } _ { 2 } \\mathsf { S }$ n. Z. Kristallogr. NCS 235 (2020) NCRS-2020-0377. \n7. Lo, K. M.; Lee, S. M.; Tiekink, E. R. T.: Crystal structure of dichlorido-bis(4-methylphenyl- $\\kappa C _ { \\mathrm { \\Delta } }$ -bis(triphenylarsine oxideκO)tin(IV), $\\mathsf C _ { 5 0 } \\mathsf H _ { 4 4 } \\mathsf A \\mathsf s _ { 2 } \\mathsf C | _ { 2 } \\mathsf { O } _ { 2 } \\mathsf s$ n. Z. Kristallogr. NCS 235 (2020) \n183–185. \n8. Tan, S. L.; Jotani, M. M.; Tiekink, E. R. T.: Utilizing Hirshfeld surface calculations, non-covalent interaction (NCI) plots and the calculation of interaction energies in the analysis of molecular packing. Acta Crystallogr. E75 (2019) 308–318. \n9. Turner, M. J.; McKinnon, J. J.; Wolff, S. K.; Grimwood, D. J.; Spackman, P. R.; Jayatilaka, D.; Spackman, M. A.: Crystal Explorer v17. The University of Western Australia, Australia (2017). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[497,83,892,332]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[650,41,895,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lee et al.: $\\mathsf C _ { 4 4 } \\mathsf H _ { 4 8 } \\mathsf C \\mathsf C \\mathsf C _ { 1 _ { 2 } } \\mathsf 0 _ { 2 } \\mathsf P _ { 2 } \\mathsf S \\mathsf n$ | 1529","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[82,41,176,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"DE GRUYTER ","text_format":null,"text_level":null,"type":"discarded"}],"string":"[\n {\n \"bbox\": \"[82,79,539,97]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"See Mun Lee, Kong Mun Lo and Edward R.T. Tiekink\\\\* \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,102,852,199]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Crystal structure of dichloridodimethylbis(tri-4- tolylphosphane oxide-κO)-tin(IV), C44H48Cl2O2P2Sn \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,234,480,436]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0787/564a6494761ddec77555cee9a3d3ffb854e5e9492eb8aba918f1b78d81782e1d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[82,455,433,495]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1515/ncrs-2020-0378 Received July 21, 2020; accepted August 18, 2020; available online August 27, 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,513,144,525]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,529,482,592]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\mathrm { C } _ { 4 4 } \\\\mathrm { H } _ { 4 8 } \\\\mathrm { C l } _ { 2 } \\\\mathrm { O } _ { 2 } \\\\mathrm { P } _ { 2 } \\\\mathrm { S n } .$ , orthorhombic, Pbca (no. 61), $a = 1 7 . 8 3 1 2 ( 1 ) \\\\textrm { \\\\AA }$ , $b = 1 2 . 0 2 9 1 ( 1 ) \\\\mathrm { ~ \\\\AA ~ }$ , $c = 1 8 . 5 8 9 5 ( 1 ) \\\\mathrm { ~ \\\\AA ~ }$ , $V = 3 9 8 7 . 3 2 ( 5 ) \\\\mathrm { ~ \\\\AA ~ } ^ { 3 }$ , $Z = 4$ , $R _ { \\\\mathrm { g t } } ( F ) = 0 . 0 1 9 6$ , $w R _ { \\\\mathrm { r e f } } ( F ^ { 2 } ) = 0 . 0 5 6 4 ;$ ， $T = 1 0 0 ( 2 ) \\\\textrm { K }$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,602,208,616]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CCDC no.: 2023888 \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,626,480,691]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The molecular structure is shown in the figure. Table 1 contains crystallographic data and Table 2 contains the list of the atoms including atomic coordinates and displacement parameters. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,706,213,720]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Source of material \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,723,480,770]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Tri(4-tolyl)phosphine oxide was prepared by the oxidation of tri(4-tolyl)phosphine (Merck) with $3 0 \\\\%$ hydrogen peroxide (Merck) in ethanol. Dimethyltin dichloride (Merck, $_ { 0 . 2 2 \\\\ \\\\mathrm { g } }$ , \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[497,261,897,422]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0193/48e5c7cdb7fb77b3834c6353e113b98e832959154ab33398126ad8fce661571d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Crystal:</td><td>Colourless prism</td></tr><tr><td>Size: Wavelength:</td><td>0.11×0.09×0.05 mm Cu Kα radiation (1.54184 A)</td></tr><tr><td></td><td></td></tr><tr><td>μ:</td><td>7.37 mm-1</td></tr><tr><td>Diffractometer,scan mode:</td><td>XtaLAB Synergy,W</td></tr><tr><td>0max,completeness:</td><td>67.1°,>99%</td></tr><tr><td>N(hkl measured,N(hkl)unique, Rint:</td><td>47255,3553,0.024</td></tr><tr><td>Criterion for lobs,N(hkl)gt:</td><td>lobs>2o(obs),3391</td></tr><tr><td>N(param)refined:</td><td>235</td></tr><tr><td>Programs:</td><td>CrysAlisPRO [1], SHELX [2,3], WinGX/ORTEP [4]</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1: Data collection and handling. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[495,490,897,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/1002/a5dd70bbd51b8c44d5f9a88d4518ea58393598803b83b2ea99565ebb89d07cbd.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Atom</td><td>X</td><td>y</td><td>Z</td><td>Uiso*/Ueq</td></tr><tr><td>Sn1</td><td>0.5</td><td>0.5</td><td>0.5</td><td>0.01216(7)</td></tr><tr><td>Cl1</td><td>0.55361(2)</td><td>0.67812(3)</td><td>0.55689(2)</td><td>0.02163(10)</td></tr><tr><td>P1</td><td>0.65744(2)</td><td>0.54160(3)</td><td>0.38148(2)</td><td>0.01201(9)</td></tr><tr><td>01</td><td>0.59770(6)</td><td>0.48389(9)</td><td>0.42508(6)</td><td>0.0160(2)</td></tr><tr><td>C1</td><td>0.68095(8)</td><td>0.45559(12)</td><td>0.30549(8)</td><td>0.0138(3)</td></tr><tr><td>C2</td><td>0.74054(10)</td><td>0.48362(14)</td><td>0.26046(9)</td><td>0.0186(3)</td></tr><tr><td>H2</td><td>0.768419</td><td>0.549541</td><td>0.269227</td><td>0.022*</td></tr><tr><td>C3</td><td>0.75929(9)</td><td>0.41574(14)</td><td>0.20297(8)</td><td>0.0188(3)</td></tr><tr><td>H3</td><td>0.799884</td><td>0.435761</td><td>0.172513</td><td>0.023*</td></tr><tr><td>C4</td><td>0.71925(9)</td><td>0.31833(13)</td><td>0.18929(8)</td><td>0.0172(3)</td></tr><tr><td>C5</td><td>0.65885(9)</td><td>0.29248(13)</td><td>0.23361(9)</td><td>0.0187(3)</td></tr><tr><td>H5</td><td>0.630181</td><td>0.227541</td><td>0.224138</td><td>0.022*</td></tr><tr><td>C6</td><td>0.63961(9)</td><td>0.35998(13)</td><td>0.29159(8)</td><td>0.0163(3)</td></tr><tr><td>H6</td><td>0.598414</td><td>0.340793</td><td>0.321517</td><td>0.020*</td></tr><tr><td>C7</td><td>0.74249(10)</td><td>0.24351(14)</td><td>0.12839(9)</td><td>0.0227(4)</td></tr><tr><td>H7A</td><td>0.725930</td><td>0.167381</td><td>0.138384</td><td>0.034*</td></tr><tr><td>H7B</td><td>0.797212</td><td>0.244893</td><td>0.123538</td><td>0.034*</td></tr><tr><td>H7C</td><td>0.719477</td><td>0.269520</td><td>0.083571</td><td>0.034*</td></tr><tr><td>C8</td><td>0.74137(8)</td><td>0.56116(13)</td><td>0.43352(8)</td><td>0.0139(3)</td></tr><tr><td>C9</td><td>0.79463(9)</td><td>0.64230(13)</td><td>0.41671(8)</td><td>0.0157(3)</td></tr><tr><td>H9</td><td>0.785775</td><td>0.692252</td><td>0.378048</td><td>0.019*</td></tr><tr><td>C10</td><td>0.86057(9)</td><td>0.65024(13)</td><td>0.45636(8)</td><td>0.0167(3)</td></tr><tr><td>H10</td><td>0.896634</td><td>0.705307</td><td>0.444298</td><td>0.020*</td></tr><tr><td>C11</td><td>0.87430(9)</td><td>0.57810(14)</td><td>0.51372(9)</td><td>0.0175(3)</td></tr><tr><td>C12</td><td>0.82115(10)</td><td>0.49717(13)</td><td>0.52984(9)</td><td>0.0192(4)</td></tr><tr><td>H12</td><td>0.830105</td><td>0.447167</td><td>0.568449</td><td>0.023*</td></tr><tr><td>C13</td><td>0.75509(12)</td><td>0.48820(14)</td><td>0.49040(9)</td><td>0.0179(4)</td></tr><tr><td>H13</td><td>0.719386</td><td>0.432482</td><td>0.502176</td><td>0.021*</td></tr><tr><td>C14</td><td>0.94453(9)</td><td>0.58833(15)</td><td>0.55813(9)</td><td>0.0232(4)</td></tr><tr><td>H14A</td><td>0.932651</td><td>0.624533</td><td>0.603959</td><td>0.035*</td></tr><tr><td>H14B</td><td>0.981554</td><td>0.632972</td><td>0.531980</td><td>0.035*</td></tr><tr><td>H14C</td><td>0.965122</td><td>0.514157</td><td>0.567357</td><td>0.035*</td></tr><tr><td>C15</td><td>0.63062(8)</td><td>0.67447(12)</td><td>0.34630(8)</td><td>0.0141(3)</td></tr><tr><td>C16</td><td>0.60132(9)</td><td>0.68328(13)</td><td>0.27686(8)</td><td>0.0168(3)</td></tr><tr><td>H16</td><td>0.600004</td><td>0.619885</td><td>0.246405</td><td>0.020*</td></tr><tr><td>C17</td><td>0.57412(9)</td><td>0.78443(14)</td><td>0.25226(9)</td><td>0.0197(3)</td></tr><tr><td>H17</td><td>0.553345</td><td>0.789359</td><td>0.205312</td><td>0.024*</td></tr><tr><td>C18</td><td>0.57689(9)</td><td>0.87852(13)</td><td>0.29541(9)</td><td>0.0186(3)</td></tr><tr><td>C19</td><td>0.60768(9)</td><td>0.86981(13)</td><td>0.36417(9)</td><td>0.0172(3)</td></tr><tr><td>H19</td><td>0.610976</td><td>0.934087</td><td>0.393697</td><td>0.021*</td></tr><tr><td>C20</td><td>0.63349(8)</td><td>0.76888(13)</td><td>0.39001(8)</td><td>0.0158(3)</td></tr><tr><td>H20</td><td>0.653141</td><td>0.763812</td><td>0.437398</td><td>0.019*</td></tr><tr><td>C21</td><td>0.54820(11)</td><td>0.98855(14)</td><td>0.26854(11)</td><td>0.0274(4)</td></tr><tr><td>H21Aa</td><td>0.554656</td><td>1.044997</td><td>0.306052</td><td>0.041*</td></tr><tr><td>H21Ba</td><td>0.576363</td><td>1.010491</td><td>0.225559</td><td>0.041*</td></tr><tr><td>H21Ca</td><td>0.494876</td><td>0.981855</td><td>0.256517</td><td>0.041*</td></tr><tr><td>H21Da</td><td>0.529274</td><td>0.979899</td><td>0.219367</td><td>0.041*</td></tr><tr><td>H21Ea</td><td>0.507567</td><td>1.014404</td><td>0.299859</td><td>0.041*</td></tr><tr><td>H21Fa</td><td>0.589054</td><td>1.043040</td><td>0.268902</td><td>0.041*</td></tr><tr><td>C22</td><td>0.44035(9)</td><td>0.59927(14)</td><td>0.42539(9)</td><td>0.0186(3)</td></tr><tr><td>H22A</td><td>0.403899</td><td>0.553064</td><td>0.399644</td><td>0.028*</td></tr><tr><td>H22B</td><td>0.475561</td><td>0.632011</td><td>0.390908</td><td>0.028*</td></tr><tr><td>H22C</td><td>0.413961</td><td>0.658687</td><td>0.451089</td><td>0.028*</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2: Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters $( \\\\\\\\mathring { \\\\\\\\mathsf { A } } ^ { 2 } )$ . \\\"]\",\n \"table_footnote\": \"[\\\"aOccupancy: 0.5. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[82,41,176,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"DE GRUYTER \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[84,805,477,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\\\\*Corresponding author: Edward R.T. Tiekink, Research Centre for Crystalline Materials, School of Science and Technology, Sunway University, Bandar Sunway 47500 , Selangor Darul Ehsan, Malaysia, e-mail: edwardt@sunway.edu.my. https://orcid.org/0000-0003- 1401-1520 See Mun Lee and Kong Mun Lo: Research Centre for Crystalline Materials, School of Science and Technology, Sunway University, Bandar Sunway 47500, Selangor Darul Ehsan, Malaysia \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[82,925,433,948]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Open Access. © 2020 See Mun Lee et al., published by De Gruyter. International License. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[638,41,915,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Z. Kristallogr. NCS 2020; 235(6): 1527–1529 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[917,41,937,63]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"a \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[435,925,512,938]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"BY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[100,105,500,467]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": \"[\\\"\\\"]\",\n \"table_footnote\": \"[\\\"\\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[102,495,500,674]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$1 . 0 \\\\ \\\\mathrm { m m o l } ,$ ) and tri $\\\\lceil p$ -tolyl)phosphine oxide $\\\\left( 0 . 6 4 \\\\ \\\\mathbf { g } , 2 . 0 \\\\ \\\\mathrm { m m o l } \\\\right)$ were heated in $9 5 \\\\%$ ethanol $\\\\mathrm { 3 0 ~ m L } )$ for 1 h and filtered. After filtration, the filtrate was evaporated slowly until a white crystalline compound was obtained. Yield: $0 . 5 2 \\\\mathrm { ~ g ~ } ( 3 0 . 2 \\\\% )$ . M. pt. (Stuart SMP30 digital melting point apparatus; uncorrected): 460–462 K. IR (Bruker Vertex 70v FTIR Spectrometer; $\\\\mathrm { c m } ^ { - 1 }$ ): 1598 $\\\\mathrm { ( m ) }$ $\\\\mathsf { v } ( \\\\mathsf { C } \\\\mathrm { = C } )$ , 1496 (m) $\\\\mathsf { v } ( \\\\mathsf { C } \\\\mathrm { = C } )$ , 1140 (s) $\\\\mathsf { v } ( \\\\mathsf { P = } 0 )$ , 1083 (s) ν(P-Ar). ${ \\\\bf \\\\delta _ { 1 } } _ { \\\\bf H }$ NMR (Bruker Ascend $4 0 0 ~ \\\\mathrm { M H z }$ NMR spectrometer; $\\\\mathrm { C D C l } _ { 3 }$ ; ppm relative to $\\\\mathbf { M e } _ { 4 } \\\\mathbf { S i }$ ): δ 2.21 (s, 6H, $\\\\mathrm { C H } _ { 3 }$ ), 2.40 (s, 18H, $\\\\mathrm { C H } _ { 3 } .$ ), 6.88–7.54 (m, 24H, Ph-H). ${ } ^ { 1 3 } { \\\\bf C } \\\\{ { \\\\bf H } \\\\}$ NMR (as for $^ 1 \\\\mathrm { H }$ NMR): 21.6 $\\\\left( \\\\mathrm { C H } _ { 3 } \\\\right)$ , 48.5 $\\\\mathrm { ( C H } _ { 3 } )$ ), 116.9, 129.2, 142.6, 149.9 (Ph—C). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[102,689,247,703]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Experimental details \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[102,707,500,788]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The C-bound H atoms were geometrically placed $\\\\left( \\\\mathrm { C - H } = 0 . 9 5 – 0 . 9 8 \\\\mathrm { \\\\ : \\\\mathring { A } } \\\\right)$ ) and refined as riding with $U _ { \\\\mathrm { i s o } } ( \\\\mathrm { H } ) { = } 1 . 2 \\\\mathrm { - }$ $1 . 5 U _ { \\\\mathrm { e q } } ( \\\\mathrm { C } )$ . The $\\\\mathrm { H }$ atoms of the C21-methyl group were found to be statistically disordered over two positions with one orientation rotated $6 0 ^ { \\\\circ }$ with respect to the other. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[102,803,171,817]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Comment \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[102,820,500,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The title compound, $\\\\mathrm { M e } _ { 2 } \\\\mathrm { S n C l } _ { 2 } \\\\mathrm { [ O = P ( 4 \\\\mathrm { - } t o l y l ) _ { 3 } ] } _ { 2 }$ , (I), was investigated in connection with recent structural studies of bis(sulphoxide) [5], bis(triorganophosphane) [6] and bis (triorganoarsane) [7] adducts of ${ \\\\mathrm { R } } _ { 2 } { \\\\mathrm { S n C l } } _ { 2 }$ . The common feature of the crystallographically determined structures of molecules of the general formula $\\\\mathrm { R } _ { 2 } \\\\mathrm { S n C l } _ { 2 } [ 0 { = } \\\\mathrm { P R } ^ { \\\\prime } { } _ { 3 } ] _ { 2 }$ is the adoption of an all-trans $\\\\mathrm { C } _ { 2 } \\\\mathrm { C l } _ { 2 } \\\\mathrm { O } _ { 2 }$ coordination geometry for Sn; see ref. [6] for a review. This is also true for the structure of (I), for which the crystal and molecular structures are described herein. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,81,914,145]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,148,915,292]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The molecular structure of (I) is shown in the figure $7 0 \\\\%$ displacement ellipsoids; unlabelled atoms are related by the symmetry operation (i) $1 - x , \\\\ 1 - y , \\\\ 1 - z )$ . The Sn atom is located on a centre of inversion and is coordinated by symmetry-related pairs of methyl-C [2.1168(15) Å], Cl [2.5735(4) Å] and oxide-O [2.2387(11) $\\\\mathring \\\\mathrm { A } ]$ atoms. The resulting $\\\\mathrm { C } _ { 2 } \\\\mathrm { C l } _ { 2 } \\\\mathrm { O } _ { 2 }$ donor set is based on an octahedron with all likeatoms being mutually trans, in accord with expectation [6]. The Sn—O1—P1 angle is bent, at $1 4 7 . 6 0 ( 7 ) ^ { \\\\circ }$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,296,915,441]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Very recently, the closely related structure formulated as $( 4 { \\\\cdot } \\\\mathrm { C l } \\\\mathrm C _ { 6 } \\\\mathrm H _ { 4 } ) _ { 2 } \\\\mathrm { S n C l } _ { 2 } [ 0 { = } \\\\mathrm { P } ( 4 { \\\\cdot } \\\\mathrm { t o l y l } ) _ { 3 } ] _ { 2 }$ was described [6]. As for (I), the Sn atom is situated on a centre on inversion. Reflecting the presence of the electron-withdrawing tin-bound 4-chlorophenyl substituents, the Sn—C [2.1441(15) Å], Sn—Cl [2.5333(4) Å] and Sn—O [2.1746(11) $\\\\mathring \\\\mathrm { A } ]$ bond lengths have elongated, contracted and contracted, respectively, compared with (I), with, relatively electropositive tin-bound methyl groups. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,443,915,654]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the crystal, tolyl- $\\\\mathrm { { C - H \\\\cdot \\\\cdot \\\\cdot C l } }$ $\\\\mathrm { [ C 1 7 - H 1 7 \\\\cdot \\\\cdot \\\\cdot C l 1 ^ { i i } }$ : $\\\\mathrm { H 1 7 \\\\cdot \\\\cdot \\\\cdot C l 1 ^ { i i } } = 2 . 7 9 \\\\mathrm { ~ \\\\AA ~ }$ , $\\\\mathrm { C 1 7 \\\\cdot \\\\cdot \\\\cdot C l 1 ^ { i i } } = 3 . 6 7 7 9 ( 1 7 ) ~ .$ Å with angle at $\\\\mathrm { H } 1 7 = 1 5 7 ^ { \\\\circ }$ for (ii) $x , ~ 3 / 2 - y , ~ - 1 / 2 + z ]$ interactions connect molecules into a supramolecular layer in the bc-plane as each molecule participates in four such interactions, i.e. two donor and two acceptor interactions per molecule. The connections between layers to consolidate the three-dimensional architecture are of the type tolyl-methyl- $\\\\mathrm { C - H } { \\\\cdot } \\\\cdot \\\\cdot \\\\pi ( \\\\mathrm { t o l y l } )$ $\\\\scriptstyle [ \\\\mathbf { C 7 - H 7 c \\\\cdot \\\\cdot \\\\cdot C g } ( \\\\mathbf { C 8 - C 1 } 3 ) ^ { \\\\mathrm { i i i } }$ : $\\\\mathrm { H 7 c } \\\\cdot \\\\cdot \\\\cdot \\\\mathrm { C g ( C 8 - C 1 3 ) ^ { i i i } } = 2 . 8 6 \\\\mathrm { \\\\normalfont ~ \\\\AA }$ with angle at $\\\\mathrm { H } 7 \\\\mathbf { c } = 1 5 4 ^ { \\\\circ }$ for (iii) $3 / 2 - x , \\\\ 1 - y , \\\\ - 1 / 2 + z ]$ and tolyl-phenyl- $\\\\operatorname { C - H } ( \\\\cdot \\\\cdot \\\\cdot \\\\pi ( \\\\operatorname { t o l y l } ) \\\\ [ \\\\operatorname { C 1 9 - H 1 9 } \\\\cdot \\\\cdot \\\\cdot \\\\operatorname { C g } ( \\\\operatorname { C 8 - C 1 3 } ) ^ { \\\\operatorname { i v } }$ : $\\\\mathrm { H 1 9 \\\\cdot \\\\cdot \\\\cdot C g ( C 8 - C 1 3 ) ^ { i v } } = 2 . 6 4$ Å with angle at ${ \\\\mathrm { H } } 1 9 = 1 5 0 ^ { \\\\circ }$ for (iv) $3 / 2 - x , 1 / 2 + y , z ]$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,656,914,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Following standard practices [8] and the program Crystal Explorer 17 [9], the molecular packing in the crystal of (I) was further analysed by calculating the Hirshfeld surface as well as the full and delineated two-dimensional fingerprint plots; there were no significant differences between the disorder models. The main contribution to the surface is due to $\\\\mathrm { H } \\\\cdot \\\\cdot \\\\cdot \\\\mathrm { H }$ contacts which account for $6 8 . 5 \\\\%$ of all contacts with the next most significant contribution being from $\\\\mathrm { H } { \\\\cdots } { \\\\bf C } / { \\\\bf C } { \\\\cdots } { \\\\bf H }$ contacts, at $1 9 . 8 \\\\%$ . After this, $\\\\mathrm { H } { \\\\cdot } \\\\cdot \\\\cdot \\\\mathrm { C l } / \\\\mathrm { C l } { \\\\cdot } \\\\cdot \\\\cdot \\\\mathrm { H }$ contacts account for $8 . 6 \\\\%$ and $\\\\mathrm { C } { \\\\cdot } \\\\cdot \\\\cdot \\\\mathrm { C }$ contacts amount to $2 . 9 \\\\%$ . These contributions may be compared with those calculated for $( 4 \\\\mathrm { - C l C _ { 6 } H _ { 4 } } ) _ { 2 } \\\\mathrm { S n C l _ { 2 } } [ \\\\mathrm { O = P } ( 4 \\\\cdot$ $\\\\operatorname { t o l y l } ) _ { 3 } ] _ { 2 }$ [6], i.e. $\\\\mathrm { H } \\\\cdot \\\\cdot \\\\cdot \\\\mathrm { H }$ $\\\\left[ 5 9 . 6 \\\\% \\\\right]$ , $\\\\mathrm { H } { \\\\cdots } { \\\\bf C } / { \\\\bf C } { \\\\cdots } { \\\\bf H }$ $[ 2 2 . 4 \\\\% ]$ and $\\\\mathrm { H } { \\\\cdot } \\\\cdot \\\\cdot \\\\mathrm { C l } / \\\\mathrm { C l } { \\\\cdot } \\\\cdot \\\\cdot \\\\mathrm { H }$ $[ 1 5 . 6 \\\\% ]$ , with the differences correlating with the presence of additional chloride substituents in the latter molecule. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[821,41,914,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"DE GRUYTER \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[104,41,349,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1528 | Lee et al.: C44H48Cl2O2P2Sn \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[84,83,480,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgements: Sunway University Sdn Bhd is thanked for financial support of this work through Grant No. STR-RCTR-RCCM-001-2019. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,166,163,179]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,194,478,332]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Rigaku Oxford Diffraction: CrysAlisPRO. Rigaku Corporation, Oxford, UK (2018). \\n2. Sheldrick, G. M.: A short history of SHELX. Acta Crystallogr. A64 (2008) 112–122. \\n3. Sheldrick, G. M.: Crystal structure refinement with SHELXL. Acta Crystallogr. C71 (2015) 3–8. \\n4. Farrugia, L. J.: WinGX and ORTEP for Windows: an update. J. Appl. Cryst. 45 (2012) 849–854. \\n5. Amin, N. A. B. M.; Hussen, R. S. D.; Lee, S. M.; Halcovitch, N. R.; Jotani, M. M.; Tiekink, E. R. T.: trans-Dichloridobis(dimethyl sulfoxide- $\\\\kappa O \\\\mathrm { , }$ )bis(4-fluorobenzyl- $\\\\mathsf { \\\\kappa } C ^ { 1 }$ )tin(IV): crystal structure and Hirshfeld surface analysis. Acta Crystallogr. E73 (2017) \\n667–672. \\n6. Lee, S. M.; Lo, K. M.; Tiekink, E. R. T.: Crystal structure of dichloridobis(tri-4-tolylphosphane oxide- $\\\\boldsymbol { \\\\kappa } O$ )-di(4-chlorophenylκC)tin(IV), $\\\\mathsf { C } _ { 5 4 } \\\\mathsf { H } _ { 5 0 } \\\\mathsf { C l } _ { 4 } 0 _ { 2 } \\\\mathsf { P } _ { 2 } \\\\mathsf { S }$ n. Z. Kristallogr. NCS 235 (2020) NCRS-2020-0377. \\n7. Lo, K. M.; Lee, S. M.; Tiekink, E. R. T.: Crystal structure of dichlorido-bis(4-methylphenyl- $\\\\kappa C _ { \\\\mathrm { \\\\Delta } }$ -bis(triphenylarsine oxideκO)tin(IV), $\\\\mathsf C _ { 5 0 } \\\\mathsf H _ { 4 4 } \\\\mathsf A \\\\mathsf s _ { 2 } \\\\mathsf C | _ { 2 } \\\\mathsf { O } _ { 2 } \\\\mathsf s$ n. Z. Kristallogr. NCS 235 (2020) \\n183–185. \\n8. Tan, S. L.; Jotani, M. M.; Tiekink, E. R. T.: Utilizing Hirshfeld surface calculations, non-covalent interaction (NCI) plots and the calculation of interaction energies in the analysis of molecular packing. Acta Crystallogr. E75 (2019) 308–318. \\n9. Turner, M. J.; McKinnon, J. J.; Wolff, S. K.; Grimwood, D. J.; Spackman, P. R.; Jayatilaka, D.; Spackman, M. A.: Crystal Explorer v17. The University of Western Australia, Australia (2017). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[497,83,892,332]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[650,41,895,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lee et al.: $\\\\mathsf C _ { 4 4 } \\\\mathsf H _ { 4 8 } \\\\mathsf C \\\\mathsf C \\\\mathsf C _ { 1 _ { 2 } } \\\\mathsf 0 _ { 2 } \\\\mathsf P _ { 2 } \\\\mathsf S \\\\mathsf n$ | 1529\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[82,41,176,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"DE GRUYTER \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1515/ncrs-2020-0378"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Chemistry"},"sha256":{"kind":"string","value":"98f6bdeaec362f73df9b6289d3b91b384419ae24a7a81762c6c8c1fe86bc6b0f"},"title":{"kind":"string","value":"Crystal structure of dichloridodimethylbis(tri-4-tolylphosphane oxide-κ<i>O</i>)-tin(IV), C<sub>44</sub>H<sub>48</sub>Cl<sub>2</sub>O<sub>2</sub>P<sub>2</sub>Sn"}}},{"rowIdx":241,"cells":{"abstract":{"kind":"string","value":""},"author":{"kind":"string","value":"Qingfei Zhang|Gaizhen Kuang|Lexiang Zhang|Yujuan Zhu"},"content_list":{"kind":"list like","value":[{"bbox":"[58,206,463,226]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nanocarriers for platinum drug delivery ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,240,557,258]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Qingfei Zhang, Gaizhen Kuang, Lexiang Zhang \\*\\*, Yujuan Zhu ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,264,811,288]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Oujiang Laboratory (Zhejiang Lab for Regenerative Medicine, Vision and Brain Health), Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, 325001, China ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[838,208,889,247]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0825/2ab5e178bc8be30a1ca52dd26e5ae928569bf0c7756e0e1d7c9f55e04989f6ff.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[58,317,193,329]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ARTICLEINFO ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[58,341,134,353]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,354,119,363]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nanocarrier ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,364,131,374]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Platinum drug ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,375,127,385]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Drug delivery ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,385,132,395]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Chemotherapy ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,397,134,408]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Cancer therapy ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[334,317,435,329]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABSTRACT ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[332,341,937,451]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Platinum drugs have been coined as one of the great success representatives in cancer chemotherapy. With the accidental discovery of cisplatin, thousands of platinum-based complexes have been synthesized, including clinically approved classical platinum(II) (Pt(II)) drugs, non-classical Pt(II) drugs, and platinum(IV) (Pt(IV)) drugs. Currently, these drugs are widely utilized in the treatment of various solid tumors in the clinic. Unfortunately, systemic toxicity and innate or acquired drug resistance greatly restrict their applications. The nanocarrier-based drug delivery systems (NDDSs) offer the possibility of targeted delivery of platinum drugs to the tumor tissue with reduced toxicity and enhanced drug efficacy. Thus, in this review, inorganic and organic nanocarriers for platinum drug delivery are introduced. The significant improvements, future challenges, and prospects of the nanocarriers toward potential clinical application are briefly discussed. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,488,163,500]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,514,485,738]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Cancer is one of the leading causes of death worldwide and is a serious public health problem [1]. Traditional chemotherapy, radiotherapy, and surgery are golden standards for cancer treatments in clinics [2]. As a systemic treatment, chemotherapy drugs can reach most tissues and organs after drug administration. Therefore, it gained good therapeutic effects regarding both potential and already metastatic middle-late cancers [3,4]. Based on the sources and chemical structures, chemotherapeutic drugs can be categorized into alkylating agents, anti-cancer antibiotics, anti-metabolic drugs, animal and plant components, anti-tumor hormones, and miscellaneous drugs [5]. Apart from plants-derived drugs such as paclitaxel, etoposide, vincristine, elemene, vincristine, vindesine, camptothecin, etc., most of the chemotherapeutic drugs are capable of being synthesized by chemical methods. Among them, chemosynthetic platinum-based antitumor agents have been effectively studied and deployed in combating diverse malignancies [6-8]. Nowadays, platinum drugs have almost accounted for more than $50\\%$ of all anti-cancer drugs in use [9,10]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,738,485,804]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Despite great achievements, platinum drugs face challenges in clinical applications, especially for toxicity and drug resistance [11,12]. In addition, low bioavailability is another major limitation inherited from poor water solubility, short blood circulation time, lack of selectivity, easy to be cleared by the reticuloendothelial system (RES), and be ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,488,937,673]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"eliminated by liver metabolism and kidney [7,13]. Nowadays, it is urgently needed to deliver platinum drugs specifically toward the target tissue and reduce their toxic side effects [14]. Compared with traditional small-molecule drugs, nanomedicines could prolong the drug circulation time and increase the bioavailability of drugs [15]. Besides, the use of nanomedicines facilitated the solubility of hydrophobic drugs and reduced potential immunogenicity [16]. In addition, the constant rate or stimuli-responsive release of the loaded drug reduces the toxic side effects and administration frequency [17]. Furthermore, nanomedicines can passively accumulate in tumor tissues, which is mainly attributable to the enhanced permeability and retention (EPR) effect [18]. Last but not least, nanomedicines can deliver drugs with different physical and chemical properties and pharmacokinetic behavior in the same systems, providing great potential for combination chemotherapy [19]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,672,937,804]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this review, we first introduce the commonly used platinum drugs including clinically approved classical platinum(II) (Pt(II)) drugs, non-classical Pt(II) drugs, and platinum(IV) (Pt(IV)) drugs [20,21]. Subsequently, an overview of nanocarrier-based drug delivery systems (NDDSs) for platinum drug delivery is summarized. The NDDSs mainly include those inorganic nanocarriers and organic nanocarriers. Finally, the perspectives and prospects of NDDSs in this area are discussed. The overall objective of this review is to discuss the biomedical potential of nanocarriers for platinum drug delivery, along with guidance for developing novel platinum drug delivery nanosystems that are clinically applicable. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[389,42,606,55]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biomedical Technology 2 (2023) 77-89 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[58,66,937,171]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"KeAi CHINESE ROOTS Biomedical Technology global IMPACT journal homepage: www.keaipublishing.com/en/journals/biomedical-technology ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,831,201,843]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"* Corresponding author. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[65,844,205,854]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"** Corresponding author. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[80,856,524,867]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"E-mail addresses: zhanglx@ucas.edu.cn (L. Zhang), zhuyujuan@ucas.ac.cn (Y. Zhu). ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[58,877,294,887]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1016/j.bmt.2022.11.011 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[58,889,630,901]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received 14 November 2022; Received in revised form 16 November 2022; Accepted 17 November 2022 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[58,902,257,912]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Available online 17 December 2022 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[58,912,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2949-723X/© 2023 The Authors. Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[58,66,181,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. Platinum drugs ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,92,485,224]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Since Rosenberg and colleagues discovered cisplatin by accident in 1965 while studying the effects of electric fields on the differentiation of $E$ coli, cisplatin has been found with anti-cancer activity [22,23]. Rapidly, the US Food and Drug Administration (FDA) approved its use for metastatic ovarian and testicular cancer in 1978 [24]. With the high success of cisplatin, the development of platinum drugs has been greatly expanded, and thousands of them have been subjected to clinical trials. According to the valence of platinum atoms either at +2 or +4 in the synthetic platinum drugs, they could be categorized as Pt(II) and Pt(IV) types [25]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,238,159,250]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.1. Pt(II) drugs ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,264,485,409]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As has been noted, cisplatin is the firstly discovered $\\mathrm{Pt(II)}$ drug [26]. Cisplatin has been widely used in treating various cancers including testicular cancer, ovarian cancer, malignant mesothelioma, bladder cancer, cervical cancer, head and neck cancer, etc., showing a broad-spectrum anti-cancer effect [27]. However, its high systemic toxicity and side effects, such as renal toxicity, gastrointestinal reaction, neurotoxicity, ototoxicity, etc., strictly limited its application in clinical [28,29]. Meanwhile, many cancer cells exhibit innate and acquired resistance to cisplatin, further limiting its chemotherapy effectiveness. These unfavorable results have sparked a new wave of platinum drug development. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,409,485,606]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"With the unremitting efforts of scientists, carboplatin as the second-generation platinum drug was approved worldwide in 1989 and primarily used for the treatment of non-small cell lung cancer (NSCLC), ovarian cancer, and head and neck cancer [30]. Carboplatin replaces the two chlorine ligands of cisplatin with 1,1-cyclobutane dicarboxylic acid as the chelating ligand [31]. Thus, the spontaneous hydration rate of carboplatin was reduced 100 times compared with cisplatin due to the double-dentate coordination leaving group ligands [32,33]. Therefore, its neurotoxicity, ototoxicity, and nephrotoxicity to the system are significantly reduced [34]. However, the action mechanism, anti-cancer activity, and anti-cancer profile of carboplatin remained similar to cisplatin, while showing cross-resistance with cisplatin [35]. Although clinically carboplatin has replaced cisplatin in the treatment of ovarian cancer and NSCLC, cisplatin is still superior to carboplatin in dealing with germinal cell cancer, bladder cancer, and head and neck cancer [36]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,607,485,751]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nedaplatin, originally known as 254-S, is another second-generation platinum drug that was granted in 1995 only in Japan [37]. Like cisplatin and carboplatin, this platinum drug has nonleaving cis ammine ligands. The difference lies in the chelating leaving glycolate ligand, which makes nedaplatin $(10\\mathrm{mg}\\mathrm{mL}^{-1})$ obtain much higher solubility than cisplatin $(2.5\\mathrm{mg}\\mathrm{mL}^{-1})$ . Besides, nedaplatin has lower gastrointestinal and nephrite toxicity after intravenous administration and a similar pharmacokinetic profile to carboplatin. Clinically, nedaplatin is mainly used in treating esophageal cancer, head and neck cancer, NSCLC, small-cell lung cancer (SCLC), and breast cancer. Clinical trials are exploring the expansion of nedaplatin usage [38]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,752,485,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Oxaliplatin, with the research name 1-OHP, is the representative third-generation platinum drug, which had been internationally approved in 2002 [39]. Oxaliplatin is composed of a nonleaving ligand of R,R-diaminocyclohexane (DACH), and a chelated leaving ligand of the oxalate group [40]. DACH has been studied as the ligand of platinum-based anticancer drugs for a long time [30]. For oxaliplatin, research results suggested that R,R stereoisomers are more effective than enantiomers S,S isomers [41]. The origin of this difference was revealed in later crystallography studies where the R,R isomers preferentially form hydrogen bonds between the pseudoequatorial NH hydrogen atoms of the R,R-DACH ligand and the O6 atoms of the $3^{\\prime}$ -dG of the plated d(GpG) lesion [42]. In addition, the cyclohexanediamine ligand in the molecular structure of oxaliplatin is larger in volume and stronger in ester affinity, thereby can be deeply embedded into DNA and preventing the self-repair ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,65,937,118]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"of damaged DNA [43]. At present, oxaliplatin is the main component of colon cancer combination chemotherapy [44]. Besides, this platinum drug also showed good curative effects on ovarian cancer, NSCLC, head and neck tumor, and malignant lymphoma [8]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,118,937,235]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heptaplatin, initially known as SKI 2053R, was discovered and entered clinical trials in the 1990s [45]. In 1999, heptaplatin was approved by the Korean FDA. The leaving group ligand of heptaplatin is malonate. 2-(1-methylethyl)-1,3-dioxolane-4,5-dimethylamine is the nonleaving group ligand, which forms a seven-membered ring structure, endowing the drug its name. It is currently marketed as SunPla and is now replaced cisplatin clinically to treat gastric carcinoma [46]. The major side effects of heptaplatin are hepatotoxicity and myelosuppression. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,237,937,354]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lobaplatin can be viewed as a derivative of heptaplatin, where the cyclobutane ring is fused to the seven-membered chelate ring instead of the functionalized dioxolane [47]. ASTA Medica in Germany originally formulated this drug under the name D-19466 [48,49]. Although clinical trials were initially performed out in numerous nations to assess the effectiveness of patients with various malignancies, only China's regulatory approval was obtained in 2010 [13]. Lobaplatin is approved primarily for combating chronic myelogenous leukemia, but also for patients with SCLC and metastatic breast cancer. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,355,937,513]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The aforementioned platinum complexes are classical clinically approved (Fig. 1 and Table 1) with have a general formula of cis- $\\left[\\mathrm{PtL}_2\\mathrm{X}_2\\right]$ , where $\\mathrm{L}_2$ represents nonleaving group ligands and $\\mathrm{X}_2$ represents leaving group ligands. Although carboplatin, oxaliplatin, and other traditional Pt(II) drugs have several advantages over cisplatin, adverse side effects and resistance still potentially exist. Besides, these drugs display low aqueous stability and higher reactivity to bioactive molecules, leading to low doses to the tumor without reaching lethal levels. Several structurally unique non-classical Pt(II) drugs were designed to solve these issues. Picoplanin, BBR3464, 56MESS, PT-ACRAMTU, etc. are the representative of these Pt(II) drugs, and some of them have already been rolled out into clinical trials (Fig. 2 and Table 2) [51-54]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,528,615,540]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.2. Pt(IV) drugs ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,554,937,778]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To circumvent the disadvantages of clinical side effects and drug resistance of cisplatin and other $\\mathrm{Pt(II)}$ drugs, scientists have been developing new platinum drugs to improve the therapeutic effect and quality of life of patients. The synthesis of $\\mathrm{Pt(IV)}$ prodrugs reached these goals to some extent [55]. The structure of the $\\mathrm{Pt(IV)}$ prodrug includes the non-leaving group L, the leaving group X, and the axial group R obtained by oxidizing the $\\mathrm{Pt(II)}$ drug into the hydroxyl group or further introducing other groups (Fig. 3a) [13]. Because of the formation of an octahedral kinetically inert structure, $\\mathrm{Pt(IV)}$ prodrugs almost do not react with cysteine, methionine, and matrix proteins that can interact with $\\mathrm{Pt(II)}$ drugs. Thus, $\\mathrm{Pt(IV)}$ configurations enable the improvement of the stability of platinum drugs, increase the blood circulation time, reduce systemic toxicity, and enhance the anti-cancer effect. Currently, the $\\mathrm{Pt(IV)}$ prodrug named Satraplatin (JM-216, Fig. 3b), which can be administered orally and has no cross-resistance with cisplatin, has entered phase III clinical trials for prostate cancer, NSCLC, and head and neck cancer therapy [56]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,778,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"According to the activation pathways and structure variations, $\\mathrm{Pt(IV)}$ can be categorized into reduction-sensitive $\\mathrm{Pt(IV)}$ prodrugs and light-sensitive $\\mathrm{Pt(IV)}$ prodrugs [57,58]. When the plane leaving group X is chlorine, the $\\mathrm{Pt(IV)}$ axial ligand R can be reduced by high-concentration reductants like glutathione (GSH), ascorbic acid (VC), and dithiothreitol (DTT) in cancer cells, destroying the rigid structure of the octahedron and conversion into $\\mathrm{Pt(II)}$ drugs (Fig. 4a) [59,60]. The $\\mathrm{Pt(II)}$ further hydrated in the cells and cross-links with DNA at different sites, and thus achieved similar cell apoptosis results as cisplatin in blocking DNA replication and transcription. When the plane leaving group ligands X is azide or iodine, $\\mathrm{Pt(IV)}$ can be degraded to $\\mathrm{Pt(II)}$ under external light stimulation. Taking the photosensitive $\\mathrm{Pt(IV)}$ containing azide group ligands as an example, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,42,129,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Q. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[752,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biomedical Technology 2 (2023) 77-89 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"78 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[210,66,786,277]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 1. Chemical structures of clinically approved Pt(II) drugs [7,34,37,38,47,49,50]. \"]","image_footnote":"[]","img_path":"images/0523/6059f97d709fa30621b39e24348df8e9e8e470c8713246049c36fccc18d8931f.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[60,346,937,500]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0624/b4ce61b2812b67c4520f89f78e376694457d772baff4b897e7a1adf8b0117651.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":"<table><tr><td>Generic Name</td><td>Research Name</td><td>Trade Name</td><td>Approval Granted</td><td>Cancer type</td><td>Side Effects</td><td>Scope of Approval</td></tr><tr><td>Cisplatin</td><td>CDDP</td><td>Platinol</td><td>1978</td><td>Testicular, Ovarian Lymphomas</td><td>Nephrotoxicity, Neurotoxicity, Ototoxicity, Nausea</td><td>Global</td></tr><tr><td>Carboplatin</td><td>JM8</td><td>Paraplatin</td><td>1989</td><td>Ovarian, Lung</td><td>Myelosuppressive</td><td>Global</td></tr><tr><td rowspan=\"2\">Nedaplatin</td><td rowspan=\"2\">254-S</td><td rowspan=\"2\">Aqupla</td><td rowspan=\"2\">1995</td><td>Head, neck, Lung, Breast, NSCLC</td><td rowspan=\"2\">Bone marrow suppression</td><td rowspan=\"2\">Japan</td></tr><tr><td>SCLC, Esophageal</td></tr><tr><td rowspan=\"2\">Heptaplatin</td><td rowspan=\"2\">SKI 2053R</td><td rowspan=\"2\">SunPla</td><td rowspan=\"2\">1999</td><td rowspan=\"2\">Advanced gastric</td><td>Hepatotoxicity</td><td rowspan=\"2\">Korea</td></tr><tr><td>Myelosuppression</td></tr><tr><td>Oxaliplatin</td><td>1-OHP</td><td>Eloxatin</td><td>2002</td><td>Colorectal</td><td>Neurotoxicity, Neutropenia</td><td>Global</td></tr><tr><td rowspan=\"2\">Lobaplatin</td><td rowspan=\"2\">D-19466</td><td rowspan=\"2\">洛铂</td><td rowspan=\"2\">2010</td><td rowspan=\"2\">Testicular, Ovarian and Lung, CML, SCLC</td><td>Thrombocytopenia</td><td rowspan=\"2\">China</td></tr><tr><td>Anemia, Leukopenia</td></tr></table>","table_caption":"[\"Table 1 Clinically approved Pt(II) drugs [7,34,37,38,47,49,50]. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[210,527,788,767]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 2. Non-classical Pt(II) drugs [51-54]. \"]","image_footnote":"[]","img_path":"images/0004/4ce654e50e5e8736fe4368d79c8da48fb3767ea89af12ba30c9c9585016b3773.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,802,487,843]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the azide ligand on the plane quickly leaves to generate three molecules of nitrogen, and then $\\mathrm{Pt(IV)}$ is converted into cytotoxic $\\mathrm{Pt(II)}$ to further play its role under light conditions (Fig. 4b) [61,62]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,857,346,871]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. Nanocarriers for platinum drugs delivery ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,883,485,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"With the rapid development of nanotechnology, NDDSs have attracted great attention in the delivery of multiple chemotherapeutic drugs [63]. Nanomedicine based on NDDSs has obvious unique advantages [64-68]: i) Prolong drug circulation time and improves ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,802,939,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pharmacokinetics; ii) Improves the solubility of insoluble drugs and protects them from early degradation; iii) By designing stimulus-responsive NDDSs, site-specific drug release and reduced systemic toxicity of drugs could be achieved; iv) Through the EPR of tumor tissue, NDDSs can be passively accumulated at the tumor tissue to improve the bioavailability of drugs; v) More effective cancer combination therapies can be achieved by loading multiple drugs, drug sensitizers, targeting ligands, etc.; vi) By co-loading with imaging reagent in the NDDSs, therapy and imaging can be integrated, real-time tracking of drug distribution and drug efficacy evaluation. NDDSs for platinum drugs ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,42,129,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Q. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[752,42,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biomedical Technology 2 (2023) 77-89 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"79 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[58,92,485,192]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0296/2ce0332c5ce664f80f7b0aff98d95c2ff05c0453f4b704acdb8b335d47d35408.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":"<table><tr><td>Generic Name</td><td>Stage</td><td>Cancer type</td></tr><tr><td rowspan=\"2\">Picoplatin</td><td>Phase II</td><td>Metastatic colorectal cancer, drug-resistant prostate cancer</td></tr><tr><td>Phase III</td><td>Recurrent or drug-resistant ovarian cancer and NSCLC</td></tr><tr><td>BBR3464</td><td>Phase II</td><td>Ovarian cancer, small cell lung cancer, NSCLC, esophageal cancer</td></tr></table>","table_caption":"[\"Table 2 Pt(II) drugs in clinical trials [51,53]. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[507,65,937,168]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"delivery mainly include inorganic nanocarriers (such as carbon dots [69], carbon nanotubes [70], graphene [71], silica nanoparticles [72], iron oxide nanoparticles $\\mathrm{(Fe_3O_4NP)}$ [73], gold nanomaterials [74], upconversion nanoparticles (UCNPs) [75], etc.) and organic nanocarriers (such as liposomes [76], vesicles [77], polymeric micelles [78], dendrimers [79]) (Fig. 5). Most studies have shown that the above NDDSs yielded better anticancer outcomes than small-molecule platinum drugs at the cellular and animal levels. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[127,235,618,486]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0699/e57939937e2efb45f680dfebddbad58b8f3aeca09b84d9250bf691fb622fadb4.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[625,234,870,486]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 3. (a) Representative structure of Pt(IV) drugs [13]. (b) The structure of JM-216 [56]. \"]","image_footnote":"[]","img_path":"images/0562/003cec909b2c514ac9b2e9849ba3adb1f028dc4d3bc5b9fb065033456701442a.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[127,532,870,689]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0279/f1a9af97d319243cbc6817569c0f6726d978410a3c9bcb260749859686d8f127.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[127,699,870,912]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 4. Mechanism of action of (a) reduction-sensitive and (b) photo-sensitive Pt(IV) prodrugs [59-62]. \"]","image_footnote":"[]","img_path":"images/0551/7297ed2e315d7b4b85d3e2fd77bd6ae7bf59696d2ca66196aaff39fc9530891a.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[58,42,129,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Q. Zhang et al. 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\"]","image_footnote":"[]","img_path":"images/0108/7d8005296026809f60d77ae8ba7facd8e5cc0b3231f2fcb6fc8d79db62fd042f.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[403,620,554,732]","code_body":null,"code_caption":null,"image_caption":"[\"Vesicle \"]","image_footnote":"[]","img_path":"images/0375/e5a05856545c515823915d1dc7c670a86a0d278fb67ff2cbac0edf82dc203bbc.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[628,615,826,728]","code_body":null,"code_caption":null,"image_caption":"[\"Polymeric Conjugate \",\"Fig. 5. Various NDDSs for platinum drugs [69-79]. \"]","image_footnote":"[]","img_path":"images/0427/c4b123457e56880a277c1a6745af6986d1f4cd0a526e209b02afa6db4912c36e.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[58,805,218,817]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1. Inorganic nanocarriers ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,831,485,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Inorganic nanoparticles generally possess suitable general properties including wide versatility, rich functionality, and potential for targeted delivery and controllable drug release. Due to the characteristics of porosity and high specific surface area, platinum drugs are often directly encapsulated in or adsorbed on the surface of inorganic nanocarriers. For example, Yamauchi et al. prepared the corresponding Cis@HPB nanocarrier by mixing the porous coordination polymeric Hollow Prussian blue (HPB) nanoparticles and the aqueous solution of cisplatin at room ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,804,937,909]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"temperature (Fig. 6a) [80]. The porous HPB material completely adsorbed the mixed cisplatin into the pore or its surface within $30\\mathrm{min}$ . In the phosphate buffer saline (PBS) at $\\mathsf{pH}7.4$ , the release of cisplatin in $\\mathrm{Cis@HPB}$ was maintained at less than $5\\%$ within $200\\mathrm{min}$ , indicating the stability of the nanocarriers. Besides, the prepared HPB nanoparticles showed good biocompatibility as indicated in Fig. 6b. The nanocarriers loaded with cisplatin (Cis@HPB) can effectively suppress the growth of bladder cancer T24 cells (Fig. 6c). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,910,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In recent years, drug-conjugated inorganic nanoparticles have been rapidly developed, and the nanocarriers used to bond platinum drugs ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,42,129,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Q. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[752,42,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biomedical Technology 2 (2023) 77-89 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"81 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[127,69,868,252]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0920/c9ff98ed7f8b36a3e12790f3afbf21c85ac8a4a52ad498db12e7809db037aeed.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[129,262,494,452]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/1005/61d1c73cd61e63f50a0657f6088ee9d32571c68a4d87e7278032044fd6462371.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[505,263,865,452]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 6. (a) An illustration representing the chemotherapy of Hollow Prussian Blue (HPB) nanoparticles. (b) MTT assays of HPB against T24 cells. (c) Comparison of MTT assays between HPB and Cis@HPB against T24 cells. Reproduced with permission [80]. Copyright 2012, Royal Society of Chemistry. \"]","image_footnote":"[]","img_path":"images/0431/ac5ff7eceaccea4915a40b06a32ae9afe2ec014be00f3ac34d8f02b8dd39bc79.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,503,487,556]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"have emerged endlessly. One typical example from Huang and coworkers synthesized mesoporous silica nanoparticles containing dicarboxylic groups in the pore channel, which were used for complexing oxaliplatin to prepare drug-loading mesoporous silica nanocarriers ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,503,937,556]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(denoted as MSN-Pt, Fig. 7) [81]. The endocytosis content of MSN-Pt was significantly enhanced, and the Pt-DNA adducts formed within $24\\mathrm{h}$ were 3.5 folds higher compared with free oxaliplatin. Therefore, the $\\mathrm{IC}_{50}$ value of MSN-Pt $(25.95\\mu \\mathrm{M})$ was significantly lower than that of oxaliplatin ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[211,582,769,677]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0596/0185aac91b4011f5e263ee4b7e3ffc99451d87a7539da60fa6a03c3296765666.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[211,682,786,901]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 7. (a) Synthesis of mesoporous silica nanoparticles containing dicarboxylic groups in the pore channel. (b) MSN nanoparticles conjugated with oxaliplatin species and the intracellular delivery and action of the platinum drug. Reproduced with permission [81]. Copyright 2013, Royal Society of Chemistry. \"]","image_footnote":"[]","img_path":"images/0516/66ccb225a175a3a02e6b55740f6be042b9be90066d4d744b2bb8a8b9fd59d986.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[60,42,129,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Q. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[752,42,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biomedical Technology 2 (2023) 77-89 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[492,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"82 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[57,65,487,105]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(39.29 $\\mu$ M) against hepatoma carcinoma HepG-2 cells. These results demonstrated that MSN-Pt promoted the intracellular accumulation of platinum drugs and simultaneously enhanced their cytotoxicity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,105,485,313]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In another demo, Liu et al. prepared Pt-PEG-GNRs by conjugating Pt(IV) prodrug to PEG-GNRs to overcome the drug resistance problem during cisplatin chemotherapy (Fig. 8a) [82]. Pt-PEG-GNRs entered cancer cells by endocytosis, so that the delivery of platinum drug in resistant cells would be not affected, avoiding the process of transporting cisplatin via copper transporter (Ctr1). Meanwhile, due to the inert structure of the Pt(IV) prodrug, the drug didn't interact with detoxication substances in cells such as Metallothionein, GSH, and other effects and inactivation. Therefore, Pt-PEG-GNRs exhibited a negligible difference in toxicity between normal lung cancer cells A549 and drug-resistant cells A549R (Fig. 8b). By contrast, the cytotoxicity of free cisplatin in A549R was much lower than that in A549. These results indicate that Pt-PEG-GNRs increased the intracellular endocytosis of platinum drugs and overcame the mechanism of intracellular platinum resistance, thus demonstrating a feasible strategy to solve the challenge of platinum drug resistance. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,316,485,486]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Another inspiring example was the innovatively applied UCNPs to deliver reduction-sensitive or photo-sensitive $\\mathrm{Pt(IV)}$ prodrugs. For the first time, the reduction-sensitive $\\mathrm{Pt(IV)}$ prodrug (DSP) with dicarboxylate was decorated onto the surface of the polyethyleneimine (PEI)-coated UCNPs $(\\mathrm{NaYF_4:Yb^{3+}/Er^{3+}})$ , and both the water dispersion and targeting ability of the nanoparticles were improved by linking another carboxyl group of dicarboxylate $\\mathrm{Pt(IV)}$ prodrug to folic acid (FA) modified polyethylene glycol (PEG-FA, Fig. 9a) [83]. The prepared NaYF4: $\\mathrm{Yb^{3+}/Er^{3+}}$ -DSP-PEG-FA nanocarriers have good cell targeting ability and high endocytosis. The cytotoxicity test revealed that the nanoparticle $(\\mathrm{IC}_{50} = 0.29~\\mu \\mathrm{g~mL}^{-1})$ significantly improved the cytokilling effect of the platinum drugs, which was 0.19 times than that of cisplatin's results $(\\mathrm{IC}_{50} = 1.51~\\mu \\mathrm{g~mL}^{-1})$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,486,485,580]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In another work, they developed UCNP-DPP-PEG nanocarriers by conjugating photo-sensitive $\\mathrm{Pt(IV)}$ prodrug (DPP) onto the surface of UCNPs (Fig. 9b) [84]. With the ability of UCNPs to convert near-infrared (NIR) light into ultraviolet (UV) to visible light, the penetration depth of the light could be improved and the photo-controlled on-demand release of the platinum drug could be realized. The UCNP-DPP-PEG administration group under NIR light irradiation showed the optimal antitumor ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,65,937,158]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"effect compared with UV-activated groups. Meanwhile, due to the presence of Gd, Yb, and Tm elements in the UCNPs, the nanocarriers achieved tri-mode imaging capabilities of nuclear magnetic resonance (MRI), computed tomography (CT), and upconversion fluorescence (UCL) imaging. Thus, the nanosystem realized NIR photo-controlled drug release behavior guided by multi-mode imaging, which has significant practical potential and theoretical guidance for cancer therapy. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,172,663,185]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2. Organic nanocarriers ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,199,937,475]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Although inorganic nanocarriers owned numerous advantages such as simple preparation, uniform size, and variety, they are not easy to degrade in vivo and have poor biocompatibility and potential biotoxicity, which limit further clinical transformation [85]. As a consequence, no clinical trial or use of inorganic nanocarriers were reported for platinum drugs at present. In stark contrast, organic nanocarriers have better biocompatibility and more safety and can carry hydrophobic and hydrophilic drugs simultaneously. Great progress has been made in organic nanocarriers for nanomedicine preparation and clinical drug delivery [86,87]. For example, several nanomedicines based on liposomes have been approved for clinical use, such as Doxil, Myocet, Caelyx, Daunoxome, and Ribodo [88-91]. It is noteworthy that several liposome nanomaterials loaded with platinum drugs have entered phase II and III clinical trials (Table 3) [92-94]. Lipoplatin, as a cisplatin-loaded liposome nanomedicine developed by Regulon, increased the solubility of cisplatin three times from $1\\mathrm{mg~mL}^{-1}$ , and extending the blood circulation duration from $6\\mathrm{h}$ to $117\\mathrm{h}$ , thus significantly increasing the tumor accumulation of the drug. The bilayer structure of liposomes promoted further endocytosis of Lipoplatin in tumor cells, boosting the tumors killing ability 200 times higher than that of normal tissues, greatly reducing the systemic toxicity of cisplatin. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,476,937,581]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In addition to organic liposome nanocarriers, polymer nanocarriers have proved with advantages of easy modification, wide source, variety, and so on, which also provided numerous possibilities for platinum drug delivery. Surprisingly, several polymer nanocarriers prepared by Kataoka (NC-6004 and NC-4016), Nowotnik (AP5346), and Schellens (AP5280), have entered phase II and III trials (Table 4) [95-97]. Among them, NC-6004 is a cisplatin-loaded polymer micellar nanomedicine, which was known for significantly improving the blood circulation time of the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[126,597,603,878]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0222/ca9fbdecb137ebe2568f1c9acdfa0879b6c1d69f741e2c57244b2b4e8ece8157.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[608,598,870,736]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0762/a067c7dc5c89a286747904317e9f056d96f423d963281a2332f294bcf06b640c.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[611,733,867,873]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 8. (a) Schematic illustration of Pt-PEG-GNRs for overcoming cisplatin resistance. (b, c) The cytotoxicity assays of (b) Pt-PEG-GNRs conjugate and (c) Cisplatin. Reproduced with permission [82]. Copyright 2012, WILEY-VCH GmbH. \"]","image_footnote":"[]","img_path":"images/0300/3978feac457c8986716aaa8b12bf1f43c0fa41d6cd29c22d33e3e0891e2b85bb.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[58,42,131,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Q. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[752,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biomedical Technology 2 (2023) 77-89 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"83 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[127,68,369,292]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0622/23bb56483d8a0d6f28b7a8624eb692c5e7ce1778dd63941086eeb9ebdfedf94a.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[374,68,870,292]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 9. Schematic illustration of UCNPs delivering (a) reduction-sensitive Pt(IV) prodrug or (b) light-sensitive Pt(IV) prodrug. (a) Reproduced with permission [83]. Copyright 2013, WILEY-VCH GmbH. (b) Reproduced with permission [84]. Copyright 2013, American Chemical Society. \"]","image_footnote":"[]","img_path":"images/0645/57a03b1debc7cd9e1ed8474a7fdb44f32e2c836800776acbe7ba0c1d418a2365.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[60,375,485,466]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/1007/79661fadb4e219c45bacff71cf603dea8b4e41161077e38e315ff61d692f4dc5.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":"<table><tr><td>Generic Name</td><td>Stage</td><td>Drug</td><td>Cancer type</td></tr><tr><td>Lipoplatin</td><td>Phase III</td><td>Cisplatin</td><td>NSCLC, stomach cancer, head and neck cancer</td></tr><tr><td>SPI-77</td><td>Phase II</td><td>Cisplatin</td><td>NSCLC, ovarian cancer</td></tr><tr><td>MBP-426</td><td>Phase II</td><td>Oxaliplatin</td><td>Gastric cancer, esophageal cancer, pancreatic cancer</td></tr></table>","table_caption":"[\"Table 3 Liposome-based platinum drug delivery nanocarriers in clinical trials [92-94]. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[60,517,485,586]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0445/3e57ec11c2abfae21bf57b4a5a49385e2b52bc3235c8074d975a5266aeedc1f0.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":"<table><tr><td>Generic Name</td><td>Stage</td><td>Drug</td><td>Carrier type</td></tr><tr><td>NC-6004</td><td>Phase II and III</td><td>Cisplatin</td><td>mPEG-b-PGA</td></tr><tr><td>NC-4016</td><td>Phase II and III</td><td>Oxaliplatin</td><td>mPEG-b-PGA</td></tr><tr><td>AP5280</td><td>Phase II</td><td>Oxaliplatin</td><td>HPMA</td></tr><tr><td>AP5346</td><td>Phase II</td><td>Cisplatin</td><td>HPMA</td></tr></table>","table_caption":"[\"Table 4 Polymer-based platinum drug delivery nanocarriers in clinical trials [95-97]. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[57,602,485,641]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"cisplatin, and slowly and continuously releasing the platinum drugs. It profoundly reduced cisplatin-related systemic toxicity and eliminated the need for hospitalization. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,641,485,669]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As mentioned above, the $\\mathrm{Pt(IV)}$ prodrugs have an octahedral inert structure so they gained low toxicity before reduction. Due to the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,341,937,604]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"reduction-sensitive or photosensitive properties and axial-modified characteristics, Pt(IV) can be loaded into the polymer-based nanocarriers through various ways, such as physical encapsulation, chemical bonding, main chain polymerization, and so on, when preparing the polymer-based nanomedicine [98,99]. To take advantage of these merits, Xiao et al. have synthesized an amphiphilic block polymer (mPEG- $b$ -PCL- $b$ -PLL) for the delivery of monocarboxylic-cisplatin, dicarboxylic-binuclear-cisplatin, and dicarboxylic-binuclear-oxaliplatin. These platinum drugs were conjugated to the polymer side chain of mPEG- $b$ -PCL- $b$ -PLL by the amide bond, and then the drug-loaded amphiphilic polymer self-assembled into micelles in aqueous (Figs. 10 and 11) [100,101]. Both cell and animal experiments confirmed that the nanomicelles had much higher endocytosis than small-molecule platinum drugs, and the former greatly increased the drug accumulation in tumors. These nanomicelles are also acidic- and reduction-sensitive. The specific release at the tumor site can be achieved through the acidic tumor environment and high reducibility conditions. Therefore, the prepared nanomicelles have better tumor treatment ability than the corresponding small-molecule Pt(II) drugs at both cellular and animal levels, leading to a reduction of systemic toxicity from platinum drugs. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,605,937,670]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Clinical transformation of polymer-based anticancer nanomedicines has confronted several challenges: 1) Regulations of composition and structure of polymer-based nanocarriers, where the batch variations are distinct; 2) Lack of direct drug monitoring capacity; 3) Lack of suitable preclinical animal models for screening and evaluating the nanomedicine ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[126,697,739,798]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0596/a5359b8760f180218bc479acc076a45648a0555f1290b832862f9d904148f789.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[124,803,870,901]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 10. (a) The synthesis processes of monocarboxylic-cisplatin. (b) Conjugation of s mPEG- $b$ -PCL- $b$ -PLL with monocarboxylic-cisplatin, and formation of monocarboxylic-cisplatin-containing micelles. Reproduced with permission [100]. Copyright 2011, Elsevier. \"]","image_footnote":"[]","img_path":"images/0965/44b908e309fa5d93244a3bed41028345294d10108c26d5cf6d8f13068b871a9f.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[58,42,129,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Q. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[752,42,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biomedical Technology 2 (2023) 77-89 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"84 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[134,78,862,361]","code_body":null,"code_caption":null,"image_caption":"[\"a \"]","image_footnote":"[]","img_path":"images/0113/0bc04a5ee1b2a8c9110b8d9bad5c56397897ab4e4144ee9aee879914bd4b66de.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[144,390,850,580]","code_body":null,"code_caption":null,"image_caption":"[\"b \",\"Fig. 11. (a) The structural formulas of dicarboxylic-binuclear-cisplatin and dicarboxylic-binuclear-oxaliplatin. (b) Conjugation of s mPEG- $b$ -PCL- $b$ -PLL with either dicarboxylic-binuclear-cisplatin or dicarboxylic-binuclear-oxaliplatin, and formation of platinum-containing micelles. Reproduced with permission [101]. Copyright 2011, Elsevier. \"]","image_footnote":"[]","img_path":"images/0364/bd96b99c327a9ce7d57e3db1d414c0348f39380f12448fa75e6840b838c37fa6.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[60,660,485,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"efficacies. To solve these problems, Cong et al. prepared a double-drug loaded nanomicelle for the delivery of cisplatin prodrug and demethylcantharidin (DMC) (Fig. 12) [102]. Firstly, they synthesized a dual-drug small-molecule prodrug via a ring-opening reaction of one molecule of cisplatin prodrug and two molecules of DMC. Then, the dual-drug small-molecule prodrug was introduced into the polymer backbone as polymeric monomers. Once the dual-drug small molecule participated in the polymerization, the proportion of drugs was determined, which was not affected by the preparation conditions and batches. The nanomicelles not only had a good therapeutic effect on the subcutaneous cervical cancer cell U14 xenograft tumor of Kunming mice but also showed the best antitumor effect on the lung squamous cell carcinoma model. In addition, the nanodrugs reduced the hematotoxicity and systemic toxicity of free cisplatin. Platinum content in the prepared nanomedicine occupied up to $12\\%$ . Due to the strong X-ray absorption ability of platinum, the distribution of the nanomedicine in the body can be directly monitored through CT imaging after injection, realizing the integration of diagnosis and therapy. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,897,485,924]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To further realize spatiotemporal controllable, site-specific, and quantitative release of drugs, Wang et al. prepared a photo-activated ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,660,937,805]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"nanocarrier by integrating the photo-sensitive $\\mathrm{Pt(IV)}$ prodrug and DMC into the polymer backbone in a similar way proposed by Cong et al. (Fig. 13) [103]. Besides similar functions as the nanomicelle from Cong et al., this nanocarrier also achieved precise photo-activated drug release at tumor sites by in situ drug tracking with CT imaging. Animal experiments further showed that the dual-drug-loaded nanoparticles (DDP NP) achieved a cure rate of $75\\%$ . Because the photo-activated release of the drug only occurred at the tumor site, the drug released in other tissues or organs was in negligible amounts. Therefore, the nanocarriers have low toxicity and almost no impact on the quality of life of mice, which had the prospect for clinical application. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,819,705,832]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. Summary and perspectives ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,844,937,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Platinum drugs have played an important role in chemotherapy. The application of platinum drugs is a particularly burgeoning area of oncology. Currently, numerous platinum complexes have been exploited for treating various cancer types. According to the difference in the valence of platinum atoms, we introduced platinum drugs from $\\mathrm{Pt(II)}$ and $\\mathrm{Pt(IV)}$ drugs categories. Specifically, $\\mathrm{Pt(II)}$ drugs include clinically ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,42,129,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Q. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[752,42,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biomedical Technology 2 (2023) 77-89 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"85 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[127,70,868,757]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 12. Schematic illustration of dual drug backboned shattering polymeric theranostic nanomedicine (DD-NP) for synergistic eradication of patient-derived lung cancer (PDLC). (a) Illustration of self-assembly and chain-shattering of DD-NP to release active Pt(II) and DMC. (b) Illustration of the establishment of PDLC model and Pt-based DMCT after intravenous injection with DD-NP. (c) Possible dual anticancer mechanisms after endocytosis of DD-NP by cancer cells. Reproduced with permission [102]. Copyright 2018, WILEY-VCH GmbH. \"]","image_footnote":"[]","img_path":"images/0532/bb0734abd46d43d0512170e3ab21351e60766cd500056e3c08909c6992fb05ea.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,828,485,894]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"approved classical platinum drugs such as cisplatin, carboplatin, oxaliplatin, etc., and non-classical platinum drugs such as picoplatin, BBR3464, 56MESS, etc. While the $\\mathrm{Pt(IV)}$ can be further divided into reduction-sensitive $\\mathrm{Pt(IV)}$ and light-sensitive $\\mathrm{Pt(IV)}$ drugs according to their activation pathway and structure difference. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,894,485,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To address many predicaments including toxic side effects, drug resistance, and bioavailability of platinum drugs, NDDSs have been widely developed and brought into research and pilot study focus. Based ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,828,937,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"on the material differences, the NDDSs could be divided into inorganic and organic nanocarriers. Although these nanocarriers have been validated with good therapeutic effects, there are still many challenges that need to be solved. Inorganic nanocarriers have been long-time used for platinum drug delivery due to their controllable size and morphology, diverse surface properties, and ingenious design. However, the disadvantages of inorganic nanomaterials are obvious because of the introduction of heavy metals. Long-term administration of such drugs would ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,42,129,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Q. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[752,42,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biomedical Technology 2 (2023) 77-89 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"86 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[211,69,786,406]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 13. Schematic diagram of the photo-activatable dual prodrug polymer nanocarrier (DPP NP) for synergistic chemotherapy. (a) Illustration of synthesis DPP. (b) Illustration of anticancer mechanisms after endocytosis of DPP NP. Reproduced with permission [103]. Copyright 2019, Elsevier. \"]","image_footnote":"[]","img_path":"images/0244/827564bb2af264d4562c9abc271dd54019d3b93a2ab790ae28c519f61bedd61c.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,453,485,571]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"easily cause damage to different tissues, thus affecting the life quality of patients. By contrast, organic nanocarriers with good biocompatibility play increasingly important roles in platinum drug delivery. Nowadays, several platinum drug-laden liposome nanocarriers (Lipoplatin, SPI-77, MBP-426) and polymeric nanocarriers (NC-6004, NC-4016, AP5346, AP5280) have entered phase II or III trials. The clinical application of these drugs has sparked the flourishing of organic nanocarriers for platinum drug delivery. Nevertheless, these organic nanocarriers still face many problems for further clinical transformation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,572,487,824]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"From intravenous injection to the target site, nanomedicines would go through five processes: blood circulation, tumor accumulation, tumor infiltration, cell uptake, and drug release. During these processes, several key courses restrict the efficacy of nanomedicines. Despite the abundant angiogenesis and lymphatic reflux defects in the tumor tissue, the EPR effect can increase the interception of nanoparticles at the tumor site. However, the absence of functional lymphatic vessels leading to increased interstitial hydraulic pressure at the tumor site will make it difficult to efficiently transport deep into tumors. Effective cellular endocytosis plays a crucial part in the efficacy of nanomedicines. Therefore, it is necessary to design actively targeted nanocarriers for platinum drug delivery. Equally important, but often overlooked, is that systemically administered nanocarriers may gradually release their loaded drugs during circulation, making carriers unable to meet the required drug concentration when they reach the tumor microenvironment. Therefore, to maximize the therapeutic effect of nanomedicines in the clinic, it is particularly important to design accurate and controllable NDDSs. Taken together, great efforts still need to be devoted to devising more efficient NDDSs for platinum drug delivery. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,836,278,849]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Declaration of competing interest ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,862,485,902]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,453,633,466]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgments ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,479,937,546]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This work was supported by the National Natural Science Foundation of China (52103196, 32201118 and 82102233), Shenzhen Fundamental Research Program (JCYJ20210324102809025), Zhejiang Provincial Natural Science Foundation of China (LGF22C100003), and Wenzhou Institute UCAS (WIUCASQD2022018 and WIUCASQD2021012). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,559,584,569]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[519,583,934,906]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[1] H. Sung, J. Ferlay, R.L. Siegel, M. Laversanne, I. Soerjomataram, A. Jemal, F. Bray, Global cancer statistics 2020: globocan estimates of incidence and mortality worldwide for 36 cancers in 185 countries, CA A Cancer J. Clin. 71 (2021) 209-249. \",\"[2] A.A. Forastiere, H. Goepfert, M. Maor, T.F. Pajak, R. Weber, W. Morrison, B. Glisson, A. Trotti, J.A. Ridge, C. Chao, Concurrent chemotherapy and radiotherapy for organ preservation in advanced laryngeal cancer, N. Engl. J. 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","text_format":null,"text_level":null,"type":"header"},{"bbox":"[752,42,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biomedical Technology 2 (2023) 77-89 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"88 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[67,66,482,559]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[71] X.-J. Liang, H. Meng, Y. Wang, H. He, J. Meng, J. Lu, P.C. Wang, Y. Zhao, X. Gao, B. Sun, Metallofullerene nanoparticles circumvent tumor resistance to cisplatin by reactivating endocytosis, Proc. Natl. Acad. Sci. USA 107 (2010) 7449-7454. \",\"[72] I.I. Slowing, B.G. Trewyn, S. Giri, V.Y. Lin, Mesoporous silica nanoparticles for drug delivery and biosensing applications, Adv. Funct. Mater. 17 (2007) 1225-1236. \",\"[73] Z. Cheng, Y. Dai, X. Kang, C. Li, S. Huang, H. Lian, Z. Hou, P. Ma, J. Lin, Gelatin-encapsulated iron oxide nanoparticles for platinum (IV) prodrug delivery, enzyme-stimulated release and MRI, Biomaterials 35 (2014) 6359-6368. \",\"[74] S. Dhar, W.L. Daniel, D.A. Giljohann, C.A. Mirkin, S.J. Lippard, Polyvalent oligonucleotide gold nanoparticle conjugates as delivery vehicles for platinum (IV) warheads, J. Am. Chem. Soc. 131 (2009) 14652-14653. \",\"[75] Y. Min, J. Li, F. Liu, E.K. Yeow, B. 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Gust, Platinum (II)-dendrimer conjugates: synthesis and investigations on cytotoxicity, cellular distribution, platinum release, DNA, and protein binding, Bioconjugate Chem. 21 (2010) 328-337. \",\"[80] H.-Y. Lian, M. Hu, C.-H. Liu, Y. Yamauchi, K.C.-W. Wu, Highly biocompatible, hollow coordination polymer nanoparticles as cisplatin carriers for efficient intracellular drug delivery, Chem. Commun. 48 (2012) 5151-5153. \",\"[81] H. He, L. Yan, F. Meng, Z. Xie, X. Jing, Y. Huang. A reduction-sensitive carrier system using mesoporous silica nanospheres with biodegradable polyester as caps, Phys. Chem. Chem. Phys. 15 (2013) 14210-14218. \",\"[82] Y. Min, C.Q. Mao, S. Chen, G. Ma, J. Wang, Y. Liu, Combating the drug resistance of cisplatin using a platinum prodrug based delivery system, Angew. Chem. 51 (2012) 6742-6747. \",\"[83] Y. Dai, X. Kang, D. Yang, X. Li, X. Zhang, C. Li, Z. Hou, Z. Cheng, P. Ma, J. 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Biotechnol. 33 (2015) 941-951. \"]","page_idx":"12","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[512,66,934,569]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[87] Q. Hu, W. Sun, C. Wang, Z. Gu, Recent advances of cocktail chemotherapy by combination drug delivery systems, Adv. Drug Deliv. Rev. 98 (2016) 19-34. \",\"[88] Y.C. Barenholz, Doxil®-The first FDA-approved nano-drug: lessons learned, J. Contr. Release 160 (2012) 117-134. \",\"[89] G. Batist, J. Barton, P. Chaikin, C. Swenson, L. Welles, Myocet (liposome-encapsulated doxorubicin citrate): a new approach in breast cancer therapy, Expet Opin. Pharmacother. 3 (2002) 1739–1751. \",\"[90] S.R.D. Johnston, M.E. Gore, Caelyx®: phase II studies in ovarian cancer, Eur. J. Cancer 37 (2001) 8-14. \",\"[91] E.A. Forssen, M.E. Ross, Daunoxome® treatment of solid tumors: preclinical and clinical investigations, J. Lip. Res. 4 (1994) 481-512. \",\"[92] T. Boulikas, Clinical overview on LipoplatinTM: a successful liposomal formulation of cisplatin, Expet Opin. Invest. Drugs 18 (2009) 1197-1218. \",\"[93] N. Seetharamu, E. Kim, H. Hochster, F. Martin, F. Muggia, Phase II study of liposomal cisplatin (SPI-77) in platinum-sensitive recurrences of ovarian cancer, Anti, Res. 30 (2010) 541-545. \",\"[94] K. Sankhala, A. Mita, R. Adinin, L. Wood, M. Beeram, S. Bullock, N. Yamagata, K. Matsuno, T. Fujisawa, A. Phan, A phase I pharmacokinetic (PK) study of MBP426, a novel liposome encapsulated oxaliplatin, J. Clin. Oncol. 27 (2009) 2535. \",\"[95] K. Endo, T. Ueno, S. Kondo, N. Wakisaka, S. Murono, M. Ito, K. Kataoka, Y. Kato, T. Yoshizaki, Tumor-targeted chemotherapy with the nanopolymer-based drug NC-6004 for oral squamous cell carcinoma, Cancer Sci. 104 (2013) 369-374. \",\"[96] J.M. Rademaker-Lakhai, C. Terret, S.B. Howell, C.M. Baud, R.F. De Boer, D. Pluim, J.H. Beijnen, J.H. Schellens, J.-P. Droz, A Phase I and pharmacological study of the platinum polymer AP5280 given as an intravenous infusion once every 3 weeks in patients with solid tumors, Clin. Cancer Res. 10 (2004) 3386-3395. \",\"[97] D.P. Nowotnik, E. Cvtikovic, ProLindact™(AP5346): a review of the development of an HPMA DACH platinum polymer therapeutic, Adv. Drug Deliv. Rev. 61 (2009) 1214-1219. \",\"[98] S. He, C. Li, Q. Zhang, J. Ding, X.J. Liang, X. Chen, H. Xiao, X. Chen, D. Zhou, Y. Huang, Tailoring platinum(IV) amphiphiles for self-targeting all-in-one assemblies as precise multimodal theranostic nanomedicine, ACS Nano 12 (2018) 7272-7281. \",\"[99] H. Lu, S. He, Q. Zhang, X. Li, Z. Xie, Z. Wang, Y. Qi, Y. Huang, Dual-sensitive dualprodrug nanoparticles with light-controlled endo/lysosomal escape for synergistic photoactivated chemotherapy, Biomater. Sci. 9 (2021) 7115-7123. \",\"[100] H. Xiao, R. Qi, S. Liu, X. Hu, T. Duan, Y. Zheng, Y. Huang, X. Jing, Biodegradable polymer-cisplatin (IV) conjugate as a pro-drug of cisplatin (II), Biomaterials 32 (2011) 7732-7739. \",\"[101] H. Xiao, H. Song, Y. Zhang, R. Qi, R. Wang, Z. Xie, Y. Huang, Y. Li, Y. Wu, X. Jing, The use of polymeric platinum (IV) prodrugs to deliver multinuclear platinum (II) drugs with reduced systemic toxicity and enhanced antitumor efficacy, Biomaterials 33 (2012) 8657-8669. \",\"[102] Y. Cong, H. Xiao, H. Xiong, Z. Wang, J. Ding, C. Li, X. Chen, X.J. Liang, D. Zhou, Y. Huang, Dual drug backboned shattering polymeric theranostic nanomedicine for synergistic eradication of patient-derived lung cancer, Adv. Mater. 30 (2018), 1706220. \",\"[103] Z. Wang, G. Kuang, Z. Yu, A. Li, D. Zhou, Y. Huang, Light-activatable dual prodrug polymer nanoparticle for precise synergistic chemotherapy guided by drug-mediated computed tomography imaging, Acta Biomater. 94 (2019) 459–468. \"]","page_idx":"12","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[60,42,129,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Q. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[752,42,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biomedical Technology 2 (2023) 77-89 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"89 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[58,206,463,226]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nanocarriers for platinum drug delivery \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,240,557,258]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Qingfei Zhang, Gaizhen Kuang, Lexiang Zhang \\\\*\\\\*, Yujuan Zhu \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,264,811,288]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Oujiang Laboratory (Zhejiang Lab for Regenerative Medicine, Vision and Brain Health), Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, 325001, China \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[838,208,889,247]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0825/2ab5e178bc8be30a1ca52dd26e5ae928569bf0c7756e0e1d7c9f55e04989f6ff.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[58,317,193,329]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ARTICLEINFO \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,341,134,353]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,354,119,363]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nanocarrier \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,364,131,374]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Platinum drug \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,375,127,385]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Drug delivery \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,385,132,395]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Chemotherapy \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,397,134,408]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Cancer therapy \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[334,317,435,329]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABSTRACT \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[332,341,937,451]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Platinum drugs have been coined as one of the great success representatives in cancer chemotherapy. With the accidental discovery of cisplatin, thousands of platinum-based complexes have been synthesized, including clinically approved classical platinum(II) (Pt(II)) drugs, non-classical Pt(II) drugs, and platinum(IV) (Pt(IV)) drugs. Currently, these drugs are widely utilized in the treatment of various solid tumors in the clinic. Unfortunately, systemic toxicity and innate or acquired drug resistance greatly restrict their applications. The nanocarrier-based drug delivery systems (NDDSs) offer the possibility of targeted delivery of platinum drugs to the tumor tissue with reduced toxicity and enhanced drug efficacy. Thus, in this review, inorganic and organic nanocarriers for platinum drug delivery are introduced. The significant improvements, future challenges, and prospects of the nanocarriers toward potential clinical application are briefly discussed. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,488,163,500]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,514,485,738]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Cancer is one of the leading causes of death worldwide and is a serious public health problem [1]. Traditional chemotherapy, radiotherapy, and surgery are golden standards for cancer treatments in clinics [2]. As a systemic treatment, chemotherapy drugs can reach most tissues and organs after drug administration. Therefore, it gained good therapeutic effects regarding both potential and already metastatic middle-late cancers [3,4]. Based on the sources and chemical structures, chemotherapeutic drugs can be categorized into alkylating agents, anti-cancer antibiotics, anti-metabolic drugs, animal and plant components, anti-tumor hormones, and miscellaneous drugs [5]. Apart from plants-derived drugs such as paclitaxel, etoposide, vincristine, elemene, vincristine, vindesine, camptothecin, etc., most of the chemotherapeutic drugs are capable of being synthesized by chemical methods. Among them, chemosynthetic platinum-based antitumor agents have been effectively studied and deployed in combating diverse malignancies [6-8]. Nowadays, platinum drugs have almost accounted for more than $50\\\\%$ of all anti-cancer drugs in use [9,10]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,738,485,804]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Despite great achievements, platinum drugs face challenges in clinical applications, especially for toxicity and drug resistance [11,12]. In addition, low bioavailability is another major limitation inherited from poor water solubility, short blood circulation time, lack of selectivity, easy to be cleared by the reticuloendothelial system (RES), and be \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,488,937,673]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"eliminated by liver metabolism and kidney [7,13]. Nowadays, it is urgently needed to deliver platinum drugs specifically toward the target tissue and reduce their toxic side effects [14]. Compared with traditional small-molecule drugs, nanomedicines could prolong the drug circulation time and increase the bioavailability of drugs [15]. Besides, the use of nanomedicines facilitated the solubility of hydrophobic drugs and reduced potential immunogenicity [16]. In addition, the constant rate or stimuli-responsive release of the loaded drug reduces the toxic side effects and administration frequency [17]. Furthermore, nanomedicines can passively accumulate in tumor tissues, which is mainly attributable to the enhanced permeability and retention (EPR) effect [18]. Last but not least, nanomedicines can deliver drugs with different physical and chemical properties and pharmacokinetic behavior in the same systems, providing great potential for combination chemotherapy [19]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,672,937,804]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this review, we first introduce the commonly used platinum drugs including clinically approved classical platinum(II) (Pt(II)) drugs, non-classical Pt(II) drugs, and platinum(IV) (Pt(IV)) drugs [20,21]. Subsequently, an overview of nanocarrier-based drug delivery systems (NDDSs) for platinum drug delivery is summarized. The NDDSs mainly include those inorganic nanocarriers and organic nanocarriers. Finally, the perspectives and prospects of NDDSs in this area are discussed. The overall objective of this review is to discuss the biomedical potential of nanocarriers for platinum drug delivery, along with guidance for developing novel platinum drug delivery nanosystems that are clinically applicable. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[389,42,606,55]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biomedical Technology 2 (2023) 77-89 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[58,66,937,171]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"KeAi CHINESE ROOTS Biomedical Technology global IMPACT journal homepage: www.keaipublishing.com/en/journals/biomedical-technology \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,831,201,843]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"* Corresponding author. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[65,844,205,854]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"** Corresponding author. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[80,856,524,867]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"E-mail addresses: zhanglx@ucas.edu.cn (L. Zhang), zhuyujuan@ucas.ac.cn (Y. Zhu). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[58,877,294,887]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1016/j.bmt.2022.11.011 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[58,889,630,901]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received 14 November 2022; Received in revised form 16 November 2022; Accepted 17 November 2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[58,902,257,912]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Available online 17 December 2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[58,912,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2949-723X/© 2023 The Authors. Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[58,66,181,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. Platinum drugs \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,92,485,224]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Since Rosenberg and colleagues discovered cisplatin by accident in 1965 while studying the effects of electric fields on the differentiation of $E$ coli, cisplatin has been found with anti-cancer activity [22,23]. Rapidly, the US Food and Drug Administration (FDA) approved its use for metastatic ovarian and testicular cancer in 1978 [24]. With the high success of cisplatin, the development of platinum drugs has been greatly expanded, and thousands of them have been subjected to clinical trials. According to the valence of platinum atoms either at +2 or +4 in the synthetic platinum drugs, they could be categorized as Pt(II) and Pt(IV) types [25]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,238,159,250]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.1. Pt(II) drugs \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,264,485,409]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As has been noted, cisplatin is the firstly discovered $\\\\mathrm{Pt(II)}$ drug [26]. Cisplatin has been widely used in treating various cancers including testicular cancer, ovarian cancer, malignant mesothelioma, bladder cancer, cervical cancer, head and neck cancer, etc., showing a broad-spectrum anti-cancer effect [27]. However, its high systemic toxicity and side effects, such as renal toxicity, gastrointestinal reaction, neurotoxicity, ototoxicity, etc., strictly limited its application in clinical [28,29]. Meanwhile, many cancer cells exhibit innate and acquired resistance to cisplatin, further limiting its chemotherapy effectiveness. These unfavorable results have sparked a new wave of platinum drug development. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,409,485,606]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"With the unremitting efforts of scientists, carboplatin as the second-generation platinum drug was approved worldwide in 1989 and primarily used for the treatment of non-small cell lung cancer (NSCLC), ovarian cancer, and head and neck cancer [30]. Carboplatin replaces the two chlorine ligands of cisplatin with 1,1-cyclobutane dicarboxylic acid as the chelating ligand [31]. Thus, the spontaneous hydration rate of carboplatin was reduced 100 times compared with cisplatin due to the double-dentate coordination leaving group ligands [32,33]. Therefore, its neurotoxicity, ototoxicity, and nephrotoxicity to the system are significantly reduced [34]. However, the action mechanism, anti-cancer activity, and anti-cancer profile of carboplatin remained similar to cisplatin, while showing cross-resistance with cisplatin [35]. Although clinically carboplatin has replaced cisplatin in the treatment of ovarian cancer and NSCLC, cisplatin is still superior to carboplatin in dealing with germinal cell cancer, bladder cancer, and head and neck cancer [36]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,607,485,751]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nedaplatin, originally known as 254-S, is another second-generation platinum drug that was granted in 1995 only in Japan [37]. Like cisplatin and carboplatin, this platinum drug has nonleaving cis ammine ligands. The difference lies in the chelating leaving glycolate ligand, which makes nedaplatin $(10\\\\mathrm{mg}\\\\mathrm{mL}^{-1})$ obtain much higher solubility than cisplatin $(2.5\\\\mathrm{mg}\\\\mathrm{mL}^{-1})$ . Besides, nedaplatin has lower gastrointestinal and nephrite toxicity after intravenous administration and a similar pharmacokinetic profile to carboplatin. Clinically, nedaplatin is mainly used in treating esophageal cancer, head and neck cancer, NSCLC, small-cell lung cancer (SCLC), and breast cancer. Clinical trials are exploring the expansion of nedaplatin usage [38]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,752,485,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Oxaliplatin, with the research name 1-OHP, is the representative third-generation platinum drug, which had been internationally approved in 2002 [39]. Oxaliplatin is composed of a nonleaving ligand of R,R-diaminocyclohexane (DACH), and a chelated leaving ligand of the oxalate group [40]. DACH has been studied as the ligand of platinum-based anticancer drugs for a long time [30]. For oxaliplatin, research results suggested that R,R stereoisomers are more effective than enantiomers S,S isomers [41]. The origin of this difference was revealed in later crystallography studies where the R,R isomers preferentially form hydrogen bonds between the pseudoequatorial NH hydrogen atoms of the R,R-DACH ligand and the O6 atoms of the $3^{\\\\prime}$ -dG of the plated d(GpG) lesion [42]. In addition, the cyclohexanediamine ligand in the molecular structure of oxaliplatin is larger in volume and stronger in ester affinity, thereby can be deeply embedded into DNA and preventing the self-repair \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,65,937,118]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"of damaged DNA [43]. At present, oxaliplatin is the main component of colon cancer combination chemotherapy [44]. Besides, this platinum drug also showed good curative effects on ovarian cancer, NSCLC, head and neck tumor, and malignant lymphoma [8]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,118,937,235]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heptaplatin, initially known as SKI 2053R, was discovered and entered clinical trials in the 1990s [45]. In 1999, heptaplatin was approved by the Korean FDA. The leaving group ligand of heptaplatin is malonate. 2-(1-methylethyl)-1,3-dioxolane-4,5-dimethylamine is the nonleaving group ligand, which forms a seven-membered ring structure, endowing the drug its name. It is currently marketed as SunPla and is now replaced cisplatin clinically to treat gastric carcinoma [46]. The major side effects of heptaplatin are hepatotoxicity and myelosuppression. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,237,937,354]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lobaplatin can be viewed as a derivative of heptaplatin, where the cyclobutane ring is fused to the seven-membered chelate ring instead of the functionalized dioxolane [47]. ASTA Medica in Germany originally formulated this drug under the name D-19466 [48,49]. Although clinical trials were initially performed out in numerous nations to assess the effectiveness of patients with various malignancies, only China's regulatory approval was obtained in 2010 [13]. Lobaplatin is approved primarily for combating chronic myelogenous leukemia, but also for patients with SCLC and metastatic breast cancer. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,355,937,513]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The aforementioned platinum complexes are classical clinically approved (Fig. 1 and Table 1) with have a general formula of cis- $\\\\left[\\\\mathrm{PtL}_2\\\\mathrm{X}_2\\\\right]$ , where $\\\\mathrm{L}_2$ represents nonleaving group ligands and $\\\\mathrm{X}_2$ represents leaving group ligands. Although carboplatin, oxaliplatin, and other traditional Pt(II) drugs have several advantages over cisplatin, adverse side effects and resistance still potentially exist. Besides, these drugs display low aqueous stability and higher reactivity to bioactive molecules, leading to low doses to the tumor without reaching lethal levels. Several structurally unique non-classical Pt(II) drugs were designed to solve these issues. Picoplanin, BBR3464, 56MESS, PT-ACRAMTU, etc. are the representative of these Pt(II) drugs, and some of them have already been rolled out into clinical trials (Fig. 2 and Table 2) [51-54]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,528,615,540]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2. Pt(IV) drugs \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,554,937,778]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To circumvent the disadvantages of clinical side effects and drug resistance of cisplatin and other $\\\\mathrm{Pt(II)}$ drugs, scientists have been developing new platinum drugs to improve the therapeutic effect and quality of life of patients. The synthesis of $\\\\mathrm{Pt(IV)}$ prodrugs reached these goals to some extent [55]. The structure of the $\\\\mathrm{Pt(IV)}$ prodrug includes the non-leaving group L, the leaving group X, and the axial group R obtained by oxidizing the $\\\\mathrm{Pt(II)}$ drug into the hydroxyl group or further introducing other groups (Fig. 3a) [13]. Because of the formation of an octahedral kinetically inert structure, $\\\\mathrm{Pt(IV)}$ prodrugs almost do not react with cysteine, methionine, and matrix proteins that can interact with $\\\\mathrm{Pt(II)}$ drugs. Thus, $\\\\mathrm{Pt(IV)}$ configurations enable the improvement of the stability of platinum drugs, increase the blood circulation time, reduce systemic toxicity, and enhance the anti-cancer effect. Currently, the $\\\\mathrm{Pt(IV)}$ prodrug named Satraplatin (JM-216, Fig. 3b), which can be administered orally and has no cross-resistance with cisplatin, has entered phase III clinical trials for prostate cancer, NSCLC, and head and neck cancer therapy [56]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,778,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"According to the activation pathways and structure variations, $\\\\mathrm{Pt(IV)}$ can be categorized into reduction-sensitive $\\\\mathrm{Pt(IV)}$ prodrugs and light-sensitive $\\\\mathrm{Pt(IV)}$ prodrugs [57,58]. When the plane leaving group X is chlorine, the $\\\\mathrm{Pt(IV)}$ axial ligand R can be reduced by high-concentration reductants like glutathione (GSH), ascorbic acid (VC), and dithiothreitol (DTT) in cancer cells, destroying the rigid structure of the octahedron and conversion into $\\\\mathrm{Pt(II)}$ drugs (Fig. 4a) [59,60]. The $\\\\mathrm{Pt(II)}$ further hydrated in the cells and cross-links with DNA at different sites, and thus achieved similar cell apoptosis results as cisplatin in blocking DNA replication and transcription. When the plane leaving group ligands X is azide or iodine, $\\\\mathrm{Pt(IV)}$ can be degraded to $\\\\mathrm{Pt(II)}$ under external light stimulation. Taking the photosensitive $\\\\mathrm{Pt(IV)}$ containing azide group ligands as an example, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,42,129,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Q. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[752,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biomedical Technology 2 (2023) 77-89 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"78 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[210,66,786,277]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 1. Chemical structures of clinically approved Pt(II) drugs [7,34,37,38,47,49,50]. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0523/6059f97d709fa30621b39e24348df8e9e8e470c8713246049c36fccc18d8931f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[60,346,937,500]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0624/b4ce61b2812b67c4520f89f78e376694457d772baff4b897e7a1adf8b0117651.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Generic Name</td><td>Research Name</td><td>Trade Name</td><td>Approval Granted</td><td>Cancer type</td><td>Side Effects</td><td>Scope of Approval</td></tr><tr><td>Cisplatin</td><td>CDDP</td><td>Platinol</td><td>1978</td><td>Testicular, Ovarian Lymphomas</td><td>Nephrotoxicity, Neurotoxicity, Ototoxicity, Nausea</td><td>Global</td></tr><tr><td>Carboplatin</td><td>JM8</td><td>Paraplatin</td><td>1989</td><td>Ovarian, Lung</td><td>Myelosuppressive</td><td>Global</td></tr><tr><td rowspan=\\\"2\\\">Nedaplatin</td><td rowspan=\\\"2\\\">254-S</td><td rowspan=\\\"2\\\">Aqupla</td><td rowspan=\\\"2\\\">1995</td><td>Head, neck, Lung, Breast, NSCLC</td><td rowspan=\\\"2\\\">Bone marrow suppression</td><td rowspan=\\\"2\\\">Japan</td></tr><tr><td>SCLC, Esophageal</td></tr><tr><td rowspan=\\\"2\\\">Heptaplatin</td><td rowspan=\\\"2\\\">SKI 2053R</td><td rowspan=\\\"2\\\">SunPla</td><td rowspan=\\\"2\\\">1999</td><td rowspan=\\\"2\\\">Advanced gastric</td><td>Hepatotoxicity</td><td rowspan=\\\"2\\\">Korea</td></tr><tr><td>Myelosuppression</td></tr><tr><td>Oxaliplatin</td><td>1-OHP</td><td>Eloxatin</td><td>2002</td><td>Colorectal</td><td>Neurotoxicity, Neutropenia</td><td>Global</td></tr><tr><td rowspan=\\\"2\\\">Lobaplatin</td><td rowspan=\\\"2\\\">D-19466</td><td rowspan=\\\"2\\\">洛铂</td><td rowspan=\\\"2\\\">2010</td><td rowspan=\\\"2\\\">Testicular, Ovarian and Lung, CML, SCLC</td><td>Thrombocytopenia</td><td rowspan=\\\"2\\\">China</td></tr><tr><td>Anemia, Leukopenia</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1 Clinically approved Pt(II) drugs [7,34,37,38,47,49,50]. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[210,527,788,767]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 2. Non-classical Pt(II) drugs [51-54]. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0004/4ce654e50e5e8736fe4368d79c8da48fb3767ea89af12ba30c9c9585016b3773.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,802,487,843]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the azide ligand on the plane quickly leaves to generate three molecules of nitrogen, and then $\\\\mathrm{Pt(IV)}$ is converted into cytotoxic $\\\\mathrm{Pt(II)}$ to further play its role under light conditions (Fig. 4b) [61,62]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,857,346,871]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. Nanocarriers for platinum drugs delivery \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,883,485,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"With the rapid development of nanotechnology, NDDSs have attracted great attention in the delivery of multiple chemotherapeutic drugs [63]. Nanomedicine based on NDDSs has obvious unique advantages [64-68]: i) Prolong drug circulation time and improves \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,802,939,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pharmacokinetics; ii) Improves the solubility of insoluble drugs and protects them from early degradation; iii) By designing stimulus-responsive NDDSs, site-specific drug release and reduced systemic toxicity of drugs could be achieved; iv) Through the EPR of tumor tissue, NDDSs can be passively accumulated at the tumor tissue to improve the bioavailability of drugs; v) More effective cancer combination therapies can be achieved by loading multiple drugs, drug sensitizers, targeting ligands, etc.; vi) By co-loading with imaging reagent in the NDDSs, therapy and imaging can be integrated, real-time tracking of drug distribution and drug efficacy evaluation. NDDSs for platinum drugs \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,42,129,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Q. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[752,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biomedical Technology 2 (2023) 77-89 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"79 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[58,92,485,192]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0296/2ce0332c5ce664f80f7b0aff98d95c2ff05c0453f4b704acdb8b335d47d35408.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Generic Name</td><td>Stage</td><td>Cancer type</td></tr><tr><td rowspan=\\\"2\\\">Picoplatin</td><td>Phase II</td><td>Metastatic colorectal cancer, drug-resistant prostate cancer</td></tr><tr><td>Phase III</td><td>Recurrent or drug-resistant ovarian cancer and NSCLC</td></tr><tr><td>BBR3464</td><td>Phase II</td><td>Ovarian cancer, small cell lung cancer, NSCLC, esophageal cancer</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2 Pt(II) drugs in clinical trials [51,53]. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[507,65,937,168]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"delivery mainly include inorganic nanocarriers (such as carbon dots [69], carbon nanotubes [70], graphene [71], silica nanoparticles [72], iron oxide nanoparticles $\\\\mathrm{(Fe_3O_4NP)}$ [73], gold nanomaterials [74], upconversion nanoparticles (UCNPs) [75], etc.) and organic nanocarriers (such as liposomes [76], vesicles [77], polymeric micelles [78], dendrimers [79]) (Fig. 5). Most studies have shown that the above NDDSs yielded better anticancer outcomes than small-molecule platinum drugs at the cellular and animal levels. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[127,235,618,486]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0699/e57939937e2efb45f680dfebddbad58b8f3aeca09b84d9250bf691fb622fadb4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[625,234,870,486]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 3. (a) Representative structure of Pt(IV) drugs [13]. (b) The structure of JM-216 [56]. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0562/003cec909b2c514ac9b2e9849ba3adb1f028dc4d3bc5b9fb065033456701442a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[127,532,870,689]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0279/f1a9af97d319243cbc6817569c0f6726d978410a3c9bcb260749859686d8f127.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[127,699,870,912]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 4. Mechanism of action of (a) reduction-sensitive and (b) photo-sensitive Pt(IV) prodrugs [59-62]. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0551/7297ed2e315d7b4b85d3e2fd77bd6ae7bf59696d2ca66196aaff39fc9530891a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[58,42,129,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Q. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[752,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biomedical Technology 2 (2023) 77-89 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"80 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[156,85,344,196]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Nanotube \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0241/58e2b58678344f5773113ad48d465a979bbd6088a14588a5aceeec08a0ebc0d2.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[421,76,576,192]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Mesoporous NP \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0590/ec239ad8489e92cf5847227ecf388e9a647b34a66ba03fb23580cc24bfb0a384.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[648,81,830,199]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Gold Nanorod \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0280/fcf8033f15d330aee45bd6d678b551b383b8bed614effb1aeb30e23622e08701.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[142,268,287,366]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Gold NP \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0078/45a48b235c092bbcb370eee578e8b2eab76a8ceca25c49a193da881833ff35b3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[322,269,478,385]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Iron oxide NP \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0513/188369956dfe7befc988b77e01f6c512d68bba8fa9d95475b32ac5df1504cbac.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[507,273,648,377]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Qdot \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0521/a9c31c01257430de3ca512b24b1f1f5c46441eaaf88cc1d47fe53c0b75755400.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n 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\"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[445,446,601,562]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Nanosphere \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/1014/91d7e3a223473680e61ba483d4fe4885521d4efd7b91ca4e6a5839e64b930ad1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[662,447,838,559]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Dendrimer \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0371/b95cfe49cf39103be8cff78d0bb14bb3730d5f2f2033ee711508ec2570c0bfe4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[157,615,342,740]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Micelle \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0108/7d8005296026809f60d77ae8ba7facd8e5cc0b3231f2fcb6fc8d79db62fd042f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[403,620,554,732]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Vesicle \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0375/e5a05856545c515823915d1dc7c670a86a0d278fb67ff2cbac0edf82dc203bbc.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[628,615,826,728]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Polymeric Conjugate \\\",\\\"Fig. 5. Various NDDSs for platinum drugs [69-79]. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0427/c4b123457e56880a277c1a6745af6986d1f4cd0a526e209b02afa6db4912c36e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[58,805,218,817]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1. Inorganic nanocarriers \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,831,485,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Inorganic nanoparticles generally possess suitable general properties including wide versatility, rich functionality, and potential for targeted delivery and controllable drug release. Due to the characteristics of porosity and high specific surface area, platinum drugs are often directly encapsulated in or adsorbed on the surface of inorganic nanocarriers. For example, Yamauchi et al. prepared the corresponding Cis@HPB nanocarrier by mixing the porous coordination polymeric Hollow Prussian blue (HPB) nanoparticles and the aqueous solution of cisplatin at room \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,804,937,909]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"temperature (Fig. 6a) [80]. The porous HPB material completely adsorbed the mixed cisplatin into the pore or its surface within $30\\\\mathrm{min}$ . In the phosphate buffer saline (PBS) at $\\\\mathsf{pH}7.4$ , the release of cisplatin in $\\\\mathrm{Cis@HPB}$ was maintained at less than $5\\\\%$ within $200\\\\mathrm{min}$ , indicating the stability of the nanocarriers. Besides, the prepared HPB nanoparticles showed good biocompatibility as indicated in Fig. 6b. The nanocarriers loaded with cisplatin (Cis@HPB) can effectively suppress the growth of bladder cancer T24 cells (Fig. 6c). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,910,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In recent years, drug-conjugated inorganic nanoparticles have been rapidly developed, and the nanocarriers used to bond platinum drugs \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,42,129,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Q. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[752,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biomedical Technology 2 (2023) 77-89 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"81 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[127,69,868,252]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0920/c9ff98ed7f8b36a3e12790f3afbf21c85ac8a4a52ad498db12e7809db037aeed.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[129,262,494,452]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/1005/61d1c73cd61e63f50a0657f6088ee9d32571c68a4d87e7278032044fd6462371.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[505,263,865,452]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 6. (a) An illustration representing the chemotherapy of Hollow Prussian Blue (HPB) nanoparticles. (b) MTT assays of HPB against T24 cells. (c) Comparison of MTT assays between HPB and Cis@HPB against T24 cells. Reproduced with permission [80]. Copyright 2012, Royal Society of Chemistry. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0431/ac5ff7eceaccea4915a40b06a32ae9afe2ec014be00f3ac34d8f02b8dd39bc79.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,503,487,556]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"have emerged endlessly. One typical example from Huang and coworkers synthesized mesoporous silica nanoparticles containing dicarboxylic groups in the pore channel, which were used for complexing oxaliplatin to prepare drug-loading mesoporous silica nanocarriers \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,503,937,556]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(denoted as MSN-Pt, Fig. 7) [81]. The endocytosis content of MSN-Pt was significantly enhanced, and the Pt-DNA adducts formed within $24\\\\mathrm{h}$ were 3.5 folds higher compared with free oxaliplatin. Therefore, the $\\\\mathrm{IC}_{50}$ value of MSN-Pt $(25.95\\\\mu \\\\mathrm{M})$ was significantly lower than that of oxaliplatin \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[211,582,769,677]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0596/0185aac91b4011f5e263ee4b7e3ffc99451d87a7539da60fa6a03c3296765666.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[211,682,786,901]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 7. (a) Synthesis of mesoporous silica nanoparticles containing dicarboxylic groups in the pore channel. (b) MSN nanoparticles conjugated with oxaliplatin species and the intracellular delivery and action of the platinum drug. Reproduced with permission [81]. Copyright 2013, Royal Society of Chemistry. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0516/66ccb225a175a3a02e6b55740f6be042b9be90066d4d744b2bb8a8b9fd59d986.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[60,42,129,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Q. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[752,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biomedical Technology 2 (2023) 77-89 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[492,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"82 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,65,487,105]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(39.29 $\\\\mu$ M) against hepatoma carcinoma HepG-2 cells. These results demonstrated that MSN-Pt promoted the intracellular accumulation of platinum drugs and simultaneously enhanced their cytotoxicity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,105,485,313]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In another demo, Liu et al. prepared Pt-PEG-GNRs by conjugating Pt(IV) prodrug to PEG-GNRs to overcome the drug resistance problem during cisplatin chemotherapy (Fig. 8a) [82]. Pt-PEG-GNRs entered cancer cells by endocytosis, so that the delivery of platinum drug in resistant cells would be not affected, avoiding the process of transporting cisplatin via copper transporter (Ctr1). Meanwhile, due to the inert structure of the Pt(IV) prodrug, the drug didn't interact with detoxication substances in cells such as Metallothionein, GSH, and other effects and inactivation. Therefore, Pt-PEG-GNRs exhibited a negligible difference in toxicity between normal lung cancer cells A549 and drug-resistant cells A549R (Fig. 8b). By contrast, the cytotoxicity of free cisplatin in A549R was much lower than that in A549. These results indicate that Pt-PEG-GNRs increased the intracellular endocytosis of platinum drugs and overcame the mechanism of intracellular platinum resistance, thus demonstrating a feasible strategy to solve the challenge of platinum drug resistance. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,316,485,486]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Another inspiring example was the innovatively applied UCNPs to deliver reduction-sensitive or photo-sensitive $\\\\mathrm{Pt(IV)}$ prodrugs. For the first time, the reduction-sensitive $\\\\mathrm{Pt(IV)}$ prodrug (DSP) with dicarboxylate was decorated onto the surface of the polyethyleneimine (PEI)-coated UCNPs $(\\\\mathrm{NaYF_4:Yb^{3+}/Er^{3+}})$ , and both the water dispersion and targeting ability of the nanoparticles were improved by linking another carboxyl group of dicarboxylate $\\\\mathrm{Pt(IV)}$ prodrug to folic acid (FA) modified polyethylene glycol (PEG-FA, Fig. 9a) [83]. The prepared NaYF4: $\\\\mathrm{Yb^{3+}/Er^{3+}}$ -DSP-PEG-FA nanocarriers have good cell targeting ability and high endocytosis. The cytotoxicity test revealed that the nanoparticle $(\\\\mathrm{IC}_{50} = 0.29~\\\\mu \\\\mathrm{g~mL}^{-1})$ significantly improved the cytokilling effect of the platinum drugs, which was 0.19 times than that of cisplatin's results $(\\\\mathrm{IC}_{50} = 1.51~\\\\mu \\\\mathrm{g~mL}^{-1})$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,486,485,580]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In another work, they developed UCNP-DPP-PEG nanocarriers by conjugating photo-sensitive $\\\\mathrm{Pt(IV)}$ prodrug (DPP) onto the surface of UCNPs (Fig. 9b) [84]. With the ability of UCNPs to convert near-infrared (NIR) light into ultraviolet (UV) to visible light, the penetration depth of the light could be improved and the photo-controlled on-demand release of the platinum drug could be realized. The UCNP-DPP-PEG administration group under NIR light irradiation showed the optimal antitumor \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,65,937,158]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"effect compared with UV-activated groups. Meanwhile, due to the presence of Gd, Yb, and Tm elements in the UCNPs, the nanocarriers achieved tri-mode imaging capabilities of nuclear magnetic resonance (MRI), computed tomography (CT), and upconversion fluorescence (UCL) imaging. Thus, the nanosystem realized NIR photo-controlled drug release behavior guided by multi-mode imaging, which has significant practical potential and theoretical guidance for cancer therapy. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,172,663,185]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2. Organic nanocarriers \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,199,937,475]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Although inorganic nanocarriers owned numerous advantages such as simple preparation, uniform size, and variety, they are not easy to degrade in vivo and have poor biocompatibility and potential biotoxicity, which limit further clinical transformation [85]. As a consequence, no clinical trial or use of inorganic nanocarriers were reported for platinum drugs at present. In stark contrast, organic nanocarriers have better biocompatibility and more safety and can carry hydrophobic and hydrophilic drugs simultaneously. Great progress has been made in organic nanocarriers for nanomedicine preparation and clinical drug delivery [86,87]. For example, several nanomedicines based on liposomes have been approved for clinical use, such as Doxil, Myocet, Caelyx, Daunoxome, and Ribodo [88-91]. It is noteworthy that several liposome nanomaterials loaded with platinum drugs have entered phase II and III clinical trials (Table 3) [92-94]. Lipoplatin, as a cisplatin-loaded liposome nanomedicine developed by Regulon, increased the solubility of cisplatin three times from $1\\\\mathrm{mg~mL}^{-1}$ , and extending the blood circulation duration from $6\\\\mathrm{h}$ to $117\\\\mathrm{h}$ , thus significantly increasing the tumor accumulation of the drug. The bilayer structure of liposomes promoted further endocytosis of Lipoplatin in tumor cells, boosting the tumors killing ability 200 times higher than that of normal tissues, greatly reducing the systemic toxicity of cisplatin. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,476,937,581]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In addition to organic liposome nanocarriers, polymer nanocarriers have proved with advantages of easy modification, wide source, variety, and so on, which also provided numerous possibilities for platinum drug delivery. Surprisingly, several polymer nanocarriers prepared by Kataoka (NC-6004 and NC-4016), Nowotnik (AP5346), and Schellens (AP5280), have entered phase II and III trials (Table 4) [95-97]. Among them, NC-6004 is a cisplatin-loaded polymer micellar nanomedicine, which was known for significantly improving the blood circulation time of the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[126,597,603,878]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0222/ca9fbdecb137ebe2568f1c9acdfa0879b6c1d69f741e2c57244b2b4e8ece8157.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[608,598,870,736]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0762/a067c7dc5c89a286747904317e9f056d96f423d963281a2332f294bcf06b640c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[611,733,867,873]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 8. (a) Schematic illustration of Pt-PEG-GNRs for overcoming cisplatin resistance. (b, c) The cytotoxicity assays of (b) Pt-PEG-GNRs conjugate and (c) Cisplatin. Reproduced with permission [82]. Copyright 2012, WILEY-VCH GmbH. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0300/3978feac457c8986716aaa8b12bf1f43c0fa41d6cd29c22d33e3e0891e2b85bb.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[58,42,131,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Q. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[752,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biomedical Technology 2 (2023) 77-89 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"83 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[127,68,369,292]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0622/23bb56483d8a0d6f28b7a8624eb692c5e7ce1778dd63941086eeb9ebdfedf94a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[374,68,870,292]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 9. Schematic illustration of UCNPs delivering (a) reduction-sensitive Pt(IV) prodrug or (b) light-sensitive Pt(IV) prodrug. (a) Reproduced with permission [83]. Copyright 2013, WILEY-VCH GmbH. (b) Reproduced with permission [84]. Copyright 2013, American Chemical Society. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0645/57a03b1debc7cd9e1ed8474a7fdb44f32e2c836800776acbe7ba0c1d418a2365.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[60,375,485,466]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/1007/79661fadb4e219c45bacff71cf603dea8b4e41161077e38e315ff61d692f4dc5.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Generic Name</td><td>Stage</td><td>Drug</td><td>Cancer type</td></tr><tr><td>Lipoplatin</td><td>Phase III</td><td>Cisplatin</td><td>NSCLC, stomach cancer, head and neck cancer</td></tr><tr><td>SPI-77</td><td>Phase II</td><td>Cisplatin</td><td>NSCLC, ovarian cancer</td></tr><tr><td>MBP-426</td><td>Phase II</td><td>Oxaliplatin</td><td>Gastric cancer, esophageal cancer, pancreatic cancer</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 3 Liposome-based platinum drug delivery nanocarriers in clinical trials [92-94]. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[60,517,485,586]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0445/3e57ec11c2abfae21bf57b4a5a49385e2b52bc3235c8074d975a5266aeedc1f0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Generic Name</td><td>Stage</td><td>Drug</td><td>Carrier type</td></tr><tr><td>NC-6004</td><td>Phase II and III</td><td>Cisplatin</td><td>mPEG-b-PGA</td></tr><tr><td>NC-4016</td><td>Phase II and III</td><td>Oxaliplatin</td><td>mPEG-b-PGA</td></tr><tr><td>AP5280</td><td>Phase II</td><td>Oxaliplatin</td><td>HPMA</td></tr><tr><td>AP5346</td><td>Phase II</td><td>Cisplatin</td><td>HPMA</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 4 Polymer-based platinum drug delivery nanocarriers in clinical trials [95-97]. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[57,602,485,641]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"cisplatin, and slowly and continuously releasing the platinum drugs. It profoundly reduced cisplatin-related systemic toxicity and eliminated the need for hospitalization. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,641,485,669]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As mentioned above, the $\\\\mathrm{Pt(IV)}$ prodrugs have an octahedral inert structure so they gained low toxicity before reduction. Due to the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,341,937,604]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"reduction-sensitive or photosensitive properties and axial-modified characteristics, Pt(IV) can be loaded into the polymer-based nanocarriers through various ways, such as physical encapsulation, chemical bonding, main chain polymerization, and so on, when preparing the polymer-based nanomedicine [98,99]. To take advantage of these merits, Xiao et al. have synthesized an amphiphilic block polymer (mPEG- $b$ -PCL- $b$ -PLL) for the delivery of monocarboxylic-cisplatin, dicarboxylic-binuclear-cisplatin, and dicarboxylic-binuclear-oxaliplatin. These platinum drugs were conjugated to the polymer side chain of mPEG- $b$ -PCL- $b$ -PLL by the amide bond, and then the drug-loaded amphiphilic polymer self-assembled into micelles in aqueous (Figs. 10 and 11) [100,101]. Both cell and animal experiments confirmed that the nanomicelles had much higher endocytosis than small-molecule platinum drugs, and the former greatly increased the drug accumulation in tumors. These nanomicelles are also acidic- and reduction-sensitive. The specific release at the tumor site can be achieved through the acidic tumor environment and high reducibility conditions. Therefore, the prepared nanomicelles have better tumor treatment ability than the corresponding small-molecule Pt(II) drugs at both cellular and animal levels, leading to a reduction of systemic toxicity from platinum drugs. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,605,937,670]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Clinical transformation of polymer-based anticancer nanomedicines has confronted several challenges: 1) Regulations of composition and structure of polymer-based nanocarriers, where the batch variations are distinct; 2) Lack of direct drug monitoring capacity; 3) Lack of suitable preclinical animal models for screening and evaluating the nanomedicine \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[126,697,739,798]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0596/a5359b8760f180218bc479acc076a45648a0555f1290b832862f9d904148f789.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[124,803,870,901]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 10. (a) The synthesis processes of monocarboxylic-cisplatin. (b) Conjugation of s mPEG- $b$ -PCL- $b$ -PLL with monocarboxylic-cisplatin, and formation of monocarboxylic-cisplatin-containing micelles. Reproduced with permission [100]. Copyright 2011, Elsevier. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0965/44b908e309fa5d93244a3bed41028345294d10108c26d5cf6d8f13068b871a9f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[58,42,129,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Q. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[752,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biomedical Technology 2 (2023) 77-89 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"84 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[134,78,862,361]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"a \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0113/0bc04a5ee1b2a8c9110b8d9bad5c56397897ab4e4144ee9aee879914bd4b66de.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[144,390,850,580]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"b \\\",\\\"Fig. 11. (a) The structural formulas of dicarboxylic-binuclear-cisplatin and dicarboxylic-binuclear-oxaliplatin. (b) Conjugation of s mPEG- $b$ -PCL- $b$ -PLL with either dicarboxylic-binuclear-cisplatin or dicarboxylic-binuclear-oxaliplatin, and formation of platinum-containing micelles. Reproduced with permission [101]. Copyright 2011, Elsevier. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0364/bd96b99c327a9ce7d57e3db1d414c0348f39380f12448fa75e6840b838c37fa6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[60,660,485,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"efficacies. To solve these problems, Cong et al. prepared a double-drug loaded nanomicelle for the delivery of cisplatin prodrug and demethylcantharidin (DMC) (Fig. 12) [102]. Firstly, they synthesized a dual-drug small-molecule prodrug via a ring-opening reaction of one molecule of cisplatin prodrug and two molecules of DMC. Then, the dual-drug small-molecule prodrug was introduced into the polymer backbone as polymeric monomers. Once the dual-drug small molecule participated in the polymerization, the proportion of drugs was determined, which was not affected by the preparation conditions and batches. The nanomicelles not only had a good therapeutic effect on the subcutaneous cervical cancer cell U14 xenograft tumor of Kunming mice but also showed the best antitumor effect on the lung squamous cell carcinoma model. In addition, the nanodrugs reduced the hematotoxicity and systemic toxicity of free cisplatin. Platinum content in the prepared nanomedicine occupied up to $12\\\\%$ . Due to the strong X-ray absorption ability of platinum, the distribution of the nanomedicine in the body can be directly monitored through CT imaging after injection, realizing the integration of diagnosis and therapy. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,897,485,924]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To further realize spatiotemporal controllable, site-specific, and quantitative release of drugs, Wang et al. prepared a photo-activated \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,660,937,805]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"nanocarrier by integrating the photo-sensitive $\\\\mathrm{Pt(IV)}$ prodrug and DMC into the polymer backbone in a similar way proposed by Cong et al. (Fig. 13) [103]. Besides similar functions as the nanomicelle from Cong et al., this nanocarrier also achieved precise photo-activated drug release at tumor sites by in situ drug tracking with CT imaging. Animal experiments further showed that the dual-drug-loaded nanoparticles (DDP NP) achieved a cure rate of $75\\\\%$ . Because the photo-activated release of the drug only occurred at the tumor site, the drug released in other tissues or organs was in negligible amounts. Therefore, the nanocarriers have low toxicity and almost no impact on the quality of life of mice, which had the prospect for clinical application. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,819,705,832]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. Summary and perspectives \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,844,937,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Platinum drugs have played an important role in chemotherapy. The application of platinum drugs is a particularly burgeoning area of oncology. Currently, numerous platinum complexes have been exploited for treating various cancer types. According to the difference in the valence of platinum atoms, we introduced platinum drugs from $\\\\mathrm{Pt(II)}$ and $\\\\mathrm{Pt(IV)}$ drugs categories. Specifically, $\\\\mathrm{Pt(II)}$ drugs include clinically \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,42,129,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Q. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[752,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biomedical Technology 2 (2023) 77-89 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"85 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[127,70,868,757]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 12. Schematic illustration of dual drug backboned shattering polymeric theranostic nanomedicine (DD-NP) for synergistic eradication of patient-derived lung cancer (PDLC). (a) Illustration of self-assembly and chain-shattering of DD-NP to release active Pt(II) and DMC. (b) Illustration of the establishment of PDLC model and Pt-based DMCT after intravenous injection with DD-NP. (c) Possible dual anticancer mechanisms after endocytosis of DD-NP by cancer cells. Reproduced with permission [102]. Copyright 2018, WILEY-VCH GmbH. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0532/bb0734abd46d43d0512170e3ab21351e60766cd500056e3c08909c6992fb05ea.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,828,485,894]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"approved classical platinum drugs such as cisplatin, carboplatin, oxaliplatin, etc., and non-classical platinum drugs such as picoplatin, BBR3464, 56MESS, etc. While the $\\\\mathrm{Pt(IV)}$ can be further divided into reduction-sensitive $\\\\mathrm{Pt(IV)}$ and light-sensitive $\\\\mathrm{Pt(IV)}$ drugs according to their activation pathway and structure difference. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,894,485,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To address many predicaments including toxic side effects, drug resistance, and bioavailability of platinum drugs, NDDSs have been widely developed and brought into research and pilot study focus. Based \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,828,937,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"on the material differences, the NDDSs could be divided into inorganic and organic nanocarriers. Although these nanocarriers have been validated with good therapeutic effects, there are still many challenges that need to be solved. Inorganic nanocarriers have been long-time used for platinum drug delivery due to their controllable size and morphology, diverse surface properties, and ingenious design. However, the disadvantages of inorganic nanomaterials are obvious because of the introduction of heavy metals. Long-term administration of such drugs would \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,42,129,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Q. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[752,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biomedical Technology 2 (2023) 77-89 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"86 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[211,69,786,406]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 13. Schematic diagram of the photo-activatable dual prodrug polymer nanocarrier (DPP NP) for synergistic chemotherapy. (a) Illustration of synthesis DPP. (b) Illustration of anticancer mechanisms after endocytosis of DPP NP. Reproduced with permission [103]. Copyright 2019, Elsevier. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0244/827564bb2af264d4562c9abc271dd54019d3b93a2ab790ae28c519f61bedd61c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,453,485,571]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"easily cause damage to different tissues, thus affecting the life quality of patients. By contrast, organic nanocarriers with good biocompatibility play increasingly important roles in platinum drug delivery. Nowadays, several platinum drug-laden liposome nanocarriers (Lipoplatin, SPI-77, MBP-426) and polymeric nanocarriers (NC-6004, NC-4016, AP5346, AP5280) have entered phase II or III trials. The clinical application of these drugs has sparked the flourishing of organic nanocarriers for platinum drug delivery. Nevertheless, these organic nanocarriers still face many problems for further clinical transformation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,572,487,824]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"From intravenous injection to the target site, nanomedicines would go through five processes: blood circulation, tumor accumulation, tumor infiltration, cell uptake, and drug release. During these processes, several key courses restrict the efficacy of nanomedicines. Despite the abundant angiogenesis and lymphatic reflux defects in the tumor tissue, the EPR effect can increase the interception of nanoparticles at the tumor site. However, the absence of functional lymphatic vessels leading to increased interstitial hydraulic pressure at the tumor site will make it difficult to efficiently transport deep into tumors. Effective cellular endocytosis plays a crucial part in the efficacy of nanomedicines. Therefore, it is necessary to design actively targeted nanocarriers for platinum drug delivery. Equally important, but often overlooked, is that systemically administered nanocarriers may gradually release their loaded drugs during circulation, making carriers unable to meet the required drug concentration when they reach the tumor microenvironment. Therefore, to maximize the therapeutic effect of nanomedicines in the clinic, it is particularly important to design accurate and controllable NDDSs. Taken together, great efforts still need to be devoted to devising more efficient NDDSs for platinum drug delivery. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,836,278,849]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Declaration of competing interest \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,862,485,902]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,453,633,466]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgments \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,479,937,546]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This work was supported by the National Natural Science Foundation of China (52103196, 32201118 and 82102233), Shenzhen Fundamental Research Program (JCYJ20210324102809025), Zhejiang Provincial Natural Science Foundation of China (LGF22C100003), and Wenzhou Institute UCAS (WIUCASQD2022018 and WIUCASQD2021012). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,559,584,569]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,583,934,906]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[1] H. 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Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[752,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biomedical Technology 2 (2023) 77-89 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"88 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[67,66,482,559]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[71] X.-J. 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Xing, Near-infrared light-mediated photoactivation of a platinum antitumor prodrug and simultaneous cellular apoptosis imaging by upconversion-luminescent nanoparticles, Angew. Chem. 126 (2014) 1030-1034. \\\",\\\"[76] S. Zalba, M.J. Garrido, Liposomes, a promising strategy for clinical application of platinum derivatives, Expet Opin. Drug Deliv. 10 (2013) 829-844. \\\",\\\"[77] E. Ambegia, S. Ansell, P. Cullis, J. Heyes, L. Palmer, I. MacLachlan, Stabilized plasmid-lipid particles containing PEG-diacylglycerols exhibit extended circulation lifetimes and tumor selective gene expression, BBA-Biomembranes 1669 (2005) 155-163. \\\",\\\"[78] N. Graf, D.R. Bielenberg, N. Kolishetti, C. Muus, J. Banyard, O.C. Farokhzad, S.J. Lippard, $\\\\\\\\alpha \\\\\\\\mathrm{V}\\\\\\\\beta 3$ integrin-targeted PLGA-PEG nanoparticles for enhanced anti-tumor efficacy of a Pt (IV) prodrug, ACS Nano 6 (2012) 4530–4539. \\\",\\\"[79] T. Kapp, A. Dullin, R. Gust, Platinum (II)-dendrimer conjugates: synthesis and investigations on cytotoxicity, cellular distribution, platinum release, DNA, and protein binding, Bioconjugate Chem. 21 (2010) 328-337. \\\",\\\"[80] H.-Y. Lian, M. Hu, C.-H. Liu, Y. Yamauchi, K.C.-W. Wu, Highly biocompatible, hollow coordination polymer nanoparticles as cisplatin carriers for efficient intracellular drug delivery, Chem. Commun. 48 (2012) 5151-5153. \\\",\\\"[81] H. He, L. Yan, F. Meng, Z. Xie, X. Jing, Y. Huang. A reduction-sensitive carrier system using mesoporous silica nanospheres with biodegradable polyester as caps, Phys. Chem. Chem. Phys. 15 (2013) 14210-14218. \\\",\\\"[82] Y. Min, C.Q. Mao, S. Chen, G. Ma, J. Wang, Y. Liu, Combating the drug resistance of cisplatin using a platinum prodrug based delivery system, Angew. Chem. 51 (2012) 6742-6747. \\\",\\\"[83] Y. Dai, X. Kang, D. Yang, X. Li, X. Zhang, C. Li, Z. Hou, Z. Cheng, P. Ma, J. Lin, Platinum (IV) pro-drug conjugated $\\\\\\\\mathrm{NaYF_4:Yb(3+)/Er(3+)}$ nanoparticles for targeted drug delivery and up-conversion cell imaging, Adv. Healthcare Mater. 2 (2013) 562-567. \\\",\\\"[84] Y. Dai, H. Xiao, J. Liu, Q. Yuan, P.a. Ma, D. Yang, C. Li, Z. Cheng, Z. Hou, P. Yang, In vivo multimodality imaging and cancer therapy by near-infrared light-triggered trans-platinum pro-drug-conjugated upconversion nanoparticles, J. Am. Chem. Soc. 135 (2013) 18920-18929. \\\",\\\"[85] H. Xiao, C. Li, Y. Dai, Z. Cheng, Z. Hou, J. Lin, Inorganic nanocarriers for platinum drug delivery, Mater, Today Off. 18 (2015) 554-564. \\\",\\\"[86] E. Blanco, H. Shen, M. Ferrari, Principles of nanoparticle design for overcoming biological barriers to drug delivery, Nat. Biotechnol. 33 (2015) 941-951. \\\"]\",\n \"page_idx\": \"12\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[512,66,934,569]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[87] Q. Hu, W. Sun, C. Wang, Z. Gu, Recent advances of cocktail chemotherapy by combination drug delivery systems, Adv. Drug Deliv. Rev. 98 (2016) 19-34. \\\",\\\"[88] Y.C. Barenholz, Doxil®-The first FDA-approved nano-drug: lessons learned, J. Contr. Release 160 (2012) 117-134. \\\",\\\"[89] G. Batist, J. Barton, P. Chaikin, C. Swenson, L. Welles, Myocet (liposome-encapsulated doxorubicin citrate): a new approach in breast cancer therapy, Expet Opin. Pharmacother. 3 (2002) 1739–1751. \\\",\\\"[90] S.R.D. Johnston, M.E. Gore, Caelyx®: phase II studies in ovarian cancer, Eur. J. Cancer 37 (2001) 8-14. \\\",\\\"[91] E.A. Forssen, M.E. Ross, Daunoxome® treatment of solid tumors: preclinical and clinical investigations, J. Lip. Res. 4 (1994) 481-512. \\\",\\\"[92] T. Boulikas, Clinical overview on LipoplatinTM: a successful liposomal formulation of cisplatin, Expet Opin. Invest. Drugs 18 (2009) 1197-1218. \\\",\\\"[93] N. Seetharamu, E. Kim, H. Hochster, F. Martin, F. Muggia, Phase II study of liposomal cisplatin (SPI-77) in platinum-sensitive recurrences of ovarian cancer, Anti, Res. 30 (2010) 541-545. \\\",\\\"[94] K. Sankhala, A. Mita, R. Adinin, L. Wood, M. Beeram, S. Bullock, N. Yamagata, K. Matsuno, T. Fujisawa, A. Phan, A phase I pharmacokinetic (PK) study of MBP426, a novel liposome encapsulated oxaliplatin, J. Clin. Oncol. 27 (2009) 2535. \\\",\\\"[95] K. Endo, T. Ueno, S. Kondo, N. Wakisaka, S. Murono, M. Ito, K. Kataoka, Y. Kato, T. Yoshizaki, Tumor-targeted chemotherapy with the nanopolymer-based drug NC-6004 for oral squamous cell carcinoma, Cancer Sci. 104 (2013) 369-374. \\\",\\\"[96] J.M. Rademaker-Lakhai, C. Terret, S.B. Howell, C.M. Baud, R.F. De Boer, D. Pluim, J.H. Beijnen, J.H. Schellens, J.-P. Droz, A Phase I and pharmacological study of the platinum polymer AP5280 given as an intravenous infusion once every 3 weeks in patients with solid tumors, Clin. Cancer Res. 10 (2004) 3386-3395. \\\",\\\"[97] D.P. Nowotnik, E. Cvtikovic, ProLindact™(AP5346): a review of the development of an HPMA DACH platinum polymer therapeutic, Adv. Drug Deliv. Rev. 61 (2009) 1214-1219. \\\",\\\"[98] S. He, C. Li, Q. Zhang, J. Ding, X.J. Liang, X. Chen, H. Xiao, X. Chen, D. Zhou, Y. Huang, Tailoring platinum(IV) amphiphiles for self-targeting all-in-one assemblies as precise multimodal theranostic nanomedicine, ACS Nano 12 (2018) 7272-7281. \\\",\\\"[99] H. Lu, S. He, Q. Zhang, X. Li, Z. Xie, Z. Wang, Y. Qi, Y. Huang, Dual-sensitive dualprodrug nanoparticles with light-controlled endo/lysosomal escape for synergistic photoactivated chemotherapy, Biomater. Sci. 9 (2021) 7115-7123. \\\",\\\"[100] H. Xiao, R. Qi, S. Liu, X. Hu, T. Duan, Y. Zheng, Y. Huang, X. Jing, Biodegradable polymer-cisplatin (IV) conjugate as a pro-drug of cisplatin (II), Biomaterials 32 (2011) 7732-7739. \\\",\\\"[101] H. Xiao, H. Song, Y. Zhang, R. Qi, R. Wang, Z. Xie, Y. Huang, Y. Li, Y. Wu, X. Jing, The use of polymeric platinum (IV) prodrugs to deliver multinuclear platinum (II) drugs with reduced systemic toxicity and enhanced antitumor efficacy, Biomaterials 33 (2012) 8657-8669. \\\",\\\"[102] Y. Cong, H. Xiao, H. Xiong, Z. Wang, J. Ding, C. Li, X. Chen, X.J. Liang, D. Zhou, Y. Huang, Dual drug backboned shattering polymeric theranostic nanomedicine for synergistic eradication of patient-derived lung cancer, Adv. Mater. 30 (2018), 1706220. \\\",\\\"[103] Z. Wang, G. Kuang, Z. Yu, A. Li, D. Zhou, Y. Huang, Light-activatable dual prodrug polymer nanoparticle for precise synergistic chemotherapy guided by drug-mediated computed tomography imaging, Acta Biomater. 94 (2019) 459–468. \\\"]\",\n \"page_idx\": \"12\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[60,42,129,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Q. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[752,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biomedical Technology 2 (2023) 77-89 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"89 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1016/j.bmt.2022.11.011"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Materials Science and Engineering/Medicine and Health Sciences"},"sha256":{"kind":"string","value":"e9801e2bd319f86f5844fe2f0fd4d2fa481e50fab2bfafcf94c0125e1e5da12b"},"title":{"kind":"string","value":"Nanocarriers for platinum drug delivery"}}},{"rowIdx":242,"cells":{"abstract":{"kind":"string","value":"interactions of potato viruses with their hosts, aphid vectors and the environment are described. | nutrients. Potato (Solanum tuberosum L.) is one of the most important food sources on the planet, and several aphid species, e.g., Myzus persicae (Sulzer) (green peach aphid) and Macrosiphum euphorbiae ( | Aphid is one of the most destructive insect pests on cultivated plants in temperate regions. Their piercing-sucking mouthparts and phloem feeding behavior directly damage crops and deplete plant | problem in potato production, inducing a wide variety of foliar and tuber symptoms, leading to severe yield reduction and loss of tuber quality. In this review, recent advances in understanding the | Thomas) (potato aphid) (Hemiptera: Aphididae) colonize potato and transmit several economically important viruses. Aphid-transmitted potato viruses have been emerging all over the world as a very serious "},"author":{"kind":"string","value":"XU, Yi|GRAY, Stewart M."},"content_list":{"kind":"list like","value":[{"bbox":"[90,224,157,237]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"REVIEW ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[90,262,897,305]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Aphids and their transmitted potato viruses: A continuous challenges in potato crops ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[853,287,897,321]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0868/14634aaa70647c43a4230fd14968c6dde23405fbb54b651ef3edc815f854bdd9.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[90,324,307,340]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"XU Yi $^{1}$ , Stewart M. GRAY $^{2,3}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,360,905,431]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"$^{1}$ Department of Plant Pathology, Nanjing Agricultural University, Nanjing 210095, P.R.China \",\"$^{2}$ Section of Plant Pathology and Plant-Microbe Biology, School of Integrated Plant Science, Cornell University, Ithaca, NY 14850, USA \",\"<sup>3</sup> Emerging Pest and Pathogens Research Unit, United States Department of Agriculture-Agricultural Research Service, Ithaca, NY 14850, USA \"]","page_idx":"0","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[90,455,159,467]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[87,469,907,592]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Aphid is one of the most destructive insect pests on cultivated plants in temperate regions. Their piercing-sucking mouthparts and phloem feeding behavior directly damage crops and deplete plant nutrients. Potato (Solanum tuberosum L.) is one of the most important food sources on the planet, and several aphid species, e.g., Myzus persicae (Sulzer) (green peach aphid) and Macrosiphum euphorbiae (Thomas) (potato aphid) (Hemiptera: Aphididae) colonize potato and transmit several economically important viruses. Aphid-transmitted potato viruses have been emerging all over the world as a very serious problem in potato production, inducing a wide variety of foliar and tuber symptoms, leading to severe yield reduction and loss of tuber quality. In this review, recent advances in understanding the interactions of potato viruses with their hosts, aphid vectors and the environment are described. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[90,604,455,618]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: aphids, virus, potato, vector, transmission ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,683,485,717]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Basic characteristics of Myzus persicae and Macrosiphum euphorbiae ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,731,485,791]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Aphids are a monophyletic insect represented by around 4400 species worldwide, and they have a very complex life cycle (Remaudière and Remaudière 1997; Blackman and Eastop 2000; Gilbert 2012; Bass et al. 2014). Aphids can ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,658,907,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"cause damage and reduce agricultural yields in several manners. They can build to high population densities in feeding plants, removing plant nutrients and plant sap to cause withering and death of the plants (Gilbert 2012). Some aphids' secretions from salivary are phytotoxic, causing stunting of the plant, leaf deformation, and gall formation. Even if otherwise asymptomatic, plant hormone balances and host metabolism can be affected to the detriment of the plant, but to the advantage of the aphid (Kaloshian 2004). Aphids M. persicae (green peach aphid) and M. euphorbiae (potato aphid) are important potato-infecting insect pests damaging potato production around the world (Kennedy et al. 1962; Blackman and Eastop 2000). These two species of aphids can be distinguished by looking at the tubercles between the base of the antennae. The tubercles of the M. euphorbiae slope outward and those ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[329,72,670,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Integrative Agriculture 2020, 19(2): 367-375 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[90,102,236,212]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"SELFIER ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[366,105,650,118]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Available online at www.sciencedirect.com ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[415,140,621,162]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ScienceDirect ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[784,96,905,212]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PITJ Journal of Integrative Agriculture (formerly Agricultural Sciences in China) Special Focus: Plant Use/Plant Management 2020 Vol.15 No.2 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,837,423,848]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received 10 July, 2019 Accepted 15 October, 2019 ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[92,850,421,862]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Correspondence XU Yi, E-mail: xuyiqpd@njau.edu.cn ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[89,866,485,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"© 2020 CAAS. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). doi: 10.1016/S2095-3119(19)62842-X ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[92,115,482,298]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"of the M. persicae converge. At most time, they undergo two stages: nymph and adult. In overwinter hosts, they both undergo three development stages: adult, nymph and egg. The adults of M. persicae have a tear-drop shape; the adults with the wing are bright green with a dark head and thorax, and a greenish abdomen with dark patches. They can secrete sticky honeydew. In contrast, M. euphorbiae has a larger and more elongated body (Fericean et al. 2011; Gilbert 2012). In addition, M. persicae infestations typically begin on the bottom of potato leaves while M. euphorbiae infestations are scattered over the plant (Blackman and Eastop 2000). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,300,482,530]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Both green peach aphid and potato aphid can produce eggs to survive winter on a primary plant host in temperate regions. Then eggs hatch and the aphids migrate to summer host plants in spring (Blackman and Eastop 2000; Sullivan 2008). Aphids take a flight to find the overwintering host plants to lay eggs, and the migration generally occurs in late summer to early autumn. In warmer climates, sexual reproduction may not occur, and females reproduce through parthenogenesis (Vorburger et al. 2003; Srinivasan and Brisson 2012). In general, one female adult can produce 20 to 50 nymphs that mature in 14 to 21 days under summer conditions with high temperature. Young nymphs periodically develop into alate (winged) adults and migrate to other plants. Green peach aphid and potato aphid both feed in plant phloem tissues which circulate carbohydrates. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,546,480,563]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. Potato diseases caused by plant viruses ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,579,482,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the fields, potatoes can be infected by many different plant viruses that can lead to yield reduction and loss of tuber quality. Potato virus diseases often can be diagnosed by some easily visible symptoms, such as mosaic patterns on leaves, stunting of the plant, leaf and tuber malformations (Hane and Hamm 1999; Tribodet et al. 2005; Xu and Nie 2006; Gray et al. 2010). However, foliar and/or tuber symptoms are not always expressed due to interactions between the virus and the potato cultivars, growing conditions, or the development stage of the plants when they are infected by viruses (Domfeh et al. 2015; Yellareddygari et al. 2018). Potato viruses are found in several viral families and one viroid (Brunt and Lawson 2001). Among them, potato viruses A, Y, and V (PVA, PVY, and PVV) are members of the genus Potyvirus (family Potyviridae). Potato leafroll virus (PLRV) is the type member of the genus Polerovirus (family Luteoviridae). Cucumber mosaic virus, alfalfa mosaic virus, and potato yellowing virus are members of the family Bromoviridae. Potato virus X is the typical member of Potexvirus, in the family of Alphaflexiviridae. Potato yellow dwarf virus is a typical member of nucleorhabdovirus, in the Rhabdoviridae family. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,115,904,237]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Potato latent virus and potato viruses M and S are found in the genus Carlavirus, Betaflexiviridae family. Potato spindle tuber viroid (PSTVd) is a pospiviroid in the family Pospiviroidae, and this virus is the first viroid to be identified (Diener 1971). Of these potato viruses, PVY, PLRV, PVX, potato mop-top virus (PMTV), tobacco rattle virus (TRV) and PSTVd will be described in detail considering they are economically important in the world currently. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,253,850,269]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. Virus description and symptoms ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,284,904,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PVY, one of the most important potato viruses, especially for seed potato production, occurs in most potato production areas around the world. PVY is the major reason for certification programs to reject or downgrade seed lots and PVY also reduces the yield and quality of tubers (Karasev and Gray 2013; Gray and Power 2018). PVY has a monopartite, linear, ssRNA (+) genome of $10\\mathrm{kb}$ in size (Berger et al. 2005). The genomic RNA is translated into polyproteins which are subsequently processed by viral-encoded proteinases into functional products (Adams et al. 2012). PVY is transmitted by numerous species of aphids, and green peach aphid is one of the most efficient vectors in a non-persistent, stylet-borne manner (Halbert et al. 2003; Karasev and Gray 2013). The virus can be transmitted in seconds to minutes and it can also be mechanically transmitted by human activity and vertically through tubers. The symptoms of PVY-infected plants vary depending on the strain of PVY and the variety of potato (Karasev and Gray 2013). Some potato varieties have a hypersensitive reaction (HR) to PVY specific strain, resulting in rapid death in the infected area (Kerlan et al. 2011; Tomczynska et al. 2014). Some potato varieties are more sensitive to PVY infection and exhibit easily visible symptoms such as mild mottling, distorted and brittle leaves (Hane and Hamm 1999; Tribodet et al. 2005). PVY distributed in most potato production areas around the world and increasing recognition of various strain types has been reported. The ordinary strain $\\mathsf{PVY}^{\\mathsf{O}}$ , was prevalent in Europe and North America before the 1990s and 2000s, respectively, and in general caused visible mosaic, necrosis, and leaf drop symptoms, although the severity of symptoms differed among potato varieties (Singh et al. 2008; Gray et al. 2010; Karasev and Gray 2013). In recent decades, PVY has rapidly evolved to become a complex of strains that evade potato fields in many regions around the world. Today the tuber necrotic strain, $\\mathsf{PVY}^{\\mathsf{NTN}}$ , predominates in Europe and another recombinant $\\mathsf{PVY}^{\\mathsf{NW}}$ predominates in North America (Lorenzen et al. 2006; Singh et al. 2008; Karasev and Gray 2013). It is noteworthy that the recombinant strain $\\mathsf{PVY}^{\\mathsf{NTN}}$ can cause the potato tuber necrotic ringspot disease (PTNRD) which seriously reduces the quality of tubers. Recently potato genome loci related ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,74,114,82]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"368 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[290,73,705,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"XU Yi et al. / Journal of Integrative Agriculture 2020, 19(2): 367-375 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[92,115,482,236]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"to PTNRD expression were identified (da Silva et al. 2017). Effective and durable single dominant resistance genes against all strains of PVY such as $Ry_{sto}$ , $Ry_{chc}$ , and $Ry_{adg}$ are available and widely used in Europe and are beginning to be incorporated into commercially acceptable cultivars in other production regions (Valkonen et al. 2017). Genetic markers exist that facilitate marker-assisted breeding and selection (Valkonen 2015; Valkonen et al. 2017). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,239,482,638]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PLRV, a typical member of the genus Polerovirus, in the family Luteoviridae, has a monopartite, ssRNA (+) genome of 5.3–5.7 kb in size with a VPg bound at the $5^{\\prime}$ end. PLRV has an isometric, non-enveloped, spherical particle with a readthrough domain (RTD) extension located on the surface of the particle (Mayo and Ziegler-Graff 1996; D'Arcy and Domier 2005). PLRV is transmitted in a persistent and circulative manner by many potato colonizing aphid species, primarily green peach aphid. Once an aphid acquires PLRV, it can transmit the virus for its entire life (Gray and Gildow 2003; Whitfield et al. 2015). RTD domain has been intensively studied, and the N-terminus of PLRV RTD is important for mediating RTP incorporation into the virion and is required for aphid transmission and interaction with aphid endosymbiont proteins (Brault et al. 1995; van den Heuvel et al. 1997; Hogenhout et al. 2000). The C-terminal region of PLRV RTD plays important roles in virus accumulation, movement, tissue tropism and symptom development in plants (Wang et al. 1995; Peter et al. 2008; Xu et al. 2018). PLRV can also be spread vertically through tubers. PLRV-infected plants develop visible symptoms include upright character and rolling of the leaves, interveinal chlorosis, leathery leaves, phloem necrosis, stunting of the plant, and net necrosis in tubers (Douglas and Pavek 1972; Peter et al. 2009). There is no effective extreme resistance to PLRV in potato. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,640,482,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PVX is in the Potexvirus genus, which is a member of Alphaflexiviridae family. Genome organization of PVX contains five open reading frames (ORF) coding for proteins RdRp, TGBp1, TGBp2, TGBp3, and CP (Huisman et al. 1988; Martelli et al. 2007). Potato plants infected PVX often develop mild symptom on foliage, but the virus can cause symptoms of chlorosis, mosaic, decreased leaf size, occasionally top necrosis and necrotic lesions in tubers. In addition, PVX can interact with PVY and other viruses in a synergistic manner to cause more severe symptoms and yield loss than either virus alone (Gonzalez-Jara et al. 2004). PVX is transmitted mechanically or vertically through infected tubers. Two resistant genes, $Rx1$ and $Rx2$ , identified from wild species S. tuberosum ssp. andigena and S. acaule, respectively provide extreme resistance to PVX (Bendahmane et al. 1999, 2000). Genetic markers exist that facilitate marker-assisted breeding and selection (Solomon-Blackburn and Barker 2001). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,115,904,405]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PMTV is a tripartite pomovirus, and the virus is vectored by the powdery scab plasmodiophoromycete Spongospora subterranea pv. Subterranean. The three genome segments, 6, 3.5 and $3\\mathrm{kb}$ in size, have a $5^{\\prime}$ cap and a $3^{\\prime}$ tRNA-like structure (Savenkov et al. 1999; Adams et al. 2017). The virus presents in many potato production areas including Europe, the Andes, Asia, Canada and the U.S (Sandgren 1995; Whitworth and Crosslin 2013; Ramesh et al. 2014; Hu et al. 2016). Foliar symptoms are cultivar- and environment-dependent and include yellow spots, arcs or chevron patterns; tuber symptoms, also cultivar- and environment-dependent, are expressed as rust-brown necrotic arcs or flecks often referred to as \"Spraing\" (Calvert and Harrison 1966). Disease caused by PMTV occurs more often under cool temperatures and in wet soils which are favorable for the germination of S. subterranean spores. The virus can survive within the resting spores of its vector for decades, making management difficult. There are no commercial PMTV-resistant potato varieties. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,407,904,668]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"TRV, a non-enveloped, rod-shaped RNA virus in the Tobravirus genus, causes corky ringspot disease on potato. TRV has a bipartite RNA genome 6.8 and $4.5\\mathrm{kb}$ in size (Harrison and Robinson 1978; Adams et al. 2017). Over 400 species of plants from 50 families are susceptible to TRV infection, which make this virus widely used as virus-induced gene silencing vector (VIGS) (Harrison and Robinson 1978; Liu et al. 2002). In potato fields, disease caused by TRV occurs more often in coarse sandy soils. Foliar symptoms are rare but similar to those caused by PMTV or AMV. Tuber symptoms are cultivar-dependent and characterized by necrotic, \"corky\" layers or necrotic flecks of tissue interspersed with rings of healthy tissue. In nature, TRV is transmitted by 'stubby-root' nematodes in the Paratrichodorus or Trichodorus genus and can also be transmitted mechanically (Ploeg et al. 1989; MacFarlane and Brown 1995). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,670,904,915]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PSTVd was the first viroid to be identified, and it is a small, single-stranded circular RNA molecule which was classified in the Pospiviroidae family. PSTVd comprises 359 nucleotides, and most of the genome displays complementary strands (Diener 1971; Gross et al. 1978). PSTVd is often transmitted by foliar contact and through tubers, but it can also be aphid-transmissible in the presence of PLRV. It is thought that the PSTVd genome is encapsidated in PLRV particles (Salazar et al. 1995; Syller et al. 1997). Symptom development after PSTVd infection is dependent upon the strain of the viroid in conjunction with the potato varieties and the stage of plant development. Infected tubers develop a spindle shape with a round cross-section. In potato fields, it has been reported that severe PSTVd strains could cause losses of up to $65\\%$ in tuber number and size. In addition, PSTVd-derived small ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[290,73,705,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"XU Yi et al. / Journal of Integrative Agriculture 2020, 19(2): 367-375 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[882,74,905,83]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"369 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[92,115,482,221]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"RNA could induce RNA silencing of several endogenous messenger RNAs during infection and silencing of these endogenous mRNAs are related to symptom development in tomato (Adkar-Purushothama et al. 2015). The disease is present in North America, South America, Europe, New Zealand, Asia, and Africa. All potatoes are susceptible to PSTVd and there is no form of natural resistance. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,237,470,254]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. Aphid transmission of potato viruses ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,269,482,668]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Many insect pests of potato are potential vectors of potato viruses, but aphids are the most important, vectoring 13 of the 40 reported viruses known to infect potato (Salazar 1996). Many of them are polyphagous and capable of transmitting potato viruses. Among 4400 aphid species, green peach aphid and potato aphid are the most efficient vectors of potato viruses. There are four modes of virus transmission: (1) non-persistent, (2) semi-persistent, (3) persistent and circulative, and (4) persistent and propagative (Nault 1997; Whitfield et al. 2015). PLRV is the only common potato virus transmitted by aphids in a persistent and circulative manner (Mayo and Ziegler-Graff 1996; Gray and Gildow 2003), while other potato viruses are generally transmitted by aphids in a non-persistent manner (i.e., stylet-borne viruses). In non-persistent mode, take PVY for example, PVY particles are quickly acquired, and there is no latency period required for virus inoculation to a new plant. These kinds of viruses are stylet-borne, and aphids are viruliferous for only a short period of time after acquisition, usually just a few minutes or hours (Karasev and Gray 2013). In contrast, when aphids acquire a persistent virus, there is a period of latency between acquisition and becoming accessible for virus transmission to a new plant. The aphids remain viruliferous and infectious for the rest of their lives and can transmit the virus each time when they feed on another plant (Gray and Gildow 2003; Whitfield et al. 2015). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,684,482,717]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5. A comprehensive view of interactions among plant, virus, vector and environment ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,733,482,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The interaction among plant, aphids and viruses has been widely studied in recent years. In general, aphids feeding on plant will activate host defenses such as jasmonate acid (JA)-dependent defense responses that are effective against aphids (De Vos et al. 2007). As a counter-reaction, aphids are able to manipulate host responses, as reflected by their ability to affect host morphology (van Emden and Harrington 2007), impact host nutrient allocation (Girousse et al. 2005), and suppress plant defense responses (Will et al. 2007). More recently, several aphid-secreted effector proteins from both green peach aphids and potato aphids have been identified (Elzinga and Jander 2013; Rodriguez ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,115,904,282]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and Bos 2013; Chaudhary et al. 2015; Naessens et al. 2015), suggesting that aphids, like other plant-associated organisms secrete effectors inside their host to manipulate host defenses (Kaloshian and Walling 2015). In addition, plant viruses have been extensively studied that could modulate plant defense system and facilitate aphid behaviors, e.g., green peach aphids are more fecund on PLRV-infected potatoes (Alvarez et al. 2007; Castle and Berger 1993). Further research will focus on how plant virus infections modulate plant resistance to insects and also how host plant resistance to insects may affect the virus infection. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,285,904,514]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Aphid-borne potato viruses are transmitted between plant hosts that involve a complex interaction among plant, virus, vector, and the environment to assure successful transmission and infection. These components are necessary in order for a virus disease to occur in any plant system. The four components are: susceptible host plant, a virulent pathogen, a capable vector, and a favorable environment (Fig. 1). There are numerous variables that may affect both the incidence and severity of the disease. These variables include plant genetic diversity, biology, and lifecycle of the host plant and pathogen, vector species and biotype, and environmental conditions (Fig. 1). The four components including plant host, virus, vector and environment are also targets for management and control of aphid and their transmitted potato viruses. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,518,904,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Within one species of potato plant there may be an incredible range of genetic diversity that remarkably influences susceptibility to aphid and potato viruses (Kang et al. 2005). If the host is resistant to a pathogen and/or insect, even when the pathogen and/or insect is present under favorable environmental conditions, a disease will not occur. For examples, several extreme resistance genes to PVY have been identified and mapped on three potato chromosomes: Ryadg identified from S. tuberosum subsp. Andigena on chromosome XI (Hamalainen et al. 1997; Herrera et al. 2018), Rysto and Ry-fsto in chromosome XII from S. stoloniferum (Flis et al. 2005; Song et al. 2005), and Rychc on chromosome IX from S. chacoense (Hosaka et al. 2001; Sato et al. 2006). Rysto-mediated extreme resistance to PVY is temperature-independent (Grech-Baran et al. 2018). Meanwhile, some plant defense responses to viruses are multifaceted and depend upon several factors including tissue type, plant development stage, and temperature. High temperature weakens Rychc-conferred resistance three potato virus Y strains $(\\mathrm{PVY}^{\\mathrm{o}}$ $\\mathrm{PVY}^{\\mathrm{n}}$ and $\\mathrm{PVY}^{\\mathrm{NTN}})$ (Ohki et al. 2018). In addition, Mi-1.2, a gene cloned from S. lycopersicum encodes a protein containing CC-NBS-LRR (coiled coil-nucleotide binding site-leucine rich repeat) domains. This gene has been shown to confer resistance to potato aphid (Milligan et al. 1998; Rossi et al. 1998). Durable dominant genes for resistance to viruses ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,73,114,83]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"370 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[290,73,705,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"XU Yi et al. / Journal of Integrative Agriculture 2020, 19(2): 367-375 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,115,485,175]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"exist in potato germplasm and provide an effective control strategy and genetic diversity in wild potatoes and related Solanum species are widely utilized to discover the resistant genes and used for potato breeding. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,177,485,391]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Furthermore, it has been demonstrated that symptoms and virus accumulation of many viruses could be affected by the age and physiological condition of the host (Fig. 1), and many plants have mature plant resistance (Develey-Riviere and Galiana 2007). The plant needs to be at a growth stage where it is susceptible to infection. Furthermore, plants need to be at a stage where viruses can not only infect, but also move to appropriate tissues to be available to aphids (Basky and Almasi 2004). Plants that are infected when most of the foliage has already developed and matured are susceptible to infection but the virus will not move easily into leaf tissue that has transitioned from sink to source, therefore it will not serve as a source of viruses yet aphids will continue to land and feed on these plants. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,393,485,624]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"All the potato viruses are RNA viruses which have high mutation rates and maintain an extremely high genetic variable population. In many cases, potato viruses can overcome host-mediated resistance and strain-specific resistance to PVY in potato. The HR resistance to PVY mediated by $Ny$ gene is strain-specific and may result in necrotic reactions in both locally and systemically infected leaves (Valkonen et al. 1996; Valkonen 2015), and other strain of PVY can easily escape from the resistance. The dominant potato gene Nytbr for HR controls ordinary PVY strains $(\\mathsf{PVY}^{\\circ})$ but is overcome by $\\mathsf{PVY}^{\\mathsf{N}}$ strains. Further studies showed a structure-function relationship in recognition of $\\mathsf{PVY}^{\\circ}$ and changing of two amino acids within the helper component proteinase could help virus escape Nytbr recognition (Tian and Valkonen 2013). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,626,485,917]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In nature, $80\\%$ of plant viruses rely on vectors for their spread (Hohn 2007). Currently, there are several available strategies to interfere with virus transmission by vectors including host genetic resistance to virus and/or insect, insecticides and integrated pest management. For example, aphid can acquire PLRV after feeding on infected plants about $10 - 30\\mathrm{min}$ , but generally requires $24 - 48\\mathrm{h}$ latency period to be able to transmit the virus. If there are timely applications of insecticides for aphid control, the aphid spread of PLRV will be blocked. In general, the ability of a given vector species to serve as a competent vector for a particular virus is determined by the combined effect of all of the physiological, ecological, and environmental factors relating vector, host, and virus (Fig. 1). Insect vectors can play a crucial role in determining the plant host range of a virus (if they are persistent viruses, the vector must have a host relationship with the plant). Transmission competency is determined by genetic components and specific molecular interactions of virus and vector (Yang et al. 2008; Cilia et al. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[529,114,890,326]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 1 Schematic representation of the interactions between the plant, virus, vector, and environmental factors. The factors that would hypothetically affect the disease formation and development are listed in each rectangle. \"]","image_footnote":"[]","img_path":"images/0477/68329a33bdb3d3fad540ff2601e779c812fd3563341db4c50021ea5ec89aa6a6.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[509,414,905,521]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2012; Tamborindeguy et al. 2013; Dietzgen et al. 2016), and potentially host plant components taken up during feeding also play some roles in this process (Pinheiro et al. 2017). A better understanding of these interactions in the whole process and the exact mechanisms of transmission will be essential for developing more effective control strategies in the future. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,525,907,917]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The role of the environment in shaping host-pathogen interactions has been attracting more and more attention. There are numerous variables in the environment that influence virus diseases incidence and severity including temperature, sunlight, moisture, relative humidity. It has been demonstrated that symptoms and virus accumulation of luteoviruses could be affected by the genotype, development stage and physiological condition of the host plant, as well as by the strain of luteovirus and the environmental conditions, such as temperature and carbon dioxide $\\left(\\mathrm{CO}_{2}\\right)$ levels (Trebicki et al. 2015). Infection rate and RNA content of PLRV in plant tissues increased as the temperature increased to $(20 \\pm 2)^{\\circ} \\mathrm{C}$ , and then declined if the temperatures continued to increase. In addition, more plants were infected by PLRV at $(30 \\pm 2)^{\\circ} \\mathrm{C}$ than at $20^{\\circ} \\mathrm{C}$ or $(25 \\pm 2)^{\\circ} \\mathrm{C}$ with high $\\mathrm{CO}_{2}$ levels $(940 \\pm 50 \\mathrm{ppm})$ (Chung et al. 2016). In $P$ . floridana plant, the PLRV infection rate was the highest at $(25 \\pm 2)^{\\circ} \\mathrm{C}$ , and greater PLRV accumulation levels were evident in plants maintained at $20-25^{\\circ} \\mathrm{C}$ (Chung et al. 2016). Changing climate conditions can also contribute to a successful spread of virus vectors and establishment of these organisms in areas that were previously unfavorable (Krishnareddy 2013; Samuel et al. 2016). Besides the physical environmental factors, biological factors such as neighbor plant, mix-infected viruses, endosymbiont, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[289,73,707,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"XU Yi et al. / Journal of Integrative Agriculture 2020, 19(2): 367-375 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[882,73,904,83]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"371 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[89,115,485,426]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and other microbes cause changes in disease patterns (Fig. 1). Plant-plant interactions are among the fundamental processes that shape the structure and function of plant communities (Brooker 2006; Antonio et al. 2015). Co-infection by different viruses in one plant occurs frequently in the field, and the interactions between the viruses are complicated, including antagonistic interactions and synergistic interactions (Syller 2012; Syller and Grupa 2016). Symbiosis which is particularly common in arthropods plays important roles in regulating vector nutrition, behavior and virus transmission (Hogenhout et al. 2000; Bourtzis and Miller 2002; Sassera et al. 2013; Jia et al. 2017). Pathogens are typically restricted to an area based on the conditions of the macroclimate. Understanding the genetic and environmental reasons why plant species vary in their susceptibility to infection, how plant/vector immune defense is intertwined with other components of host physiology, and how interactions with pathogens shape the evolution of host immunity will help us develop strategies for management and control of aphid and virus diseases on potatoes. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[90,442,285,458]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgements ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,474,485,565]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We are grateful to Prof. Tao Xiaorong from Nanjing Agricultural University, China, for providing comments and helpful suggestions on the manuscript. This work was supported by the grants from the Startup Fund for Distinguished Scholars, Nanjing Agricultural University, China. 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Discussion paper: The \"]","page_idx":"7","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[90,73,114,83]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"374 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[290,73,707,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"XU Yi et al. / Journal of Integrative Agriculture 2020, 19(2): 367-375 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[92,115,485,797]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"naming of Potato virus Y strains infecting potato. Archive of Virology, 153, 1-13. \",\"Solomon-Blackburn R M, Barker H. 2001. Breeding virus resistant potatoes (Solanum tuberosum): A review of traditional and molecular approaches. Heredity (Edinb) 86, 17-35. \",\"Song Y S, Hepting L, Schweizer G, Hartl L, Wenzel G, Schwarzfischer A. 2005. Mapping of extreme resistance to PVY (Ry (sto)) on chromosome XII using anther-culture-derived primary dihaploid potato lines. Theoretical and Applied Genetics, 111, 879-887. \",\"Srinivasan D G, Brisson J A. 2012. Aphids: A model for polyphenism and epigenetics. Genetics Research International, 2012, 431531. \",\"Sullivan D J. 2008. Aphids (Hemiptera: Aphididae). In: Capinera JL, ed., Encyclopedia of Entomology. Springer, Dordrecht. \",\"Syller J. 2012. Facilitative and antagonistic interactions between plant viruses in mixed infections. Molecular Plant Pathology, 13, 204-216. \",\"Syller J, Grupa A. 2016. Antagonistic within-host interactions between plant viruses: Molecular basis and impact on viral and host fitness. Molecular Plant Pathology, 17, 769-782. \",\"Syller J, Marczewski W, Pawlowsicz J. 1997. Transmission by aphids of potato spindle tuber viroid encapsidated by potato leafroll luteovirus particles. European Journal of Plant Pathology, 103, 285-289. \",\"Tamborindeguy C, Bereman M S, DeBlasio S, Igwe D, Smith D M, White F, MacCoss M J, Gray S M, Cilia M. 2013. Genomic and proteomic analysis of Schizaphis graminum reveals cyclophilin proteins are involved in the transmission of cereal Yellow dwarf virus. PLoS ONE, 8, e71620. \",\"Tian Y P, Valkonen J P. 2013. Genetic determinants of Potato virus Y required to overcome or trigger hypersensitive resistance to PVY strain group O controlled by the gene Ny in potato. Molecular Plant-Microbe Interactions, 26, 297-305. \",\"Tomczynska I, Jupe F, Hein I, Marczewski W, Sliwka J. 2014. Hypersensitive response to Potato virus Y in potato cultivar Sarpo Mira is conferred by the Ny-Smira gene located on the long arm of chromosome IX. Molecular Breeding, 34, 471-480. \",\"Trebicki P, Nancarrow N, Cole E, Bosque-Perez N A, Constable F E, Freeman A J, Rodoni B, Yen A L, Luck J E, Fitzgerald G J. 2015. Virus disease in wheat predicted to increase with a changing climate. Global Change Biology, 21, 3511-3519. \",\"Tribodet M, Glais L, Kerlan C, Jacquot E. 2005. Characterization of Potato virus Y (PVY) molecular determinants involved in the vein necrosis symptom induced by PVYN isolates in infected Nicotiana tabacum cv. Xanthi. Journal of General Virology, 86, 2101-2105. \"]","page_idx":"8","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[512,115,905,784]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Valkonen J P T. 2015. Elucidation of virus-host interactions to enhance resistance breeding for control of virus diseases in potato. Breeding Science, 65, 69-76. \",\"Valkonen J P T, Jones R A C, Slack S A, Watanabe K N. 1996. Resistance specificity to viruses in potato: Standardization of nomenclature. Plant Breeding, 115, 433-438. \",\"Valkonen J P T, Zimnoch-Guzowska E G C, Watanabe K N. 2017. Resistance to Potato virus Y in potato. In: Lacomme C, Glais L, Bellstedt D, Dupuis B, Karasev A, Jacquot E, eds., Potato Virus Y: Biodiversity, Pathogenicity, Epidemiology and Management. Springer International Publishing, Cham. pp. 207-241. \",\"Vorburger C, Lancaster M, Sunnucks P. 2003. Environmentally related patterns of reproductive modes in the aphid Myzus persicae and the predominance of two 'superclones' in Victoria, Australia. Molecular Ecology, 12, 3493-3504. \",\"De Vos M, Kim J H, Jander G. 2007. Biochemistry and molecular biology of Arabidopsis-aphid interactions. Bioessays, 29, 871-883. \",\"Wang J Y, Chay C, Gildow F E, Gray S M. 1995. Readthrough protein associated with virions of Barley yellow dwarf luteovirus and its potential role in regulating the efficiency of aphid transmission. Virology, 206, 954-962. \",\"Whitfield A E, Falk B W, Rotenberg D. 2015. Insect vector-mediated transmission of plant viruses. Virology, 479-480, 278-289. \",\"Whitworth J L, Crosslin J M. 2013. Detection of Potato mop top virus (Furovirus) on potato in southeast Idaho. Plant Disease, 97, 149. \",\"Will T, Tjallingii W F, Thönnessen A, Van Bel A J E. 2007. Molecular sabotage of plant defense by aphid saliva. Proceedings of the National Academy of Sciences of the United States of America, 104, 10536-10541. \",\"Xu H, Nie J. 2006. Identification, characterization, and molecular detection of Alfalfa mosaic virus in potato. Phytopathology, 96, 1237-1242. \",\"Xu Y, Da Silva W L, Qian Y, Gray S M. 2018. An aromatic amino acid and associated helix in the C-terminus of the potato leafroll virus minor capsid protein regulate systemic infection and symptom expression. PLoS Pathogens, 14, e1007451. \",\"Yang X, Thannhauser T W, Burrows M, Cox-Foster D, Gildow F E, Gray S M. 2008. Coupling genetics and proteomics to identify aphid proteins associated with vector-specific transmission of polerovirus (luteoviridae). Journal of Virology, 82, 291-299. \",\"Yellareddygari S K R, Whitworth J L, Gudmestad N C. 2018. Assessing potato cultivar sensitivity to tuber necrosis caused by Potato mop-top virus. Plant Disease, 102, 1148-1153. \"]","page_idx":"8","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[289,73,707,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"XU Yi et al. / Journal of Integrative Agriculture 2020, 19(2): 367-375 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[882,73,905,83]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"375 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[638,812,905,825]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Executive Editor-in-Chief WAN Fang-hao ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[710,826,904,838]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Managing editor SUN Lu-juan ","text_format":null,"text_level":null,"type":"footer"}],"string":"[\n {\n \"bbox\": \"[90,224,157,237]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"REVIEW \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[90,262,897,305]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Aphids and their transmitted potato viruses: A continuous challenges in potato crops \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[853,287,897,321]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0868/14634aaa70647c43a4230fd14968c6dde23405fbb54b651ef3edc815f854bdd9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[90,324,307,340]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"XU Yi $^{1}$ , Stewart M. GRAY $^{2,3}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,360,905,431]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"$^{1}$ Department of Plant Pathology, Nanjing Agricultural University, Nanjing 210095, P.R.China \\\",\\\"$^{2}$ Section of Plant Pathology and Plant-Microbe Biology, School of Integrated Plant Science, Cornell University, Ithaca, NY 14850, USA \\\",\\\"<sup>3</sup> Emerging Pest and Pathogens Research Unit, United States Department of Agriculture-Agricultural Research Service, Ithaca, NY 14850, USA \\\"]\",\n \"page_idx\": \"0\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[90,455,159,467]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[87,469,907,592]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Aphid is one of the most destructive insect pests on cultivated plants in temperate regions. Their piercing-sucking mouthparts and phloem feeding behavior directly damage crops and deplete plant nutrients. Potato (Solanum tuberosum L.) is one of the most important food sources on the planet, and several aphid species, e.g., Myzus persicae (Sulzer) (green peach aphid) and Macrosiphum euphorbiae (Thomas) (potato aphid) (Hemiptera: Aphididae) colonize potato and transmit several economically important viruses. Aphid-transmitted potato viruses have been emerging all over the world as a very serious problem in potato production, inducing a wide variety of foliar and tuber symptoms, leading to severe yield reduction and loss of tuber quality. In this review, recent advances in understanding the interactions of potato viruses with their hosts, aphid vectors and the environment are described. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[90,604,455,618]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: aphids, virus, potato, vector, transmission \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,683,485,717]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Basic characteristics of Myzus persicae and Macrosiphum euphorbiae \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,731,485,791]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Aphids are a monophyletic insect represented by around 4400 species worldwide, and they have a very complex life cycle (Remaudière and Remaudière 1997; Blackman and Eastop 2000; Gilbert 2012; Bass et al. 2014). Aphids can \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,658,907,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"cause damage and reduce agricultural yields in several manners. They can build to high population densities in feeding plants, removing plant nutrients and plant sap to cause withering and death of the plants (Gilbert 2012). Some aphids' secretions from salivary are phytotoxic, causing stunting of the plant, leaf deformation, and gall formation. Even if otherwise asymptomatic, plant hormone balances and host metabolism can be affected to the detriment of the plant, but to the advantage of the aphid (Kaloshian 2004). Aphids M. persicae (green peach aphid) and M. euphorbiae (potato aphid) are important potato-infecting insect pests damaging potato production around the world (Kennedy et al. 1962; Blackman and Eastop 2000). These two species of aphids can be distinguished by looking at the tubercles between the base of the antennae. The tubercles of the M. euphorbiae slope outward and those \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[329,72,670,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Integrative Agriculture 2020, 19(2): 367-375 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[90,102,236,212]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"SELFIER \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[366,105,650,118]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Available online at www.sciencedirect.com \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[415,140,621,162]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ScienceDirect \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[784,96,905,212]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PITJ Journal of Integrative Agriculture (formerly Agricultural Sciences in China) Special Focus: Plant Use/Plant Management 2020 Vol.15 No.2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,837,423,848]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received 10 July, 2019 Accepted 15 October, 2019 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[92,850,421,862]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Correspondence XU Yi, E-mail: xuyiqpd@njau.edu.cn \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[89,866,485,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"© 2020 CAAS. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). doi: 10.1016/S2095-3119(19)62842-X \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[92,115,482,298]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"of the M. persicae converge. At most time, they undergo two stages: nymph and adult. In overwinter hosts, they both undergo three development stages: adult, nymph and egg. The adults of M. persicae have a tear-drop shape; the adults with the wing are bright green with a dark head and thorax, and a greenish abdomen with dark patches. They can secrete sticky honeydew. In contrast, M. euphorbiae has a larger and more elongated body (Fericean et al. 2011; Gilbert 2012). In addition, M. persicae infestations typically begin on the bottom of potato leaves while M. euphorbiae infestations are scattered over the plant (Blackman and Eastop 2000). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,300,482,530]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Both green peach aphid and potato aphid can produce eggs to survive winter on a primary plant host in temperate regions. Then eggs hatch and the aphids migrate to summer host plants in spring (Blackman and Eastop 2000; Sullivan 2008). Aphids take a flight to find the overwintering host plants to lay eggs, and the migration generally occurs in late summer to early autumn. In warmer climates, sexual reproduction may not occur, and females reproduce through parthenogenesis (Vorburger et al. 2003; Srinivasan and Brisson 2012). In general, one female adult can produce 20 to 50 nymphs that mature in 14 to 21 days under summer conditions with high temperature. Young nymphs periodically develop into alate (winged) adults and migrate to other plants. Green peach aphid and potato aphid both feed in plant phloem tissues which circulate carbohydrates. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,546,480,563]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. Potato diseases caused by plant viruses \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,579,482,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the fields, potatoes can be infected by many different plant viruses that can lead to yield reduction and loss of tuber quality. Potato virus diseases often can be diagnosed by some easily visible symptoms, such as mosaic patterns on leaves, stunting of the plant, leaf and tuber malformations (Hane and Hamm 1999; Tribodet et al. 2005; Xu and Nie 2006; Gray et al. 2010). However, foliar and/or tuber symptoms are not always expressed due to interactions between the virus and the potato cultivars, growing conditions, or the development stage of the plants when they are infected by viruses (Domfeh et al. 2015; Yellareddygari et al. 2018). Potato viruses are found in several viral families and one viroid (Brunt and Lawson 2001). Among them, potato viruses A, Y, and V (PVA, PVY, and PVV) are members of the genus Potyvirus (family Potyviridae). Potato leafroll virus (PLRV) is the type member of the genus Polerovirus (family Luteoviridae). Cucumber mosaic virus, alfalfa mosaic virus, and potato yellowing virus are members of the family Bromoviridae. Potato virus X is the typical member of Potexvirus, in the family of Alphaflexiviridae. Potato yellow dwarf virus is a typical member of nucleorhabdovirus, in the Rhabdoviridae family. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,115,904,237]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Potato latent virus and potato viruses M and S are found in the genus Carlavirus, Betaflexiviridae family. Potato spindle tuber viroid (PSTVd) is a pospiviroid in the family Pospiviroidae, and this virus is the first viroid to be identified (Diener 1971). Of these potato viruses, PVY, PLRV, PVX, potato mop-top virus (PMTV), tobacco rattle virus (TRV) and PSTVd will be described in detail considering they are economically important in the world currently. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,253,850,269]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. Virus description and symptoms \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,284,904,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PVY, one of the most important potato viruses, especially for seed potato production, occurs in most potato production areas around the world. PVY is the major reason for certification programs to reject or downgrade seed lots and PVY also reduces the yield and quality of tubers (Karasev and Gray 2013; Gray and Power 2018). PVY has a monopartite, linear, ssRNA (+) genome of $10\\\\mathrm{kb}$ in size (Berger et al. 2005). The genomic RNA is translated into polyproteins which are subsequently processed by viral-encoded proteinases into functional products (Adams et al. 2012). PVY is transmitted by numerous species of aphids, and green peach aphid is one of the most efficient vectors in a non-persistent, stylet-borne manner (Halbert et al. 2003; Karasev and Gray 2013). The virus can be transmitted in seconds to minutes and it can also be mechanically transmitted by human activity and vertically through tubers. The symptoms of PVY-infected plants vary depending on the strain of PVY and the variety of potato (Karasev and Gray 2013). Some potato varieties have a hypersensitive reaction (HR) to PVY specific strain, resulting in rapid death in the infected area (Kerlan et al. 2011; Tomczynska et al. 2014). Some potato varieties are more sensitive to PVY infection and exhibit easily visible symptoms such as mild mottling, distorted and brittle leaves (Hane and Hamm 1999; Tribodet et al. 2005). PVY distributed in most potato production areas around the world and increasing recognition of various strain types has been reported. The ordinary strain $\\\\mathsf{PVY}^{\\\\mathsf{O}}$ , was prevalent in Europe and North America before the 1990s and 2000s, respectively, and in general caused visible mosaic, necrosis, and leaf drop symptoms, although the severity of symptoms differed among potato varieties (Singh et al. 2008; Gray et al. 2010; Karasev and Gray 2013). In recent decades, PVY has rapidly evolved to become a complex of strains that evade potato fields in many regions around the world. Today the tuber necrotic strain, $\\\\mathsf{PVY}^{\\\\mathsf{NTN}}$ , predominates in Europe and another recombinant $\\\\mathsf{PVY}^{\\\\mathsf{NW}}$ predominates in North America (Lorenzen et al. 2006; Singh et al. 2008; Karasev and Gray 2013). It is noteworthy that the recombinant strain $\\\\mathsf{PVY}^{\\\\mathsf{NTN}}$ can cause the potato tuber necrotic ringspot disease (PTNRD) which seriously reduces the quality of tubers. Recently potato genome loci related \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,74,114,82]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"368 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[290,73,705,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"XU Yi et al. / Journal of Integrative Agriculture 2020, 19(2): 367-375 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[92,115,482,236]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"to PTNRD expression were identified (da Silva et al. 2017). Effective and durable single dominant resistance genes against all strains of PVY such as $Ry_{sto}$ , $Ry_{chc}$ , and $Ry_{adg}$ are available and widely used in Europe and are beginning to be incorporated into commercially acceptable cultivars in other production regions (Valkonen et al. 2017). Genetic markers exist that facilitate marker-assisted breeding and selection (Valkonen 2015; Valkonen et al. 2017). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,239,482,638]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PLRV, a typical member of the genus Polerovirus, in the family Luteoviridae, has a monopartite, ssRNA (+) genome of 5.3–5.7 kb in size with a VPg bound at the $5^{\\\\prime}$ end. PLRV has an isometric, non-enveloped, spherical particle with a readthrough domain (RTD) extension located on the surface of the particle (Mayo and Ziegler-Graff 1996; D'Arcy and Domier 2005). PLRV is transmitted in a persistent and circulative manner by many potato colonizing aphid species, primarily green peach aphid. Once an aphid acquires PLRV, it can transmit the virus for its entire life (Gray and Gildow 2003; Whitfield et al. 2015). RTD domain has been intensively studied, and the N-terminus of PLRV RTD is important for mediating RTP incorporation into the virion and is required for aphid transmission and interaction with aphid endosymbiont proteins (Brault et al. 1995; van den Heuvel et al. 1997; Hogenhout et al. 2000). The C-terminal region of PLRV RTD plays important roles in virus accumulation, movement, tissue tropism and symptom development in plants (Wang et al. 1995; Peter et al. 2008; Xu et al. 2018). PLRV can also be spread vertically through tubers. PLRV-infected plants develop visible symptoms include upright character and rolling of the leaves, interveinal chlorosis, leathery leaves, phloem necrosis, stunting of the plant, and net necrosis in tubers (Douglas and Pavek 1972; Peter et al. 2009). There is no effective extreme resistance to PLRV in potato. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,640,482,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PVX is in the Potexvirus genus, which is a member of Alphaflexiviridae family. Genome organization of PVX contains five open reading frames (ORF) coding for proteins RdRp, TGBp1, TGBp2, TGBp3, and CP (Huisman et al. 1988; Martelli et al. 2007). Potato plants infected PVX often develop mild symptom on foliage, but the virus can cause symptoms of chlorosis, mosaic, decreased leaf size, occasionally top necrosis and necrotic lesions in tubers. In addition, PVX can interact with PVY and other viruses in a synergistic manner to cause more severe symptoms and yield loss than either virus alone (Gonzalez-Jara et al. 2004). PVX is transmitted mechanically or vertically through infected tubers. Two resistant genes, $Rx1$ and $Rx2$ , identified from wild species S. tuberosum ssp. andigena and S. acaule, respectively provide extreme resistance to PVX (Bendahmane et al. 1999, 2000). Genetic markers exist that facilitate marker-assisted breeding and selection (Solomon-Blackburn and Barker 2001). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,115,904,405]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PMTV is a tripartite pomovirus, and the virus is vectored by the powdery scab plasmodiophoromycete Spongospora subterranea pv. Subterranean. The three genome segments, 6, 3.5 and $3\\\\mathrm{kb}$ in size, have a $5^{\\\\prime}$ cap and a $3^{\\\\prime}$ tRNA-like structure (Savenkov et al. 1999; Adams et al. 2017). The virus presents in many potato production areas including Europe, the Andes, Asia, Canada and the U.S (Sandgren 1995; Whitworth and Crosslin 2013; Ramesh et al. 2014; Hu et al. 2016). Foliar symptoms are cultivar- and environment-dependent and include yellow spots, arcs or chevron patterns; tuber symptoms, also cultivar- and environment-dependent, are expressed as rust-brown necrotic arcs or flecks often referred to as \\\"Spraing\\\" (Calvert and Harrison 1966). Disease caused by PMTV occurs more often under cool temperatures and in wet soils which are favorable for the germination of S. subterranean spores. The virus can survive within the resting spores of its vector for decades, making management difficult. There are no commercial PMTV-resistant potato varieties. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,407,904,668]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"TRV, a non-enveloped, rod-shaped RNA virus in the Tobravirus genus, causes corky ringspot disease on potato. TRV has a bipartite RNA genome 6.8 and $4.5\\\\mathrm{kb}$ in size (Harrison and Robinson 1978; Adams et al. 2017). Over 400 species of plants from 50 families are susceptible to TRV infection, which make this virus widely used as virus-induced gene silencing vector (VIGS) (Harrison and Robinson 1978; Liu et al. 2002). In potato fields, disease caused by TRV occurs more often in coarse sandy soils. Foliar symptoms are rare but similar to those caused by PMTV or AMV. Tuber symptoms are cultivar-dependent and characterized by necrotic, \\\"corky\\\" layers or necrotic flecks of tissue interspersed with rings of healthy tissue. In nature, TRV is transmitted by 'stubby-root' nematodes in the Paratrichodorus or Trichodorus genus and can also be transmitted mechanically (Ploeg et al. 1989; MacFarlane and Brown 1995). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,670,904,915]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PSTVd was the first viroid to be identified, and it is a small, single-stranded circular RNA molecule which was classified in the Pospiviroidae family. PSTVd comprises 359 nucleotides, and most of the genome displays complementary strands (Diener 1971; Gross et al. 1978). PSTVd is often transmitted by foliar contact and through tubers, but it can also be aphid-transmissible in the presence of PLRV. It is thought that the PSTVd genome is encapsidated in PLRV particles (Salazar et al. 1995; Syller et al. 1997). Symptom development after PSTVd infection is dependent upon the strain of the viroid in conjunction with the potato varieties and the stage of plant development. Infected tubers develop a spindle shape with a round cross-section. In potato fields, it has been reported that severe PSTVd strains could cause losses of up to $65\\\\%$ in tuber number and size. In addition, PSTVd-derived small \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[290,73,705,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"XU Yi et al. / Journal of Integrative Agriculture 2020, 19(2): 367-375 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[882,74,905,83]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"369 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[92,115,482,221]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"RNA could induce RNA silencing of several endogenous messenger RNAs during infection and silencing of these endogenous mRNAs are related to symptom development in tomato (Adkar-Purushothama et al. 2015). The disease is present in North America, South America, Europe, New Zealand, Asia, and Africa. All potatoes are susceptible to PSTVd and there is no form of natural resistance. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,237,470,254]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. Aphid transmission of potato viruses \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,269,482,668]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Many insect pests of potato are potential vectors of potato viruses, but aphids are the most important, vectoring 13 of the 40 reported viruses known to infect potato (Salazar 1996). Many of them are polyphagous and capable of transmitting potato viruses. Among 4400 aphid species, green peach aphid and potato aphid are the most efficient vectors of potato viruses. There are four modes of virus transmission: (1) non-persistent, (2) semi-persistent, (3) persistent and circulative, and (4) persistent and propagative (Nault 1997; Whitfield et al. 2015). PLRV is the only common potato virus transmitted by aphids in a persistent and circulative manner (Mayo and Ziegler-Graff 1996; Gray and Gildow 2003), while other potato viruses are generally transmitted by aphids in a non-persistent manner (i.e., stylet-borne viruses). In non-persistent mode, take PVY for example, PVY particles are quickly acquired, and there is no latency period required for virus inoculation to a new plant. These kinds of viruses are stylet-borne, and aphids are viruliferous for only a short period of time after acquisition, usually just a few minutes or hours (Karasev and Gray 2013). In contrast, when aphids acquire a persistent virus, there is a period of latency between acquisition and becoming accessible for virus transmission to a new plant. The aphids remain viruliferous and infectious for the rest of their lives and can transmit the virus each time when they feed on another plant (Gray and Gildow 2003; Whitfield et al. 2015). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,684,482,717]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5. A comprehensive view of interactions among plant, virus, vector and environment \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,733,482,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The interaction among plant, aphids and viruses has been widely studied in recent years. In general, aphids feeding on plant will activate host defenses such as jasmonate acid (JA)-dependent defense responses that are effective against aphids (De Vos et al. 2007). As a counter-reaction, aphids are able to manipulate host responses, as reflected by their ability to affect host morphology (van Emden and Harrington 2007), impact host nutrient allocation (Girousse et al. 2005), and suppress plant defense responses (Will et al. 2007). More recently, several aphid-secreted effector proteins from both green peach aphids and potato aphids have been identified (Elzinga and Jander 2013; Rodriguez \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,115,904,282]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and Bos 2013; Chaudhary et al. 2015; Naessens et al. 2015), suggesting that aphids, like other plant-associated organisms secrete effectors inside their host to manipulate host defenses (Kaloshian and Walling 2015). In addition, plant viruses have been extensively studied that could modulate plant defense system and facilitate aphid behaviors, e.g., green peach aphids are more fecund on PLRV-infected potatoes (Alvarez et al. 2007; Castle and Berger 1993). Further research will focus on how plant virus infections modulate plant resistance to insects and also how host plant resistance to insects may affect the virus infection. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,285,904,514]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Aphid-borne potato viruses are transmitted between plant hosts that involve a complex interaction among plant, virus, vector, and the environment to assure successful transmission and infection. These components are necessary in order for a virus disease to occur in any plant system. The four components are: susceptible host plant, a virulent pathogen, a capable vector, and a favorable environment (Fig. 1). There are numerous variables that may affect both the incidence and severity of the disease. These variables include plant genetic diversity, biology, and lifecycle of the host plant and pathogen, vector species and biotype, and environmental conditions (Fig. 1). The four components including plant host, virus, vector and environment are also targets for management and control of aphid and their transmitted potato viruses. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,518,904,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Within one species of potato plant there may be an incredible range of genetic diversity that remarkably influences susceptibility to aphid and potato viruses (Kang et al. 2005). If the host is resistant to a pathogen and/or insect, even when the pathogen and/or insect is present under favorable environmental conditions, a disease will not occur. For examples, several extreme resistance genes to PVY have been identified and mapped on three potato chromosomes: Ryadg identified from S. tuberosum subsp. Andigena on chromosome XI (Hamalainen et al. 1997; Herrera et al. 2018), Rysto and Ry-fsto in chromosome XII from S. stoloniferum (Flis et al. 2005; Song et al. 2005), and Rychc on chromosome IX from S. chacoense (Hosaka et al. 2001; Sato et al. 2006). Rysto-mediated extreme resistance to PVY is temperature-independent (Grech-Baran et al. 2018). Meanwhile, some plant defense responses to viruses are multifaceted and depend upon several factors including tissue type, plant development stage, and temperature. High temperature weakens Rychc-conferred resistance three potato virus Y strains $(\\\\mathrm{PVY}^{\\\\mathrm{o}}$ $\\\\mathrm{PVY}^{\\\\mathrm{n}}$ and $\\\\mathrm{PVY}^{\\\\mathrm{NTN}})$ (Ohki et al. 2018). In addition, Mi-1.2, a gene cloned from S. lycopersicum encodes a protein containing CC-NBS-LRR (coiled coil-nucleotide binding site-leucine rich repeat) domains. This gene has been shown to confer resistance to potato aphid (Milligan et al. 1998; Rossi et al. 1998). Durable dominant genes for resistance to viruses \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,73,114,83]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"370 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[290,73,705,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"XU Yi et al. / Journal of Integrative Agriculture 2020, 19(2): 367-375 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,115,485,175]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"exist in potato germplasm and provide an effective control strategy and genetic diversity in wild potatoes and related Solanum species are widely utilized to discover the resistant genes and used for potato breeding. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,177,485,391]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Furthermore, it has been demonstrated that symptoms and virus accumulation of many viruses could be affected by the age and physiological condition of the host (Fig. 1), and many plants have mature plant resistance (Develey-Riviere and Galiana 2007). The plant needs to be at a growth stage where it is susceptible to infection. Furthermore, plants need to be at a stage where viruses can not only infect, but also move to appropriate tissues to be available to aphids (Basky and Almasi 2004). Plants that are infected when most of the foliage has already developed and matured are susceptible to infection but the virus will not move easily into leaf tissue that has transitioned from sink to source, therefore it will not serve as a source of viruses yet aphids will continue to land and feed on these plants. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,393,485,624]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"All the potato viruses are RNA viruses which have high mutation rates and maintain an extremely high genetic variable population. In many cases, potato viruses can overcome host-mediated resistance and strain-specific resistance to PVY in potato. The HR resistance to PVY mediated by $Ny$ gene is strain-specific and may result in necrotic reactions in both locally and systemically infected leaves (Valkonen et al. 1996; Valkonen 2015), and other strain of PVY can easily escape from the resistance. The dominant potato gene Nytbr for HR controls ordinary PVY strains $(\\\\mathsf{PVY}^{\\\\circ})$ but is overcome by $\\\\mathsf{PVY}^{\\\\mathsf{N}}$ strains. Further studies showed a structure-function relationship in recognition of $\\\\mathsf{PVY}^{\\\\circ}$ and changing of two amino acids within the helper component proteinase could help virus escape Nytbr recognition (Tian and Valkonen 2013). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,626,485,917]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In nature, $80\\\\%$ of plant viruses rely on vectors for their spread (Hohn 2007). Currently, there are several available strategies to interfere with virus transmission by vectors including host genetic resistance to virus and/or insect, insecticides and integrated pest management. For example, aphid can acquire PLRV after feeding on infected plants about $10 - 30\\\\mathrm{min}$ , but generally requires $24 - 48\\\\mathrm{h}$ latency period to be able to transmit the virus. If there are timely applications of insecticides for aphid control, the aphid spread of PLRV will be blocked. In general, the ability of a given vector species to serve as a competent vector for a particular virus is determined by the combined effect of all of the physiological, ecological, and environmental factors relating vector, host, and virus (Fig. 1). Insect vectors can play a crucial role in determining the plant host range of a virus (if they are persistent viruses, the vector must have a host relationship with the plant). Transmission competency is determined by genetic components and specific molecular interactions of virus and vector (Yang et al. 2008; Cilia et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[529,114,890,326]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 1 Schematic representation of the interactions between the plant, virus, vector, and environmental factors. The factors that would hypothetically affect the disease formation and development are listed in each rectangle. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0477/68329a33bdb3d3fad540ff2601e779c812fd3563341db4c50021ea5ec89aa6a6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[509,414,905,521]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2012; Tamborindeguy et al. 2013; Dietzgen et al. 2016), and potentially host plant components taken up during feeding also play some roles in this process (Pinheiro et al. 2017). A better understanding of these interactions in the whole process and the exact mechanisms of transmission will be essential for developing more effective control strategies in the future. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,525,907,917]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The role of the environment in shaping host-pathogen interactions has been attracting more and more attention. There are numerous variables in the environment that influence virus diseases incidence and severity including temperature, sunlight, moisture, relative humidity. It has been demonstrated that symptoms and virus accumulation of luteoviruses could be affected by the genotype, development stage and physiological condition of the host plant, as well as by the strain of luteovirus and the environmental conditions, such as temperature and carbon dioxide $\\\\left(\\\\mathrm{CO}_{2}\\\\right)$ levels (Trebicki et al. 2015). Infection rate and RNA content of PLRV in plant tissues increased as the temperature increased to $(20 \\\\pm 2)^{\\\\circ} \\\\mathrm{C}$ , and then declined if the temperatures continued to increase. In addition, more plants were infected by PLRV at $(30 \\\\pm 2)^{\\\\circ} \\\\mathrm{C}$ than at $20^{\\\\circ} \\\\mathrm{C}$ or $(25 \\\\pm 2)^{\\\\circ} \\\\mathrm{C}$ with high $\\\\mathrm{CO}_{2}$ levels $(940 \\\\pm 50 \\\\mathrm{ppm})$ (Chung et al. 2016). In $P$ . floridana plant, the PLRV infection rate was the highest at $(25 \\\\pm 2)^{\\\\circ} \\\\mathrm{C}$ , and greater PLRV accumulation levels were evident in plants maintained at $20-25^{\\\\circ} \\\\mathrm{C}$ (Chung et al. 2016). Changing climate conditions can also contribute to a successful spread of virus vectors and establishment of these organisms in areas that were previously unfavorable (Krishnareddy 2013; Samuel et al. 2016). Besides the physical environmental factors, biological factors such as neighbor plant, mix-infected viruses, endosymbiont, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[289,73,707,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"XU Yi et al. / Journal of Integrative Agriculture 2020, 19(2): 367-375 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[882,73,904,83]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"371 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[89,115,485,426]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and other microbes cause changes in disease patterns (Fig. 1). Plant-plant interactions are among the fundamental processes that shape the structure and function of plant communities (Brooker 2006; Antonio et al. 2015). Co-infection by different viruses in one plant occurs frequently in the field, and the interactions between the viruses are complicated, including antagonistic interactions and synergistic interactions (Syller 2012; Syller and Grupa 2016). Symbiosis which is particularly common in arthropods plays important roles in regulating vector nutrition, behavior and virus transmission (Hogenhout et al. 2000; Bourtzis and Miller 2002; Sassera et al. 2013; Jia et al. 2017). Pathogens are typically restricted to an area based on the conditions of the macroclimate. Understanding the genetic and environmental reasons why plant species vary in their susceptibility to infection, how plant/vector immune defense is intertwined with other components of host physiology, and how interactions with pathogens shape the evolution of host immunity will help us develop strategies for management and control of aphid and virus diseases on potatoes. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[90,442,285,458]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgements \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,474,485,565]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We are grateful to Prof. Tao Xiaorong from Nanjing Agricultural University, China, for providing comments and helpful suggestions on the manuscript. This work was supported by the grants from the Startup Fund for Distinguished Scholars, Nanjing Agricultural University, China. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[90,583,203,598]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[90,613,485,917]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Adams M J, Adkins S, Bragard C, Gilmer D, Li D, MacFarlane S A, Wong S M, Melcher U, Ratti C, Ryu K H. 2017. ICTV virus taxonomy profile: Virgaviridae. 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Small deletions in the potato leafroll virus readthrough protein affect particle morphology, aphid transmission, virus movement and accumulation. Journal of General Virology, 89, 2037-2045. \\\"]\",\n \"page_idx\": \"7\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[512,115,907,917]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Peter K A, Gildow F, Palukaitis P, Gray S M. 2009. The C terminus of the polerovirus p5 readthrough domain limits virus infection to the phloem. Journal of Virology, 83, 5419-5429. \\\",\\\"Pinheiro P V, Ghanim M, Alexander M, Rebelo A R, Santos R S, Orsburn B C, Gray S M, Cilia M. 2017. Host plants indirectly influence plant virus transmission by altering gut cysteine protease activity of aphid vectors. Molecular & Cell Proteomics, 16, S230-S243. \\\",\\\"Ploeg A T, Brown D J F, Robinson D J. 1989. Transmission of tobraviruses by trichodorid nematodes. EPPO Bulletin, 19, 605-610. \\\",\\\"Ramesh S V, Raikhy G, Brown C R, Whitworth J L, Pappu H R. 2014. Complete genomic characterization of a potato mop-top virus isolate from the United States. *Archieve of Virology*, 159, 3427-3433. \\\",\\\"Remaudière G, Remaudière R. 1997. Catalogue des Aphididae du Monde, Homoptera Aphidoidea. Institut National de la Recherche Agronomique, Paris. p. 473. (in French) \\\",\\\"Rodriguez P A, Bos J I B. 2013. Toward understanding the role of aphid effectors in plant infestation. Molecular Plant-Microbe Interaction, 26, 25-30. \\\",\\\"Rossi M, Goggin F L, Milligan S B, Kaloshian I, Ullman D E, Williamson V M. 1998. The nematode resistance gene $M_i$ of tomato confers resistance against the potato aphid. Proceedings of the National Academy of Sciences of the United States of America, 95, 9750-9754. \\\",\\\"Salazar L. 1996. Potato Virus and Their Control. International Potato Center (CIP), Lima. \\\",\\\"Salazar L F, Querci M, Bartolini I, Lazarte V. 1995. Aphid transmission of potato spindle tuber viroid assisted by potato leafroll virus. Fitopatologia, 30, 56-58. \\\",\\\"Samuel G H, Adelman Z N, Myles K M. 2016. Temperature-dependent effects on the replication and transmission of arthropod-borne viruses in their insect hosts. Current Opinion in Insect Science, 16, 108-113. \\\",\\\"Sandgren M. 1995. Potato mop-top virus (PMTV): Distribution in Sweden, development of symptoms during storage and cultivar trials in field and glasshouse. *Potato Research*, 38, 379-389. \\\",\\\"Sassera D, Epis S, Pajoro M, Bandi C. 2013. Microbial symbiosis and the control of vector-borne pathogens in tsetse flies, human lice, and triatomine bugs. *Pathogens and Global Health*, 107, 285-292. \\\",\\\"Sato M, Nishikawa K, Komura K, Hosaka K. 2006. Potato virus Y resistance gene, $Ry_{\\\\\\\\mathrm{chc}}$ , mapped to the distal end of potato chromosome 9. *Euphytica*, 149, 367-372. \\\",\\\"Savenkov E I, Sandgren M, Valkonen J P. 1999. Complete sequence of RNA 1 and the presence of tRNA-like structures in all RNAs of Potato mop-top virus, genus Pomovirus. Journal of General Virology, 80, 2779-2784. \\\",\\\"da Silva W L, Ingram J, Hackett C A, Coombs J J, Douches D, Bryan G J, De Jong W, Gray S M. 2017. Mapping loci that control tuber and foliar symptoms caused by PVY in autotetraploid potato (Solanum tuberosum L.). G3 (Bethesda), 7, 3587-3595. \\\",\\\"Singh R P, Valkonen J P, Gray S M, Boonham N, Jones R A, Kerlan C, Schubert J. 2008. Discussion paper: The \\\"]\",\n \"page_idx\": \"7\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[90,73,114,83]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"374 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[290,73,707,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"XU Yi et al. / Journal of Integrative Agriculture 2020, 19(2): 367-375 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[92,115,485,797]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"naming of Potato virus Y strains infecting potato. Archive of Virology, 153, 1-13. \\\",\\\"Solomon-Blackburn R M, Barker H. 2001. Breeding virus resistant potatoes (Solanum tuberosum): A review of traditional and molecular approaches. Heredity (Edinb) 86, 17-35. \\\",\\\"Song Y S, Hepting L, Schweizer G, Hartl L, Wenzel G, Schwarzfischer A. 2005. Mapping of extreme resistance to PVY (Ry (sto)) on chromosome XII using anther-culture-derived primary dihaploid potato lines. Theoretical and Applied Genetics, 111, 879-887. \\\",\\\"Srinivasan D G, Brisson J A. 2012. Aphids: A model for polyphenism and epigenetics. Genetics Research International, 2012, 431531. \\\",\\\"Sullivan D J. 2008. Aphids (Hemiptera: Aphididae). In: Capinera JL, ed., Encyclopedia of Entomology. Springer, Dordrecht. \\\",\\\"Syller J. 2012. Facilitative and antagonistic interactions between plant viruses in mixed infections. Molecular Plant Pathology, 13, 204-216. \\\",\\\"Syller J, Grupa A. 2016. Antagonistic within-host interactions between plant viruses: Molecular basis and impact on viral and host fitness. Molecular Plant Pathology, 17, 769-782. \\\",\\\"Syller J, Marczewski W, Pawlowsicz J. 1997. Transmission by aphids of potato spindle tuber viroid encapsidated by potato leafroll luteovirus particles. European Journal of Plant Pathology, 103, 285-289. \\\",\\\"Tamborindeguy C, Bereman M S, DeBlasio S, Igwe D, Smith D M, White F, MacCoss M J, Gray S M, Cilia M. 2013. Genomic and proteomic analysis of Schizaphis graminum reveals cyclophilin proteins are involved in the transmission of cereal Yellow dwarf virus. PLoS ONE, 8, e71620. \\\",\\\"Tian Y P, Valkonen J P. 2013. Genetic determinants of Potato virus Y required to overcome or trigger hypersensitive resistance to PVY strain group O controlled by the gene Ny in potato. Molecular Plant-Microbe Interactions, 26, 297-305. \\\",\\\"Tomczynska I, Jupe F, Hein I, Marczewski W, Sliwka J. 2014. Hypersensitive response to Potato virus Y in potato cultivar Sarpo Mira is conferred by the Ny-Smira gene located on the long arm of chromosome IX. Molecular Breeding, 34, 471-480. \\\",\\\"Trebicki P, Nancarrow N, Cole E, Bosque-Perez N A, Constable F E, Freeman A J, Rodoni B, Yen A L, Luck J E, Fitzgerald G J. 2015. Virus disease in wheat predicted to increase with a changing climate. Global Change Biology, 21, 3511-3519. \\\",\\\"Tribodet M, Glais L, Kerlan C, Jacquot E. 2005. Characterization of Potato virus Y (PVY) molecular determinants involved in the vein necrosis symptom induced by PVYN isolates in infected Nicotiana tabacum cv. Xanthi. Journal of General Virology, 86, 2101-2105. \\\"]\",\n \"page_idx\": \"8\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[512,115,905,784]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Valkonen J P T. 2015. Elucidation of virus-host interactions to enhance resistance breeding for control of virus diseases in potato. Breeding Science, 65, 69-76. \\\",\\\"Valkonen J P T, Jones R A C, Slack S A, Watanabe K N. 1996. Resistance specificity to viruses in potato: Standardization of nomenclature. Plant Breeding, 115, 433-438. \\\",\\\"Valkonen J P T, Zimnoch-Guzowska E G C, Watanabe K N. 2017. Resistance to Potato virus Y in potato. In: Lacomme C, Glais L, Bellstedt D, Dupuis B, Karasev A, Jacquot E, eds., Potato Virus Y: Biodiversity, Pathogenicity, Epidemiology and Management. Springer International Publishing, Cham. pp. 207-241. \\\",\\\"Vorburger C, Lancaster M, Sunnucks P. 2003. Environmentally related patterns of reproductive modes in the aphid Myzus persicae and the predominance of two 'superclones' in Victoria, Australia. Molecular Ecology, 12, 3493-3504. \\\",\\\"De Vos M, Kim J H, Jander G. 2007. Biochemistry and molecular biology of Arabidopsis-aphid interactions. Bioessays, 29, 871-883. \\\",\\\"Wang J Y, Chay C, Gildow F E, Gray S M. 1995. Readthrough protein associated with virions of Barley yellow dwarf luteovirus and its potential role in regulating the efficiency of aphid transmission. Virology, 206, 954-962. \\\",\\\"Whitfield A E, Falk B W, Rotenberg D. 2015. Insect vector-mediated transmission of plant viruses. Virology, 479-480, 278-289. \\\",\\\"Whitworth J L, Crosslin J M. 2013. Detection of Potato mop top virus (Furovirus) on potato in southeast Idaho. Plant Disease, 97, 149. \\\",\\\"Will T, Tjallingii W F, Thönnessen A, Van Bel A J E. 2007. Molecular sabotage of plant defense by aphid saliva. Proceedings of the National Academy of Sciences of the United States of America, 104, 10536-10541. \\\",\\\"Xu H, Nie J. 2006. Identification, characterization, and molecular detection of Alfalfa mosaic virus in potato. Phytopathology, 96, 1237-1242. \\\",\\\"Xu Y, Da Silva W L, Qian Y, Gray S M. 2018. An aromatic amino acid and associated helix in the C-terminus of the potato leafroll virus minor capsid protein regulate systemic infection and symptom expression. PLoS Pathogens, 14, e1007451. \\\",\\\"Yang X, Thannhauser T W, Burrows M, Cox-Foster D, Gildow F E, Gray S M. 2008. Coupling genetics and proteomics to identify aphid proteins associated with vector-specific transmission of polerovirus (luteoviridae). Journal of Virology, 82, 291-299. \\\",\\\"Yellareddygari S K R, Whitworth J L, Gudmestad N C. 2018. Assessing potato cultivar sensitivity to tuber necrosis caused by Potato mop-top virus. Plant Disease, 102, 1148-1153. \\\"]\",\n \"page_idx\": \"8\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[289,73,707,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"XU Yi et al. / Journal of Integrative Agriculture 2020, 19(2): 367-375 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[882,73,905,83]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"375 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[638,812,905,825]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Executive Editor-in-Chief WAN Fang-hao \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[710,826,904,838]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Managing editor SUN Lu-juan \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1016/s2095-3119(19)62842-x"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Life Sciences"},"sha256":{"kind":"string","value":"f2f81b80d8fc5c469cfa05e3c24ce4e970515f844896d418f1a07931c27ada1f"},"title":{"kind":"string","value":"Aphids and their transmitted potato viruses: A continuous challenges in potato crops"}}},{"rowIdx":243,"cells":{"abstract":{"kind":"string","value":""},"author":{"kind":"string","value":"Stepan Saenko, Katharina J. Hoff, Mario Stanke"},"content_list":{"kind":"list like","value":[{"bbox":"[184,165,816,218]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Annotation of 200 Insect Genomes with BRAKER for Consistent Comparisons across Species ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[269,233,727,253]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Stepan Saenko<sup>1</sup>, Katharina J. Hoff<sup>1,2</sup>, Mario Stanke<sup>1,2</sup> ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[181,263,815,282]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{1}$ Institute of Mathematics and Computer Science, University of Greifswald, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[377,284,617,299]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Greifswald, 17489, Germany ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[148,299,846,330]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{2}$ Center for Functional Genomics of Microbes, University of Greifswald, Greifswald, 17489, Germany ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[145,364,250,383]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,396,849,441]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The annotation of genomes lags behind their sequencing and assembly. For example, of 5,092 insect species in GenBank, as one of the most widely used databases, only 375 currently have annotated genomes within this database. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,441,849,516]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Additionally, species that were previously annotated can benefit from reannotation using RNA-Seq and protein data that have been added since their last annotation, as well as from state-of-the-art annotation methods, whose accuracy has improved. Heterogeneous annotations performed with different tools and protein databases can introduce artifactual differences when comparing gene sets or gene structures between species. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,518,849,652]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Recently, the BRAKER3 annotation pipeline was introduced that integrates evidence from RNA-Seq and from a protein database. It was benchmarked as one of the most accurate annotation methods. Here, we introduce an automated genome annotation workflow that allows to annotate a list of species with BRAKER3 and VARUS for RNA-Seq retrieval, or in the absence of transcriptome data, with BRAKER2, with minimal manual intervention. We selected a diverse set of 200 insect species from different families, including 85 species previously lacking annotations in GenBank. Using currently available RNA-Seq and protein sequence data, we applied our automated workflow to annotate these genomes and conducted downstream analyses typically performed in comparative genomics studies. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,654,849,683]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We present the resulting gene structures, protein sequences, gene ontology terms, orthologous gene groups and a species tree. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[145,705,429,728]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Background & Summary ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,737,849,813]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Over the past two decades, the number of sequenced insect genomes has increased dramatically, from just twenty species twenty years ago to over 6,000 today, according to GenBank statistics [1]. Additionally, other large-scale initiatives and external databases, such as Tree of Life [2], contribute to this growing pool of genomic data. However, having access to raw data is only the first step—accurate and comprehensive genome annotations are essential to address key biological ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,2,910,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[493,847,503,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,849,150]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"questions and challenges in phylogenetics, comparative genomics, evolutionary biology, the analysis of gene functions and the study of developmental pathways. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,151,849,196]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"While the number of insect species with scaffold- or chromosome-level assemblies in GenBank has risen to 3,062 as of January 2025, the percentage of species with annotations at GenBank has decreased to only $10\\%$ , underscoring a significant annotation bottleneck (Figure 1). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[238,214,756,449]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 1: Total number of insect species in GenBank with at least scaffold level assembly and the percentage that has an annotation at GenBank \"]","image_footnote":"[]","img_path":"images/0339/fb691b205acaa906ac153bb1f52836f230b0a72b305afc1bd093596e054e4b26.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[142,516,849,621]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To maximize the benefit of genomic data, annotation pipelines must meet several criteria: algorithms must be up-to-date, raw data should be accessible, and the entire process must be reproducible; additionally, annotations must be high quality, standardized, and comparable between species. Comparability, in this context, means that observed genomic differences, such as gene truncations, the presence or absence of exons or even whole genes, or variations in gene structure, should reflect true biological distinctions rather than errors or missing genes or splice forms introduced by differing annotation methods or the use of other data sets (e.g., proteins or RNA-Seq). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,622,851,787]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Algorithm development has recently been shown to lead to improved accuracy [3-5], in addition to the progress that can be achieved when applying old algorithms to additional data. For example, the average increases in F1 scores when identifying complete protein-coding transcripts in eleven species were 4 percent points from BRAKER1 to BRAKER2 and an additional 24 percent points from BRAKER2 to BRAKER3. The latter achieved an average transcript-level F1 score of about $60\\%$ . Unfortunately, the current state of eukaryotic genome annotation is still not precise enough to ensure that all, or even most, of the structural differences identified between the annotations of closely related species can be reliably interpreted as biological variations. In addition, the problem of false positive differences can be exacerbated when annotations are generated by a variety of methods. For example, such heterogeneity in annotation methods has been shown to dramatically increase the apparent number of lineage-specific genes [6]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,787,849,816]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The recently developed BRAKER3 [4] integrates evidence from RNA-Seq in addition to evidence from a protein database, which was already integrated by BRAKER2 [7]. In both these run modes, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,2,910,36]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[493,847,503,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,849,210]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the BRAKER pipeline automatically trains the parameters of hidden Markov models using the genome and the provided evidence and predicts protein-coding genes using the evidence again, including alternative splice forms. BRAKER3 was benchmarked under controlled conditions on the similarity between database and target proteins on 11 species, including Drosophila melanogaster, Bombus terrestris and Parasteatoda tepidariorum. It performed best among the pipelines compared [4]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,210,849,376]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The BRAKER pipeline can be started with a single command line and, contrary to MAKER [8], for example, does not require manual steps. However, the RNA-Seq data and a protein database have to be provided by a user and the input genome should be repeat masked. In addition, it is advisable to perform quality control steps after annotation, such as the execution of BUSCO [9] and OMArk [10]. As such preprocessing and postprocessing steps to annotation can require substantial manual effort if done for a large number of species, we have developed an automated VARUS-BRAKER workflow that performs them automatically and integrates multiple tools: VARUS [11], which automatically collects, selects, and aligns RNA-Seq data; repeat masking; BRAKER2 [7] and BRAKER3 [4], as well as downstream tools for quality control. As a result, the new VARUS-BRAKER workflow used in this study requires minimal manual effort per genome. In its user-friendlyst run mode, only the binomial names of the species need to be input. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,377,849,436]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For the insect annotation data presented here, we focused on Holometabola and a diverse set of their outgroups, as our goal was the study of evolutionary innovations along the branch leading to the most recent ancestor of Holometabola. However, the annotation data and the orthologous groups of genes presented here can serve as a foundation for diverse other studies of insect genomics. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,436,849,587]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Holometabolous insects exhibit a unique larval stage that is morphologically distinct from the adult form. They undergo a complex transformation, with extensive reorganization and dedifferentiation of larval organs during the prepupal and pupal stages [12]. In contrast, hemimetabolous insects undergo a more gradual developmental process: their embryogenesis produces an adult-like larva that transitions into the adult form through a series of molts, with wings and genitalia typically appearing in the final molt. The origin of complete metamorphosis dates back approximately 400 million years [13] to the early Devonian period, an era marked by significant evolutionary innovations, including the emergence of winged insects (Pterygota), the advent of insect flight, and the development of holometaboly - an adaptation that likely contributed to the evolutionary success of these insects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,588,849,679]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We here present whole-genome annotations of the protein-coding genes of 200 insect species, 85 of which did not have annotations in GenBank. Gene structures were predicted with BRAKER. RNA-Seq data was integrated for all species where it was available as well as evidence from protein homology. All 4,259,838 identified proteins were functionally annotated with GO terms. We identified groups of orthologs in the whole set of 200 proteomes, and subsequently constructed multiple sequence alignments of these protein families and a maximum likelihood species tree. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[145,700,250,718]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,731,849,823]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The primary goal of this study was to address the gap in insect genome annotations by employing state-of-the-art tools, ensuring consistent annotation quality. Using the BRAKER3 pipeline [4], our objective was to minimize artifacts arising from heterogeneous annotation methods and incorporate the most current data, including protein and RNA-Seq datasets. To highlight the need for updates, we assessed the age of existing annotations using metadata from the NCBI RefSeq database, which provides reliable timestamps. Our analysis revealed a wide range of submission dates, with many ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,2,910,36]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[493,847,504,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,849,196]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"annotations dating back several years. Specifically, out of the dataset examined, approximately $75\\%$ were submitted prior to 2022. The genome annotations presented in this work were generated using publicly available genome, RNA-Seq, and protein datasets. The analysis was carried out in three key stages: input specification, structural genome annotation, and downstream processing. An overview of the analysis workflow is shown in Figure 2. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[183,207,815,712]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 2: The scheme of the VARUS-BRAKER workflow. \"]","image_footnote":"[]","img_path":"images/0809/f12e3f2d0cc02b7acc835dc8c339aedc71bbf306eca932099cbba9b6060db9c5.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[143,756,849,816]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the first stage, input specification, the user prepares a text table with pointers to the genomes and optionally to the RNA-Seq data. Each line in the table specifies one genome to be annotated. There are several ways to specify the input data. As a minimum, when genome and RNA-Seq data are accessible from Genbank and Sequence Read Archive (SRA, https://www.ncbi.nlm.nih.gov/ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,2,910,36]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[493,847,504,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,851,195]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"sra/), it is sufficient if a row just contains the species name, e.g. Aphis mellifera. In general, the table has the following columns: species name (mandatory), optional link to the genome file (file path or URL) and optional list of links for RNA-Seq data or a list of SRA IDs. If there are no genome data provided, datasets from NCBI (v14.16.0) [14] will be used to download the assembly from GenBank, giving preference to assemblies tagged 'reference'. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,196,851,301]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The second stage, structural genome annotation, encompasses all automatic steps up to and including the gene prediction. Initially, RepeatModeler2 [15] and RepeatMasker [16] generate a species-specific repeat library and soft-mask the genome. If no specific RNA-Seq data was specified, VARUS (v1.0.0) is used to automatically obtain RNA-Seq evidence. Varus uses NCBI's fastq-dump to retrieve reads from SRA. The RNA-Seq reads are then aligned to the genome with HISAT2 [17]. The resulting SAM files are converted to BAM format, merged if multiple libraries were used, sorted, and indexed using SAMtools [18]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[148,301,851,602]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To obtain data to exploit homology with known proteins, the workflow automatically determines a suitable section of OrthoDB v12 [19] from the species name and using NCBI's Taxonomy (https://www.ncbi.nlm.nih.gov/taxonomy/). This protein database is downloaded, unless already present, from https://bioinf.uni-greifswald.de/bioinf/partitioned_odb12. Then the gene models are called by the BRAKER pipeline (v3.0.3), which itself entails steps to train GeneMark-ETP [20] and AUGUSTUS [21] and predict evidence-based gene structures with them. If RNA-Seq data is available the BRAKER3 mode is used, otherwise the BRAKER2 mode to predict protein-coding gene structures from the soft-masked genome. The BRAKER3 mode requires RNA-Seq and is preferred as it was benchmarked to be significantly more accurate than BRAKER2 [4]. In BRAKER3 mode it utilizes GeneMark-ETP [22], which processes RNA-Seq alignments through StringTie2 [23] to assemble transcripts. GeneMarkS-T screens the assembled transcripts for potential genes. Additionally, DIAMOND [24] and GeneMark-EP+’s protein evidence pipeline are used to filter genes. GeneMark-ETP performs ab initio gene predictions based on self-training. Finally, AUGUSTUS is being trained on a reliable subset of predicted genes, and the final gene set is being consolidated using TSEBRA [25]. Protein evidence was incorporated during annotation, regardless whether BRAKER3 mode or BRAKER2 mode was used. This mode involves GeneMark-EP+, which self-trained GeneMark-ES to identify seed gene sequences. These sequences are then aligned to the protein database using DIAMOND, followed by accurate spliced alignment using Spaln2 [26]. The intermediate gene set generated by GeneMark-EP+ based on protein evidence was refined with AUGUSTUS. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,603,851,678]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Benchmark results comparisons to BRAKER3, when run with manually selected whole RNA-Seq libraries, are available in Section Technical Validation. Based on the experimental results, we chose a VARUS batch size of 75,000 bp and a maximum batch length of 600 bp. Increasing these parameters did not improve accuracy or precision; it only increased processing time. The optimal VARUS runtime was less than four hours. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,679,851,753]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the third and final stage, downstream processing, the workflow performs quality assessment and functional annotation. BUSCO [9] is used to assess in particular the completeness of the predicted proteomes with regards to universal single-copy genes. In addition, FANTASIA [27] is used to determine functional annotations, integrating gene ontology terms and protein-domain annotations to enhance accuracy and completeness. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,2,910,36]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[493,845,504,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,118,313,135]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Species Selection ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,143,849,218]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As basis for selecting a sample of species, we used a phylogenetic tree derived from NCBI's Taxonomy, afterwards we used the NCBITaxa module from the ete3 package [28] to handle taxonomy data, which included all insect species from the table at https://ftp.ncbi.nlm.nih.gov/genomes/GENOME_REPORTS/eukaryotes.txt with an assembly level higher than \"contig,\" resulting in a set of 3,062 species. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[148,219,851,430]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"First, a subset of species was manually selected. The remaining species were then automatically selected to maximize diversity. Manual selection used two criteria: the number of citations in Google Scholar, reflecting their scientific relevance, and the availability of RNA-Seq data in the Sequence Read Archive (SRA), ensuring sufficient transcriptomic evidence for robust annotation. To obtain the remaining species, we developed and run a custom script that identifies for a given tree, set of manually selected leaves $A$ and a given total number $n$ a set $S$ of leaves such that $A$ and $S$ together contain $n$ leaves, and the tree restricted to $S \\cup A$ and its ancestors has maximum total branch length, where the length of a branch is the number of taxonomic levels it spans. This script maxSubtreeSet.pl is included in the BRAKER-VARUS repository on GitHub. This approach maximized diversity while including species that are suitable for comparative benchmarking or that are otherwise important. The choice also strikes a balance between reannotations (115) and annotations of previously unannotated genomes (85). Species with available RNA-Seq (169) were preferred over species without (31), as the accuracy of BRAKER is much higher in the former than in the latter [4]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,430,851,565]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"With the above approach, initially, a total of 220 insect genome assemblies were retrieved from NCBI GenBank using the NCBI datasets [14] tool. The data set includes genomic data from 77 families across 14 orders. Later, we had to exclude some species from the data set due to their unsatisfactory predicted protein completeness level. All the remaining 200 species obtain $85\\%$ completeness. Nevertheless, we were able to maintain a balance between diversity and redundancy. Specifically, our taxon sampling includes the following species distributions: 40 from Lepidoptera, 34 from Hymenoptera, 24 from Hemiptera, and 20 from Coleoptera. A comprehensive list containing species, genus and accession numbers for the species' genome assemblies, is provided in Supplementary Material 1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,2,910,36]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[493,847,503,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[246,116,750,506]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 3: The taxonomy of the 200 selected species. A bright/dark blue label at the periphery of the circle marks whether annotations were done with BRAKER2 or BRAKER3, respectively. \"]","image_footnote":"[]","img_path":"images/0073/68c8d40c42067b2df3a651d04d67ee0c85d29c056bea3001b9ef74eb8c577d86.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[143,584,436,601]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Structural genome annotation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,609,849,669]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"All genome assemblies were processed with the VARUS-BRAKER workflow described above. In this use case with insects genomes, the workflow automatically retrieved the Arthropoda partition from OrthoDB v11 [19] from https://bioinf.uni-greifswald.de/bioinf/partitioned_odb11/Arthropoda.fa.gz. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,670,849,731]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The average running time of the workflow per species was approximately 20 hours, and 16 minutes, utilizing 36 CPUs, the runtime ranges from $5\\mathrm{h}09\\mathrm{min}$ for Goniozus legneri to $78\\mathrm{h}34\\mathrm{min}$ for Periplaneta americana. This includes the time for automatic download of RNA-Seq data from NCBI, which varies due to the responsiveness of the SRA server. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,748,334,766]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Orthology Analysis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,773,849,820]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The proteins predicted by BRAKER as part of the above workflow were grouped into orthogroups, representing sets of genes descended from a common ancestor. After annotating the 200 species listed in the Supplementary Table S1, we proceeded to find orthologous gene groups (orthogroups) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,3,910,36]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[493,847,503,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,851,165]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"in the whole set of 4,259,838 transcripts with OrthoFinder2 (v2.5.5) [29], which performed an all-versus-all comparison of protein sequences. OrthoFinder2 was executed with the following command: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,176,781,191]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"python orthofinder.py -f species_proteins_dir/ -M msa -A mafft -t 36 -a 36 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,200,849,244]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Here, the -M msa flag specifies that multiple sequence alignment (MSA)-based orthogroup inference is used, and -A mafft indicates that MAFFT is the chosen alignment tool. The options -t 36 and -a 36 specify the number of threads allocated for the analysis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,244,851,381]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Along the orthogroup analysis protein multiple sequence alignments with MAFFT v7.505 [30] were constructed, the corresponding protein multiple sequence alignments files were used to construct a phylogenetic tree with RAxML Next Generation (RAxML-NG) [31], using the LG+G8+F substitution model. This model consists of the fixed LG empirical amino acid substitution matrix, empirical amino acid frequencies inferred from the alignment (+F), and rate heterogeneity modeled with 8 discrete categories of a gamma distribution (+G8). Phylogenetic inference was performed with 200 bootstrap replicates. The resulting tree (200_insects_raxml.{pdf,nwk}) and the input alignment (SpeciesTreeAlignment.fa) are provided in the data deposited at figshare https://figshare.com/s/fca8b91b7c3e1871d2ae. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[169,382,517,396]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The tree was built with the following command: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,407,823,452]","code_body":"raxml-ng --all --model LG+G8+F/WAG+G8+F --tree pars{10} \\\n--bs-trees 200 --threads 36 \\\n--msa OrthoFinder2/Results/MultipleSequenceAlignments/SpeciesTreeAlignment.fa","code_caption":"[]","image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":"code","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"code"},{"bbox":"[143,462,849,492]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Among the analyzed groups, all Endopterygota species were united into a hierarchical orthogroup, highlighting their shared evolutionary history. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,492,849,551]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The entire data processing workflow, including genome annotation, functional annotation, and orthology analysis, was implemented using standardized tools and versions, as documented in the Methods section. All software and parameters used for processing are provided in Supplementary Materials. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[145,571,367,587]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Functional Annotation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,595,849,656]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Functional annotation was performed for all 200 species using the FANTASIA pipeline [27], which assigns Gene Ontology (GO) [32] IDs to transcripts. Multiple GO terms were assigned for some transcripts, reflecting their diverse functions. At the core of the FANTASIA pipeline is goPred-Sim[33], a similarity-based method for GO prediction. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,657,849,717]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"FANTASIA provides Gene Ontology terms for each protein sequence. However, these identifiers are not human-readable. To enhance interpretability, we applied an R-based solution with a package topGO [34] for translating GO IDs into human-readable terms. GO terms are classified into three categories: Biological Process (BP), Molecular Function (MF), and Cellular Component (CC). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,717,849,762]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An example of applying this approach and analyzing the functional annotation data using GO terms is demonstrated in Figure 4. We obtained human-readable terms for the GO IDs and filtered by labels having insect, larva, or pupa in the name. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,2,910,36]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[493,847,503,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[212,119,795,743]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 4: Visualization of an excerpt of the functional annotation. For selected biological processes as specified in gene ontology, the number of genes with this GO term annotation is shown. \"]","image_footnote":"[]","img_path":"images/0118/15753940ba153af4a88537bb241b4c833a66e8373ff24a06bebb8bf020bd058d.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[81,3,913,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[493,847,504,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"9 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[145,116,305,133]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data Records ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,147,849,237]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The dataset contains structural and functional annotations for 200 insect species. A taxonomic tree illustrating the relationships among these species is shown in Figure 3. The Orthofinder2 pipeline also constructs a species tree with the STAG method (Species Tree inferred from All Orthogroups). The tree topologies of this tree and the tree constructed using RAXML-NG have a Robinson-Foulds distance [35]) of $4.9\\%$ , i.e. $95.1\\%$ of all possible splits that are induced by the edges of either tree are shared by the other tree. Both trees are available in the deposited data. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,239,849,284]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figures 5 and 6 show the distributions of genome sizes and protein lengths. The average genome size is 413,245,217 bp, and the sizes range between a minimum of 86 Mb *Propsilocerus akamusi* and a maximum of 3 Gb for Periplaneta americana. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[148,297,491,458]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 5: Distribution of genome sizes \"]","image_footnote":"[]","img_path":"images/0786/8fa827ceaab2ef4866654b0e7967fc635b7dd5a5fe7a9d3339a87613454e20ee.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[503,297,846,459]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 6: Distribution of predicted protein sizes \"]","image_footnote":"[]","img_path":"images/1019/6221bcbba802f33ad76fa341e4d504beb34d46e0141f8776c2cf58a4991d7543.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[143,503,849,535]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The 200 selected species are distributed across major insect clades as follows: Endopterygota (167 species), Paraneoptera (27), Polyneoptera (3), and Palaeoptera (3). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[145,551,313,569]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data Availability ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,577,849,667]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We have deposited the dataset, including annotations, protein sequences, and OrthoFinder2 analysis in the figshare repository. All species-specific data are stored in separate .tar.gz archives. Each such archive contains four files: (i) predicted protein sequences including all isoforms, (ii) predicted protein sequences containing only the longest isoform per gene, (iii) a structural annotation file, and (iv) a structural annotation file decorated with Gene Ontology terms in .gff3.gz format. For example, Drosophila_melanogaster.tar.gz contains the four files ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,667,607,683]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Drosophila_melanogaster{. FAA,_longest.faa,.gtf,.gff3}. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,683,849,758]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Additionally, for user convenience, the structural annotation files decorated with Gene Ontology terms (.gff3.gz) have also been uploaded separately to allow direct automated access. This results in duplication, as the .gff3 files are available both individually and within the respective species archives. Furthermore, the results of OrthoFinder2 are provided in the archive OrthoFinder2_Results.tar.gz. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,758,849,804]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The genome sequences used as input for these annotations were obtained from NCBI. Details of the corresponding accession numbers, the specific BRAKER version used and whether the genomes had prior annotations are listed in Supplementary Table S1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,2,910,36]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,845,508,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,851,181]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Regrettably, it was not possible to make the annotations produced in this study available via a third party annotation (TPA) submission to GenBank. The International Nucleotide Sequence Database Collaboration had announced in September 2024 [36] that third party annotations are not accepted anymore from January 2025. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[145,203,382,220]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Technical Validation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[145,234,395,253]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Gene Structure Accuracy ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,260,849,486]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"BRAKER3 was recently evaluated and compared against other pipelines in another study by comparing the predictions against reference annotations of 11 species [4]. In doing so, input protein evidence data from species closely related to the respective evaluation species were withheld. This was done to benchmark the application use case in which a new genome should be annotated. While Gabriel et al. [4] manually selected complete RNA-Seq libraries, the BRAKER-VARUS workflow used here automatically samples from RNA-Seq data with VARUS [11]. We therefore performed comparative tests of our results against those from the original BRAKER3 publication. We selected nine model organisms as benchmarks: Danio rerio, Drosophila melanogaster, Gallus gallus, Mus musculus, Populus trichocarpa, Medicago truncatula, Parasteatoda tepidariorum, Arabidopsis thaliana, and Caenorhabditis elegans. In addition, we evaluated variations in batch size and the number of RNA-Seq datasets. Unlike the original BRAKER3 approach, in which SRA datasets were manually selected prior to testing, the RNA data provision process in this study was fully automated. Below test aimed to demonstrate that the automatic selection of RNA-Seq datasets and their alignment to a reference genome does not compromise the quality of the results. The evaluated metrics were sensitivity, specificity, and the F1-score. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,487,849,607]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The results of the benchmarking are available in Table 1. Averaging over the nine species, the accuracy of the BRAKER-VARUS workflow with automatic RNA-Seq sampling from among all libraries in SRA is very close to the accuracy of BRAKER3 when complete libraries were chosen manually. Gene- and transcript-level accuracy are slightly better in the automated workflow, and exon-level accuracy is slightly worse, all differences are at most 0.6 percent points. We therefore conclude that our fully automated BRAKER-VARUS workflow, which only requires the binomial names as manually prepared input, is on average as good as a semi-automatic approach, where RNA-Seq libraries are prepared manually. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[168,607,666,622]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The following formulas were used to calculate the evaluation metrics: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[168,633,848,732]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- Sensitivity $(\\\\mathrm{Sn}) = \\\\frac{TP}{TP + FN}$ , where $TP$ is the number of true positives, and $FN$ is the number of false negatives. \",\"- Precision $(\\\\mathrm{Pr}) = \\\\frac{TP}{TP + FP}$ , where $TP$ is the number of true positives, and $FP$ is the number of false positives. \",\"F1-score $= 2\\\\times \\\\frac{\\\\mathrm{Pr}\\\\times\\\\mathrm{Sn}}{\\\\mathrm{Pr} + \\\\mathrm{Sn}}$ \"]","page_idx":"10","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[78,2,910,36]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,845,506,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"11 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[215,116,782,619]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0996/55bef63b6c616c24772a717d9765c7604c433b6a8362a306c62d0baa3b0b933f.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":"<table><tr><td></td><td colspan=\"2\">Gene</td><td colspan=\"2\">Transcript</td><td colspan=\"2\">Exon</td></tr><tr><td></td><td>Sn</td><td>Pr</td><td>Sn</td><td>Pr</td><td>Sn</td><td>Pr</td></tr><tr><td colspan=\"7\">Caenorhabditis elegans</td></tr><tr><td>BRAKER-VARUS workflow</td><td>71.54</td><td>85.34</td><td>54.21</td><td>76.23</td><td>78.67</td><td>94.84</td></tr><tr><td>BRAKER3</td><td>68.22</td><td>85.54</td><td>51.86</td><td>77.64</td><td>75.25</td><td>95.45</td></tr><tr><td colspan=\"7\">Arabidopsis thaliana</td></tr><tr><td>BRAKER-VARUS workflow</td><td>82.64</td><td>83.08</td><td>57.64</td><td>78.14</td><td>82.12</td><td>94.08</td></tr><tr><td>BRAKER3</td><td>81.80</td><td>87.23</td><td>57.01</td><td>83.85</td><td>81.72</td><td>95.80</td></tr><tr><td colspan=\"7\">Populus trichocarpa</td></tr><tr><td>BRAKER-VARUS workflow</td><td>78.33</td><td>88.62</td><td>63.40</td><td>81.52</td><td>85.59</td><td>94.82</td></tr><tr><td>BRAKER3</td><td>77.75</td><td>88.31</td><td>63.08</td><td>82.00</td><td>85.08</td><td>94.99</td></tr><tr><td colspan=\"7\">Medicago truncatula</td></tr><tr><td>BRAKER-VARUS workflow</td><td>50.56</td><td>72.95</td><td>50.56</td><td>65.56</td><td>77.71</td><td>88.46</td></tr><tr><td>BRAKER3</td><td>49.62</td><td>73.14</td><td>49.62</td><td>66.57</td><td>76.89</td><td>88.98</td></tr><tr><td colspan=\"7\">Parasteatoda tepidariorum</td></tr><tr><td>BRAKER-VARUS workflow</td><td>44.78</td><td>59.56</td><td>37.73</td><td>54.08</td><td>49.65</td><td>87.50</td></tr><tr><td>BRAKER3</td><td>48.64</td><td>59.63</td><td>42.14</td><td>54.05</td><td>58.53</td><td>86.7</td></tr><tr><td colspan=\"7\">Danio rerio</td></tr><tr><td>BRAKER-VARUS workflow</td><td>56.84</td><td>71.11</td><td>35.30</td><td>68.06</td><td>65.85</td><td>92.73</td></tr><tr><td>BRAKER3</td><td>56.91</td><td>66.60</td><td>35.83</td><td>58.23</td><td>65.15</td><td>90.79</td></tr><tr><td colspan=\"7\">Drosophila Melanogaster</td></tr><tr><td>BRAKER-VARUS workflow</td><td>87.85</td><td>90.31</td><td>61.19</td><td>83.11</td><td>84.16</td><td>95.43</td></tr><tr><td>BRAKER3</td><td>85.67</td><td>89.89</td><td>58.66</td><td>83.69</td><td>82.88</td><td>95.75</td></tr><tr><td colspan=\"7\">Gallus Gallus</td></tr><tr><td>BRAKER-VARUS workflow</td><td>83.75</td><td>79.49</td><td>74.31</td><td>70.73</td><td>92.72</td><td>94.64</td></tr><tr><td>BRAKER3</td><td>84.87</td><td>79.57</td><td>75.95</td><td>70.07</td><td>93.92</td><td>94.52</td></tr><tr><td colspan=\"7\">Mus Musculus</td></tr><tr><td>BRAKER-VARUS workflow</td><td>72.11</td><td>83.15</td><td>72.11</td><td>80.39</td><td>77.77</td><td>97.62</td></tr><tr><td>BRAKER3</td><td>79.62</td><td>81.50</td><td>79.61</td><td>71.91</td><td>85.37</td><td>96.40</td></tr><tr><td colspan=\"7\">Average</td></tr><tr><td>BRAKER-VARUS workflow</td><td>67.51</td><td>78.71</td><td>51.43</td><td>72.39</td><td>74.82</td><td>92.55</td></tr><tr><td>BRAKER3</td><td>66.94</td><td>78.62</td><td>51.17</td><td>72.29</td><td>75.07</td><td>92.64</td></tr></table>","table_caption":"[\"Table 1: Gene Structure Accuracy (Sn=sensitivity, Pr=precision). \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[145,667,383,686]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proteome Completeness ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,693,857,756]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To obtain one quality measure about proteome completeness, we can BUSCO [9]. For each species the predicted proteomes were evaluated using a lineage-specific dataset, such as hymenoptera_odb10, lepidoptera_odb10, diptera_odb10. For the selected genomes, BUSCO showed an annotation completeness level of at least $85\\%$ . The BUSCO results are shown in Supplementary Figure S1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,3,913,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,845,509,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"12 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,118,470,135]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Overprediction or Contamination ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,143,851,189]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To obtain a second opinion on proteome completeness and to get information on overprediction or contamination, we run OMArk. OMArk reports an average completeness level of $92\\%$ and shows low contamination level (Supplementary Figure S2). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,210,344,231]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Code Availability ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,242,851,316]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The complete genome annotation workflow, including scripts and configurations for data processing, annotation, phylogenetic analysis with OrthoFinder, and Gene Ontology terms predictions with FANTASIA is available on GitHub at https://github.com/Gaius-Augustus/varus-braker/. Further details on the workflow and additional custom scripts can be found in the repository documentation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[145,340,271,358]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[147,371,851,811]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1. NCBI. Eukaryotic Genome Annotation at NCBI https://www.ncbi.nlm.nih.gov/genome/annotation_euk/. Accessed 26 February 2025. \",\"2. Maddison, D. R., Schulz, K.-S. & Maddison, W. P. The Tree of Life Web Project. Tree of Life Web Project. http://tolweb.org (2007). \",\"3. Vuruputoor, V. S. et al. Welcome to the big leaves: Best practices for improving genome annotation in non-model plant genomes. Applications in Plant Sciences 11. This article is part of the special issue \\\"Bioinformatics for Plant Biology.\\\", e11533. https://doi.org/10.1002/aps3.11533 (2023). \",\"4. Gabriel, L. et al. BRAKER3: Fully automated genome annotation using RNA-seq and protein evidence with GeneMark-ETP, AUGUSTUS, and TSEBRA. Genome Research (2024). \",\"5. Gabriel, L., Becker, F., Hoff, K. J. & Stanke, M. Tiberius: end-to-end deep learning with an HMM for gene prediction. Bioinformatics 40, btae685 (2024). \",\"6. Weisman, C. M., Murray, A. W. & Eddy, S. R. Mixing genome annotation methods in a comparative analysis inflates the apparent number of lineage-specific genes. *Current Biology* 32, 2632-2639.e2. ISSN: 0960-9822. https://doi.org/10.1016/j.cub.2022.04.085 (2022). \",\"7. Brūna, T., Hoff, K. J., Lomsadze, A., Stanke, M. & Borodovsky, M. BRAKER2: automatic eukaryotic genome annotation with GeneMark-EP+ and AUGUSTUS supported by a protein database. NAR Genomics and Bioinformatics 3, lqaa108 (2021). \",\"8. Cantarel, B. 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Nature biotechnology 43, 124-133 (2025). \"]","page_idx":"12","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[78,2,910,36]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,845,506,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"13 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[145,119,869,768]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"11. Stanke, M., Bruhn, W., Becker, F. & Hoff, K. J. VARUS: sampling complementary RNA reads from the sequence read archive. BMC bioinformatics (2019). \",\"12. Konopova, B., Smykal, V. & Jindra, M. Common and Distinct Roles of Juvenile Hormone Signaling Genes in Metamorphosis of Holometabolous and Hemimetabolous Insects. PLoS ONE 6, e28728. https://doi.org/10.1371/journal.pone.0028728 (2011). \",\"13. Thomas, Dohmen & Hughes. Gene content evolution in the arthropods. 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Sensitive protein alignments at tree-of-life scale using DIAMOND. Nature Methods 18, 366-368 (2021). \",\"25. Gabriel, Hoff & Brüna. TSEBRA: transcript selector for BRAKER. BMC bioinformatics (2021). \",\"26. Gotoh, O. in Multiple Sequence Alignment (ed Katoh, K.) 139-151 (Humana, New York, NY, 2021). \"]","page_idx":"13","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[78,2,910,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,845,508,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"14 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[145,119,851,595]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"27. Martínez-Redondo, G. I., Barrios-Núñez, I., Vázquez-Valls, M., Rojas, A. M. & Fernández, R. Illuminating the functional landscape of the dark proteome across the Animal Tree of Life through natural language processing models. bioRxiv. eprint: https://www.biorxiv.org/content/early/2024/05/29/2024.02.28.582465.full.pdf. https://www.biorxiv.org/content/early/2024/05/29/2024.02.28.582465 (2024). \",\"28. Huerta-Cepas, J., Serra, F. & Bork, P. ETE 3: Reconstruction, Analysis, and Visualization of Phylogenomic Data. Molecular Biology and Evolution 33, 1635-1638. https://doi.org/10.1093/molbev/msw046 (2016). \",\"29. Emms & Kelly. OrthoFinder: phylogenetic orthology inference for comparative genomics. Genome Biol (2019). \",\"30. Katoh & Standley. MAFFT multiple sequence alignment software version 7: improvements in performance and usability. Mol Biol Evol (2013). \",\"31. Kozlov, A. M., Darriba, D., Flouri, T., Morel, B. & Stamatakis, A. RAXML-NG: A fast, scalable, and user-friendly tool for maximum likelihood phylogenetic inference. Bioinformatics 35, 4453-4455 (2019). \",\"32. Ashburner, M. et al. Gene ontology: tool for the unification of biology. Nature Genetics 25, 25-29 (2000). \",\"33. Littmann, M., Heinzinger, M., Dallago, C., et al. Embeddings from deep learning transfer GO annotations beyond homology. *Scientific Reports* 11. https://doi.org/10.1038/s41598-020-80786-0 (2021). \",\"34. Alexa, A. & Rahnenuhrer, J. topGO: Enrichment Analysis for Gene Ontology https://bioconductor.org/packages/topGO/. R package version 2.58.0. 2024. \",\"35. Robinson, D. & Foulds, L. Comparison of phylogenetic trees. Mathematical Biosciences 53, 131-147. ISSN: 0025-5564. https://www.sciencedirect.com/science/article/pii/0025556481900432 (1981). \",\"36. INDSC. From January 2025 TPA-Exp and TPA-Inf submission types will no longer be accepted as new submissions 2024. https://www.insdc.org/news/from-january-2025-tpa-exp-and-tpa-inf-submission-types-will-no-longer-be-accepted-as-new-submissions-03-09-2024/ (2025). \"]","page_idx":"14","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[145,617,364,638]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgements ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,648,851,739]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The work was funded in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - STA 1009/15-1. The computational analyses were performed using the HPC resources provided by Greifswald University and Munster University; for the latter, we thank the group of Erich Bornberg-Bauer. We also thank Elias Dohmen for providing the instructions to the HPC resources and discussing the OrthoFinder2 workflow for orthogroup analysis, and Gregor Bucher and Lena Reim for phylogeny. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[145,761,511,780]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Author contributions statement ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,792,852,823]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S.S. implemented and ran the workflow and analyzed the data. K.H. contributed to the creation of the workflow and structure annotation postprocessing. S.S. and M.S. designed the experiments. S.S. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,2,910,36]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,845,508,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"15 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,849,137]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and M.S. wrote the draft manuscript. All authors reviewed, revised, and approved the manuscript. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[145,157,380,180]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Competing interests ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[145,190,462,205]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The authors declare no competing interests. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,2,910,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,845,508,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"16 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[184,165,816,218]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Annotation of 200 Insect Genomes with BRAKER for Consistent Comparisons across Species \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[269,233,727,253]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Stepan Saenko<sup>1</sup>, Katharina J. Hoff<sup>1,2</sup>, Mario Stanke<sup>1,2</sup> \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[181,263,815,282]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{1}$ Institute of Mathematics and Computer Science, University of Greifswald, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[377,284,617,299]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Greifswald, 17489, Germany \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[148,299,846,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{2}$ Center for Functional Genomics of Microbes, University of Greifswald, Greifswald, 17489, Germany \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,364,250,383]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,396,849,441]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The annotation of genomes lags behind their sequencing and assembly. For example, of 5,092 insect species in GenBank, as one of the most widely used databases, only 375 currently have annotated genomes within this database. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,441,849,516]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Additionally, species that were previously annotated can benefit from reannotation using RNA-Seq and protein data that have been added since their last annotation, as well as from state-of-the-art annotation methods, whose accuracy has improved. Heterogeneous annotations performed with different tools and protein databases can introduce artifactual differences when comparing gene sets or gene structures between species. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,518,849,652]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Recently, the BRAKER3 annotation pipeline was introduced that integrates evidence from RNA-Seq and from a protein database. It was benchmarked as one of the most accurate annotation methods. Here, we introduce an automated genome annotation workflow that allows to annotate a list of species with BRAKER3 and VARUS for RNA-Seq retrieval, or in the absence of transcriptome data, with BRAKER2, with minimal manual intervention. We selected a diverse set of 200 insect species from different families, including 85 species previously lacking annotations in GenBank. Using currently available RNA-Seq and protein sequence data, we applied our automated workflow to annotate these genomes and conducted downstream analyses typically performed in comparative genomics studies. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,654,849,683]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We present the resulting gene structures, protein sequences, gene ontology terms, orthologous gene groups and a species tree. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,705,429,728]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Background & Summary \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,737,849,813]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Over the past two decades, the number of sequenced insect genomes has increased dramatically, from just twenty species twenty years ago to over 6,000 today, according to GenBank statistics [1]. Additionally, other large-scale initiatives and external databases, such as Tree of Life [2], contribute to this growing pool of genomic data. However, having access to raw data is only the first step—accurate and comprehensive genome annotations are essential to address key biological \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,2,910,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[493,847,503,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,849,150]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"questions and challenges in phylogenetics, comparative genomics, evolutionary biology, the analysis of gene functions and the study of developmental pathways. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,151,849,196]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"While the number of insect species with scaffold- or chromosome-level assemblies in GenBank has risen to 3,062 as of January 2025, the percentage of species with annotations at GenBank has decreased to only $10\\\\%$ , underscoring a significant annotation bottleneck (Figure 1). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[238,214,756,449]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 1: Total number of insect species in GenBank with at least scaffold level assembly and the percentage that has an annotation at GenBank \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0339/fb691b205acaa906ac153bb1f52836f230b0a72b305afc1bd093596e054e4b26.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[142,516,849,621]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To maximize the benefit of genomic data, annotation pipelines must meet several criteria: algorithms must be up-to-date, raw data should be accessible, and the entire process must be reproducible; additionally, annotations must be high quality, standardized, and comparable between species. Comparability, in this context, means that observed genomic differences, such as gene truncations, the presence or absence of exons or even whole genes, or variations in gene structure, should reflect true biological distinctions rather than errors or missing genes or splice forms introduced by differing annotation methods or the use of other data sets (e.g., proteins or RNA-Seq). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,622,851,787]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Algorithm development has recently been shown to lead to improved accuracy [3-5], in addition to the progress that can be achieved when applying old algorithms to additional data. For example, the average increases in F1 scores when identifying complete protein-coding transcripts in eleven species were 4 percent points from BRAKER1 to BRAKER2 and an additional 24 percent points from BRAKER2 to BRAKER3. The latter achieved an average transcript-level F1 score of about $60\\\\%$ . Unfortunately, the current state of eukaryotic genome annotation is still not precise enough to ensure that all, or even most, of the structural differences identified between the annotations of closely related species can be reliably interpreted as biological variations. In addition, the problem of false positive differences can be exacerbated when annotations are generated by a variety of methods. For example, such heterogeneity in annotation methods has been shown to dramatically increase the apparent number of lineage-specific genes [6]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,787,849,816]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The recently developed BRAKER3 [4] integrates evidence from RNA-Seq in addition to evidence from a protein database, which was already integrated by BRAKER2 [7]. In both these run modes, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,2,910,36]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[493,847,503,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,849,210]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the BRAKER pipeline automatically trains the parameters of hidden Markov models using the genome and the provided evidence and predicts protein-coding genes using the evidence again, including alternative splice forms. BRAKER3 was benchmarked under controlled conditions on the similarity between database and target proteins on 11 species, including Drosophila melanogaster, Bombus terrestris and Parasteatoda tepidariorum. It performed best among the pipelines compared [4]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,210,849,376]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The BRAKER pipeline can be started with a single command line and, contrary to MAKER [8], for example, does not require manual steps. However, the RNA-Seq data and a protein database have to be provided by a user and the input genome should be repeat masked. In addition, it is advisable to perform quality control steps after annotation, such as the execution of BUSCO [9] and OMArk [10]. As such preprocessing and postprocessing steps to annotation can require substantial manual effort if done for a large number of species, we have developed an automated VARUS-BRAKER workflow that performs them automatically and integrates multiple tools: VARUS [11], which automatically collects, selects, and aligns RNA-Seq data; repeat masking; BRAKER2 [7] and BRAKER3 [4], as well as downstream tools for quality control. As a result, the new VARUS-BRAKER workflow used in this study requires minimal manual effort per genome. In its user-friendlyst run mode, only the binomial names of the species need to be input. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,377,849,436]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For the insect annotation data presented here, we focused on Holometabola and a diverse set of their outgroups, as our goal was the study of evolutionary innovations along the branch leading to the most recent ancestor of Holometabola. However, the annotation data and the orthologous groups of genes presented here can serve as a foundation for diverse other studies of insect genomics. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,436,849,587]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Holometabolous insects exhibit a unique larval stage that is morphologically distinct from the adult form. They undergo a complex transformation, with extensive reorganization and dedifferentiation of larval organs during the prepupal and pupal stages [12]. In contrast, hemimetabolous insects undergo a more gradual developmental process: their embryogenesis produces an adult-like larva that transitions into the adult form through a series of molts, with wings and genitalia typically appearing in the final molt. The origin of complete metamorphosis dates back approximately 400 million years [13] to the early Devonian period, an era marked by significant evolutionary innovations, including the emergence of winged insects (Pterygota), the advent of insect flight, and the development of holometaboly - an adaptation that likely contributed to the evolutionary success of these insects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,588,849,679]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We here present whole-genome annotations of the protein-coding genes of 200 insect species, 85 of which did not have annotations in GenBank. Gene structures were predicted with BRAKER. RNA-Seq data was integrated for all species where it was available as well as evidence from protein homology. All 4,259,838 identified proteins were functionally annotated with GO terms. We identified groups of orthologs in the whole set of 200 proteomes, and subsequently constructed multiple sequence alignments of these protein families and a maximum likelihood species tree. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,700,250,718]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,731,849,823]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The primary goal of this study was to address the gap in insect genome annotations by employing state-of-the-art tools, ensuring consistent annotation quality. Using the BRAKER3 pipeline [4], our objective was to minimize artifacts arising from heterogeneous annotation methods and incorporate the most current data, including protein and RNA-Seq datasets. To highlight the need for updates, we assessed the age of existing annotations using metadata from the NCBI RefSeq database, which provides reliable timestamps. Our analysis revealed a wide range of submission dates, with many \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,2,910,36]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[493,847,504,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,849,196]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"annotations dating back several years. Specifically, out of the dataset examined, approximately $75\\\\%$ were submitted prior to 2022. The genome annotations presented in this work were generated using publicly available genome, RNA-Seq, and protein datasets. The analysis was carried out in three key stages: input specification, structural genome annotation, and downstream processing. An overview of the analysis workflow is shown in Figure 2. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[183,207,815,712]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 2: The scheme of the VARUS-BRAKER workflow. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0809/f12e3f2d0cc02b7acc835dc8c339aedc71bbf306eca932099cbba9b6060db9c5.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[143,756,849,816]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the first stage, input specification, the user prepares a text table with pointers to the genomes and optionally to the RNA-Seq data. Each line in the table specifies one genome to be annotated. There are several ways to specify the input data. As a minimum, when genome and RNA-Seq data are accessible from Genbank and Sequence Read Archive (SRA, https://www.ncbi.nlm.nih.gov/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,2,910,36]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[493,847,504,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,851,195]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"sra/), it is sufficient if a row just contains the species name, e.g. Aphis mellifera. In general, the table has the following columns: species name (mandatory), optional link to the genome file (file path or URL) and optional list of links for RNA-Seq data or a list of SRA IDs. If there are no genome data provided, datasets from NCBI (v14.16.0) [14] will be used to download the assembly from GenBank, giving preference to assemblies tagged 'reference'. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,196,851,301]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The second stage, structural genome annotation, encompasses all automatic steps up to and including the gene prediction. Initially, RepeatModeler2 [15] and RepeatMasker [16] generate a species-specific repeat library and soft-mask the genome. If no specific RNA-Seq data was specified, VARUS (v1.0.0) is used to automatically obtain RNA-Seq evidence. Varus uses NCBI's fastq-dump to retrieve reads from SRA. The RNA-Seq reads are then aligned to the genome with HISAT2 [17]. The resulting SAM files are converted to BAM format, merged if multiple libraries were used, sorted, and indexed using SAMtools [18]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[148,301,851,602]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To obtain data to exploit homology with known proteins, the workflow automatically determines a suitable section of OrthoDB v12 [19] from the species name and using NCBI's Taxonomy (https://www.ncbi.nlm.nih.gov/taxonomy/). This protein database is downloaded, unless already present, from https://bioinf.uni-greifswald.de/bioinf/partitioned_odb12. Then the gene models are called by the BRAKER pipeline (v3.0.3), which itself entails steps to train GeneMark-ETP [20] and AUGUSTUS [21] and predict evidence-based gene structures with them. If RNA-Seq data is available the BRAKER3 mode is used, otherwise the BRAKER2 mode to predict protein-coding gene structures from the soft-masked genome. The BRAKER3 mode requires RNA-Seq and is preferred as it was benchmarked to be significantly more accurate than BRAKER2 [4]. In BRAKER3 mode it utilizes GeneMark-ETP [22], which processes RNA-Seq alignments through StringTie2 [23] to assemble transcripts. GeneMarkS-T screens the assembled transcripts for potential genes. Additionally, DIAMOND [24] and GeneMark-EP+’s protein evidence pipeline are used to filter genes. GeneMark-ETP performs ab initio gene predictions based on self-training. Finally, AUGUSTUS is being trained on a reliable subset of predicted genes, and the final gene set is being consolidated using TSEBRA [25]. Protein evidence was incorporated during annotation, regardless whether BRAKER3 mode or BRAKER2 mode was used. This mode involves GeneMark-EP+, which self-trained GeneMark-ES to identify seed gene sequences. These sequences are then aligned to the protein database using DIAMOND, followed by accurate spliced alignment using Spaln2 [26]. The intermediate gene set generated by GeneMark-EP+ based on protein evidence was refined with AUGUSTUS. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,603,851,678]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Benchmark results comparisons to BRAKER3, when run with manually selected whole RNA-Seq libraries, are available in Section Technical Validation. Based on the experimental results, we chose a VARUS batch size of 75,000 bp and a maximum batch length of 600 bp. Increasing these parameters did not improve accuracy or precision; it only increased processing time. The optimal VARUS runtime was less than four hours. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,679,851,753]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the third and final stage, downstream processing, the workflow performs quality assessment and functional annotation. BUSCO [9] is used to assess in particular the completeness of the predicted proteomes with regards to universal single-copy genes. In addition, FANTASIA [27] is used to determine functional annotations, integrating gene ontology terms and protein-domain annotations to enhance accuracy and completeness. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,2,910,36]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[493,845,504,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,118,313,135]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Species Selection \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,143,849,218]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As basis for selecting a sample of species, we used a phylogenetic tree derived from NCBI's Taxonomy, afterwards we used the NCBITaxa module from the ete3 package [28] to handle taxonomy data, which included all insect species from the table at https://ftp.ncbi.nlm.nih.gov/genomes/GENOME_REPORTS/eukaryotes.txt with an assembly level higher than \\\"contig,\\\" resulting in a set of 3,062 species. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[148,219,851,430]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"First, a subset of species was manually selected. The remaining species were then automatically selected to maximize diversity. Manual selection used two criteria: the number of citations in Google Scholar, reflecting their scientific relevance, and the availability of RNA-Seq data in the Sequence Read Archive (SRA), ensuring sufficient transcriptomic evidence for robust annotation. To obtain the remaining species, we developed and run a custom script that identifies for a given tree, set of manually selected leaves $A$ and a given total number $n$ a set $S$ of leaves such that $A$ and $S$ together contain $n$ leaves, and the tree restricted to $S \\\\cup A$ and its ancestors has maximum total branch length, where the length of a branch is the number of taxonomic levels it spans. This script maxSubtreeSet.pl is included in the BRAKER-VARUS repository on GitHub. This approach maximized diversity while including species that are suitable for comparative benchmarking or that are otherwise important. The choice also strikes a balance between reannotations (115) and annotations of previously unannotated genomes (85). Species with available RNA-Seq (169) were preferred over species without (31), as the accuracy of BRAKER is much higher in the former than in the latter [4]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,430,851,565]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"With the above approach, initially, a total of 220 insect genome assemblies were retrieved from NCBI GenBank using the NCBI datasets [14] tool. The data set includes genomic data from 77 families across 14 orders. Later, we had to exclude some species from the data set due to their unsatisfactory predicted protein completeness level. All the remaining 200 species obtain $85\\\\%$ completeness. Nevertheless, we were able to maintain a balance between diversity and redundancy. Specifically, our taxon sampling includes the following species distributions: 40 from Lepidoptera, 34 from Hymenoptera, 24 from Hemiptera, and 20 from Coleoptera. A comprehensive list containing species, genus and accession numbers for the species' genome assemblies, is provided in Supplementary Material 1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,2,910,36]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[493,847,503,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[246,116,750,506]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 3: The taxonomy of the 200 selected species. A bright/dark blue label at the periphery of the circle marks whether annotations were done with BRAKER2 or BRAKER3, respectively. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0073/68c8d40c42067b2df3a651d04d67ee0c85d29c056bea3001b9ef74eb8c577d86.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[143,584,436,601]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Structural genome annotation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,609,849,669]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"All genome assemblies were processed with the VARUS-BRAKER workflow described above. In this use case with insects genomes, the workflow automatically retrieved the Arthropoda partition from OrthoDB v11 [19] from https://bioinf.uni-greifswald.de/bioinf/partitioned_odb11/Arthropoda.fa.gz. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,670,849,731]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The average running time of the workflow per species was approximately 20 hours, and 16 minutes, utilizing 36 CPUs, the runtime ranges from $5\\\\mathrm{h}09\\\\mathrm{min}$ for Goniozus legneri to $78\\\\mathrm{h}34\\\\mathrm{min}$ for Periplaneta americana. This includes the time for automatic download of RNA-Seq data from NCBI, which varies due to the responsiveness of the SRA server. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,748,334,766]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Orthology Analysis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,773,849,820]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The proteins predicted by BRAKER as part of the above workflow were grouped into orthogroups, representing sets of genes descended from a common ancestor. After annotating the 200 species listed in the Supplementary Table S1, we proceeded to find orthologous gene groups (orthogroups) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,3,910,36]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[493,847,503,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,851,165]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"in the whole set of 4,259,838 transcripts with OrthoFinder2 (v2.5.5) [29], which performed an all-versus-all comparison of protein sequences. OrthoFinder2 was executed with the following command: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,176,781,191]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"python orthofinder.py -f species_proteins_dir/ -M msa -A mafft -t 36 -a 36 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,200,849,244]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Here, the -M msa flag specifies that multiple sequence alignment (MSA)-based orthogroup inference is used, and -A mafft indicates that MAFFT is the chosen alignment tool. The options -t 36 and -a 36 specify the number of threads allocated for the analysis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,244,851,381]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Along the orthogroup analysis protein multiple sequence alignments with MAFFT v7.505 [30] were constructed, the corresponding protein multiple sequence alignments files were used to construct a phylogenetic tree with RAxML Next Generation (RAxML-NG) [31], using the LG+G8+F substitution model. This model consists of the fixed LG empirical amino acid substitution matrix, empirical amino acid frequencies inferred from the alignment (+F), and rate heterogeneity modeled with 8 discrete categories of a gamma distribution (+G8). Phylogenetic inference was performed with 200 bootstrap replicates. The resulting tree (200_insects_raxml.{pdf,nwk}) and the input alignment (SpeciesTreeAlignment.fa) are provided in the data deposited at figshare https://figshare.com/s/fca8b91b7c3e1871d2ae. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[169,382,517,396]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The tree was built with the following command: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,407,823,452]\",\n \"code_body\": \"raxml-ng --all --model LG+G8+F/WAG+G8+F --tree pars{10} \\\\\\n--bs-trees 200 --threads 36 \\\\\\n--msa OrthoFinder2/Results/MultipleSequenceAlignments/SpeciesTreeAlignment.fa\",\n \"code_caption\": \"[]\",\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": \"code\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"code\"\n },\n {\n \"bbox\": \"[143,462,849,492]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Among the analyzed groups, all Endopterygota species were united into a hierarchical orthogroup, highlighting their shared evolutionary history. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,492,849,551]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The entire data processing workflow, including genome annotation, functional annotation, and orthology analysis, was implemented using standardized tools and versions, as documented in the Methods section. All software and parameters used for processing are provided in Supplementary Materials. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,571,367,587]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Functional Annotation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,595,849,656]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Functional annotation was performed for all 200 species using the FANTASIA pipeline [27], which assigns Gene Ontology (GO) [32] IDs to transcripts. Multiple GO terms were assigned for some transcripts, reflecting their diverse functions. At the core of the FANTASIA pipeline is goPred-Sim[33], a similarity-based method for GO prediction. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,657,849,717]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"FANTASIA provides Gene Ontology terms for each protein sequence. However, these identifiers are not human-readable. To enhance interpretability, we applied an R-based solution with a package topGO [34] for translating GO IDs into human-readable terms. GO terms are classified into three categories: Biological Process (BP), Molecular Function (MF), and Cellular Component (CC). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,717,849,762]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An example of applying this approach and analyzing the functional annotation data using GO terms is demonstrated in Figure 4. We obtained human-readable terms for the GO IDs and filtered by labels having insect, larva, or pupa in the name. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,2,910,36]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[493,847,503,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[212,119,795,743]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 4: Visualization of an excerpt of the functional annotation. For selected biological processes as specified in gene ontology, the number of genes with this GO term annotation is shown. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0118/15753940ba153af4a88537bb241b4c833a66e8373ff24a06bebb8bf020bd058d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[81,3,913,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[493,847,504,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"9 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[145,116,305,133]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data Records \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,147,849,237]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The dataset contains structural and functional annotations for 200 insect species. A taxonomic tree illustrating the relationships among these species is shown in Figure 3. The Orthofinder2 pipeline also constructs a species tree with the STAG method (Species Tree inferred from All Orthogroups). The tree topologies of this tree and the tree constructed using RAXML-NG have a Robinson-Foulds distance [35]) of $4.9\\\\%$ , i.e. $95.1\\\\%$ of all possible splits that are induced by the edges of either tree are shared by the other tree. Both trees are available in the deposited data. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,239,849,284]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figures 5 and 6 show the distributions of genome sizes and protein lengths. The average genome size is 413,245,217 bp, and the sizes range between a minimum of 86 Mb *Propsilocerus akamusi* and a maximum of 3 Gb for Periplaneta americana. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[148,297,491,458]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 5: Distribution of genome sizes \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0786/8fa827ceaab2ef4866654b0e7967fc635b7dd5a5fe7a9d3339a87613454e20ee.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[503,297,846,459]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 6: Distribution of predicted protein sizes \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/1019/6221bcbba802f33ad76fa341e4d504beb34d46e0141f8776c2cf58a4991d7543.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[143,503,849,535]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The 200 selected species are distributed across major insect clades as follows: Endopterygota (167 species), Paraneoptera (27), Polyneoptera (3), and Palaeoptera (3). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,551,313,569]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data Availability \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,577,849,667]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We have deposited the dataset, including annotations, protein sequences, and OrthoFinder2 analysis in the figshare repository. All species-specific data are stored in separate .tar.gz archives. Each such archive contains four files: (i) predicted protein sequences including all isoforms, (ii) predicted protein sequences containing only the longest isoform per gene, (iii) a structural annotation file, and (iv) a structural annotation file decorated with Gene Ontology terms in .gff3.gz format. For example, Drosophila_melanogaster.tar.gz contains the four files \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,667,607,683]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Drosophila_melanogaster{. FAA,_longest.faa,.gtf,.gff3}. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,683,849,758]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Additionally, for user convenience, the structural annotation files decorated with Gene Ontology terms (.gff3.gz) have also been uploaded separately to allow direct automated access. This results in duplication, as the .gff3 files are available both individually and within the respective species archives. Furthermore, the results of OrthoFinder2 are provided in the archive OrthoFinder2_Results.tar.gz. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,758,849,804]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The genome sequences used as input for these annotations were obtained from NCBI. Details of the corresponding accession numbers, the specific BRAKER version used and whether the genomes had prior annotations are listed in Supplementary Table S1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,2,910,36]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,845,508,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,851,181]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Regrettably, it was not possible to make the annotations produced in this study available via a third party annotation (TPA) submission to GenBank. The International Nucleotide Sequence Database Collaboration had announced in September 2024 [36] that third party annotations are not accepted anymore from January 2025. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,203,382,220]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Technical Validation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,234,395,253]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Gene Structure Accuracy \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,260,849,486]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"BRAKER3 was recently evaluated and compared against other pipelines in another study by comparing the predictions against reference annotations of 11 species [4]. In doing so, input protein evidence data from species closely related to the respective evaluation species were withheld. This was done to benchmark the application use case in which a new genome should be annotated. While Gabriel et al. [4] manually selected complete RNA-Seq libraries, the BRAKER-VARUS workflow used here automatically samples from RNA-Seq data with VARUS [11]. We therefore performed comparative tests of our results against those from the original BRAKER3 publication. We selected nine model organisms as benchmarks: Danio rerio, Drosophila melanogaster, Gallus gallus, Mus musculus, Populus trichocarpa, Medicago truncatula, Parasteatoda tepidariorum, Arabidopsis thaliana, and Caenorhabditis elegans. In addition, we evaluated variations in batch size and the number of RNA-Seq datasets. Unlike the original BRAKER3 approach, in which SRA datasets were manually selected prior to testing, the RNA data provision process in this study was fully automated. Below test aimed to demonstrate that the automatic selection of RNA-Seq datasets and their alignment to a reference genome does not compromise the quality of the results. The evaluated metrics were sensitivity, specificity, and the F1-score. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,487,849,607]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The results of the benchmarking are available in Table 1. Averaging over the nine species, the accuracy of the BRAKER-VARUS workflow with automatic RNA-Seq sampling from among all libraries in SRA is very close to the accuracy of BRAKER3 when complete libraries were chosen manually. Gene- and transcript-level accuracy are slightly better in the automated workflow, and exon-level accuracy is slightly worse, all differences are at most 0.6 percent points. We therefore conclude that our fully automated BRAKER-VARUS workflow, which only requires the binomial names as manually prepared input, is on average as good as a semi-automatic approach, where RNA-Seq libraries are prepared manually. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[168,607,666,622]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The following formulas were used to calculate the evaluation metrics: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[168,633,848,732]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- Sensitivity $(\\\\\\\\mathrm{Sn}) = \\\\\\\\frac{TP}{TP + FN}$ , where $TP$ is the number of true positives, and $FN$ is the number of false negatives. \\\",\\\"- Precision $(\\\\\\\\mathrm{Pr}) = \\\\\\\\frac{TP}{TP + FP}$ , where $TP$ is the number of true positives, and $FP$ is the number of false positives. \\\",\\\"F1-score $= 2\\\\\\\\times \\\\\\\\frac{\\\\\\\\mathrm{Pr}\\\\\\\\times\\\\\\\\mathrm{Sn}}{\\\\\\\\mathrm{Pr} + \\\\\\\\mathrm{Sn}}$ \\\"]\",\n \"page_idx\": \"10\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[78,2,910,36]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,845,506,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"11 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[215,116,782,619]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0996/55bef63b6c616c24772a717d9765c7604c433b6a8362a306c62d0baa3b0b933f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td></td><td colspan=\\\"2\\\">Gene</td><td colspan=\\\"2\\\">Transcript</td><td colspan=\\\"2\\\">Exon</td></tr><tr><td></td><td>Sn</td><td>Pr</td><td>Sn</td><td>Pr</td><td>Sn</td><td>Pr</td></tr><tr><td colspan=\\\"7\\\">Caenorhabditis elegans</td></tr><tr><td>BRAKER-VARUS workflow</td><td>71.54</td><td>85.34</td><td>54.21</td><td>76.23</td><td>78.67</td><td>94.84</td></tr><tr><td>BRAKER3</td><td>68.22</td><td>85.54</td><td>51.86</td><td>77.64</td><td>75.25</td><td>95.45</td></tr><tr><td colspan=\\\"7\\\">Arabidopsis thaliana</td></tr><tr><td>BRAKER-VARUS workflow</td><td>82.64</td><td>83.08</td><td>57.64</td><td>78.14</td><td>82.12</td><td>94.08</td></tr><tr><td>BRAKER3</td><td>81.80</td><td>87.23</td><td>57.01</td><td>83.85</td><td>81.72</td><td>95.80</td></tr><tr><td colspan=\\\"7\\\">Populus trichocarpa</td></tr><tr><td>BRAKER-VARUS workflow</td><td>78.33</td><td>88.62</td><td>63.40</td><td>81.52</td><td>85.59</td><td>94.82</td></tr><tr><td>BRAKER3</td><td>77.75</td><td>88.31</td><td>63.08</td><td>82.00</td><td>85.08</td><td>94.99</td></tr><tr><td colspan=\\\"7\\\">Medicago truncatula</td></tr><tr><td>BRAKER-VARUS workflow</td><td>50.56</td><td>72.95</td><td>50.56</td><td>65.56</td><td>77.71</td><td>88.46</td></tr><tr><td>BRAKER3</td><td>49.62</td><td>73.14</td><td>49.62</td><td>66.57</td><td>76.89</td><td>88.98</td></tr><tr><td colspan=\\\"7\\\">Parasteatoda tepidariorum</td></tr><tr><td>BRAKER-VARUS workflow</td><td>44.78</td><td>59.56</td><td>37.73</td><td>54.08</td><td>49.65</td><td>87.50</td></tr><tr><td>BRAKER3</td><td>48.64</td><td>59.63</td><td>42.14</td><td>54.05</td><td>58.53</td><td>86.7</td></tr><tr><td colspan=\\\"7\\\">Danio rerio</td></tr><tr><td>BRAKER-VARUS workflow</td><td>56.84</td><td>71.11</td><td>35.30</td><td>68.06</td><td>65.85</td><td>92.73</td></tr><tr><td>BRAKER3</td><td>56.91</td><td>66.60</td><td>35.83</td><td>58.23</td><td>65.15</td><td>90.79</td></tr><tr><td colspan=\\\"7\\\">Drosophila Melanogaster</td></tr><tr><td>BRAKER-VARUS workflow</td><td>87.85</td><td>90.31</td><td>61.19</td><td>83.11</td><td>84.16</td><td>95.43</td></tr><tr><td>BRAKER3</td><td>85.67</td><td>89.89</td><td>58.66</td><td>83.69</td><td>82.88</td><td>95.75</td></tr><tr><td colspan=\\\"7\\\">Gallus Gallus</td></tr><tr><td>BRAKER-VARUS workflow</td><td>83.75</td><td>79.49</td><td>74.31</td><td>70.73</td><td>92.72</td><td>94.64</td></tr><tr><td>BRAKER3</td><td>84.87</td><td>79.57</td><td>75.95</td><td>70.07</td><td>93.92</td><td>94.52</td></tr><tr><td colspan=\\\"7\\\">Mus Musculus</td></tr><tr><td>BRAKER-VARUS workflow</td><td>72.11</td><td>83.15</td><td>72.11</td><td>80.39</td><td>77.77</td><td>97.62</td></tr><tr><td>BRAKER3</td><td>79.62</td><td>81.50</td><td>79.61</td><td>71.91</td><td>85.37</td><td>96.40</td></tr><tr><td colspan=\\\"7\\\">Average</td></tr><tr><td>BRAKER-VARUS workflow</td><td>67.51</td><td>78.71</td><td>51.43</td><td>72.39</td><td>74.82</td><td>92.55</td></tr><tr><td>BRAKER3</td><td>66.94</td><td>78.62</td><td>51.17</td><td>72.29</td><td>75.07</td><td>92.64</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1: Gene Structure Accuracy (Sn=sensitivity, Pr=precision). \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[145,667,383,686]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proteome Completeness \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,693,857,756]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To obtain one quality measure about proteome completeness, we can BUSCO [9]. For each species the predicted proteomes were evaluated using a lineage-specific dataset, such as hymenoptera_odb10, lepidoptera_odb10, diptera_odb10. For the selected genomes, BUSCO showed an annotation completeness level of at least $85\\\\%$ . The BUSCO results are shown in Supplementary Figure S1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,3,913,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,845,509,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"12 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,118,470,135]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Overprediction or Contamination \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,143,851,189]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To obtain a second opinion on proteome completeness and to get information on overprediction or contamination, we run OMArk. OMArk reports an average completeness level of $92\\\\%$ and shows low contamination level (Supplementary Figure S2). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,210,344,231]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Code Availability \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,242,851,316]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The complete genome annotation workflow, including scripts and configurations for data processing, annotation, phylogenetic analysis with OrthoFinder, and Gene Ontology terms predictions with FANTASIA is available on GitHub at https://github.com/Gaius-Augustus/varus-braker/. Further details on the workflow and additional custom scripts can be found in the repository documentation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,340,271,358]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[147,371,851,811]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1. NCBI. Eukaryotic Genome Annotation at NCBI https://www.ncbi.nlm.nih.gov/genome/annotation_euk/. Accessed 26 February 2025. \\\",\\\"2. Maddison, D. R., Schulz, K.-S. & Maddison, W. P. The Tree of Life Web Project. Tree of Life Web Project. http://tolweb.org (2007). \\\",\\\"3. Vuruputoor, V. S. et al. Welcome to the big leaves: Best practices for improving genome annotation in non-model plant genomes. Applications in Plant Sciences 11. This article is part of the special issue \\\\\\\"Bioinformatics for Plant Biology.\\\\\\\", e11533. https://doi.org/10.1002/aps3.11533 (2023). \\\",\\\"4. Gabriel, L. et al. BRAKER3: Fully automated genome annotation using RNA-seq and protein evidence with GeneMark-ETP, AUGUSTUS, and TSEBRA. Genome Research (2024). \\\",\\\"5. Gabriel, L., Becker, F., Hoff, K. J. & Stanke, M. Tiberius: end-to-end deep learning with an HMM for gene prediction. Bioinformatics 40, btae685 (2024). \\\",\\\"6. Weisman, C. M., Murray, A. W. & Eddy, S. R. Mixing genome annotation methods in a comparative analysis inflates the apparent number of lineage-specific genes. *Current Biology* 32, 2632-2639.e2. ISSN: 0960-9822. https://doi.org/10.1016/j.cub.2022.04.085 (2022). \\\",\\\"7. Brūna, T., Hoff, K. J., Lomsadze, A., Stanke, M. & Borodovsky, M. BRAKER2: automatic eukaryotic genome annotation with GeneMark-EP+ and AUGUSTUS supported by a protein database. NAR Genomics and Bioinformatics 3, lqaa108 (2021). \\\",\\\"8. Cantarel, B. L. et al. MAKER: an easy-to-use annotation pipeline designed for emerging model organism genomes. Genome research 18, 188-196 (2008). \\\",\\\"9. Manni, M., Berkeley, M. R., Seppey, M., Simão, F. A. & Zdobnov, E. M. BUSCO Update: Novel and Streamlined Workflows along with Broader and Deeper Phylogenetic Coverage for Scoring of Eukaryotic, Prokaryotic, and Viral Genomes. Molecular Biology and Evolution 38, 4647-4654 (2021). \\\",\\\"10. Nevers, Y. et al. Quality assessment of gene repertoire annotations with OMArk. Nature biotechnology 43, 124-133 (2025). \\\"]\",\n \"page_idx\": \"12\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[78,2,910,36]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,845,506,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"13 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[145,119,869,768]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"11. Stanke, M., Bruhn, W., Becker, F. & Hoff, K. J. VARUS: sampling complementary RNA reads from the sequence read archive. BMC bioinformatics (2019). \\\",\\\"12. Konopova, B., Smykal, V. & Jindra, M. 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ISSN: 2047-217X. eprint: https://academic.oup.com/gigascience/article-pdf/10/2/giab008/36332246/giab008.pdf. https://doi.org/10.1093/gigascience/giab008(Feb.2021). \\\",\\\"19. Zdobnov, E. M. et al. OrthoDB in 2020: evolutionary and functional annotations of orthologs. Nucleic Acids Research 49, D389-D393. ISSN: 0305-1048. eprint: https://academic.oup.com/nar/article-pdf/49/D1/D389/35363966/gkaa1009.pdf. https://doi.org/10.1093/nar/gkaa1009 (Nov. 2020). \\\",\\\"20. Brūna, T., Lomsadze, A. & Borodovsky, M. GeneMark-ETP significantly improves the accuracy of automatic annotation of large eukaryotic genomes. Genome Research 34, 757-768 (2024). \\\",\\\"21. Stanke, M., Diekhans, M., Baertsch, R. & Haussler, D. Using native and syntenically mapped cDNA alignments to improve de novo gene finding. Bioinformatics 24, 637-644 (2008). \\\",\\\"22. Brūna, T., Lomsadze, A. & Borodovsky, M. GeneMark-ETP significantly improves the accuracy of automatic annotation of large eukaryotic genomes. 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Gotoh, O. in Multiple Sequence Alignment (ed Katoh, K.) 139-151 (Humana, New York, NY, 2021). \\\"]\",\n \"page_idx\": \"13\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[78,2,910,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,845,508,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"14 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[145,119,851,595]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"27. Martínez-Redondo, G. I., Barrios-Núñez, I., Vázquez-Valls, M., Rojas, A. M. & Fernández, R. Illuminating the functional landscape of the dark proteome across the Animal Tree of Life through natural language processing models. bioRxiv. eprint: https://www.biorxiv.org/content/early/2024/05/29/2024.02.28.582465.full.pdf. https://www.biorxiv.org/content/early/2024/05/29/2024.02.28.582465 (2024). \\\",\\\"28. Huerta-Cepas, J., Serra, F. & Bork, P. ETE 3: Reconstruction, Analysis, and Visualization of Phylogenomic Data. Molecular Biology and Evolution 33, 1635-1638. https://doi.org/10.1093/molbev/msw046 (2016). \\\",\\\"29. Emms & Kelly. OrthoFinder: phylogenetic orthology inference for comparative genomics. Genome Biol (2019). \\\",\\\"30. Katoh & Standley. MAFFT multiple sequence alignment software version 7: improvements in performance and usability. Mol Biol Evol (2013). \\\",\\\"31. Kozlov, A. M., Darriba, D., Flouri, T., Morel, B. & Stamatakis, A. RAXML-NG: A fast, scalable, and user-friendly tool for maximum likelihood phylogenetic inference. Bioinformatics 35, 4453-4455 (2019). \\\",\\\"32. Ashburner, M. et al. Gene ontology: tool for the unification of biology. Nature Genetics 25, 25-29 (2000). \\\",\\\"33. Littmann, M., Heinzinger, M., Dallago, C., et al. Embeddings from deep learning transfer GO annotations beyond homology. *Scientific Reports* 11. https://doi.org/10.1038/s41598-020-80786-0 (2021). \\\",\\\"34. Alexa, A. & Rahnenuhrer, J. topGO: Enrichment Analysis for Gene Ontology https://bioconductor.org/packages/topGO/. R package version 2.58.0. 2024. \\\",\\\"35. Robinson, D. & Foulds, L. Comparison of phylogenetic trees. Mathematical Biosciences 53, 131-147. ISSN: 0025-5564. https://www.sciencedirect.com/science/article/pii/0025556481900432 (1981). \\\",\\\"36. INDSC. From January 2025 TPA-Exp and TPA-Inf submission types will no longer be accepted as new submissions 2024. https://www.insdc.org/news/from-january-2025-tpa-exp-and-tpa-inf-submission-types-will-no-longer-be-accepted-as-new-submissions-03-09-2024/ (2025). \\\"]\",\n \"page_idx\": \"14\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[145,617,364,638]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgements \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,648,851,739]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The work was funded in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - STA 1009/15-1. The computational analyses were performed using the HPC resources provided by Greifswald University and Munster University; for the latter, we thank the group of Erich Bornberg-Bauer. We also thank Elias Dohmen for providing the instructions to the HPC resources and discussing the OrthoFinder2 workflow for orthogroup analysis, and Gregor Bucher and Lena Reim for phylogeny. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,761,511,780]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Author contributions statement \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,792,852,823]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S.S. implemented and ran the workflow and analyzed the data. K.H. contributed to the creation of the workflow and structure annotation postprocessing. S.S. and M.S. designed the experiments. S.S. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,2,910,36]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,845,508,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"15 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,849,137]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and M.S. wrote the draft manuscript. All authors reviewed, revised, and approved the manuscript. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,157,380,180]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Competing interests \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,190,462,205]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The authors declare no competing interests. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,2,910,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.04.17.649312; this version posted April 20, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,845,508,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"16 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":""},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Life Sciences"},"sha256":{"kind":"string","value":"118a2bac1f55d85e17bed140dc1fb493a9bffb0af74345ab0a717ae6e81646ab"},"title":{"kind":"string","value":"Annotation of 200 Insect Genomes with BRAKER for Consistent Comparisons across Species"}}},{"rowIdx":244,"cells":{"abstract":{"kind":"string","value":""},"author":{"kind":"string","value":"Alan P. Morrison|Samuel Olówósejéjé|Paul Leahy"},"content_list":{"kind":"list like","value":[{"bbox":"[62,209,771,250]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A practical approach for increased electrification, lower emissions and lower energy costs in Africa ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,262,514,279]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Samuel Olówósejéjé $^ { \\mathrm { a , b , * } }$ , Paul Leahy a,c , Alan P. Morrison d ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,287,647,330]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"a School of Engineering, University College Cork, College Road, Cork, Ireland \nb Nigerian Electricity Management Services Agency (NEMSA), Wuse 2, Abuja, Nigeria \nc Marine Renewable Energy Ireland Research Centre, University College Cork, Ringaskiddy, Co. Cork, Ireland \nd Department of Electrical and Electronic Engineering, School of Engineering, University College Cork, College Road, Cork, Ireland ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[63,359,228,373]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"a r t i c l e i n f o ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[337,360,455,373]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"a b s t r a c t ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,385,179,460]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: \nBeneficial electrification \nEconomic cost \nGHG emissions \nGrid defection \nPhotovoltaic \nUrban electrification ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[339,385,939,601]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The limited access to affordable, reliable and sustainable energy in sub-Saharan Africa could inhibit the region’s realisation of the United Nations Sustainable Development Goals by 2030. The intermittency and unreliability of power supply in the region has led countries, especially in the eastern sub-region, to implement sustainable energy solutions for rural electrification, thereby improving electricity supply access to underserved and unserved communities. With this focus on rural electrification, a deficit in electricity supply to urban settlements could arise, owing to the economic feasibility of extending the power grid towards securing electricity access for a growing population and the increasing number of rural-urban migrators. This paper reviews existing literature on electrifying sub-Saharan Africa, highlighting the prescriptions for deploying energy solutions in the region. Consequently, a country-level case study on grid defection solutions for Nigerian commercial centres assessing 14 different designs of Integrated Power Systems’ (IPS) operations against the three impact metrics of cost implication (\\$/lifetime), greenhouse gas (GHG) emissions $\\mathrm { C O } _ { 2 }$ tonnes/yr.) and surplus energy (MWh/yr.), is presented. The systematic analysis demonstrates that an integrated hybrid-solar-photovoltaics (PV)-based system (IHSS) without battery storage, serving $5 6 \\%$ of its load from solar-PV and $4 4 \\%$ from fossil-fuelled generators provides the lowest cost power supply option. The modelled system generated 25 MWh/yr. in surplus energy and emitted $5 3 \\%$ fewer GHG emissions than the largest emitter. A compelling case is made whereby augmenting existing infrastructure with an appropriately sized PV plant will significantly reduce costs and simultaneously have a significant impact on GHG emissions. The generation of surplus energy also presents an opportunity to augment urban electrification through custom-fit sustainable energy solutions and the formation of a transactive electricity market. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,633,161,645]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,659,485,778]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sub-Saharan Africa’s (SSAs) electric power supply-to-demand shortfall has been widely documented [1–3]. The electrification rate of most countries in SSA excluding South-Africa is less than $3 0 \\%$ with an average electrification rate of $1 6 \\%$ in rural communities [3]. The paucity of electricity supply in the region is quite alarming, with the World Bank estimating that over $5 0 \\%$ of the 1 billion people without access to electricity reside in SSA [2,3]. Consequently, over $7 0 \\%$ of primary energy is sourced from traditional biomass (fuelwood and charcoal), with more than half of SSA’s electricity generated from large hydropower [4]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,779,485,829]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the eastern sub-region, electricity consumption in 2015 for the EA-8 (Burundi, Kenya, Malawi, Mozambique, Rwanda, Tanzania, Uganda including South-Africa) stood at 261 TWh, with South-Africa consuming 227 TWh of the total figure [6]. In comparison, Italy consumed ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,633,937,803]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"310 TWh within the same period, despite having a fifth of the ${ \\tt E A } { \\cdot } 8 { ' } s$ total population [6]. At the country-level, Nigeria – the most populous nation on the continent – still has to electrify over half its population [5] and improve the quality of power delivered to electrified areas. According to the World Bank, Nigerians with power supply access experience 33 power outages a month at an average outage duration of $^ { 8 \\mathrm { h } }$ [2]. The need for reliable power has resulted in the proliferation of smallmedium scale fossil-fuel generators of different models and capacities, giving rise to electricity costs and air pollution in the multi-sectors (commercial, industrial and residential) [7,8]. The region’s limited access to an affordable, reliable and sustainable source of power has inhibited its socioeconomic development, with attendant consequences on quality of life, public health, climate change, economic growth and prosperity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,805,937,829]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Public health in SSA is of concern on two fronts: in rural communities and settlements where indoor air pollution is a growing prob-","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,70,941,174]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Contents lists available at ScienceDirect Sustainable Futures Sustainable Futures journal homepage: www.elsevier.com/locate/sftr ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,897,732,944]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1016/j.sftr.2020.100022 Received 15 December 2019; Accepted 2 April 2020 2666-1888 $' ( ©$ 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[63,863,794,887]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"∗ Corresponding author at: School of Engineering, University College Cork, College Road, Cork, Ireland. E-mail addresses: kunle.olowosejeje@gmail.com (S. Olówósejéjé), paul.leahy@ucc.ie (P. Leahy), a.morrison@ucc.ie (A.P. Morrison). ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[838,211,887,248]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Check for updates ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[400,45,600,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable Futures 2 (2020) 100022 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[67,76,485,500]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nomenclature \nBOS balance of system \nC&I commercial and Industrial \nDG diesel generator \nDisCo distribution companies \nEA-8 East Africa [8] \nGHG greenhouse gas \nGHI global horizontal irradiance \nGS generator system \nHVDC high voltage direct current \nIHGS integrated hybrid generator based system \nIHSBS integrated hybrid solar and battery based system \nIHSS integrated hybrid solar based system \nIPS integrated power system \nkW kilowatt \nkWh kilowatt hour \nLCCA Life-cycle cost analysis \nMW megawatt \nMWh/yr. megawatt hour per year \nNEM net energy metering \nNWA non-wire alternative \nPG petrol generator \nPV photovoltaic \nRE renewable energy \nRES renewable energy system \nRET renewable energy technology \nSDG sustainable development goal \nSHS solar home system \nSSA sub-Saharan Africa \nTEM transactive electricity market ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,519,485,728]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"lem, with $6 5 \\%$ of primary energy (cooking, heating and lightning) in the EA-8 sourced from solid biomass [6], and in urban regions where diesel/petrol fuelled generators are employed in ameliorating the effect of electric power supply unreliability on the quality of life. The air quality impacts from both situations could adversely impact human health [6,9,20,26]. SSA’s electricity crisis presents an opportunity to address the electricity access deficit in tandem with climate change. The region is already considered a non-significant contributor to global greenhouse gas (GHG) emissions with its global contributions at $2 \\mathrm { - } 3 \\%$ attributed to energy related and industrial activities [10]. Furthermore, about $6 0 \\%$ of the countries on the continent have committed to climate change mitigation by ratifying the “Paris Climate Accord” [1,11]. However, South-Africa with an electrification rate of approximately $8 8 \\%$ is looking to bring about 12 GW of coal-powered plants online, with Malawi and Zimbabwe also making considerable investments in coal-power generation capacities [3]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,731,485,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Climate policies and an enabling regulatory environment will be required in realising country-level and regional climate change mitigation commitments. The transition to a low-carbon economy has garnered some level of success in the eastern sub-region [16], with countries implementing sustainable energy solutions for rural electrification [3]. A notable industry leader in SSA is M-Kopa – a Kenyan solar energy company, serving Kenya, Tanzania and Uganda. According to the company, they have been able to develop solar home systems (SHSs) for over 600,000 low-income households in these countries, providing them with affordable and cleaner access to energy [12]. They have also been able to pioneer a pay-as-you-go mobile payment system for collecting returns on their services and in remotely monitoring (communicating with) their physical asset. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,902,485,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As the discourse on SSA’s electricity paucity centres on providing electricity supply access to underserved and unserved communities particularly in rural areas, urban regions could experience an electricity supply deficit resulting from natural population growth and rural-urban migration. With over $5 0 \\%$ of the African population predicted to be living in cities by 2030 and $6 0 \\%$ by 2050, urbanisation is a social phenomenon that could influence access to electricity by putting pressure on energy resources and infrastructure [3]. At the country-level, Nigeria is predicted to add about 212 million people to its urban population between 2014 and 2050 [1]. The success recorded so far through the deployment of low-carbon technology for rural electrification in eastern Africa, presents an opportunity for exploring sustainable energy solutions in extending power supply access, improving power quality and sustaining the duration of electricity supply to a growing urban region (commercial, industrial and residential) in SSA. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,70,937,226]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,228,939,320]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In light of these conditions, further discussions in this paper are structured as follows: Section 2 covers a review of the literature on the energy solutions and drivers to energy access in SSA. Section 3 presents the method adopted, outlining the case study on Nigerian commercial centres and defining system operations design. Section 4 covers the results of the case study analysis with Section 5 discussing the implications of the results. Section 6 concludes the paper. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,335,702,346]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. Review of relevant studies ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,360,937,517]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The literature on SSA’s electricity supply paucity and the energy solutions that could bridge the power supply to demand deficit is extensive, with discussions highlighting power supply access and reliability as a nexus to the region’s socioeconomic development. Documented energy solutions for electrifying SSA’s unserved and underserved communities favour sustainable energy solutions due to their minimal to zero adverse impact on public health and the environment, amongst other factors. Consequently, literature on SSA’s electric power supply unreliability is reviewed accounting for the western, eastern and southern Africa sub-regions, with discussions split into energy solutions for increasing electrification and the drivers for improving electricity supply access. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,533,635,544]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.1. Energy solutions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[515,561,937,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"With the electrification rate of most countries in SSA excluding South-Africa below $3 0 \\%$ and an average electrification rate of $1 6 \\%$ in rural communities [3], existing literature on energy solutions for the region mainly focus on implementing sustainable solutions for rural settlements towards meeting their primary energy needs i.e. cooking, heating and lighting. Okoye and Oranekwu-Okoye [14] advocated the economic viability of solar-photovoltaic (PV) systems for rural electrification in SSA, using rural Gusau, Nigeria as a case study. Other studies by Azimoh et al. [23] on rural Namibia and Boamah and Rothfub [19] on Ghana analysed the successes of the hybrid (solar-diesel) minigrid system in operation and the government-led solar home system (SHS) initiative respectively. Considering the wider benefits of “electrification beyond lighting”, Schwerhoff and Sy [20] identified large-scale renewable energy developmental projects requiring substantial capital as integral to electrifying SSA and accelerating the transition to sustainable energy solutions. Barasa et al. [21] demonstrated the cost suitability of renewable energy (RE) systems delivering power through a high voltage direct current (HVDC) grid and their potential in increasing regional electrification through interconnected grid systems. Presley et al. [13] disputed the immediate focus on deploying sustainable solutions for electrification by arguing that the transition should only occur once conventional energy has been scaled up and utilised in achieving the “benchmark” of reducing energy poverty and accelerating economic growth and development. Adhekpukoli [29] presented the democratisation of Nigeria’s electricity industry by further deregulating the sector to accommodate disparate electric power producers as a solution to the ‘decades-long’ electricity supply deficit. There is a need for sharing the emphasis on Africa’s electrification agenda between the rural deficient and increasing electricity supply access to urban regions, particularly economic drivers like the commercial and industrial (C&I) sectors. A cost-benefit analysis by Olówósejéjé et al. [25] on Nigeria’s industrial sector realised that industries could make significant cost savings if they transitioned to solar-PV based systems instead of complementing unreliable grid power with diesel generation. Sustainable energy solutions are being favoured for narrowing the electricity supply shortfall in rural SSA because they address the global issue of climate change. Chakamera and Alagidede [16] emphasised the need to mitigate the adverse effect of climate change by decreasing electricity production from nonrenewable energy sources and increasing production from renewable energy sources in the long term. Ouedraogo [17] stated that the economic, social and environmental benefits of deploying renewable energy technology and infrastructure outweighed its capital-intensive nature. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[766,45,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable Futures 2 (2020) 100022 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,45,258,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Olówósejéjé, P. Leahy and A.P. Morrison ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,70,485,240]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,242,485,424]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Rose et al. [35] evaluated the potential of solar-PV (combined with reservoir hydropower) grid connected systems in displacing diesel generation in Kenya. They suggested that these large-scale RE systems are more impactful investments in providing sustainable energy solutions and significantly reducing carbon emissions. The United Nations 2030 target of ensuring access to affordable, reliable, sustainable and modern energy for all might have to be revised due to the rate at which SSA is being electrified. To support this point, Bazilian et al. [22] considered regional electrification targets in line with that of the Sustainable Development Goals (SDGs) as quite ambitious, stating that power generation capacity has not kept pace with population growth. They also put forward the contrasting level of commitment to power development projects amongst countries in the region as a significant issue in realising the SDGs within the stipulated time period. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,440,210,452]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.2. Energy access drivers ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,467,485,861]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The unavailability of and inaccessibility to data on the energy sector in SSA critically inhibits effective electricity supply planning and implementation. Trotter et al. [15] identified a major problem of electricity planning as the lack and unreliability of data. Bazilian [24] in discussing the role of international institutions in fostering SSA’s electrification, implored the establishment of an information sharing mechanism towards improving the delivery of financial instruments and initiatives to the region. Ateba and Prinsloo [33] in identifying an effective approach towards electricity supply sustainability in South Africa, recommended the development of an integrated strategic management framework for sectoral planning informed by the holistic and comprehensive analyses of grid operations. The necessity for accessible energy data cannot be overemphasised as energy policies are informed by available data on the production, distribution and consumption of energy. Trotter et al. [15] listed the enabling factors for sustaining SSA’s electrification drive as adequate policy design, sufficient finance, securing social benefits, a favourable political situation, community engagement together with human capital development. Azimoh et al. [23] listed government support, involvement of the local community, capacity development of same, sensitisation towards energy efficient practices, prepaid metering and the adoption of a progressive electricity tariff system as factors that have sustained the operation of the mini-grid system in Tsumkwe village, Namibia. In another study, Jain and Jain [32] presented political instability, contrasting energy strategies, technical ineptitude and grid infrastructure modification/integration as issues to be addressed in electrifying rural localities through renewable energy technology (RET). Adesanya and Schelly [26] concluded that renewable energy uptake in Nigeria is subject to supporting energy policies and an awareness drive through synergies amongst the government, financial institutions, private investors and stakeholders. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,862,485,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It is imperative that the renewable energy industry in SSA is derisked to promote investments in renewable energy technology (RET) by private investors, multilateral financial organisations and international development partners. Obeng-Darko [28] in discussing the impeding factors to Ghana utilising renewable energy and energy efficient technologies in achieving a $1 0 \\%$ penetration of national electricity production by 2020, highlighted deficiencies in legislative and regulatory frameworks as risk escalators deterring investments in renewable energy development projects and initiatives. Consolidating discussions in [28], Aliyu et al. [30] highlighted the importance of renewable energy policy mechanisms such as feed-in-tariffs and net energy metering in promoting and incentivising investments in renewable energy technology. Moner-Girona et al. [34] recommended the implementation of RETspecific tariffs for incentivising national and international investments in RETs. Social factors and societal behaviours have to be considered in the deployment of energy solutions and more particularly innovative solutions and new technology. Boamah and Rothfub [19] stated that the inter-relationship between energy and society is an important factor in implementing energy development projects. Wojuola and Alant [27] inferred the integration of sustainable development in education, science and technology policies towards fostering a national sustainable development culture, after realising a low level of knowledge on RETs in their survey of Ibadan, Nigeria. They also recommended that energy education should encompass all knowledge delivery systems. Misplacing priorities on energy development projects could scupper the rate at which continent-wide social and economic development is achieved. Trotter and Abdullah [18] proposed that international involvement in Africa’s energy sector be redirected towards focussing on making public aid available for rural electrification, promoting local content through dissemination of technology and relaxing the conditions on foreign aid in order to support state-driven leadership. Simone and Bazilian [24] also proposed that international institutions channel their efforts into supporting the development of sound energy policies, sectoral reforms, corporate governance and ensuring transparency best practices. Renewably-powered systems for rural electrification could be faced with sustainability challenges, if the after services are not functional. Azimoh et al. [31] surveyed rural households in South Africa to investigate the impact of the SHS programme on the community. They argued that although the programme had facilitated the illumination of households thereby increasing study and business hours, it was not sustainable in the offing. This was due to the inadequacies of the fee for service payment model, the system’s limited power supply, improper system use, equipment theft and the rising cost of doing business for the energy service companies. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,69,939,571]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,586,662,597]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.3. Gaps in the literature ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,612,937,703]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A review of the literature shows solar-power based systems as the preferred energy solution (due to a continent-wide resource abundance) in facilitating SSA’s electrification. Their deployment either in standalone configurations or in complementarity with fossil-fuel based systems were consistent in the discourse. Also consistent in the literature was the mode in which these RETs were implemented (SHSs and minigrid systems). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,704,937,887]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Following the extensive literature review, we present three stages/enablers to energy supply access. The first stage encompasses a politically stable environment, reliable data that is readily accessible and energy policies, with policy actions supported by an enabling legislative and regulatory infrastructure. Access to RE development finance, mechanisms incentivising RET investments, dissemination of RET, energy sector reforms and effective payment models for collecting returns on RET services constitute the second stage. The third stage focusses on community engagement in determining the best-fit innovative solutions as well as in inculcating a community-wide technology sustenance culture post-project implementation. The first stage serves as the building blocks for the successful implementation of the second stage with the final stage ensuring the sustenance of the project after completion. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,889,937,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Throughout the breadth of the literature, discussions have centred on implementing grid defection solutions (small-scale SHSs and minigrid systems) for the electrification of rural SSA. With an electrification rate of less than $3 0 \\%$ in most SSA countries [3], it is important that electrifying rural areas is in tandem with extending and improving the quality of power delivered to urban regions. It is also important that electrification goes beyond lighting and provides the quality of power required in meeting the operational demands of urban-domiciled commercial centres and industries. This study seeks to address this gap in literature by analysing the economic and environmental viability of hybrid scalable PV-centric grid defection solutions for urban commercial centres (with urban regions comprising of commercial, industrial and residential sectors) towards a collective electrification drive i.e. increasing urban electrification and sustaining rural electrification efforts. A systematic analysis is carried out on 14 stand-alone integrated power system designs in meeting the electricity demand of urban commercial sectors and by extension, augmenting electricity supply access to the residential sector. There is an opportunity for surplus energy generated from these hybrid systems to power the residential sectors through industrial and commercial coalition formations. As a sustainable approach in terms of economic viability, the non-essentiality of energy storage systems in these hybrid configurations based on regional location is also elicited. The focus on the commercial sector stems from the fact that small and medium scale enterprises are the mainstay of an economy. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[766,45,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable Futures 2 (2020) 100022 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,45,258,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Olówósejéjé, P. Leahy and A.P. Morrison ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[231,97,769,292]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0720/85c9b6eb979f8e6510d10dc5a297fb30a6356593e8b269f7756fbed5d1acdfcd.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":"<table><tr><td rowspan=\"2\">IPS</td><td colspan=\"3\">Capacity (kW)</td><td>Capacity (kWh)</td></tr><tr><td>Solar-photovoltaic (PV)</td><td>Diesel generator (DG)</td><td>Petrol generator (PG)</td><td>Battery array</td></tr><tr><td>RES</td><td>100</td><td>=</td><td>=</td><td>82</td></tr><tr><td>GS</td><td>1</td><td>15.5</td><td>2.2</td><td>1</td></tr><tr><td>IHSS</td><td>30</td><td>15.5</td><td>2.2</td><td>=</td></tr><tr><td>IHSBS 1</td><td>20</td><td>15.5</td><td>1</td><td>12</td></tr><tr><td>IHSBS 2</td><td>30</td><td>15.5</td><td>1</td><td>12</td></tr><tr><td>IHSBS3</td><td>40</td><td>15.5</td><td></td><td>12</td></tr><tr><td>IHSBS 4</td><td>50</td><td>15.5</td><td></td><td>12</td></tr><tr><td>IHSBS 5</td><td>60</td><td>15.5</td><td></td><td>28</td></tr><tr><td>IHSBS 6</td><td>70</td><td>15.5</td><td></td><td>42</td></tr><tr><td>IHSBS7</td><td>80</td><td>15.5</td><td></td><td>42</td></tr><tr><td>IHSBS8</td><td>90</td><td>15.5</td><td>二</td><td>42</td></tr><tr><td>IHGS 1</td><td>10</td><td>15.5</td><td>2.2</td><td>1</td></tr><tr><td>IHGS 2</td><td>10</td><td>15.5</td><td>2.2</td><td>12</td></tr><tr><td>IHGS 3</td><td>10</td><td>15.5</td><td>1</td><td>12</td></tr></table>","table_caption":"[\"Table 1 Summary of the IPS’ system capacities. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[62,315,485,578]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,596,131,607]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. Method ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,621,485,832]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This study was guided by three fundamental pillars: affordability, reliability and sustainability. Commercial centres in Abuja’s (Nigeria) metropolis were surveyed to establish their most commonly-occurring commercial activities, which informed load demand projections. Subsequently, Olowos Plaza, a model single commercial centre housing the commercial outlets that cater to these activities was created and modelled in detail as a case study. A systematic analysis was performed on 14 different integrated power systems (IPSs): (a renewable energy system (RES); a fossil-fuel generator system (GS); an integrated hybrid solarbased system (IHSS); eight integrated hybrid solar and battery-based systems (IHSBS); and three integrated hybrid generator-based systems (IHGS)). In realising a viable solution, the power systems were analysed against three impact/performance metrics: cost implication (\\$/lifetime over 20 years), GHG emissions $\\mathrm { C O } _ { 2 }$ tonnes/yr.) and surplus energy (MWh/yr.). Table 1 summarises the system capacities of the $1 4 ~ \\mathrm { I P S } ^ { \\prime }$ operations designs. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[63,849,258,861]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1. Survey on commercial centres ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,876,485,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Forty commercial centres in Abuja were surveyed to establish the most commonly-occurring commercial activities in these centres. A checklist was designed with 31 out of the 40 centres surveyed accommodating commercial outlets that engage in three or more of its listed activities, namely: cyber café businesses, boutiques, salons, tailoring businesses and grocery shops. These results informed the creation of Olowos Plaza, located in Abuja and housing a cyber café, boutique, salon, tailoring and grocery shop. See Supplementary material 1 for the survey checklist. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,316,939,366]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,389,774,401]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1.1. Load demand projection/determination ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[515,402,939,558]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The weekly load demand of Olowos Plaza was realised based on the power requirements of the five commercial outlets. Olowos Plaza is open for business seven days a week with reduced business hours on Sundays. Some commercial outlets (cyber café, boutique and tailoring shops) are not operational on Sundays. Business operations are from 9 a.m. to $1 0 \\ \\mathrm { p . m . }$ ., Mondays to Saturdays, and from noon to $5 \\ \\mathrm { p . m }$ . on Sundays. Business times are representative of most commercial centres in Nigeria. Fig. 1 indicates the hourly load demand (kW) for Olowos plaza for a typical weekday, Saturday and Sunday. See Supplementary material 2, 3 and 4 for the typical week (weekdays and weekend) power consumption breakdown, equipment model and power rating, as well as business operation assumptions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,580,800,591]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2. Power system selection and cost consideration ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,605,937,670]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The three main power system components (although with different system compositions, and in different capacities and operations configuration) analysed in meeting Olowos Plaza’s load demand were a solarphotovoltaic (PV) system, a battery storage system and a fossil-fuel generator system. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,692,647,703]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2.1. Solar-PV system ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[515,704,939,847]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Solar-PV system operations was designed using Abuja’s global horizontal irradiation (GHI) data for year 2017 sourced from Copernicus Atmosphere Monitoring Service [36]. $1 0 0 \\mathsf { W _ { p } }$ $( V _ { o c } \\mathrm { ~ - ~ } 2 2 . 3 \\mathrm { ~ V } ; I _ { s c } \\mathrm { ~ - ~ }$ 6A; $V _ { m p } - 1 8 ~ \\mathrm { V } ;$ ; $I _ { m p } - 5 . 5 6 A .$ ; $\\eta - 1 9 . 2 \\% )$ monocrystalline solar-PV panels (considering the technical data specific to the panel’s power rating) were selected and sized for every $1 0 \\mathrm { k W }$ capacity increment, for systems’ operation design in the $1 0 \\mathrm { k W _ { p } } – 1 0 0 \\mathrm { k W _ { p } }$ capacity range. For practicality, $\\ \" 4 8 \\nabla ^ { \\mathrm { 3 } }$ string array configurations were considered i.e. to limit the systems’ current-carrying capacity, thereby limiting the systems’ protection sizing. See Supplementary material 5 for a full listing of operations design assumptions and considerations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,849,939,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Solar-PV system cost consideration: A 20 year operational lifetime was considered when determining system cost prices. The PV panels’ costs were based on wholesale prices [37]. The other costs taken into account for the PV system include the land costs, balance of system (BOS) costs (excluding battery storage costs) and PV panel maintenance costs. Maintenance costs (cleaning schedules) were considered due to the location of Olowos Plaza and its susceptibility to seasonal dust accumulation [38]. Eq. (1) was used in determining the lifetime (Lt) costs for the solar-PV systems’ capacities. See Supplementary material 6 for a full listing of the systems’ cost assumptions and considerations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[766,45,939,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable Futures 2 (2020) 100022 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,45,258,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Olówósejéjé, P. Leahy and A.P. Morrison ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[63,70,625,253]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 1. Olowos plaza hourly load demand for a typical weekday, Saturday and Sunday. \"]","image_footnote":"[]","img_path":"images/0557/2e1e7b122b0b02daf9e7211f8abaf8f8504eb13ad20d95f71cfd11b0b5b19daa.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[62,287,485,326]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,337,485,350]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Total Cost $=$ Capital $^ +$ Maintenance $^ +$ Replacement Costs $^ +$ Land Cost (1) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,366,228,378]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2.2. Battery storage system ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,380,485,563]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Flooded, deep-cycle, lead-acid batteries (the industry workhorse) were selected as the technology for the battery storage system. “Rolls” batteries were selected due to capacity and cost considerations. We employed brute-force search in determining the battery capacity for our system array. The search compared $6 \\mathrm { ~ V ~ }$ and $^ { 1 2 \\mathrm { ~ V ~ } }$ battery types from three battery manufacturers (others being “Trojan” and “Crown” batteries) against possible application ${ } ^ { \\mathfrak { s } } \\mathbf { C }$ -rates” $\\mathrm { . 1 0 h r }$ , 13hr and 15hr) and depth of discharge $1 0 \\%$ , $2 0 \\%$ , $3 0 \\%$ and $4 0 \\%$ ). We opted for a $4 8 \\mathrm { \\ : V }$ system and limited an array to three parallel connections, with reference to the “Rolls” battery manual [39]. Also referencing the manual [39], we employed a multi-stage (bulk, absorption and float) battery charge for the “charging” phase in the battery array’s operation cycle. See Supplementary material 5 for further details on the battery storage system’s operation design. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,564,485,630]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Battery storage system cost consideration: The capital, replacement and maintenance costs for a 20 year operational lifetime were considered for the battery storage systems. Eq. (2) was employed in realising the lifetime costs for the different battery storage capacities. See Supplementary material 6 for further details on battery storage system costs. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,641,383,653]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Total Cost $=$ Capital $^ +$ Maintenance $^ +$ Replacement Costs ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,670,201,682]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2.3. Generator system ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,683,485,800]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The fossil-fuelled generator system consists of one “19.3kVA/15.5kW” diesel-fuelled and one “2.8kVA/2.2kW” petrolfuelled generator installed at the canopy level operating in prime power mode. 3-phase, direct-injection generators with a rotation speed of $1 5 0 0 \\mathrm { r p m }$ were considered for the system. Pertaining to system lifetime, we were guided by “HOMER” – a software on distributed generation power system design and optimisation [40], whilst considering the system’s mode of operations. See Supplementary material 5 for further details on the generator system’s operation design. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,802,485,866]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Generator system cost consideration: The capital, replacement, fuel and maintenance costs for a 20 year operational lifetime were considered for the generator system. Eq. (3) was used in determining the generator system’s lifetime costs. See Supplementary material 6 for further details on these costs. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,877,425,890]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Total ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,902,485,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A life-cycle cost analysis (LCCA) was carried out on the different IPS for their operational lifetime. The real discount rate was calculated considering inflation at $1 1 . 4 \\%$ and nominal interest rate at $1 4 \\%$ [41,42]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[532,287,821,300]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For the calculations, we employed the equation: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,303,613,329]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0659/2c306d7cd31a93c04465d7bc52b95da6ab385170791c479ea1ff1767525f7022.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\operatorname { r } = \\left( { \\frac { 1 + i } { 1 + n } } \\right) - 1\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[514,332,554,344]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[532,354,808,393]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$r =$ real discount/interest rate; $i =$ nominal interest rate; and $n =$ inflation rate, taken as $2 \\%$ representative. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,403,939,480]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This rate was used in calculating the present value of the maintenance, operations and replacement costs for the lifetime of the $1 4 ~ \\mathrm { I P S }$ analysed. Diesel and petrol costs [43,44] were considered for the generator system. The solar-PV system cost accounts for the BOS components costs, as well as the charge controllers and inverter capital and replacement costs. Supplementary material 7 details the LCCA on the IPSs. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,494,754,506]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.3. System operations of the different IPS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,519,939,585]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figs. 2, 3 and 4 indicate the hourly system operations of the different IPS for a typical weekday, Saturday and Sunday, respectively. In these representations, the following codes are used to indicate the main power source for each hour of the day: Photovoltaic – PV; Battery – Batt; Diesel Generator – DG and Petrol Generator – PG. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,598,579,610]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. Results ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,625,939,728]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"From our analysis, the “IHSS” variant is the cheapest (\\$162,225) IPS of the 14 power systems analysed. Olowos Plaza will make power system cost (capital, replacement, operations and maintenance) savings of up to $5 5 \\%$ when compared to the average power system costs (\\$358,578) for its operational lifetime. The plaza will make further power system cost savings of up to $2 6 \\%$ when compared to the “RES” – the most costly (\\$867,436) power system for the analysis. Fig. 5 represents the various IPS’ costs. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,731,939,875]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Informed by power distribution companies’ (DisCos) unwillingness to transact with embedded generators (with proferred excuses of network maintenance and rehabilitation), and with all but one of the power systems generating surplus energy (MWh/yr.), we factored in the surplus energy performance metric. We hypothesise that the inability to capitalise on the surplus energy generated by Olowos Plaza power systems’ operations would be more impactful to the systems at the upper limit of the surplus energy metric. The plaza is also permitted to operate without a power distribution license in all the power system capacities considered [45]. Fig. 6 represents the IPS’ costs and surplus energy relationship. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,876,937,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The “GS” is the only power system of the 14 analysed that generated no surplus energy through its operations. As an outlier it was not included in calculations determining the average surplus energy (56 MWh/yr.). The “RES” through its operations, generated the most surplus energy (126 MWh/yr.) of the systems’. With no operational transactive electricity market (TEM) in place, we considered the systems with surplus energy generation above average as non-feasible with precedence set on system operations efficiency i.e. closely matched supply-demand ratio (systems generating below the average surplus energy). In light of these, eight of the fourteen IPS analysed were found to generate surplus energy below the average. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[766,45,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable Futures 2 (2020) 100022 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,45,258,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Olówósejéjé, P. Leahy and A.P. Morrison ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[119,70,884,278]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0074/5daf7f48b41670d20bef5d2290da89072a71faac56bfef96181485636857b3bf.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[119,308,887,514]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0642/87d0825e0a06224235585d2b80b6b10724310fa9a1e0c89cf3a3afa0eb0d73be.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[119,552,885,759]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 4. Hourly system operations of the different IPS for a typical Sunday. \"]","image_footnote":"[]","img_path":"images/0169/46ef5ff481d01afbb6540a640d84be5316031366bcb5e1b75dee32cd5cab94c0.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[62,809,485,887]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,889,485,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In determining the $\\mathrm { C O } _ { 2 }$ (tonnes/year) value for the different IPS, we worked with the assumption of diesel fuel emitting $2 . 6 8 ~ \\mathrm { k g }$ per litre consumption and petrol emitting $2 . 3 1 ~ \\mathrm { k g }$ per litre consumption [46]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,809,937,836]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Fig. 7 ( hockey stick graph) represents the IPS’ costs and GHG emissions relationship. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,837,939,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The “RES” is the only power system of the 14 analysed that emitted no greenhouse gases through its operations. As an outlier it was not included in calculations determining the average GHG emissions $( 2 2 \\mathsf { C O } _ { 2 }$ tonnes/year). The “GS” through its operations, generated the most GHG emissions (47 $\\mathrm { C O } _ { 2 }$ tonnes/year) of the systems. Furthermore, and with emphasis on GHG emissions, the following power systems were feasible: IHSS, IHSBS 2, IHSBS 3, IHSBS 4, IHSBS 5, IHSBS 6, IHSBS 7, IHSBS 8 and RES. The following were also feasible when assessing the systems for cost implication: GS, IHGS 1, IHGS 2, IHGS 3, IHSS, IHSBS 1, IHSBS 2, IHSBS 3 and IHSBS 4, with a review on the systems’ surplus energy returning these: GS, IHGS 1, IHGS 3, IHSS, IHSBS 1, IHSBS 2, IHSBS 3 and IHSBS 4, as practicable. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[766,45,939,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable Futures 2 (2020) 100022 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,45,258,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Olówósejéjé, P. Leahy and A.P. Morrison ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[139,70,867,383]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 5. Total lifetime cost of all IPS, in descending order of percentage renewable contribution. \"]","image_footnote":"[]","img_path":"images/0483/bc2ff2c3be47c73190d54dde7047332cb4e13afc51a2fd495deb62e900d49702.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[124,423,882,812]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 6. IPS’ costs and surplus energy relationship in ascending order of surplus energy generated. \"]","image_footnote":"[]","img_path":"images/0780/975cd5fa3d0787f553aa2503dba0b884a443bd54f68341bf04db40bbbeeba170.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[62,860,487,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,860,939,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Considering all impact/performance metrics, we realised a feasible solutions (“sweet spot”) region for Olowos Plaza. The region comprises hybrid power systems, with one solar-PV based system (IHSS) and three solar-PV and battery based systems (IHSBS 2, IHSBS 3 and IHSBS 4). In light of these, the “IHSS” is the most viable power system solution of the 14 integrated power system operations analysed. It best satisfied the conditions of the impact assessment defined by the three impact metrics of; cost implication (\\$/lifetime (20 years)), GHG emissions $\\mathrm { C O } _ { 2 }$ tonnes/yr.) and surplus energy (MWh/yr.) – Figs. 5, 6 and 7, respectively. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[766,45,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable Futures 2 (2020) 100022 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,45,258,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Olówósejéjé, P. Leahy and A.P. Morrison ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[121,73,884,438]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 7. IPS’ costs and GHG emissions relationship in descending order of percentage renewable contribution. \"]","image_footnote":"[]","img_path":"images/0222/56f9b2095fa51ccf0e131ae997a11227baf8d61ff5b7b34dc324f3e8c10d096c.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[62,486,485,552]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,552,485,578]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Summarising the result of our analysis, we present the following salient points: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,586,487,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"i. The “IHSS” is the cheapest power system option, with surplus energy of 25 MWh/yr., $8 0 \\%$ less than the largest surplus energy generator and emitting $5 3 \\%$ less GHG emissions than the largest emitter. \nii. With a tariff of $\\$ 0.12/4W h$ for commercial (single and 3-phase) customers [47], an average of $3 5 . 8 \\mathrm { ~ h ~ }$ of electricity per week [48] and commercial centre residents incurring an extra $\\$ 0.20$ $- \\ 0 . 3 0 / \\mathrm { k W h }$ on generators for security of supply [48], the GS, IHGS 1, IHGS 2, IHGS 3, IHSS, IHSBS 1, IHSBS 2, IHSBS 3 and IHSBS 4 all provide off-grid power solutions that are reliable with cheaper-to-similar costs as the commercial centres’ current power systems. (See Supplementary material 6 for conversion rates.) \niii. The choice of a petrol generator over a battery storage system led to significant lifetime cost savings for the “IHSS” to the sum of $\\$ 74,446$ when compared with the “IHSBS $2 ^ { \\prime \\prime }$ . Although, the “IHSBS $2 ^ { \\prime \\prime }$ performed slightly better than the “IHSS” against the other impact metrics i.e. generated approximately 1 MWh/yr. less surplus energy, emitting 6 tonnes fewer $\\mathrm { C O } _ { 2 }$ emissions. \niv. Focussing on the IHSBS’ and referring to Fig. 7, we observe a distinct transition from IHSBS 4 – IHSBS 5, an inflection point in our systems analysis with feasibility ramifications. The marginal cost of increasing the renewable percentage contribution begins to increase at the transition from IHSBS 4 – IHSBS 5. \nv. Guided by Luckow et al.’s [49] report, we introduced a carbon tax $\\left( \\$ 25\\right)$ on the generator (GS) and hybrid generator-based systems (IHGS 1, IHGS 2 and IHGS 3) and still found them costcompetitive (average increase of $\\$ 0.03/40$ in levelised cost of ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[552,486,937,511]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"energy (LCOE)) when compared to commercial centres’ current power systems. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[532,513,939,604]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"vi. The design and installation of a generator system at the canopy level for commercial centres allows for easier monitoring of air quality and implementing carbon air filter technologies. It also addresses the proliferation of small-scale petrol generators from shop to shop and floor to floor, improving air quality and mitigating the adverse effect of generator fumes on the health [6,9, 20]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[529,605,939,696]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"vii. Renewably-powered commercial centres, vanguard a transition to smart energy systems that ensures commercial centre residents energy consumption and usage are cost-reflective. For Olowos Plaza, this would result in commercial outlet 1 paying $4 7 \\%$ of the Plaza’s total yearly electricity costs, outlet $3 \\mathrm { - } 4 1 \\%$ , outlet $5 { - } 1 0 \\%$ and outlets 2 and 4 paying $1 \\%$ , respectively. Refer to Supplementary material 4 for the commercial outlets activities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,717,601,728]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5. Discussion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[515,744,937,875]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results from our case study analysis demonstrate beneficial electrification for the commercial sector through PV-centric grid defection solutions. Total grid defection solutions also present an opportunity for the DisCos to increase the duration and improve the quality of electricity supply to the residential sector by reducing the number of energy intensive C&I customers connected to their network. These non-wire alternatives (NWA) could also be explored in partial grid defection configurations by incentivising surplus energy generation through policy mechanisms like net energy metering (NEM). It would mean electricity is made available during periods of peak demand and in emergencies. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,876,939,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In bolstering economic development, surplus energy generation could yet be pivotal in propelling the formation of a transactive electricity market (TEM) through C&I coalition formations that could further develop into hubs, clusters and villages. Reiterating recommendations by Adhekpukoli [29], further deregulation of the electricity sector to accommodate more independent power producers, embedded and captive power generators could be pivotal to increasing urban and rural electrification. As such, TEM would have to be backed by policy and an adequate regulatory infrastructure. The democratisation of the electricity sector to involve more nonconventional power producers by introducing different pathways (generation to consumers) as opposed to the traditional power delivery structure (generation to transmission to distribution to utilisation) increases business competition (through direct competition or partnerships) with the DisCos that could drive customers electricity supply costs down. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[766,45,939,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable Futures 2 (2020) 100022 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,45,258,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Olówósejéjé, P. Leahy and A.P. Morrison ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,70,485,200]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,203,485,424]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We posit that the C&I sectors transitioning to prosumers generating excess electricity could by extension electrify the residential sectors provided adequate legislative and regulatory frameworks are in place. We refer to this initiative as “Commercial Electrification of the Residential Sector (Comtridential)”. This could be in partnership with the DisCos (requiring further investments in revamping and modifying their electricity infrastructure/networks) or directly with the residential sector focussing on residential estates. The latter would require significant investments in the deployment of power distribution infrastructure. The potential for this energy solution could be measured by the willingness of residential estates (middle to high income earners) in maintaining access to an electricity supply network and increasing the duration of supplied hours. Given the electricity supply situation, an example of customer willingness in remaining electrified draws from the collective efforts of estate residents in funding the replacement of damaged service transformers resulting from power surges due to grid unreliability and intermittency. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,427,485,596]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The transition to sustainable solutions as a means in electrifying the various sectors that contribute to the socioeconomic development of a nation is possible and is being exemplified in Nigeria through a public sector led initiative. The Nigerian government through its rural electrification agency (REA), in partnership with private investors and multilateral finance institutions (The World Bank and African Development Bank) are deploying solar-PV powered utility-scale (stand-alone) systems in improving electricity supply to the commercial, industrial, education and health sectors [50]. These solutions are being implemented under two initiatives (Energising Economies and Energising Education), underscoring the importance of non-fragmented finance by international donor organisations and multilateral institutions as elicited by Simone and Bazilian [24]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,612,157,624]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6. Conclusions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,638,485,914]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The results of this analysis show that a practical approach of adopting hybrid systems with PV, batteries and fossil fuel generation in urban commercial settings in Nigeria will greatly reduce lifetime energy costs and deliver reliable power to loads. These would be achieved while simultaneously contributing to decarbonisation and improving air quality by reducing overall reliance on fossil fuel self-generation. It also elicited the non-essentiality of energy storage systems (high cost considerations) in regions of abundant solar energy resource especially for hybrid energy systems that also incorporate non-renewable sources of power generation. The IHSS evidenced this, by best satisfying the economic and environmental metrics of our analysis i.e. being the cheapest power system option and emitting $5 3 \\%$ less GHG emissions than the largest emitter. Also, from this study, we realised that disparate energy solutions would have to be explored in meeting country-level and regional electrification targets in the medium to long term. Our case study results further highlighted total to partial sustainable grid defection solutions as practicable solutions for urban electrification. A unique case was presented for the commercial electrification of the residential sector (comtridential) through commercial and industrial coalition formations taking advantage of the generation of surplus energy from hybrid renewable energy systems operating in a liberated transactive electricity market. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,915,485,940]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Our case study on commercial centres informed the reality that most project developers assess their project feasibility solely on its cost implication, disregarding its social and environmental effects. Therefore without adequate climate policies, the generator and three generator-based hybrid systems (GS, IHGS1, IHGS2 and IHGS3) emitting 47, 44, 40 and $3 8 \\thinspace \\mathrm { C O _ { 2 } }$ tonnes/year respectively, would have been considered feasible. Focussing on the issue of climate change, sustainable energy solutions are being favoured in electrifying rural SSA. The deployment of sustainable energy solutions addresses the regional electrification crisis in tandem with mitigating the effect of climate change. Energy policy formulation that serves as a proper deterrent to carbon-intensive processes of the commercial, industrial and power sectors present a more impactful approach in reducing carbon emissions and mitigating the effect of climate change beyond small-scale, PV-centric, grid defection solutions. Consequently, the role of individual nation’s government in improving regional electrification rates, both in urban and rural areas, cannot be overemphasised. Government support through policy actions and ensuring an enabling regulatory environment are essential in driving the energy transition through the implementation of sustainable energy solutions. These precursors form the bedrock to improving access to finance, implementing policy mechanisms, dissemination of information & technology, initiating sectoral reforms and community engagement. Ready access to reliable data across the region is also important in informing financial investments and implementing sustainable development projects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,70,937,372]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,374,939,518]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In light of these, if the United Nations SDGs are to be met by 2030, it is important that SSA’s rural electrification agenda goes beyond lighting and provides the required energy that could stimulate socioeconomic activities towards the collective development of communities, broader countries and the wider region. Sustainable electrification targeting core urban sectors (commercial, industrial and residential), are channelled measures in addressing the attendant consequences of urbanisation and spurring economic development through industrialisation. Therefore, it is critical that rural electrification is sustained alongside efforts of extending electrification, improving the quality of power delivered and increasing the duration of electricity supply access to urban areas. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,532,732,544]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Declaration Competing of Interest ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[534,558,756,569]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"No conflict of interest to be declared. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,586,631,597]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgement ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,612,937,636]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This work was supported by the Petroleum Technology Development Fund (PTDF): [Grant Number PTDF/ED/PHD/ SAO/776/15]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,651,675,663]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Supplementary materials ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,678,939,703]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.sftr.2020.100022. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,715,584,726]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[521,738,939,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"[1] International Bank for Reconstruction and Development, in: The State of Electricity Access Report, The World Bank Group, 2017, pp. 1–80. \n[2] The Economist Intelligence Unit, Power up: delivering renewable energy in Africa, The Economist Group. 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Wilson, in: Carbon Dioxide Price Forecast, Synapse Energy Economics Inc., Massachusetts, USA, 2015, pp. 1–32. \n[50] Rural Electrification Agency, in: Highlighting the Rural Electrification Agency’s Impact, REA, 2019, pp. 1–19. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[766,45,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable Futures 2 (2020) 100022 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,45,258,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Olówósejéjé, P. Leahy and A.P. Morrison ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[60,66,487,617]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,71,939,619]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[766,45,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable Futures 2 (2020) 100022 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,44,258,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Olówósejéjé, P. Leahy and A.P. Morrison ","text_format":null,"text_level":null,"type":"discarded"}],"string":"[\n {\n \"bbox\": \"[62,209,771,250]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A practical approach for increased electrification, lower emissions and lower energy costs in Africa \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,262,514,279]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Samuel Olówósejéjé $^ { \\\\mathrm { a , b , * } }$ , Paul Leahy a,c , Alan P. Morrison d \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,287,647,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"a School of Engineering, University College Cork, College Road, Cork, Ireland \\nb Nigerian Electricity Management Services Agency (NEMSA), Wuse 2, Abuja, Nigeria \\nc Marine Renewable Energy Ireland Research Centre, University College Cork, Ringaskiddy, Co. Cork, Ireland \\nd Department of Electrical and Electronic Engineering, School of Engineering, University College Cork, College Road, Cork, Ireland \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[63,359,228,373]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"a r t i c l e i n f o \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[337,360,455,373]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"a b s t r a c t \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,385,179,460]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: \\nBeneficial electrification \\nEconomic cost \\nGHG emissions \\nGrid defection \\nPhotovoltaic \\nUrban electrification \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[339,385,939,601]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The limited access to affordable, reliable and sustainable energy in sub-Saharan Africa could inhibit the region’s realisation of the United Nations Sustainable Development Goals by 2030. The intermittency and unreliability of power supply in the region has led countries, especially in the eastern sub-region, to implement sustainable energy solutions for rural electrification, thereby improving electricity supply access to underserved and unserved communities. With this focus on rural electrification, a deficit in electricity supply to urban settlements could arise, owing to the economic feasibility of extending the power grid towards securing electricity access for a growing population and the increasing number of rural-urban migrators. This paper reviews existing literature on electrifying sub-Saharan Africa, highlighting the prescriptions for deploying energy solutions in the region. Consequently, a country-level case study on grid defection solutions for Nigerian commercial centres assessing 14 different designs of Integrated Power Systems’ (IPS) operations against the three impact metrics of cost implication (\\\\$/lifetime), greenhouse gas (GHG) emissions $\\\\mathrm { C O } _ { 2 }$ tonnes/yr.) and surplus energy (MWh/yr.), is presented. The systematic analysis demonstrates that an integrated hybrid-solar-photovoltaics (PV)-based system (IHSS) without battery storage, serving $5 6 \\\\%$ of its load from solar-PV and $4 4 \\\\%$ from fossil-fuelled generators provides the lowest cost power supply option. The modelled system generated 25 MWh/yr. in surplus energy and emitted $5 3 \\\\%$ fewer GHG emissions than the largest emitter. A compelling case is made whereby augmenting existing infrastructure with an appropriately sized PV plant will significantly reduce costs and simultaneously have a significant impact on GHG emissions. The generation of surplus energy also presents an opportunity to augment urban electrification through custom-fit sustainable energy solutions and the formation of a transactive electricity market. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,633,161,645]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,659,485,778]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sub-Saharan Africa’s (SSAs) electric power supply-to-demand shortfall has been widely documented [1–3]. The electrification rate of most countries in SSA excluding South-Africa is less than $3 0 \\\\%$ with an average electrification rate of $1 6 \\\\%$ in rural communities [3]. The paucity of electricity supply in the region is quite alarming, with the World Bank estimating that over $5 0 \\\\%$ of the 1 billion people without access to electricity reside in SSA [2,3]. Consequently, over $7 0 \\\\%$ of primary energy is sourced from traditional biomass (fuelwood and charcoal), with more than half of SSA’s electricity generated from large hydropower [4]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,779,485,829]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the eastern sub-region, electricity consumption in 2015 for the EA-8 (Burundi, Kenya, Malawi, Mozambique, Rwanda, Tanzania, Uganda including South-Africa) stood at 261 TWh, with South-Africa consuming 227 TWh of the total figure [6]. In comparison, Italy consumed \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,633,937,803]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"310 TWh within the same period, despite having a fifth of the ${ \\\\tt E A } { \\\\cdot } 8 { ' } s$ total population [6]. At the country-level, Nigeria – the most populous nation on the continent – still has to electrify over half its population [5] and improve the quality of power delivered to electrified areas. According to the World Bank, Nigerians with power supply access experience 33 power outages a month at an average outage duration of $^ { 8 \\\\mathrm { h } }$ [2]. The need for reliable power has resulted in the proliferation of smallmedium scale fossil-fuel generators of different models and capacities, giving rise to electricity costs and air pollution in the multi-sectors (commercial, industrial and residential) [7,8]. The region’s limited access to an affordable, reliable and sustainable source of power has inhibited its socioeconomic development, with attendant consequences on quality of life, public health, climate change, economic growth and prosperity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,805,937,829]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Public health in SSA is of concern on two fronts: in rural communities and settlements where indoor air pollution is a growing prob-\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,70,941,174]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Contents lists available at ScienceDirect Sustainable Futures Sustainable Futures journal homepage: www.elsevier.com/locate/sftr \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,897,732,944]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1016/j.sftr.2020.100022 Received 15 December 2019; Accepted 2 April 2020 2666-1888 $' ( ©$ 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[63,863,794,887]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"∗ Corresponding author at: School of Engineering, University College Cork, College Road, Cork, Ireland. E-mail addresses: kunle.olowosejeje@gmail.com (S. Olówósejéjé), paul.leahy@ucc.ie (P. Leahy), a.morrison@ucc.ie (A.P. Morrison). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[838,211,887,248]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Check for updates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[400,45,600,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable Futures 2 (2020) 100022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[67,76,485,500]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nomenclature \\nBOS balance of system \\nC&I commercial and Industrial \\nDG diesel generator \\nDisCo distribution companies \\nEA-8 East Africa [8] \\nGHG greenhouse gas \\nGHI global horizontal irradiance \\nGS generator system \\nHVDC high voltage direct current \\nIHGS integrated hybrid generator based system \\nIHSBS integrated hybrid solar and battery based system \\nIHSS integrated hybrid solar based system \\nIPS integrated power system \\nkW kilowatt \\nkWh kilowatt hour \\nLCCA Life-cycle cost analysis \\nMW megawatt \\nMWh/yr. megawatt hour per year \\nNEM net energy metering \\nNWA non-wire alternative \\nPG petrol generator \\nPV photovoltaic \\nRE renewable energy \\nRES renewable energy system \\nRET renewable energy technology \\nSDG sustainable development goal \\nSHS solar home system \\nSSA sub-Saharan Africa \\nTEM transactive electricity market \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,519,485,728]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"lem, with $6 5 \\\\%$ of primary energy (cooking, heating and lightning) in the EA-8 sourced from solid biomass [6], and in urban regions where diesel/petrol fuelled generators are employed in ameliorating the effect of electric power supply unreliability on the quality of life. The air quality impacts from both situations could adversely impact human health [6,9,20,26]. SSA’s electricity crisis presents an opportunity to address the electricity access deficit in tandem with climate change. The region is already considered a non-significant contributor to global greenhouse gas (GHG) emissions with its global contributions at $2 \\\\mathrm { - } 3 \\\\%$ attributed to energy related and industrial activities [10]. Furthermore, about $6 0 \\\\%$ of the countries on the continent have committed to climate change mitigation by ratifying the “Paris Climate Accord” [1,11]. However, South-Africa with an electrification rate of approximately $8 8 \\\\%$ is looking to bring about 12 GW of coal-powered plants online, with Malawi and Zimbabwe also making considerable investments in coal-power generation capacities [3]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,731,485,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Climate policies and an enabling regulatory environment will be required in realising country-level and regional climate change mitigation commitments. The transition to a low-carbon economy has garnered some level of success in the eastern sub-region [16], with countries implementing sustainable energy solutions for rural electrification [3]. A notable industry leader in SSA is M-Kopa – a Kenyan solar energy company, serving Kenya, Tanzania and Uganda. According to the company, they have been able to develop solar home systems (SHSs) for over 600,000 low-income households in these countries, providing them with affordable and cleaner access to energy [12]. They have also been able to pioneer a pay-as-you-go mobile payment system for collecting returns on their services and in remotely monitoring (communicating with) their physical asset. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,902,485,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As the discourse on SSA’s electricity paucity centres on providing electricity supply access to underserved and unserved communities particularly in rural areas, urban regions could experience an electricity supply deficit resulting from natural population growth and rural-urban migration. With over $5 0 \\\\%$ of the African population predicted to be living in cities by 2030 and $6 0 \\\\%$ by 2050, urbanisation is a social phenomenon that could influence access to electricity by putting pressure on energy resources and infrastructure [3]. At the country-level, Nigeria is predicted to add about 212 million people to its urban population between 2014 and 2050 [1]. The success recorded so far through the deployment of low-carbon technology for rural electrification in eastern Africa, presents an opportunity for exploring sustainable energy solutions in extending power supply access, improving power quality and sustaining the duration of electricity supply to a growing urban region (commercial, industrial and residential) in SSA. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,70,937,226]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,228,939,320]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In light of these conditions, further discussions in this paper are structured as follows: Section 2 covers a review of the literature on the energy solutions and drivers to energy access in SSA. Section 3 presents the method adopted, outlining the case study on Nigerian commercial centres and defining system operations design. Section 4 covers the results of the case study analysis with Section 5 discussing the implications of the results. Section 6 concludes the paper. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,335,702,346]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. Review of relevant studies \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,360,937,517]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The literature on SSA’s electricity supply paucity and the energy solutions that could bridge the power supply to demand deficit is extensive, with discussions highlighting power supply access and reliability as a nexus to the region’s socioeconomic development. Documented energy solutions for electrifying SSA’s unserved and underserved communities favour sustainable energy solutions due to their minimal to zero adverse impact on public health and the environment, amongst other factors. Consequently, literature on SSA’s electric power supply unreliability is reviewed accounting for the western, eastern and southern Africa sub-regions, with discussions split into energy solutions for increasing electrification and the drivers for improving electricity supply access. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,533,635,544]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.1. Energy solutions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,561,937,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"With the electrification rate of most countries in SSA excluding South-Africa below $3 0 \\\\%$ and an average electrification rate of $1 6 \\\\%$ in rural communities [3], existing literature on energy solutions for the region mainly focus on implementing sustainable solutions for rural settlements towards meeting their primary energy needs i.e. cooking, heating and lighting. Okoye and Oranekwu-Okoye [14] advocated the economic viability of solar-photovoltaic (PV) systems for rural electrification in SSA, using rural Gusau, Nigeria as a case study. Other studies by Azimoh et al. [23] on rural Namibia and Boamah and Rothfub [19] on Ghana analysed the successes of the hybrid (solar-diesel) minigrid system in operation and the government-led solar home system (SHS) initiative respectively. Considering the wider benefits of “electrification beyond lighting”, Schwerhoff and Sy [20] identified large-scale renewable energy developmental projects requiring substantial capital as integral to electrifying SSA and accelerating the transition to sustainable energy solutions. Barasa et al. [21] demonstrated the cost suitability of renewable energy (RE) systems delivering power through a high voltage direct current (HVDC) grid and their potential in increasing regional electrification through interconnected grid systems. Presley et al. [13] disputed the immediate focus on deploying sustainable solutions for electrification by arguing that the transition should only occur once conventional energy has been scaled up and utilised in achieving the “benchmark” of reducing energy poverty and accelerating economic growth and development. Adhekpukoli [29] presented the democratisation of Nigeria’s electricity industry by further deregulating the sector to accommodate disparate electric power producers as a solution to the ‘decades-long’ electricity supply deficit. There is a need for sharing the emphasis on Africa’s electrification agenda between the rural deficient and increasing electricity supply access to urban regions, particularly economic drivers like the commercial and industrial (C&I) sectors. A cost-benefit analysis by Olówósejéjé et al. [25] on Nigeria’s industrial sector realised that industries could make significant cost savings if they transitioned to solar-PV based systems instead of complementing unreliable grid power with diesel generation. Sustainable energy solutions are being favoured for narrowing the electricity supply shortfall in rural SSA because they address the global issue of climate change. Chakamera and Alagidede [16] emphasised the need to mitigate the adverse effect of climate change by decreasing electricity production from nonrenewable energy sources and increasing production from renewable energy sources in the long term. Ouedraogo [17] stated that the economic, social and environmental benefits of deploying renewable energy technology and infrastructure outweighed its capital-intensive nature. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[766,45,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable Futures 2 (2020) 100022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,45,258,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Olówósejéjé, P. Leahy and A.P. Morrison \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,70,485,240]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,242,485,424]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Rose et al. [35] evaluated the potential of solar-PV (combined with reservoir hydropower) grid connected systems in displacing diesel generation in Kenya. They suggested that these large-scale RE systems are more impactful investments in providing sustainable energy solutions and significantly reducing carbon emissions. The United Nations 2030 target of ensuring access to affordable, reliable, sustainable and modern energy for all might have to be revised due to the rate at which SSA is being electrified. To support this point, Bazilian et al. [22] considered regional electrification targets in line with that of the Sustainable Development Goals (SDGs) as quite ambitious, stating that power generation capacity has not kept pace with population growth. They also put forward the contrasting level of commitment to power development projects amongst countries in the region as a significant issue in realising the SDGs within the stipulated time period. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,440,210,452]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2. Energy access drivers \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,467,485,861]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The unavailability of and inaccessibility to data on the energy sector in SSA critically inhibits effective electricity supply planning and implementation. Trotter et al. [15] identified a major problem of electricity planning as the lack and unreliability of data. Bazilian [24] in discussing the role of international institutions in fostering SSA’s electrification, implored the establishment of an information sharing mechanism towards improving the delivery of financial instruments and initiatives to the region. Ateba and Prinsloo [33] in identifying an effective approach towards electricity supply sustainability in South Africa, recommended the development of an integrated strategic management framework for sectoral planning informed by the holistic and comprehensive analyses of grid operations. The necessity for accessible energy data cannot be overemphasised as energy policies are informed by available data on the production, distribution and consumption of energy. Trotter et al. [15] listed the enabling factors for sustaining SSA’s electrification drive as adequate policy design, sufficient finance, securing social benefits, a favourable political situation, community engagement together with human capital development. Azimoh et al. [23] listed government support, involvement of the local community, capacity development of same, sensitisation towards energy efficient practices, prepaid metering and the adoption of a progressive electricity tariff system as factors that have sustained the operation of the mini-grid system in Tsumkwe village, Namibia. In another study, Jain and Jain [32] presented political instability, contrasting energy strategies, technical ineptitude and grid infrastructure modification/integration as issues to be addressed in electrifying rural localities through renewable energy technology (RET). Adesanya and Schelly [26] concluded that renewable energy uptake in Nigeria is subject to supporting energy policies and an awareness drive through synergies amongst the government, financial institutions, private investors and stakeholders. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,862,485,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It is imperative that the renewable energy industry in SSA is derisked to promote investments in renewable energy technology (RET) by private investors, multilateral financial organisations and international development partners. Obeng-Darko [28] in discussing the impeding factors to Ghana utilising renewable energy and energy efficient technologies in achieving a $1 0 \\\\%$ penetration of national electricity production by 2020, highlighted deficiencies in legislative and regulatory frameworks as risk escalators deterring investments in renewable energy development projects and initiatives. Consolidating discussions in [28], Aliyu et al. [30] highlighted the importance of renewable energy policy mechanisms such as feed-in-tariffs and net energy metering in promoting and incentivising investments in renewable energy technology. Moner-Girona et al. [34] recommended the implementation of RETspecific tariffs for incentivising national and international investments in RETs. Social factors and societal behaviours have to be considered in the deployment of energy solutions and more particularly innovative solutions and new technology. Boamah and Rothfub [19] stated that the inter-relationship between energy and society is an important factor in implementing energy development projects. Wojuola and Alant [27] inferred the integration of sustainable development in education, science and technology policies towards fostering a national sustainable development culture, after realising a low level of knowledge on RETs in their survey of Ibadan, Nigeria. They also recommended that energy education should encompass all knowledge delivery systems. Misplacing priorities on energy development projects could scupper the rate at which continent-wide social and economic development is achieved. Trotter and Abdullah [18] proposed that international involvement in Africa’s energy sector be redirected towards focussing on making public aid available for rural electrification, promoting local content through dissemination of technology and relaxing the conditions on foreign aid in order to support state-driven leadership. Simone and Bazilian [24] also proposed that international institutions channel their efforts into supporting the development of sound energy policies, sectoral reforms, corporate governance and ensuring transparency best practices. Renewably-powered systems for rural electrification could be faced with sustainability challenges, if the after services are not functional. Azimoh et al. [31] surveyed rural households in South Africa to investigate the impact of the SHS programme on the community. They argued that although the programme had facilitated the illumination of households thereby increasing study and business hours, it was not sustainable in the offing. This was due to the inadequacies of the fee for service payment model, the system’s limited power supply, improper system use, equipment theft and the rising cost of doing business for the energy service companies. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,69,939,571]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,586,662,597]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.3. Gaps in the literature \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,612,937,703]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A review of the literature shows solar-power based systems as the preferred energy solution (due to a continent-wide resource abundance) in facilitating SSA’s electrification. Their deployment either in standalone configurations or in complementarity with fossil-fuel based systems were consistent in the discourse. Also consistent in the literature was the mode in which these RETs were implemented (SHSs and minigrid systems). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,704,937,887]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Following the extensive literature review, we present three stages/enablers to energy supply access. The first stage encompasses a politically stable environment, reliable data that is readily accessible and energy policies, with policy actions supported by an enabling legislative and regulatory infrastructure. Access to RE development finance, mechanisms incentivising RET investments, dissemination of RET, energy sector reforms and effective payment models for collecting returns on RET services constitute the second stage. The third stage focusses on community engagement in determining the best-fit innovative solutions as well as in inculcating a community-wide technology sustenance culture post-project implementation. The first stage serves as the building blocks for the successful implementation of the second stage with the final stage ensuring the sustenance of the project after completion. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,889,937,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Throughout the breadth of the literature, discussions have centred on implementing grid defection solutions (small-scale SHSs and minigrid systems) for the electrification of rural SSA. With an electrification rate of less than $3 0 \\\\%$ in most SSA countries [3], it is important that electrifying rural areas is in tandem with extending and improving the quality of power delivered to urban regions. It is also important that electrification goes beyond lighting and provides the quality of power required in meeting the operational demands of urban-domiciled commercial centres and industries. This study seeks to address this gap in literature by analysing the economic and environmental viability of hybrid scalable PV-centric grid defection solutions for urban commercial centres (with urban regions comprising of commercial, industrial and residential sectors) towards a collective electrification drive i.e. increasing urban electrification and sustaining rural electrification efforts. A systematic analysis is carried out on 14 stand-alone integrated power system designs in meeting the electricity demand of urban commercial sectors and by extension, augmenting electricity supply access to the residential sector. There is an opportunity for surplus energy generated from these hybrid systems to power the residential sectors through industrial and commercial coalition formations. As a sustainable approach in terms of economic viability, the non-essentiality of energy storage systems in these hybrid configurations based on regional location is also elicited. The focus on the commercial sector stems from the fact that small and medium scale enterprises are the mainstay of an economy. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[766,45,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable Futures 2 (2020) 100022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,45,258,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Olówósejéjé, P. Leahy and A.P. Morrison \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[231,97,769,292]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0720/85c9b6eb979f8e6510d10dc5a297fb30a6356593e8b269f7756fbed5d1acdfcd.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=\\\"2\\\">IPS</td><td colspan=\\\"3\\\">Capacity (kW)</td><td>Capacity (kWh)</td></tr><tr><td>Solar-photovoltaic (PV)</td><td>Diesel generator (DG)</td><td>Petrol generator (PG)</td><td>Battery array</td></tr><tr><td>RES</td><td>100</td><td>=</td><td>=</td><td>82</td></tr><tr><td>GS</td><td>1</td><td>15.5</td><td>2.2</td><td>1</td></tr><tr><td>IHSS</td><td>30</td><td>15.5</td><td>2.2</td><td>=</td></tr><tr><td>IHSBS 1</td><td>20</td><td>15.5</td><td>1</td><td>12</td></tr><tr><td>IHSBS 2</td><td>30</td><td>15.5</td><td>1</td><td>12</td></tr><tr><td>IHSBS3</td><td>40</td><td>15.5</td><td></td><td>12</td></tr><tr><td>IHSBS 4</td><td>50</td><td>15.5</td><td></td><td>12</td></tr><tr><td>IHSBS 5</td><td>60</td><td>15.5</td><td></td><td>28</td></tr><tr><td>IHSBS 6</td><td>70</td><td>15.5</td><td></td><td>42</td></tr><tr><td>IHSBS7</td><td>80</td><td>15.5</td><td></td><td>42</td></tr><tr><td>IHSBS8</td><td>90</td><td>15.5</td><td>二</td><td>42</td></tr><tr><td>IHGS 1</td><td>10</td><td>15.5</td><td>2.2</td><td>1</td></tr><tr><td>IHGS 2</td><td>10</td><td>15.5</td><td>2.2</td><td>12</td></tr><tr><td>IHGS 3</td><td>10</td><td>15.5</td><td>1</td><td>12</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1 Summary of the IPS’ system capacities. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[62,315,485,578]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,596,131,607]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. Method \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,621,485,832]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This study was guided by three fundamental pillars: affordability, reliability and sustainability. Commercial centres in Abuja’s (Nigeria) metropolis were surveyed to establish their most commonly-occurring commercial activities, which informed load demand projections. Subsequently, Olowos Plaza, a model single commercial centre housing the commercial outlets that cater to these activities was created and modelled in detail as a case study. A systematic analysis was performed on 14 different integrated power systems (IPSs): (a renewable energy system (RES); a fossil-fuel generator system (GS); an integrated hybrid solarbased system (IHSS); eight integrated hybrid solar and battery-based systems (IHSBS); and three integrated hybrid generator-based systems (IHGS)). In realising a viable solution, the power systems were analysed against three impact/performance metrics: cost implication (\\\\$/lifetime over 20 years), GHG emissions $\\\\mathrm { C O } _ { 2 }$ tonnes/yr.) and surplus energy (MWh/yr.). Table 1 summarises the system capacities of the $1 4 ~ \\\\mathrm { I P S } ^ { \\\\prime }$ operations designs. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[63,849,258,861]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1. Survey on commercial centres \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,876,485,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Forty commercial centres in Abuja were surveyed to establish the most commonly-occurring commercial activities in these centres. A checklist was designed with 31 out of the 40 centres surveyed accommodating commercial outlets that engage in three or more of its listed activities, namely: cyber café businesses, boutiques, salons, tailoring businesses and grocery shops. These results informed the creation of Olowos Plaza, located in Abuja and housing a cyber café, boutique, salon, tailoring and grocery shop. See Supplementary material 1 for the survey checklist. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,316,939,366]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,389,774,401]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1.1. Load demand projection/determination \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,402,939,558]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The weekly load demand of Olowos Plaza was realised based on the power requirements of the five commercial outlets. Olowos Plaza is open for business seven days a week with reduced business hours on Sundays. Some commercial outlets (cyber café, boutique and tailoring shops) are not operational on Sundays. Business operations are from 9 a.m. to $1 0 \\\\ \\\\mathrm { p . m . }$ ., Mondays to Saturdays, and from noon to $5 \\\\ \\\\mathrm { p . m }$ . on Sundays. Business times are representative of most commercial centres in Nigeria. Fig. 1 indicates the hourly load demand (kW) for Olowos plaza for a typical weekday, Saturday and Sunday. See Supplementary material 2, 3 and 4 for the typical week (weekdays and weekend) power consumption breakdown, equipment model and power rating, as well as business operation assumptions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,580,800,591]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2. Power system selection and cost consideration \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,605,937,670]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The three main power system components (although with different system compositions, and in different capacities and operations configuration) analysed in meeting Olowos Plaza’s load demand were a solarphotovoltaic (PV) system, a battery storage system and a fossil-fuel generator system. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,692,647,703]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2.1. Solar-PV system \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,704,939,847]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Solar-PV system operations was designed using Abuja’s global horizontal irradiation (GHI) data for year 2017 sourced from Copernicus Atmosphere Monitoring Service [36]. $1 0 0 \\\\mathsf { W _ { p } }$ $( V _ { o c } \\\\mathrm { ~ - ~ } 2 2 . 3 \\\\mathrm { ~ V } ; I _ { s c } \\\\mathrm { ~ - ~ }$ 6A; $V _ { m p } - 1 8 ~ \\\\mathrm { V } ;$ ; $I _ { m p } - 5 . 5 6 A .$ ; $\\\\eta - 1 9 . 2 \\\\% )$ monocrystalline solar-PV panels (considering the technical data specific to the panel’s power rating) were selected and sized for every $1 0 \\\\mathrm { k W }$ capacity increment, for systems’ operation design in the $1 0 \\\\mathrm { k W _ { p } } – 1 0 0 \\\\mathrm { k W _ { p } }$ capacity range. For practicality, $\\\\ \\\" 4 8 \\\\nabla ^ { \\\\mathrm { 3 } }$ string array configurations were considered i.e. to limit the systems’ current-carrying capacity, thereby limiting the systems’ protection sizing. See Supplementary material 5 for a full listing of operations design assumptions and considerations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,849,939,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Solar-PV system cost consideration: A 20 year operational lifetime was considered when determining system cost prices. The PV panels’ costs were based on wholesale prices [37]. The other costs taken into account for the PV system include the land costs, balance of system (BOS) costs (excluding battery storage costs) and PV panel maintenance costs. Maintenance costs (cleaning schedules) were considered due to the location of Olowos Plaza and its susceptibility to seasonal dust accumulation [38]. Eq. (1) was used in determining the lifetime (Lt) costs for the solar-PV systems’ capacities. See Supplementary material 6 for a full listing of the systems’ cost assumptions and considerations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[766,45,939,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable Futures 2 (2020) 100022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,45,258,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Olówósejéjé, P. Leahy and A.P. Morrison \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[63,70,625,253]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 1. Olowos plaza hourly load demand for a typical weekday, Saturday and Sunday. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0557/2e1e7b122b0b02daf9e7211f8abaf8f8504eb13ad20d95f71cfd11b0b5b19daa.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[62,287,485,326]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,337,485,350]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Total Cost $=$ Capital $^ +$ Maintenance $^ +$ Replacement Costs $^ +$ Land Cost (1) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,366,228,378]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2.2. Battery storage system \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,380,485,563]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Flooded, deep-cycle, lead-acid batteries (the industry workhorse) were selected as the technology for the battery storage system. “Rolls” batteries were selected due to capacity and cost considerations. We employed brute-force search in determining the battery capacity for our system array. The search compared $6 \\\\mathrm { ~ V ~ }$ and $^ { 1 2 \\\\mathrm { ~ V ~ } }$ battery types from three battery manufacturers (others being “Trojan” and “Crown” batteries) against possible application ${ } ^ { \\\\mathfrak { s } } \\\\mathbf { C }$ -rates” $\\\\mathrm { . 1 0 h r }$ , 13hr and 15hr) and depth of discharge $1 0 \\\\%$ , $2 0 \\\\%$ , $3 0 \\\\%$ and $4 0 \\\\%$ ). We opted for a $4 8 \\\\mathrm { \\\\ : V }$ system and limited an array to three parallel connections, with reference to the “Rolls” battery manual [39]. Also referencing the manual [39], we employed a multi-stage (bulk, absorption and float) battery charge for the “charging” phase in the battery array’s operation cycle. See Supplementary material 5 for further details on the battery storage system’s operation design. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,564,485,630]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Battery storage system cost consideration: The capital, replacement and maintenance costs for a 20 year operational lifetime were considered for the battery storage systems. Eq. (2) was employed in realising the lifetime costs for the different battery storage capacities. See Supplementary material 6 for further details on battery storage system costs. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,641,383,653]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Total Cost $=$ Capital $^ +$ Maintenance $^ +$ Replacement Costs \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,670,201,682]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2.3. Generator system \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,683,485,800]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The fossil-fuelled generator system consists of one “19.3kVA/15.5kW” diesel-fuelled and one “2.8kVA/2.2kW” petrolfuelled generator installed at the canopy level operating in prime power mode. 3-phase, direct-injection generators with a rotation speed of $1 5 0 0 \\\\mathrm { r p m }$ were considered for the system. Pertaining to system lifetime, we were guided by “HOMER” – a software on distributed generation power system design and optimisation [40], whilst considering the system’s mode of operations. See Supplementary material 5 for further details on the generator system’s operation design. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,802,485,866]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Generator system cost consideration: The capital, replacement, fuel and maintenance costs for a 20 year operational lifetime were considered for the generator system. Eq. (3) was used in determining the generator system’s lifetime costs. See Supplementary material 6 for further details on these costs. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,877,425,890]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Total \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,902,485,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A life-cycle cost analysis (LCCA) was carried out on the different IPS for their operational lifetime. The real discount rate was calculated considering inflation at $1 1 . 4 \\\\%$ and nominal interest rate at $1 4 \\\\%$ [41,42]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[532,287,821,300]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For the calculations, we employed the equation: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,303,613,329]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0659/2c306d7cd31a93c04465d7bc52b95da6ab385170791c479ea1ff1767525f7022.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\operatorname { r } = \\\\left( { \\\\frac { 1 + i } { 1 + n } } \\\\right) - 1\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[514,332,554,344]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[532,354,808,393]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$r =$ real discount/interest rate; $i =$ nominal interest rate; and $n =$ inflation rate, taken as $2 \\\\%$ representative. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,403,939,480]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This rate was used in calculating the present value of the maintenance, operations and replacement costs for the lifetime of the $1 4 ~ \\\\mathrm { I P S }$ analysed. Diesel and petrol costs [43,44] were considered for the generator system. The solar-PV system cost accounts for the BOS components costs, as well as the charge controllers and inverter capital and replacement costs. Supplementary material 7 details the LCCA on the IPSs. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,494,754,506]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.3. System operations of the different IPS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,519,939,585]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figs. 2, 3 and 4 indicate the hourly system operations of the different IPS for a typical weekday, Saturday and Sunday, respectively. In these representations, the following codes are used to indicate the main power source for each hour of the day: Photovoltaic – PV; Battery – Batt; Diesel Generator – DG and Petrol Generator – PG. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,598,579,610]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. Results \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,625,939,728]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"From our analysis, the “IHSS” variant is the cheapest (\\\\$162,225) IPS of the 14 power systems analysed. Olowos Plaza will make power system cost (capital, replacement, operations and maintenance) savings of up to $5 5 \\\\%$ when compared to the average power system costs (\\\\$358,578) for its operational lifetime. The plaza will make further power system cost savings of up to $2 6 \\\\%$ when compared to the “RES” – the most costly (\\\\$867,436) power system for the analysis. Fig. 5 represents the various IPS’ costs. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,731,939,875]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Informed by power distribution companies’ (DisCos) unwillingness to transact with embedded generators (with proferred excuses of network maintenance and rehabilitation), and with all but one of the power systems generating surplus energy (MWh/yr.), we factored in the surplus energy performance metric. We hypothesise that the inability to capitalise on the surplus energy generated by Olowos Plaza power systems’ operations would be more impactful to the systems at the upper limit of the surplus energy metric. The plaza is also permitted to operate without a power distribution license in all the power system capacities considered [45]. Fig. 6 represents the IPS’ costs and surplus energy relationship. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,876,937,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The “GS” is the only power system of the 14 analysed that generated no surplus energy through its operations. As an outlier it was not included in calculations determining the average surplus energy (56 MWh/yr.). The “RES” through its operations, generated the most surplus energy (126 MWh/yr.) of the systems’. With no operational transactive electricity market (TEM) in place, we considered the systems with surplus energy generation above average as non-feasible with precedence set on system operations efficiency i.e. closely matched supply-demand ratio (systems generating below the average surplus energy). In light of these, eight of the fourteen IPS analysed were found to generate surplus energy below the average. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[766,45,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable Futures 2 (2020) 100022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,45,258,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Olówósejéjé, P. Leahy and A.P. Morrison \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[119,70,884,278]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0074/5daf7f48b41670d20bef5d2290da89072a71faac56bfef96181485636857b3bf.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[119,308,887,514]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0642/87d0825e0a06224235585d2b80b6b10724310fa9a1e0c89cf3a3afa0eb0d73be.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[119,552,885,759]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 4. Hourly system operations of the different IPS for a typical Sunday. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0169/46ef5ff481d01afbb6540a640d84be5316031366bcb5e1b75dee32cd5cab94c0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[62,809,485,887]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,889,485,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In determining the $\\\\mathrm { C O } _ { 2 }$ (tonnes/year) value for the different IPS, we worked with the assumption of diesel fuel emitting $2 . 6 8 ~ \\\\mathrm { k g }$ per litre consumption and petrol emitting $2 . 3 1 ~ \\\\mathrm { k g }$ per litre consumption [46]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,809,937,836]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Fig. 7 ( hockey stick graph) represents the IPS’ costs and GHG emissions relationship. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,837,939,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The “RES” is the only power system of the 14 analysed that emitted no greenhouse gases through its operations. As an outlier it was not included in calculations determining the average GHG emissions $( 2 2 \\\\mathsf { C O } _ { 2 }$ tonnes/year). The “GS” through its operations, generated the most GHG emissions (47 $\\\\mathrm { C O } _ { 2 }$ tonnes/year) of the systems. Furthermore, and with emphasis on GHG emissions, the following power systems were feasible: IHSS, IHSBS 2, IHSBS 3, IHSBS 4, IHSBS 5, IHSBS 6, IHSBS 7, IHSBS 8 and RES. The following were also feasible when assessing the systems for cost implication: GS, IHGS 1, IHGS 2, IHGS 3, IHSS, IHSBS 1, IHSBS 2, IHSBS 3 and IHSBS 4, with a review on the systems’ surplus energy returning these: GS, IHGS 1, IHGS 3, IHSS, IHSBS 1, IHSBS 2, IHSBS 3 and IHSBS 4, as practicable. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[766,45,939,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable Futures 2 (2020) 100022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,45,258,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Olówósejéjé, P. Leahy and A.P. Morrison \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[139,70,867,383]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 5. Total lifetime cost of all IPS, in descending order of percentage renewable contribution. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0483/bc2ff2c3be47c73190d54dde7047332cb4e13afc51a2fd495deb62e900d49702.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[124,423,882,812]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 6. IPS’ costs and surplus energy relationship in ascending order of surplus energy generated. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0780/975cd5fa3d0787f553aa2503dba0b884a443bd54f68341bf04db40bbbeeba170.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[62,860,487,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,860,939,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Considering all impact/performance metrics, we realised a feasible solutions (“sweet spot”) region for Olowos Plaza. The region comprises hybrid power systems, with one solar-PV based system (IHSS) and three solar-PV and battery based systems (IHSBS 2, IHSBS 3 and IHSBS 4). In light of these, the “IHSS” is the most viable power system solution of the 14 integrated power system operations analysed. It best satisfied the conditions of the impact assessment defined by the three impact metrics of; cost implication (\\\\$/lifetime (20 years)), GHG emissions $\\\\mathrm { C O } _ { 2 }$ tonnes/yr.) and surplus energy (MWh/yr.) – Figs. 5, 6 and 7, respectively. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[766,45,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable Futures 2 (2020) 100022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,45,258,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Olówósejéjé, P. Leahy and A.P. Morrison \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[121,73,884,438]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 7. IPS’ costs and GHG emissions relationship in descending order of percentage renewable contribution. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0222/56f9b2095fa51ccf0e131ae997a11227baf8d61ff5b7b34dc324f3e8c10d096c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[62,486,485,552]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,552,485,578]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Summarising the result of our analysis, we present the following salient points: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,586,487,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"i. The “IHSS” is the cheapest power system option, with surplus energy of 25 MWh/yr., $8 0 \\\\%$ less than the largest surplus energy generator and emitting $5 3 \\\\%$ less GHG emissions than the largest emitter. \\nii. With a tariff of $\\\\$ 0.12/4W h$ for commercial (single and 3-phase) customers [47], an average of $3 5 . 8 \\\\mathrm { ~ h ~ }$ of electricity per week [48] and commercial centre residents incurring an extra $\\\\$ 0.20$ $- \\\\ 0 . 3 0 / \\\\mathrm { k W h }$ on generators for security of supply [48], the GS, IHGS 1, IHGS 2, IHGS 3, IHSS, IHSBS 1, IHSBS 2, IHSBS 3 and IHSBS 4 all provide off-grid power solutions that are reliable with cheaper-to-similar costs as the commercial centres’ current power systems. (See Supplementary material 6 for conversion rates.) \\niii. The choice of a petrol generator over a battery storage system led to significant lifetime cost savings for the “IHSS” to the sum of $\\\\$ 74,446$ when compared with the “IHSBS $2 ^ { \\\\prime \\\\prime }$ . Although, the “IHSBS $2 ^ { \\\\prime \\\\prime }$ performed slightly better than the “IHSS” against the other impact metrics i.e. generated approximately 1 MWh/yr. less surplus energy, emitting 6 tonnes fewer $\\\\mathrm { C O } _ { 2 }$ emissions. \\niv. Focussing on the IHSBS’ and referring to Fig. 7, we observe a distinct transition from IHSBS 4 – IHSBS 5, an inflection point in our systems analysis with feasibility ramifications. The marginal cost of increasing the renewable percentage contribution begins to increase at the transition from IHSBS 4 – IHSBS 5. \\nv. Guided by Luckow et al.’s [49] report, we introduced a carbon tax $\\\\left( \\\\$ 25\\\\right)$ on the generator (GS) and hybrid generator-based systems (IHGS 1, IHGS 2 and IHGS 3) and still found them costcompetitive (average increase of $\\\\$ 0.03/40$ in levelised cost of \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[552,486,937,511]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"energy (LCOE)) when compared to commercial centres’ current power systems. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[532,513,939,604]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"vi. The design and installation of a generator system at the canopy level for commercial centres allows for easier monitoring of air quality and implementing carbon air filter technologies. It also addresses the proliferation of small-scale petrol generators from shop to shop and floor to floor, improving air quality and mitigating the adverse effect of generator fumes on the health [6,9, 20]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[529,605,939,696]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"vii. Renewably-powered commercial centres, vanguard a transition to smart energy systems that ensures commercial centre residents energy consumption and usage are cost-reflective. For Olowos Plaza, this would result in commercial outlet 1 paying $4 7 \\\\%$ of the Plaza’s total yearly electricity costs, outlet $3 \\\\mathrm { - } 4 1 \\\\%$ , outlet $5 { - } 1 0 \\\\%$ and outlets 2 and 4 paying $1 \\\\%$ , respectively. Refer to Supplementary material 4 for the commercial outlets activities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,717,601,728]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5. Discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,744,937,875]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results from our case study analysis demonstrate beneficial electrification for the commercial sector through PV-centric grid defection solutions. Total grid defection solutions also present an opportunity for the DisCos to increase the duration and improve the quality of electricity supply to the residential sector by reducing the number of energy intensive C&I customers connected to their network. These non-wire alternatives (NWA) could also be explored in partial grid defection configurations by incentivising surplus energy generation through policy mechanisms like net energy metering (NEM). It would mean electricity is made available during periods of peak demand and in emergencies. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,876,939,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In bolstering economic development, surplus energy generation could yet be pivotal in propelling the formation of a transactive electricity market (TEM) through C&I coalition formations that could further develop into hubs, clusters and villages. Reiterating recommendations by Adhekpukoli [29], further deregulation of the electricity sector to accommodate more independent power producers, embedded and captive power generators could be pivotal to increasing urban and rural electrification. As such, TEM would have to be backed by policy and an adequate regulatory infrastructure. The democratisation of the electricity sector to involve more nonconventional power producers by introducing different pathways (generation to consumers) as opposed to the traditional power delivery structure (generation to transmission to distribution to utilisation) increases business competition (through direct competition or partnerships) with the DisCos that could drive customers electricity supply costs down. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[766,45,939,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable Futures 2 (2020) 100022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,45,258,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Olówósejéjé, P. Leahy and A.P. Morrison \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,70,485,200]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,203,485,424]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We posit that the C&I sectors transitioning to prosumers generating excess electricity could by extension electrify the residential sectors provided adequate legislative and regulatory frameworks are in place. We refer to this initiative as “Commercial Electrification of the Residential Sector (Comtridential)”. This could be in partnership with the DisCos (requiring further investments in revamping and modifying their electricity infrastructure/networks) or directly with the residential sector focussing on residential estates. The latter would require significant investments in the deployment of power distribution infrastructure. The potential for this energy solution could be measured by the willingness of residential estates (middle to high income earners) in maintaining access to an electricity supply network and increasing the duration of supplied hours. Given the electricity supply situation, an example of customer willingness in remaining electrified draws from the collective efforts of estate residents in funding the replacement of damaged service transformers resulting from power surges due to grid unreliability and intermittency. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,427,485,596]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The transition to sustainable solutions as a means in electrifying the various sectors that contribute to the socioeconomic development of a nation is possible and is being exemplified in Nigeria through a public sector led initiative. The Nigerian government through its rural electrification agency (REA), in partnership with private investors and multilateral finance institutions (The World Bank and African Development Bank) are deploying solar-PV powered utility-scale (stand-alone) systems in improving electricity supply to the commercial, industrial, education and health sectors [50]. These solutions are being implemented under two initiatives (Energising Economies and Energising Education), underscoring the importance of non-fragmented finance by international donor organisations and multilateral institutions as elicited by Simone and Bazilian [24]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,612,157,624]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6. Conclusions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,638,485,914]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The results of this analysis show that a practical approach of adopting hybrid systems with PV, batteries and fossil fuel generation in urban commercial settings in Nigeria will greatly reduce lifetime energy costs and deliver reliable power to loads. These would be achieved while simultaneously contributing to decarbonisation and improving air quality by reducing overall reliance on fossil fuel self-generation. It also elicited the non-essentiality of energy storage systems (high cost considerations) in regions of abundant solar energy resource especially for hybrid energy systems that also incorporate non-renewable sources of power generation. The IHSS evidenced this, by best satisfying the economic and environmental metrics of our analysis i.e. being the cheapest power system option and emitting $5 3 \\\\%$ less GHG emissions than the largest emitter. Also, from this study, we realised that disparate energy solutions would have to be explored in meeting country-level and regional electrification targets in the medium to long term. Our case study results further highlighted total to partial sustainable grid defection solutions as practicable solutions for urban electrification. A unique case was presented for the commercial electrification of the residential sector (comtridential) through commercial and industrial coalition formations taking advantage of the generation of surplus energy from hybrid renewable energy systems operating in a liberated transactive electricity market. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,915,485,940]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Our case study on commercial centres informed the reality that most project developers assess their project feasibility solely on its cost implication, disregarding its social and environmental effects. Therefore without adequate climate policies, the generator and three generator-based hybrid systems (GS, IHGS1, IHGS2 and IHGS3) emitting 47, 44, 40 and $3 8 \\\\thinspace \\\\mathrm { C O _ { 2 } }$ tonnes/year respectively, would have been considered feasible. Focussing on the issue of climate change, sustainable energy solutions are being favoured in electrifying rural SSA. The deployment of sustainable energy solutions addresses the regional electrification crisis in tandem with mitigating the effect of climate change. Energy policy formulation that serves as a proper deterrent to carbon-intensive processes of the commercial, industrial and power sectors present a more impactful approach in reducing carbon emissions and mitigating the effect of climate change beyond small-scale, PV-centric, grid defection solutions. Consequently, the role of individual nation’s government in improving regional electrification rates, both in urban and rural areas, cannot be overemphasised. Government support through policy actions and ensuring an enabling regulatory environment are essential in driving the energy transition through the implementation of sustainable energy solutions. These precursors form the bedrock to improving access to finance, implementing policy mechanisms, dissemination of information & technology, initiating sectoral reforms and community engagement. Ready access to reliable data across the region is also important in informing financial investments and implementing sustainable development projects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,70,937,372]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,374,939,518]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In light of these, if the United Nations SDGs are to be met by 2030, it is important that SSA’s rural electrification agenda goes beyond lighting and provides the required energy that could stimulate socioeconomic activities towards the collective development of communities, broader countries and the wider region. Sustainable electrification targeting core urban sectors (commercial, industrial and residential), are channelled measures in addressing the attendant consequences of urbanisation and spurring economic development through industrialisation. Therefore, it is critical that rural electrification is sustained alongside efforts of extending electrification, improving the quality of power delivered and increasing the duration of electricity supply access to urban areas. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,532,732,544]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Declaration Competing of Interest \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[534,558,756,569]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"No conflict of interest to be declared. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,586,631,597]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgement \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,612,937,636]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This work was supported by the Petroleum Technology Development Fund (PTDF): [Grant Number PTDF/ED/PHD/ SAO/776/15]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,651,675,663]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Supplementary materials \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,678,939,703]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.sftr.2020.100022. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,715,584,726]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[521,738,939,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"[1] International Bank for Reconstruction and Development, in: The State of Electricity Access Report, The World Bank Group, 2017, pp. 1–80. \\n[2] The Economist Intelligence Unit, Power up: delivering renewable energy in Africa, The Economist Group. 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Leahy, A Morrison, Combined effects of dust accumulation and array tilt angle on the energy yield of photovoltaic systems, in: Proceedings of Energy Systems Conference, London, 2018 19th–20th June 2018. \\n[39] Rolls Battery Engineering (n.d). Battery User Manual. Surrette Battery Company Limited. pp. 7, 9 and 10 – 14. 2019 \\n[40] HOMER Energy (2018). Generator Lifetime [online] available from https://www.homerenergy.com/products/pro/docs/3.11/generator_lifetime.html [20th September 2018] \\n[41] Nigeria Inflation Rate (2018). Trading Economics [online] available from https://tradingeconomics.com/nigeria/inflation-cpi [5th December 2018] \\n[42] Nigeria Interest Rate (2018). Trading Economics [online] available from https://tradingeconomics.com/nigeria/interest-rate [5th December 2018] \\n[43] GlobalPetrolPrices (2018). Diesel Prices [online] available from https://www.globalpetrolprices.com/diesel_prices/ [15th December 2018] \\n[44] GlobalPetrolPrices (2018). Gasoline Prices [online] available from https://www.globalpetrolprices.com/gasoline_prices/ [15th December 2018] \\n[45] Nigerian Electricity Regulatory Commission, in: Handbook on Application for Licences, NERC: Licensing, 2018, pp. 2–15. \\n[46] Davies, T.W. (2005). Energy Conversion: Calculation of CO2 Emissions from Fuels [online] available from http://people.exeter.ac.uk/TWDavies/ energy_conversion.htm [20th January 2017] \\n[47] Abuja Electricity Distribution Company (2016). Commercial – Single and 3-phase [online] available from http://www.abujaelectricity.com/?page_id=29 [10th January 2019] \\n[48] W. Arowolo, P. Blechinger, C. Cader, Y Perez, Seeking workable solutions to the electrification challenge in Nigeria: minigrid, reverse auctions and institutional adaptation, Energy Strategy Rev. 23 (2019) 114–141. \\n[49] P. Luckow, E.A. Stanton, S. Fields, B. Biewald, S. Jackson, J. Fisher, R. Wilson, in: Carbon Dioxide Price Forecast, Synapse Energy Economics Inc., Massachusetts, USA, 2015, pp. 1–32. \\n[50] Rural Electrification Agency, in: Highlighting the Rural Electrification Agency’s Impact, REA, 2019, pp. 1–19. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[766,45,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable Futures 2 (2020) 100022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,45,258,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. 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Morrison \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[60,66,487,617]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,71,939,619]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[766,45,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable Futures 2 (2020) 100022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,44,258,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Olówósejéjé, P. Leahy and A.P. Morrison \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1016/j.sftr.2020.100022"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Earth and Atmospheric Sciences"},"sha256":{"kind":"string","value":"f82df72b96df264c570ab3c6fba4d85ca3aef4bdd1543b93e0788bcfe8ab8863"},"title":{"kind":"string","value":"A practical approach for increased electrification, lower emissions and lower energy costs in Africa"}}},{"rowIdx":245,"cells":{"abstract":{"kind":"string","value":"A series of diatomite supported Cu/Ni bimetallic catalysts were prepared using the co-impregnation method to improve the efficiency and selectivity toward methyl 12-hydroxystearate in the hydrogenation of methyl ricinoleate. The catalysts were characterized using X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy and energy dispersive X-ray spectroscopy (SEM-EDS), X-ray photoelectron spectroscopy (XPS) and temperature programmed reduction (H$_2$-TPR). All the characterization results verified the formation of highly dispersed Cu/Ni alloy on support. Moreover, by subtly regulating the Ni/Cu molar ratio as well as the reaction parameters, the hydrogenation of methyl ricinoleate to methyl 12-hydroxystearate proceeded efficiently and selectively, affording 97% yield of methyl 12-hydroxystearate and nearly equivalent conversion of methyl ricinoleate under 2 MPa H$_2$pressure and at 130 ℃ in 4 h with only 1 wt% of the catalyst Ni$_7$Cu$_1$/diatomite (based on methyl ricinoleate). Besides, the supported Cu–Ni bimetallic catalyst is stable during recycle and reuse. After five cycles of reuse, much catalytic activity is still preserved. Therefore, this low-cost and stable bimetallic catalyst would be promising for the hydrogenation of methyl ricinoleate to methyl 12-hydroxystearate, representing an example of green catalysis for efficiently conversion of biomass to value-added chemicals and materials.<$<img>$>img0000<$<\\img>$>"},"author":{"kind":"string","value":"Feng-Ge Zhao|Xiao Zhang|Liang-Nian He|Hong-Ru Li|Xiao-Ying Cui|Feng Ye"},"content_list":{"kind":"list like","value":[{"bbox":"[70,190,122,203]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,213,766,255]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green process for hydrogenation of methyl ricinoleate to methyl 12-hydroxystearate over diatomite supported Cu/Ni bimetallic catalyst ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[828,214,879,251]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0722/f38cafcd7b8020a1f6447509e1f70068f106e9a173a9f658453688789817d78e.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[68,267,759,285]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Xiao Zhang<sup>a</sup>, Hong-Ru Li<sup>b, *</sup>, Feng-Ge Zhao<sup>a</sup>, Xiao-Ying Cui<sup>c</sup>, Feng Ye<sup>c</sup>, Liang-Nian He<sup>a, *</sup> ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,292,658,325]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"$^{a}$ State Key Laboratory and Institute of Elemento-Organic Chemistry, College of Chemistry, Nankai University, Tianjin, 300071, China \",\"b College of Pharmacy, Nankai University, Tianjin, 300353, China \",\"c Nankai University Engineering Research Center for Castor, Tianjin, 300071, China \"]","page_idx":"0","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[70,353,189,362]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HIGHLIGHTS","text_format":null,"text_level":"1","type":"text"},{"bbox":"[71,377,292,485]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Hydrogenation of methyl ricinoleate was performed using a Cu/Ni bimetallic catalyst. \",\"- The formation of highly dispersed Cu/Ni alloy on catalyst surface was verified. \",\"- Methyl 12-hydroxystearate was obtained with high yield and selectivity. \",\"- This protocol represents a green catalysis for efficient conversion of biomass. \"]","page_idx":"0","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[339,353,549,364]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"GRAPHICAL ABSTRACT ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[341,381,759,514]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0577/d1001079ce1b83d18aa19051c5a951fd7072937c197a6cf5d181ab4791aa51f2.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[70,550,202,561]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ARTICLEINFO ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[70,575,120,585]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,586,112,593]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biomass ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,596,138,606]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green process ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,607,143,617]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Hydrogenation ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,618,199,628]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methyl 12-hydroxystearate ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,629,209,638]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Supported bimetallic catalyst ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,639,174,649]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable chemistry ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[339,550,436,561]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABSTRACT ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[336,574,926,740]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A series of diatomite supported $\\mathrm{Cu / N_i}$ bimetallic catalysts were prepared using the co-impregnation method to improve the efficiency and selectivity toward methyl 12-hydroxystearate in the hydrogenation of methyl ricinoleate. The catalysts were characterized using X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy and energy dispersive X-ray spectroscopy (SEM-EDS), X-ray photoelectron spectroscopy (XPS) and temperature programmed reduction $(\\mathrm{H}_2$ TPR). All the characterization results verified the formation of highly dispersed $\\mathrm{Cu / N_i}$ alloy on support. Moreover, by subtly regulating the $\\mathrm{Ni / Cu}$ molar ratio as well as the reaction parameters, the hydrogenation of methyl ricinoleate to methyl 12-hydroxystearate proceeded efficiently and selectively, affording $97\\%$ yield of methyl 12-hydroxystearate and nearly equivalent conversion of methyl ricinoleate under $2\\mathrm{MPaH_2}$ pressure and at $130^{\\circ}\\mathrm{C}$ in $4\\mathrm{h}$ with only $1\\mathrm{wt}\\%$ of the catalyst $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite (based on methyl ricinoleate). Besides, the supported $\\mathrm{Cu - N_i}$ bimetallic catalyst is stable during recycle and reuse. After five cycles of reuse, much catalytic activity is still preserved. Therefore, this low-cost and stable bimetallic catalyst would be promising for the hydrogenation of methyl ricinoleate to methyl 12-hydroxystearate, representing an example of green catalysis for efficiently conversion of biomass to value-added chemicals and materials. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,776,173,788]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,802,485,814]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The resource depletion and environmental pollution are becoming ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,776,926,816]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"increasingly serious with the rapid development of global industry. In this context, the renewable biomass has attracted much concern as the alternative to non-renewable fossil resources [1,2]. By now, many chemicals, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[372,51,622,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green Chemical Engineering 2 (2021) 187-196 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[70,102,171,133]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"KeAi ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[71,134,173,149]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CHINESE ROOTS GLOBAL IMPACT ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[385,85,617,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Contents lists available at ScienceDirect ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[356,114,647,135]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green Chemical Engineering ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[233,153,766,166]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"journal homepage: www.kaipublishing.com/en/journals/green-chemical-engineering ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[831,76,926,167]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green Chemical Engineering ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[78,835,210,848]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"* Corresponding author. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[89,848,532,860]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"E-mail addresses: lihongru@nankai.edu.cn (H.-R. Li), heln@nankai.edu.cn (L.-N. He). ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[70,869,297,881]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1016/j.gce.2020.09.011 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[68,892,266,904]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Available online 28 September 2020 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[68,904,924,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2666-9528/© 2020 Institute of Process Engineering, Chinese Academy of Sciences. Publishing services by Elsevier B.V. on behalf of KeAi Communication Co. Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[68,74,485,125]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"which were traditionally obtained from fossil fuels, a depleting resource, can be derived from biomass such as cellulose, lignin and vegetable oil [3]. Moreover, for certain specific chemicals with unique structure and properties, biomass serves as the only source [4,5]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,125,485,255]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The castor oil, which is produced from castor beans of Ricinus communis, has become an appealing non-food biomass for its unique structure and properties [6-8]. The main component exists in castor oil is triglyceride 12-hydroxy-9-octadecenoic acid (ricinoleic acid) [9]. The unique structure of ricinoleic acid, for example, the unsaturated bond as well as a secondary -OH group at its 12 carbon, makes castor oil a useful platform chemical. Up to now, the derivatives of castor oil have been applied in many nonfood fields [10-13], whereby methyl 12-hydroxystearate is an important basic raw material used in medicine, cosmetics and other industries for synthesizing surfactants, thickeners, and dispersants [14,15]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,255,486,462]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Up to now, methyl 12-hydroxystearate is produced via transesterification and subsequent hydrogenation or hydrogenation followed by transesterification starting from castor oil as shown in Scheme 1, wherein the hydrogenation step has been intensively investigated to improve the efficiency and selectivity toward the target product. So far, the $\\mathrm{Pd / C}$ catalyst [16], nickel supported catalyst [17] and Pt-based catalysts [18-20] have already been developed for the hydrogenation of castor oil or methyl ricinoleate to produce the hydrogenated castor oil or methyl 12-hydroxystearate. However, the product via $\\mathrm{Pd / C}$ catalysis generally contains dehydration impurities albeit the reaction can proceed at moderate $\\mathrm{H}_{2}$ pressure. The nickel monometallic supported catalyst has good selectivity but the product yield and catalyst reusability need to be further improved. On the other hand, Pt-based catalysts are expensive and not applicable for commercial production. As a consequence, developing inexpensive catalysts with high efficient and selectivity for industrial production of methyl 12-hydroxystearate is still highly desired. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,462,486,630]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Here we focus attention on bimetallic supported catalysts. As compared to monometallic supported catalyst, the bimetallic supported catalysts demonstrate enhanced activity, product selectivity, and catalyst stability. For example, the $\\mathrm{Ni / Cu}$ bimetallic catalysts supported onto $\\mathrm{Al_2O_3}$ and zeolite have been applied in oleic acid and palm oil hydrogenation [21,22] and hydrogenation of furfural to 2-methylfuran as well [23]. The results of these examples show that regulating the composition of catalysts may facilitate $\\mathrm{H}_{2}$ dissociation and selective substrate adsorption and thus enhance the catalytic activity and product selectivity. The in-depth mechanism study reveals that doping a second metal can alter the surface properties by forming alloy, therefore resulting in surprising effect [24-27]. In view of this, we envisioned that the $\\mathrm{Cu / Ni}$ supported bimetallic catalysts may efficiently work for the selective ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[542,76,893,296]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 1. XRD patterns of $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite, Ni/diatomite, calcined diatomite and untreated diatomite. \"]","image_footnote":"[]","img_path":"images/0196/ec9a15bb21130e8eddbaac21c72bf990ccd3d78154c1148b3d214d4cfc98bfbc.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[508,369,924,395]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"hydrogenation of $\\mathrm{C = C}$ bond in methyl ricinoleate to produce methyl 12-hydroxystearate. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[508,395,926,537]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this work, the supported $\\mathrm{Cu / Ni}$ bimetallic catalyst was prepared using the cheap and available support diatomite and applied in the hydrogenation of methyl ricinoleate. As expected, almost equivalent conversion of methyl ricinoleate and $97\\%$ yield of methyl 12-hydroxystearate were obtained. In addition to the remarkable catalytic activity and selectivity, the bimetallic catalyst also showed excellent reusability. The high efficiency and selectivity of this catalyst can be rationalized by the formation of alloy on the surface of catalyst, which has been confirmed by different characterization methods. Moreover, the stability of the $\\mathrm{Cu / Ni}$ bimetallic supported catalyst in reuse was also verified by catalyst characterization and related study. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,550,617,562]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. Experimental ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,576,594,588]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.1. Materials ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[508,602,926,629]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nickel sulfate, copper sulfate and sodium carbonate were purchased from Tianjin Guangfu Technology Development Co. Ltd. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[192,654,805,908]","code_body":null,"code_caption":null,"image_caption":"[\"Scheme 1. Synthesis of methyl 12- hydroxystearate from castor oil. \"]","image_footnote":"[]","img_path":"images/0553/00d1dbf0e76271bc3490af85d4f5e2f70d808f68e81c92cf546272511590e7b6.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[70,51,140,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"X. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[712,51,926,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green Chemical Engineering 2 (2021) 187-196 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,941,509,951]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"188 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[179,88,493,244]","code_body":null,"code_caption":null,"image_caption":"[\"a \"]","image_footnote":"[]","img_path":"images/0183/e20a77d34555020eb18b0c8c73e140cc40291b453583c575cced72b62a25fc03.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[519,88,834,244]","code_body":null,"code_caption":null,"image_caption":"[\"b \"]","image_footnote":"[]","img_path":"images/0312/e48381bd1d32864923e3a55532093bfe9185893086acc238953be30d22d1f8c5.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[178,256,493,419]","code_body":null,"code_caption":null,"image_caption":"[\"C \",\"Ni Ka1 \"]","image_footnote":"[]","img_path":"images/0659/f89a826a08e42093d3f1a22fcac1933906a9cc53a9f23e399efcb8631caff3aa.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[522,253,836,420]","code_body":null,"code_caption":null,"image_caption":"[\"d \",\"Cu Ka1 \",\"Fig. 2. (a) (b) SEM images of $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst at different magnifications, (c) (d) EDS mapping images of Ni and Cu in $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst. \"]","image_footnote":"[]","img_path":"images/0463/4b715427fa7315fc0eb199a4fb8da9bff3762a2021c941d41e6cc98453a27642.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[176,487,493,645]","code_body":null,"code_caption":null,"image_caption":"[\"a \"]","image_footnote":"[]","img_path":"images/0201/86f7820ed4398c17e305b928cb3167520b826692ae2e69764e9b2eb113f4a35c.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[516,487,831,646]","code_body":null,"code_caption":null,"image_caption":"[\"b \"]","image_footnote":"[]","img_path":"images/0336/507256fdeef0250b1a4981cdab291319caec1739f37d62e9228039ca7e3a1c7e.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[176,659,493,825]","code_body":null,"code_caption":null,"image_caption":"[\"C \",\"Si Ka1 \"]","image_footnote":"[]","img_path":"images/0889/75eba0a68d8a6588e6ec6642c3f9657850dae36a0db1f1da3ceac97a854699f4.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[521,660,834,825]","code_body":null,"code_caption":null,"image_caption":"[\"d \",\"Ni Ka1 \",\"Fig. 3. (a) SEM images of Ni/diatomite catalyst at different magnifications, (c) EDS mapping images of Ni and Si in Ni/diatomite catalyst. \"]","image_footnote":"[]","img_path":"images/0790/1190389599af774937a831baaedd89f1cc910f860d6ff0fda10e18f58fb9aad2.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[68,879,488,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Diatomite was bought from Energy Chemical. Methyl ricinoleate was prepared by the transesterification of castor oil with methanol and purified by distillation (for details, see SI). The castor oil was ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[508,879,924,917]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"supported by Tianjin No. 6 chemical reagent Factory and $\\mathrm{H}_{2}$ with a purity of $99.99\\%$ was supplied by Liquefied Air (Tianjin). All chemicals were used as received. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[71,51,140,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"X. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[712,51,926,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green Chemical Engineering 2 (2021) 187-196 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,941,509,951]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"189 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[196,77,495,230]","code_body":null,"code_caption":null,"image_caption":"[\"a \"]","image_footnote":"[]","img_path":"images/0372/0d914266778e8caaeab7fd281fe4c48896cd572aceda0890a9378a22b75c72a1.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[519,80,820,230]","code_body":null,"code_caption":null,"image_caption":"[\"b \"]","image_footnote":"[]","img_path":"images/0668/5abe1f431cf6992503af8075c92d00092a635e22fe79227677dbe6c59487c14a.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[196,240,493,393]","code_body":null,"code_caption":null,"image_caption":"[\"C \"]","image_footnote":"[]","img_path":"images/0645/451765934af221fe41de508925680671aaafd33c2fa483b7fc23c2a2c524b1da.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[519,240,820,392]","code_body":null,"code_caption":null,"image_caption":"[\"d \",\"Fig. 4. (a) TEM images of $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst at different magnifications, (c) (d) TEM images of Ni/diatomite catalyst at different magnifications. \"]","image_footnote":"[]","img_path":"images/0161/d4e6dba5e925701eaec2bd566fe122c50e98be3c715a27e74527344820cbe572.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[189,458,491,628]","code_body":null,"code_caption":null,"image_caption":"[\"a \"]","image_footnote":"[]","img_path":"images/0806/7dedc7442b149f09b69cadf9bce203d42ee45978cc91dde534182ad940471146.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[516,460,820,627]","code_body":null,"code_caption":null,"image_caption":"[\"b \"]","image_footnote":"[]","img_path":"images/0478/e2bcd6c3c9dcbe4f3c74404e262def1d752d71883cd9622f651ff28292530f90.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[186,628,488,806]","code_body":null,"code_caption":null,"image_caption":"[\"C \"]","image_footnote":"[]","img_path":"images/0298/c67d969da446b48557dbc9e1409c7a4092dc1caa18f3d5766d4f08b028902136.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[509,629,820,806]","code_body":null,"code_caption":null,"image_caption":"[\"d \",\"Fig. 5. Nitrogen adsorption-desorption isotherms and pore size distribution of (a) (b) $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst and (c) (d) Ni/diatomite catalyst. \"]","image_footnote":"[]","img_path":"images/0962/aa29685f1251dd26e489c56c0439dfe5a7a9c8ccf8854f874e47523e8826a0db.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[70,846,307,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.2. Cu/Ni/diatomite catalyst preparation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,872,486,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A series of diatomite supported bimetallic Cu/Ni catalysts with different Cu/Ni molar ratio and monometallic Ni or Cu catalyst were synthesized via a co-impregnation method [28]. Briefly, $8.805\\mathrm{g}$ diatomite and $50~\\mathrm{mL}~1~\\mathrm{mol}~\\mathrm{L}^{-1}\\mathrm{Na}_2\\mathrm{CO}_3$ were added to a three-necked ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[508,845,926,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"flask and stirred at $70^{\\circ}\\mathrm{C}$ for $0.5\\mathrm{h}$ . Then the pre-prepared $0.6\\mathrm{mol}L^{-1}$ nickel sulfate aqueous solution and $0.2\\mathrm{mol}L^{-1}$ copper sulfate aqueous solution were mixed well according to the calculated volume and added dropwise to the above diatomite suspension under vigorous stirring. After that, the $\\mathsf{pH}$ of the suspension was adjusted to 8-9 using $1\\mathrm{mol}L^{-1}\\mathrm{Na}_2\\mathrm{CO}_3$ aqueous solution. Then the precipitate was aged for ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[71,51,140,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"X. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[712,51,926,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green Chemical Engineering 2 (2021) 187-196 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,941,509,951]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"190 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[71,100,486,193]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0246/084e511086c02d1062274facfafdb4f38c412bfd38abd01a3110c62af0b27b55.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":"<table><tr><td rowspan=\"2\">Catalyst</td><td rowspan=\"2\">SBET/(m2g-1)</td><td rowspan=\"2\">Pore volume /(cm3g-1)</td><td rowspan=\"2\">Pore size /nm</td><td colspan=\"2\">Metal loadinga/(wt%)</td></tr><tr><td>Ni</td><td>Cu</td></tr><tr><td>Ni/SiO2</td><td>17.2</td><td>0.04</td><td>4.82</td><td>16.5</td><td>-</td></tr><tr><td>Ni7Cu1/SiO2</td><td>19.8</td><td>0.06</td><td>5.47</td><td>17.2</td><td>2.3</td></tr></table>","table_caption":"[\"Table 1 The physicochemical properties of Ni/diatomite and $\\\\mathrm{Ni_7Cu_1 / }$ diatomite catalysts. \"]","table_footnote":"[\"a Metal loading determined by ICP-OES. The deviations between the actual and calculated values originate from the metal loss in precipitation process and the different precipitate rates between the Cu, Ni in catalyst preparation. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[68,256,486,400]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$4\\mathrm{h}$ at $70^{\\circ}\\mathrm{C}$ and the resulting dark green suspension was filtered and the precipitate was washed with distilled water repeatedly to neutral, followed by drying at $120^{\\circ}\\mathrm{C}$ for $4\\mathrm{h}$ in a vacuum oven to remove the residual moisture. Next, the catalyst was transferred to a tube furnace and dried at $70^{\\circ}\\mathrm{C}$ for $2\\mathrm{h}$ , followed by calcined at $340^{\\circ}\\mathrm{C}$ for $2\\mathrm{h}$ in nitrogen atmosphere and reduced in hydrogen at $360^{\\circ}\\mathrm{C}$ for $2\\mathrm{h}$ . Then the resulting supported catalyst was cooled under $\\mathbf{N}_2$ flow. In the supported catalyst preparation, the total metal Cu and Ni loading was fixed at $20\\mathrm{wt}\\%$ and the catalyst with different $\\mathrm{Cu / Ni}$ ratio can be prepared by changing the volume of nickel sulfate and copper sulfate aqueous solution. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,418,302,430]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.3. Catalyst characterization techniques ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,443,486,649]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A MimFlex600 diffractometer was used to record the X-ray diffraction (XRD) patterns of the catalysts. In the characterization, $\\mathrm{CuK}\\alpha$ radiation is at $45\\mathrm{kV}$ and $200\\mathrm{mA}$ and a scanning rate of $0.5^{\\circ}\\mathrm{min}^{-1}$ was set in the 20 range of $5^{\\circ}\\sim 80^{\\circ}$ . Scanning electron microscopy and energy dispersive X-ray spectroscopy (SEM-EDS) of the supported catalyst were performed on JEOL-JSM Model 6380 LA instrument with a $200\\mathrm{kV}$ operating voltage. To avoid the charges accumulation and improve the conductivity, gold spraying was performed before placing on the sample table. Transmission electron microscopy (TEM) was carried out on a Tecnai G2 F20 transmission electron microscopy, operating at $200\\mathrm{kV}$ . Before TEM analysis, the sample particles were dispersed in ethanol and then loaded on carbon-coated copper grids to evaporate the solvent. Xray photoelectron spectroscopy (XPS) analysis was performed on a Kratos Axis Ultra DLD spectrometer with a monochromatized Al Ka X-ray source $(\\mathrm{hn} = 1486.6\\mathrm{eV})$ . The C 1s peak $(284.6\\mathrm{eV})$ was used as the reference standard for the binding energy. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,650,486,791]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The nitrogen adsorption desorption experiment was performed on BELSORP Max instrument. Before the experiment, a vacuum pretreatment was applied to the samples at $423\\mathrm{K}$ for $8\\mathrm{h}$ first and then the adsorption desorption isotherms was determined at $77\\mathrm{K}$ . The specific surface area and pore volume and pore size distribution were calculated according to the Brunauer-Emmett-Teller (BET) model and nonlocal density functional theory (NLDFT) method respectively. The inductively coupled plasma-optical emission spectroscopy (ICP-OES) was used to measure the actual loading of metal Cu and Ni in different catalysts on an Agilent 730 device. Before analysis, a mixture of HCl and $\\mathrm{HNO}_3$ with molar ratio of 3:1 was employed to dissolve the catalysts. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,792,486,908]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The $\\mathrm{H}_{2}$ temperature programmed reduction of the catalyst $(\\mathrm{H}_{2}$ TPR) was recorded on a Micromeritics Chemisorb 2750 device equipped with a thermal conductivity detector (TCD) from Micromeritics Instrument (Shanghai) Ltd. In the characterization, the samples were firstly pretreated at $350^{\\circ}\\mathrm{C}$ for $2\\mathrm{h}$ , and then the temperature decreased to $25^{\\circ}\\mathrm{C}$ with an argon flow of $10~\\mathrm{mL~min}^{-1}$ . After that, the atmosphere was switched to $10\\%$ hydrogen/ $90\\%$ argon and the reactor was heated to $800^{\\circ}\\mathrm{C}$ at a ramp rate of $10^{\\circ}\\mathrm{C~min}^{-1}$ to begin the $\\mathrm{H}_{2}$ temperature programmed reduction. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,75,859,88]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.4. General procedure for hydrogenation of methyl ricinoleate ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[506,100,924,138]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The catalytic activity was evaluated by the yield and selectivity toward methyl 12-hydroxystearate in the hydrogenation of methyl ricinoleate. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[506,139,926,372]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The prepared catalysts were pelleted, crushed, and screened out with 20-40 meshes. The hydrogenation reaction was performed in batch mode with a magnetically stirred $50~\\mathrm{mL}$ autoclave. Before the reaction, about $1\\mathrm{g}$ methyl ricinoleate and a certain amount of the supported catalyst were loaded in the autoclave, then the air in the reactor was expelled and pure $\\mathrm{H}_{2}$ was fed into the reactor to maintain a reaction pressure. Subsequently, the reactor was heated to the preset temperature to begin the reaction. After a period of reaction, the reactor was cooled to room temperature. The resulting mixture was dissolved in ethyl acetate and the solid catalyst was separated by filtration. The reused catalyst was characterization by SEM, TEM, XRD and XPS. The filtrate was analyzed by GC and GC-MS to determine the conversion of methyl ricinoleate and the yield of methyl 12-hydroxystearate as well as the composition of the crude reaction mixture respectively. To test the reusability of the supported catalyst, the catalyst recovered by filtration was washed with ethanol and dried under vacuum, and then used for next cycle. Simultaneously, the recovered catalyst was also characterized using different technique to inspect its stability in reuse. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,390,633,403]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.5. Analysis method ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[506,416,926,661]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The conversion of methyl ricinoleate and yield of products were determined by gas chromatography equipped with SH-Rtx-5 capillary column and a FID detector using biphenyl as internal standard (Shimadzu, GC-2014). The carrier gas was nitrogen, and the temperature of the injector and detector were $280^{\\circ}\\mathrm{C}$ and $300^{\\circ}\\mathrm{C}$ respectively. The temperature program was from $120^{\\circ}\\mathrm{C}$ to $280^{\\circ}\\mathrm{C}$ at a ramp of $10^{\\circ}\\mathrm{C}\\mathrm{min}^{-1}$ , holding $20\\mathrm{min}$ at $280^{\\circ}\\mathrm{C}$ . The composition of the reaction mixture after hydrogenation was identified on a GC-MS system (Shimadzu GCMS-QP2010) in the electronic impact ionization mode at $70\\mathrm{eV}$ and equipped with a RTX-5 MS capillary column. The temperature of the oven was programmed from $50^{\\circ}\\mathrm{C}$ to $300^{\\circ}\\mathrm{C}$ at a ramp of $20^{\\circ}\\mathrm{C}\\mathrm{min}^{-1}$ , and kept at $300^{\\circ}\\mathrm{C}$ for $30\\mathrm{min}$ . The data are given as mass units per charge $(m / z)$ . FTIR was performed on Bruker Tensor 27 FT-IR instrument spectrophotometer with KBr pellets and the wavenumber range of $4000 - 400~\\mathrm{cm}^{-1}$ . ${}^{1}\\mathrm{H}$ NMR and ${}^{13}\\mathrm{C}$ NMR were recorded on $400\\mathrm{MHz}$ and $100.6\\mathrm{MHz}$ spectrometers using $\\mathrm{CDCl}_3$ as solvent referenced to $\\mathrm{CDCl}_3$ (7.26 ppm for ${}^{1}\\mathrm{H}$ NMR and $77.00~\\mathrm{ppm}$ for ${}^{13}\\mathrm{C}$ NMR). The high resolution mass spectrometry was used to determine the molecular weight of analyte on a Varian 7.0 T FTICR-MS with ESI technique. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,676,673,687]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. Results and discussion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,701,679,714]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1. Catalyst characterization ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[506,727,926,908]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To investigate the surface morphology and composition of the catalysts, the XRD patterns of the as-synthesized $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite (the subscript means the molar ratio of the two metals in the catalyst), Ni/ diatomite, calcined diatomite and untreated diatomite powders were detected and depicted in Fig. 1. It can be seen that the structure of diatomite is retained in the catalyst preparation process. For the Ni/ diatomite catalyst, the characteristic peaks for metallic nickel phase (JCPDS #04-0850) at $2\\theta = 45^{\\circ}$ , $53^{\\circ}$ , $78^{\\circ}$ are observed, which reveals the existence of metallic Ni(0). After doping a certain amount of copper, the shift and attenuation of the crystal diffraction peak were observed in Fig. 1, which means that the copper-nickel bimetal alloy was formed and the formed metal particles are too small to be detected. Thus we inferred that the metal dispersion on the carrier was enhanced by doping a small amount of copper. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[71,51,140,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"X. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[712,51,926,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green Chemical Engineering 2 (2021) 187-196 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,941,508,951]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"191 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[78,77,500,334]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0297/1e7030d942db03061397d34c441dd098de3c23872e453750fdba3e93cdb2a597.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[509,76,913,337]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0033/df988beaaba3c31864d205f6f99b4ada0920aa15418a6ea7fab7ed0135b112c0.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[76,335,493,597]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0537/09dc33a3d92d8b414c9cc1d8109db80a663a1b2046e7d96ac9ba40d67c238aab.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[506,337,921,600]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 6. (a) XPS survey spectra of Ni/diatomite and $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite, (b) XPS spectra for Cu 2p of $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite, (c) XPS spectra for Ni 2p of Ni/diatomite, (d) XPS spectra for Ni 2p of $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite. \"]","image_footnote":"[]","img_path":"images/0635/75d5337d5b8a6b65ca80d4d2c0372f0bced86d379ba2271510e36e3dd33ec53c.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[68,667,485,845]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The micromorphology and structures of the $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite and Ni/diatomite catalysts were determined by SEM-EDS and TEM. The SEM-EDS results in Fig. 2 and Fig. 3 showed that there were uniformly distributed nano-scale open pores in the surface of disk-like diatomite, which can endow the supported catalyst with sufficient specific surface area. For $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite catalyst, EDS mapping indicated that Cu and Ni X-ray signals were uniformly mixed together. The consistent distribution of Cu and Ni hinted a good fusion performance of Ni and Cu in the $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite catalyst, which was in consistence with the XRD results. By contrast, for the Ni/diatomite catalyst, the relative large Ni metal particles can be found on the surface of carrier, which indicated poor dispersion of metal on diatomite. Therefore, it was concluded that the dispersion of metals on the support is improved with the addition of Cu. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,848,488,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The TEM results in Fig. 4 also confirmed that Ni/Cu alloy homogeneously dispersed on the diatomite with an average particle size of $20\\mathrm{nm}$ . As compared with the monometallic Ni/diatomite catalyst, the Ni/Cu alloy particle was much smaller, which implies that the addition of the Cu can reduce the particle size and increase the dispersion of metals on the carrier. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[506,667,926,796]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The specific surface area, pore volume and average pore diameter of $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite and Ni/diatomite catalysts were calculated according to the nitrogen adsorption desorption results. As shown in Fig. 5, the isotherm of $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite and Ni/diatomite exhibit typical IUPAC type IV pattern with H1-type hysteresis loop, which indicates a mesoporous nature of the supported catalyst. As shown in Table 1, the specific surface area, pore volume and average pore diameter of the $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite catalyst were slightly larger than those of Ni/diatomite, which was supposed to benefit from the enhanced metal dispersion on the carrier for $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite catalyst. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[506,796,928,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The XPS analysis was performed to obtain the detailed information on the surface chemical composition and chemical states in the reduced supported catalyst. The XPS survey spectra showed that both supported metal and $\\mathrm{SiO}_2$ coexist on the catalyst surface. The high resolution spectra of Ni 2p and Cu 2p photoelectron lines for $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite and Ni/diatomite were shown in Fig. 6. Two peaks can be found for the Cu $2\\mathrm{p}_{3/2}$ spectra of $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite catalysts. The peak at 932.4 eV represents metallic Cu, and the peak at 933.7 eV is associated with $\\mathrm{Cu}^{2+}$ in CuO. Similarly, for the Ni $2\\mathrm{p}_{3/2}$ spectra, two peaks at 852.7 eV and 858.9 eV were detected, which can be related to metallic Ni and $\\mathrm{Ni}^{2+}$ in ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[71,51,140,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"X. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[712,51,926,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green Chemical Engineering 2 (2021) 187-196 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,941,509,951]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"192 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[133,76,424,262]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 7. $\\\\mathrm{H}_2$ -TPR profiles of $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite and Ni/diatomite catalysts. \"]","image_footnote":"[]","img_path":"images/0835/f89e1a46ff0ac252c6e4c2d95e631367e7fd74e8e9378834595e74754c1dcd70.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[68,313,485,417]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"NiO, respectively. The results of XPS analysis showed that $\\mathrm{Ni}^0$ and $\\mathrm{Ni}^{2+}$ species coexist on the surface of supported Ni/diatomite and $\\mathrm{Ni}^0$ , $\\mathrm{Ni}^{2+}$ , $\\mathrm{Cu}^0$ and $\\mathrm{Cu}^{2+}$ species present on the surface of $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite. The existence of oxidized metal on the catalyst surface is ascribed to the reoxidation of reduced metal when exposed to air as well as the incomplete reduction in the tube furnace. In XRD characterization, no oxide species were detected due to the good dispersion of these species on the catalysts surface. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,418,486,560]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To detect the change of atomic environment in Ni/diatomite and $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite catalysts, the $\\mathrm{H}_2$ -TPR analysis was carried out before the reduction of catalysts and the resulting profiles are shown in Fig. 7. For Ni/diatomite, a single reduction peak between $170^{\\circ}\\mathrm{C}$ and $358^{\\circ}\\mathrm{C}$ with a reduction in the approximate temperature of $233^{\\circ}\\mathrm{C}$ was observed. For bimetallic $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite catalyst, four isolated reduction peaks were observed, which implied a complex composition on the surface of the bimetallic catalyst; presumably due to different precipitate rates between the Cu, Ni. Although different metal oxide species coexisted on the diatomite surface, the shift of main reduction peak (at $199^{\\circ}\\mathrm{C}$ ) toward low temperature meant the change of atomic environment for at least ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[508,75,926,127]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"part of Ni, which confirmed the formation of the Cu-Ni alloy. The other two minor reduction processes occurred between $140^{\\circ}\\mathrm{C} - 150^{\\circ}\\mathrm{C}$ might be ascribed to the reduction of copper oxide [29] and the reduction peak presented at $375^{\\circ}\\mathrm{C}$ , being associated with the reduction of NiO. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,141,901,155]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2. Hydrogenation of methyl ricinoleate to methyl 12-hydroxystearate ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,167,741,180]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2.1. Performances of different catalysts ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[508,180,926,464]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Having obtained the supported monometallic and bimetallic catalysts, the hydrogenation of methyl ricinoleate was performed under a relatively low pressure (2 MPa). And the results were listed in Table 2. It can be seen that in the absence of catalyst or using $\\mathrm{Cu}$ /diatomite as catalyst, no hydrogenation occurred (entries 1-2). The $\\mathrm{Ni}$ /diatomite and $\\mathrm{Ni} / \\mathrm{Cu}$ /diatomite catalyst can promote the hydrogenation. However, the usage of monometallic catalyst should be much higher than that of the bimetallic ones (entries 3-5 vs. 6-8, Table 2) to achieve comparable conversion and yield. This meant that the catalytic activity was enhanced by adding $\\mathrm{Cu}$ . It was also noteworthy that the disparity between the conversion of methyl ricinoleate and the yield of methyl 12-hydroxystearate can be observed for some reactions (entries 3-7), which means the by-product formation. Gratifyingly, by regulating the content of $\\mathrm{Cu}$ in the bimetallic catalyst, the by-product can be reduced (entries 8-11). When the $\\mathrm{Ni} / \\mathrm{Cu}$ atom ratio was 7:1, nearly equivalent conversion and up to $97\\%$ yield of product can be obtained. Therefore, the catalyst $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite was optimum for this reaction. The results showed that both the efficiency and selectivity of the catalyst toward methyl 12-hydroxystearate was improved by doping a small amount of $\\mathrm{Cu}$ . The enhanced activity and selectivity of the bimetallic catalyst may be originated from its improved ability to activate hydrogen and the specific site adsorption of the substrate on the alloy surface. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[508,464,928,567]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"With $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite as catalyst, we further studied the effect of catalyst amount on the hydrogenation reaction. It was found that both of the conversion of methyl ricinoleate and the yield of methyl 12-hydroxystearate decreased when reducing the catalyst amount (entries 8-11). Even so, $82\\%$ yield of product can still be obtained when the catalyst was reduced to $0.2\\mathrm{wt}\\%$ , being corroborated the high efficiency of the bimetallic catalyst. To maintain a high conversion and product yield, $1\\mathrm{wt}\\%$ $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite was used as catalyst in the following experiments. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,620,718,701]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0875/0dffbd41c35f1dddde142a7bb887adfa564171559ca843f59d4f3da824743ad6.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[71,723,926,865]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0779/adf73971845a9df4c8d54bafeae5720cde2a44d7190d918ddd1b4bfe96b61969.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":"<table><tr><td>Entry</td><td>Catalyst</td><td>Catalyst, wt%</td><td>Conversion, %a</td><td>Yield, %a</td></tr><tr><td>1</td><td>None</td><td>-</td><td>0</td><td>0</td></tr><tr><td>2</td><td>Cu/diatomite</td><td>1</td><td>0</td><td>0</td></tr><tr><td>3</td><td>Ni/diatomite</td><td>1</td><td>47</td><td>40</td></tr><tr><td>4</td><td>Ni/diatomite</td><td>5</td><td>92</td><td>85</td></tr><tr><td>5</td><td>Ni/diatomite</td><td>8</td><td>>99</td><td>93</td></tr><tr><td>6</td><td>Ni3Cu1/diatomite</td><td>1</td><td>>99</td><td>91</td></tr><tr><td>7</td><td>Ni5Cu1/diatomite</td><td>1</td><td>>99</td><td>95</td></tr><tr><td>8</td><td>Ni7Cu1/diatomite</td><td>1</td><td>>99</td><td>97</td></tr><tr><td>9</td><td>Ni7Cu1/diatomite</td><td>0.5</td><td>88</td><td>87</td></tr><tr><td>10</td><td>Ni7Cu1/diatomite</td><td>0.3</td><td>85</td><td>83</td></tr><tr><td>11</td><td>Ni7Cu1/diatomite</td><td>0.2</td><td>83</td><td>82</td></tr></table>","table_caption":"[\"Table 2 Catalyst screening for hydrogenation of methyl ricinoleate. \"]","table_footnote":"[\"Reaction conditions: methyl ricinoleate $(3.2\\\\mathrm{mmol},1.00\\\\mathrm{g})$ $\\\\mathrm{H}_2$ 2 MPa), $130^{\\\\circ}\\\\mathrm{C}$ 10 h. \",\"a Determined by GC with biphenyl as internal standard. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[71,51,140,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"X. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[712,51,926,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green Chemical Engineering 2 (2021) 187-196 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,941,509,951]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"193 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[230,80,803,293]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 8. Effect of reaction parameters on the hydrogenation of methyl ricinoleate. Reactions were performed with methyl ricinoleate (3.2 mmol, 1.00 g), $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite (1 wt% relative to methyl ricinoleate). \"]","image_footnote":"[]","img_path":"images/0484/fb52577cc3a97a0bc672a9cf11ceeb24cdd5024b19e3bb4d7465f666825938f0.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[68,346,292,359]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2.2. Effect of the reaction parameters ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,359,485,397]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"With the selected catalyst in hand, we further optimized the other reaction conditions containing the hydrogen pressure, temperature and reaction time for the reaction. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,398,485,577]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The effect of $\\mathrm{H}_2$ pressure on the hydrogenation of methyl ricinoleate was investigated with the reaction temperature and reaction time set at $130^{\\circ}\\mathrm{C}$ and $9.5\\mathrm{h}$ . Similarly, the reaction temperature was screened by fixing the $\\mathrm{H}_2$ pressure and reaction time at $2\\mathrm{MPa}$ and $9.5\\mathrm{h}$ , respectively. The results in Fig. 8 showed that the reaction is sensitive to the $\\mathrm{H}_2$ pressure as well as the reaction temperature. When the $\\mathrm{H}_2$ pressure is below $1\\mathrm{MPa}$ and the temperature is less than $100^{\\circ}\\mathrm{C}$ , the hydrogenation of methyl ricinoleate cannot occur. Increasing the $\\mathrm{H}_2$ pressure and reaction temperature improved the conversion of methyl ricinoleate. However, the $\\mathrm{H}_2$ pressure higher than $2\\mathrm{MPa}$ and temperature above $130^{\\circ}\\mathrm{C}$ reduced the product selectivity. Therefore, the optimal $\\mathrm{H}_2$ pressure and reaction temperature were set at $2\\mathrm{MPa}$ and $130^{\\circ}\\mathrm{C}$ , respectively. Under these optimized conditions, up to $97\\%$ yield of target product can be obtained. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,579,486,630]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the subsequent investigation of reaction time, an obvious induction time was observed. After the induction time, the conversion of methyl ricinoleate and yield of methyl 12-hydroxystearate increased sharply. When the reaction time was prolonged to more than $4\\mathrm{h}$ , the conversion ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,670,478,883]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 9. Reusability of the $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst. Reaction conditions: methyl ricinoleate (3.2 mmol, $1.00\\\\mathrm{g}$ ), $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite (10 mg), $\\\\mathrm{H}_2$ (2 MPa), $130^{\\\\circ}\\\\mathrm{C}, 4\\\\mathrm{h}$ . \"]","image_footnote":"[]","img_path":"images/0517/ade61dc009f7a009cdaa9f8dd5e794100c26e6e1e8084d66888b28388f0c80fe.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[506,346,926,488]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"remained unchanged but the product yield decreased. Simultaneously, the by-product methyl stearate was detected (the by-product has been verified by GC-MS spectra of the crude reaction mixture and the details can be found in SI). It is inferred that the induction time is the result of catalyst reactivation as the bimetallic catalyst exposed to air can be easily deactivated. Actually, in the XPS characterization of the catalyst, the oxidized Cu and Ni species was detected. After the catalyst was reactivated in the reaction system, the hydrogenation proceeded quickly and almost equivalent conversion of methyl ricinoleate can be achieved. With the increase of reaction time, side reactions occurred and the yield of target product decreased. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[508,501,846,514]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2.3. Reusability of the supported Cu/Ni bimetallic catalyst ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[506,514,926,669]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As the recyclability and reusability are the key features for the heterogeneous catalyst, the stability and reusability of the $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite catalyst was assessed for this hydrogenation reaction and the results were presented in Fig. 9. In this set of experiments, the hydrogenation reaction was conducted under the optimal conditions. When the reaction was completed, the mixture was dissolved in ethyl acetate. Then the catalyst was recovered by filtrating the reaction mixture. After appropriate treatment (as mentioned in Section 2.3), the catalyst was reused in the next run. It can be seen from Fig. 9 that after five runs of reaction, $92\\%$ of the catalytic activity was retained, which means that the supported bimetallic catalyst has satisfying stability and reusability. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[506,669,928,787]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To further verify the stability of the catalyst in reused, the $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite catalyst after five rounds of recycle was characterized by SEM, TEM, XRD and XPS. The results in Fig. 10 showed that the morphology and composition of the catalyst were stable during the reuse, which supported the excellent reusability of the supported bimetallic catalyst. The improved stability of this bimetallic catalyst can be attributed to the formation of $\\mathrm{Cu} / \\mathrm{Ni}$ alloy, which inhibited the migration and aggregation of Ni atom during the exothermic process and thus keep the even distribution of catalytic sites on the surface of support. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,800,609,809]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. Conclusions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[506,824,926,914]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In summary, a high efficient diatomite supported $\\mathrm{Cu / Ni}$ bimetallic catalyst was developed for selective hydrogenation of methyl ricinoleate to methyl 12-hydroxystearate. The results showed that the $\\mathrm{Cu / Ni}$ ratio of 7:1 in the supported bimetallic catalyst is optimum and the characterization results of XRD, SEM-EDS, TEM, XPS and $\\mathrm{H}_2$ -TPR showed that the highly dispersed $\\mathrm{Cu / Ni}$ alloy was formed on the surface of carrier, which might promote double bond adsorption and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[71,51,140,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"X. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[712,51,926,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green Chemical Engineering 2 (2021) 187-196 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,941,509,951]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"194 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[202,87,514,235]","code_body":null,"code_caption":null,"image_caption":"[\"a \",\"b \"]","image_footnote":"[]","img_path":"images/0812/c6f13b5370d5ce9890fdb9e752bfcb2d9909db382df9ade4e2927cc9c3098191.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[542,87,836,235]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0969/4698f898a460d1e8c4223dcea8cff3ccec6923aceb8c625ce0fc809da6a58cfd.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[176,254,500,472]","code_body":null,"code_caption":null,"image_caption":"[\"c \"]","image_footnote":"[]","img_path":"images/0060/16ef50770594cd1ec3fb526f8ee4ccdd9fd2f6a32919f8400f607dcb179ed85f.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[540,254,834,471]","code_body":null,"code_caption":null,"image_caption":"[\"d \"]","image_footnote":"[]","img_path":"images/0214/6802893906ab0adbbf4a07a750431abd8c4b02aa7bb041d4aa1607ee958ed430.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[161,488,488,709]","code_body":null,"code_caption":null,"image_caption":"[\"e \",\"Fig. 10. (a) SEM, (b) TEM images of reused $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst after five catalytic cycles, (c) XRD spectra of fresh and used $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst, (d) XPS survey spectra for Cu 2p and (e) Ni 2p of the reused $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst after five catalytic cycles. \"]","image_footnote":"[]","img_path":"images/0757/5cc7583bfa224edf67d7b939b7f9f06cd0a304785916a576245886e956c3c90c.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[68,751,488,906]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\mathrm{H}_2$ activation on the catalyst and therefore result in its superior catalytic activity and selectivity as compared with the supported Ni monometallic catalyst. Under the optimal reaction conditions, i.e. $2\\mathrm{MPa}$ of $\\mathrm{H}_2$ pressure, $130^{\\circ}\\mathrm{C}$ and $1\\mathrm{wt}\\%$ catalyst, up to $97\\%$ yield of methyl 12-hydroxystearate and equivalent conversion of methyl ricinoleate can be achieved in $4\\mathrm{h}$ . In addition, the heterogeneous $\\mathrm{Ni}_7\\mathrm{Cu}_1/$ diatomite catalyst could be easily recovered and reused without significant loss of activity. Therefore, this $\\mathrm{Cu} / \\mathrm{Ni}$ bimetallic supported catalyst proves to be efficient for commercial production of methyl 12-hydroxystearate from methyl ricinoleate. Therefore, this work will pave new avenue for developing green process for upgrading of biomass to industrial useful chemicals and materials. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,751,723,765]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Declaration of competing interest ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[508,777,926,818]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,829,635,843]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgements ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[508,855,928,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This work was financially supported by the National Program on Key Research Project (2016YFA0602900) and Nankai University Engineering Research Center for Castor and also supported by \"the Fundamental Research Funds for the Central Universities\", Nankai University (000082). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[71,51,140,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"X. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[712,51,926,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green Chemical Engineering 2 (2021) 187-196 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,941,509,951]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"195 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[71,75,143,86]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[71,100,483,434]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[1] R. 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Technol. 179 (2018) 135-142. \",\"[28] P. Pecchia, I. Galasso, S. Mapelli, P. Bondioli, F. Zaccheria, N. Ravasio, Stabilisation of camelina oil methyl esters through selective hydrogenation, Ind. Crop. Prod. 51 (2013) 306-309. \",\"[29] Z. Zhang, H. Chen, C. Wang, K. Chen, X. Lu, P. Ouyang, J. Fu, Efficient and stable Cu-Ni/ZrO $_2$ catalysts for in situ hydrogenation and deoxygenation of oleic acid into heptadecane using methanol as a hydrogen donor, Fuel 230 (2018) 211-217. \"]","page_idx":"9","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[71,51,140,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"X. Zhang et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[712,51,926,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green Chemical Engineering 2 (2021) 187-196 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,941,509,951]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"196 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[70,190,122,203]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,213,766,255]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green process for hydrogenation of methyl ricinoleate to methyl 12-hydroxystearate over diatomite supported Cu/Ni bimetallic catalyst \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[828,214,879,251]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0722/f38cafcd7b8020a1f6447509e1f70068f106e9a173a9f658453688789817d78e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[68,267,759,285]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Xiao Zhang<sup>a</sup>, Hong-Ru Li<sup>b, *</sup>, Feng-Ge Zhao<sup>a</sup>, Xiao-Ying Cui<sup>c</sup>, Feng Ye<sup>c</sup>, Liang-Nian He<sup>a, *</sup> \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,292,658,325]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"$^{a}$ State Key Laboratory and Institute of Elemento-Organic Chemistry, College of Chemistry, Nankai University, Tianjin, 300071, China \\\",\\\"b College of Pharmacy, Nankai University, Tianjin, 300353, China \\\",\\\"c Nankai University Engineering Research Center for Castor, Tianjin, 300071, China \\\"]\",\n \"page_idx\": \"0\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[70,353,189,362]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HIGHLIGHTS\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[71,377,292,485]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Hydrogenation of methyl ricinoleate was performed using a Cu/Ni bimetallic catalyst. \\\",\\\"- The formation of highly dispersed Cu/Ni alloy on catalyst surface was verified. \\\",\\\"- Methyl 12-hydroxystearate was obtained with high yield and selectivity. \\\",\\\"- This protocol represents a green catalysis for efficient conversion of biomass. \\\"]\",\n \"page_idx\": \"0\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[339,353,549,364]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"GRAPHICAL ABSTRACT \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[341,381,759,514]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0577/d1001079ce1b83d18aa19051c5a951fd7072937c197a6cf5d181ab4791aa51f2.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[70,550,202,561]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ARTICLEINFO \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,575,120,585]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,586,112,593]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biomass \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,596,138,606]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green process \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,607,143,617]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Hydrogenation \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,618,199,628]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methyl 12-hydroxystearate \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,629,209,638]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Supported bimetallic catalyst \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,639,174,649]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable chemistry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[339,550,436,561]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABSTRACT \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[336,574,926,740]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A series of diatomite supported $\\\\mathrm{Cu / N_i}$ bimetallic catalysts were prepared using the co-impregnation method to improve the efficiency and selectivity toward methyl 12-hydroxystearate in the hydrogenation of methyl ricinoleate. The catalysts were characterized using X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy and energy dispersive X-ray spectroscopy (SEM-EDS), X-ray photoelectron spectroscopy (XPS) and temperature programmed reduction $(\\\\mathrm{H}_2$ TPR). All the characterization results verified the formation of highly dispersed $\\\\mathrm{Cu / N_i}$ alloy on support. Moreover, by subtly regulating the $\\\\mathrm{Ni / Cu}$ molar ratio as well as the reaction parameters, the hydrogenation of methyl ricinoleate to methyl 12-hydroxystearate proceeded efficiently and selectively, affording $97\\\\%$ yield of methyl 12-hydroxystearate and nearly equivalent conversion of methyl ricinoleate under $2\\\\mathrm{MPaH_2}$ pressure and at $130^{\\\\circ}\\\\mathrm{C}$ in $4\\\\mathrm{h}$ with only $1\\\\mathrm{wt}\\\\%$ of the catalyst $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite (based on methyl ricinoleate). Besides, the supported $\\\\mathrm{Cu - N_i}$ bimetallic catalyst is stable during recycle and reuse. After five cycles of reuse, much catalytic activity is still preserved. Therefore, this low-cost and stable bimetallic catalyst would be promising for the hydrogenation of methyl ricinoleate to methyl 12-hydroxystearate, representing an example of green catalysis for efficiently conversion of biomass to value-added chemicals and materials. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,776,173,788]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,802,485,814]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The resource depletion and environmental pollution are becoming \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,776,926,816]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"increasingly serious with the rapid development of global industry. In this context, the renewable biomass has attracted much concern as the alternative to non-renewable fossil resources [1,2]. By now, many chemicals, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[372,51,622,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green Chemical Engineering 2 (2021) 187-196 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[70,102,171,133]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"KeAi \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[71,134,173,149]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CHINESE ROOTS GLOBAL IMPACT \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[385,85,617,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Contents lists available at ScienceDirect \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[356,114,647,135]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green Chemical Engineering \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[233,153,766,166]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"journal homepage: www.kaipublishing.com/en/journals/green-chemical-engineering \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[831,76,926,167]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green Chemical Engineering \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[78,835,210,848]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"* Corresponding author. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[89,848,532,860]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"E-mail addresses: lihongru@nankai.edu.cn (H.-R. Li), heln@nankai.edu.cn (L.-N. He). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[70,869,297,881]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1016/j.gce.2020.09.011 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[68,892,266,904]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Available online 28 September 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[68,904,924,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2666-9528/© 2020 Institute of Process Engineering, Chinese Academy of Sciences. Publishing services by Elsevier B.V. on behalf of KeAi Communication Co. Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[68,74,485,125]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"which were traditionally obtained from fossil fuels, a depleting resource, can be derived from biomass such as cellulose, lignin and vegetable oil [3]. Moreover, for certain specific chemicals with unique structure and properties, biomass serves as the only source [4,5]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,125,485,255]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The castor oil, which is produced from castor beans of Ricinus communis, has become an appealing non-food biomass for its unique structure and properties [6-8]. The main component exists in castor oil is triglyceride 12-hydroxy-9-octadecenoic acid (ricinoleic acid) [9]. The unique structure of ricinoleic acid, for example, the unsaturated bond as well as a secondary -OH group at its 12 carbon, makes castor oil a useful platform chemical. Up to now, the derivatives of castor oil have been applied in many nonfood fields [10-13], whereby methyl 12-hydroxystearate is an important basic raw material used in medicine, cosmetics and other industries for synthesizing surfactants, thickeners, and dispersants [14,15]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,255,486,462]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Up to now, methyl 12-hydroxystearate is produced via transesterification and subsequent hydrogenation or hydrogenation followed by transesterification starting from castor oil as shown in Scheme 1, wherein the hydrogenation step has been intensively investigated to improve the efficiency and selectivity toward the target product. So far, the $\\\\mathrm{Pd / C}$ catalyst [16], nickel supported catalyst [17] and Pt-based catalysts [18-20] have already been developed for the hydrogenation of castor oil or methyl ricinoleate to produce the hydrogenated castor oil or methyl 12-hydroxystearate. However, the product via $\\\\mathrm{Pd / C}$ catalysis generally contains dehydration impurities albeit the reaction can proceed at moderate $\\\\mathrm{H}_{2}$ pressure. The nickel monometallic supported catalyst has good selectivity but the product yield and catalyst reusability need to be further improved. On the other hand, Pt-based catalysts are expensive and not applicable for commercial production. As a consequence, developing inexpensive catalysts with high efficient and selectivity for industrial production of methyl 12-hydroxystearate is still highly desired. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,462,486,630]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Here we focus attention on bimetallic supported catalysts. As compared to monometallic supported catalyst, the bimetallic supported catalysts demonstrate enhanced activity, product selectivity, and catalyst stability. For example, the $\\\\mathrm{Ni / Cu}$ bimetallic catalysts supported onto $\\\\mathrm{Al_2O_3}$ and zeolite have been applied in oleic acid and palm oil hydrogenation [21,22] and hydrogenation of furfural to 2-methylfuran as well [23]. The results of these examples show that regulating the composition of catalysts may facilitate $\\\\mathrm{H}_{2}$ dissociation and selective substrate adsorption and thus enhance the catalytic activity and product selectivity. The in-depth mechanism study reveals that doping a second metal can alter the surface properties by forming alloy, therefore resulting in surprising effect [24-27]. In view of this, we envisioned that the $\\\\mathrm{Cu / Ni}$ supported bimetallic catalysts may efficiently work for the selective \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[542,76,893,296]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 1. XRD patterns of $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite, Ni/diatomite, calcined diatomite and untreated diatomite. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0196/ec9a15bb21130e8eddbaac21c72bf990ccd3d78154c1148b3d214d4cfc98bfbc.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[508,369,924,395]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"hydrogenation of $\\\\mathrm{C = C}$ bond in methyl ricinoleate to produce methyl 12-hydroxystearate. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[508,395,926,537]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this work, the supported $\\\\mathrm{Cu / Ni}$ bimetallic catalyst was prepared using the cheap and available support diatomite and applied in the hydrogenation of methyl ricinoleate. As expected, almost equivalent conversion of methyl ricinoleate and $97\\\\%$ yield of methyl 12-hydroxystearate were obtained. In addition to the remarkable catalytic activity and selectivity, the bimetallic catalyst also showed excellent reusability. The high efficiency and selectivity of this catalyst can be rationalized by the formation of alloy on the surface of catalyst, which has been confirmed by different characterization methods. Moreover, the stability of the $\\\\mathrm{Cu / Ni}$ bimetallic supported catalyst in reuse was also verified by catalyst characterization and related study. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,550,617,562]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. Experimental \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,576,594,588]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.1. Materials \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[508,602,926,629]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nickel sulfate, copper sulfate and sodium carbonate were purchased from Tianjin Guangfu Technology Development Co. Ltd. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[192,654,805,908]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Scheme 1. Synthesis of methyl 12- hydroxystearate from castor oil. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0553/00d1dbf0e76271bc3490af85d4f5e2f70d808f68e81c92cf546272511590e7b6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[70,51,140,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"X. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[712,51,926,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green Chemical Engineering 2 (2021) 187-196 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,941,509,951]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"188 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[179,88,493,244]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"a \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0183/e20a77d34555020eb18b0c8c73e140cc40291b453583c575cced72b62a25fc03.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[519,88,834,244]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"b \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0312/e48381bd1d32864923e3a55532093bfe9185893086acc238953be30d22d1f8c5.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[178,256,493,419]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"C \\\",\\\"Ni Ka1 \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0659/f89a826a08e42093d3f1a22fcac1933906a9cc53a9f23e399efcb8631caff3aa.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[522,253,836,420]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"d \\\",\\\"Cu Ka1 \\\",\\\"Fig. 2. (a) (b) SEM images of $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite catalyst at different magnifications, (c) (d) EDS mapping images of Ni and Cu in $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite catalyst. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0463/4b715427fa7315fc0eb199a4fb8da9bff3762a2021c941d41e6cc98453a27642.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[176,487,493,645]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"a \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0201/86f7820ed4398c17e305b928cb3167520b826692ae2e69764e9b2eb113f4a35c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[516,487,831,646]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"b \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0336/507256fdeef0250b1a4981cdab291319caec1739f37d62e9228039ca7e3a1c7e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[176,659,493,825]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"C \\\",\\\"Si Ka1 \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0889/75eba0a68d8a6588e6ec6642c3f9657850dae36a0db1f1da3ceac97a854699f4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[521,660,834,825]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"d \\\",\\\"Ni Ka1 \\\",\\\"Fig. 3. (a) SEM images of Ni/diatomite catalyst at different magnifications, (c) EDS mapping images of Ni and Si in Ni/diatomite catalyst. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0790/1190389599af774937a831baaedd89f1cc910f860d6ff0fda10e18f58fb9aad2.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[68,879,488,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Diatomite was bought from Energy Chemical. Methyl ricinoleate was prepared by the transesterification of castor oil with methanol and purified by distillation (for details, see SI). The castor oil was \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[508,879,924,917]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"supported by Tianjin No. 6 chemical reagent Factory and $\\\\mathrm{H}_{2}$ with a purity of $99.99\\\\%$ was supplied by Liquefied Air (Tianjin). All chemicals were used as received. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[71,51,140,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"X. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[712,51,926,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green Chemical Engineering 2 (2021) 187-196 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,941,509,951]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"189 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[196,77,495,230]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"a \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0372/0d914266778e8caaeab7fd281fe4c48896cd572aceda0890a9378a22b75c72a1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[519,80,820,230]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"b \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0668/5abe1f431cf6992503af8075c92d00092a635e22fe79227677dbe6c59487c14a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[196,240,493,393]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"C \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0645/451765934af221fe41de508925680671aaafd33c2fa483b7fc23c2a2c524b1da.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[519,240,820,392]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"d \\\",\\\"Fig. 4. (a) TEM images of $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite catalyst at different magnifications, (c) (d) TEM images of Ni/diatomite catalyst at different magnifications. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0161/d4e6dba5e925701eaec2bd566fe122c50e98be3c715a27e74527344820cbe572.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[189,458,491,628]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"a \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0806/7dedc7442b149f09b69cadf9bce203d42ee45978cc91dde534182ad940471146.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[516,460,820,627]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"b \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0478/e2bcd6c3c9dcbe4f3c74404e262def1d752d71883cd9622f651ff28292530f90.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[186,628,488,806]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"C \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0298/c67d969da446b48557dbc9e1409c7a4092dc1caa18f3d5766d4f08b028902136.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[509,629,820,806]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"d \\\",\\\"Fig. 5. Nitrogen adsorption-desorption isotherms and pore size distribution of (a) (b) $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite catalyst and (c) (d) Ni/diatomite catalyst. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0962/aa29685f1251dd26e489c56c0439dfe5a7a9c8ccf8854f874e47523e8826a0db.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[70,846,307,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2. Cu/Ni/diatomite catalyst preparation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,872,486,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A series of diatomite supported bimetallic Cu/Ni catalysts with different Cu/Ni molar ratio and monometallic Ni or Cu catalyst were synthesized via a co-impregnation method [28]. Briefly, $8.805\\\\mathrm{g}$ diatomite and $50~\\\\mathrm{mL}~1~\\\\mathrm{mol}~\\\\mathrm{L}^{-1}\\\\mathrm{Na}_2\\\\mathrm{CO}_3$ were added to a three-necked \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[508,845,926,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"flask and stirred at $70^{\\\\circ}\\\\mathrm{C}$ for $0.5\\\\mathrm{h}$ . Then the pre-prepared $0.6\\\\mathrm{mol}L^{-1}$ nickel sulfate aqueous solution and $0.2\\\\mathrm{mol}L^{-1}$ copper sulfate aqueous solution were mixed well according to the calculated volume and added dropwise to the above diatomite suspension under vigorous stirring. After that, the $\\\\mathsf{pH}$ of the suspension was adjusted to 8-9 using $1\\\\mathrm{mol}L^{-1}\\\\mathrm{Na}_2\\\\mathrm{CO}_3$ aqueous solution. Then the precipitate was aged for \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[71,51,140,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"X. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[712,51,926,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green Chemical Engineering 2 (2021) 187-196 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,941,509,951]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"190 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[71,100,486,193]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0246/084e511086c02d1062274facfafdb4f38c412bfd38abd01a3110c62af0b27b55.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=\\\"2\\\">Catalyst</td><td rowspan=\\\"2\\\">SBET/(m2g-1)</td><td rowspan=\\\"2\\\">Pore volume /(cm3g-1)</td><td rowspan=\\\"2\\\">Pore size /nm</td><td colspan=\\\"2\\\">Metal loadinga/(wt%)</td></tr><tr><td>Ni</td><td>Cu</td></tr><tr><td>Ni/SiO2</td><td>17.2</td><td>0.04</td><td>4.82</td><td>16.5</td><td>-</td></tr><tr><td>Ni7Cu1/SiO2</td><td>19.8</td><td>0.06</td><td>5.47</td><td>17.2</td><td>2.3</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1 The physicochemical properties of Ni/diatomite and $\\\\\\\\mathrm{Ni_7Cu_1 / }$ diatomite catalysts. \\\"]\",\n \"table_footnote\": \"[\\\"a Metal loading determined by ICP-OES. The deviations between the actual and calculated values originate from the metal loss in precipitation process and the different precipitate rates between the Cu, Ni in catalyst preparation. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[68,256,486,400]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$4\\\\mathrm{h}$ at $70^{\\\\circ}\\\\mathrm{C}$ and the resulting dark green suspension was filtered and the precipitate was washed with distilled water repeatedly to neutral, followed by drying at $120^{\\\\circ}\\\\mathrm{C}$ for $4\\\\mathrm{h}$ in a vacuum oven to remove the residual moisture. Next, the catalyst was transferred to a tube furnace and dried at $70^{\\\\circ}\\\\mathrm{C}$ for $2\\\\mathrm{h}$ , followed by calcined at $340^{\\\\circ}\\\\mathrm{C}$ for $2\\\\mathrm{h}$ in nitrogen atmosphere and reduced in hydrogen at $360^{\\\\circ}\\\\mathrm{C}$ for $2\\\\mathrm{h}$ . Then the resulting supported catalyst was cooled under $\\\\mathbf{N}_2$ flow. In the supported catalyst preparation, the total metal Cu and Ni loading was fixed at $20\\\\mathrm{wt}\\\\%$ and the catalyst with different $\\\\mathrm{Cu / Ni}$ ratio can be prepared by changing the volume of nickel sulfate and copper sulfate aqueous solution. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,418,302,430]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.3. Catalyst characterization techniques \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,443,486,649]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A MimFlex600 diffractometer was used to record the X-ray diffraction (XRD) patterns of the catalysts. In the characterization, $\\\\mathrm{CuK}\\\\alpha$ radiation is at $45\\\\mathrm{kV}$ and $200\\\\mathrm{mA}$ and a scanning rate of $0.5^{\\\\circ}\\\\mathrm{min}^{-1}$ was set in the 20 range of $5^{\\\\circ}\\\\sim 80^{\\\\circ}$ . Scanning electron microscopy and energy dispersive X-ray spectroscopy (SEM-EDS) of the supported catalyst were performed on JEOL-JSM Model 6380 LA instrument with a $200\\\\mathrm{kV}$ operating voltage. To avoid the charges accumulation and improve the conductivity, gold spraying was performed before placing on the sample table. Transmission electron microscopy (TEM) was carried out on a Tecnai G2 F20 transmission electron microscopy, operating at $200\\\\mathrm{kV}$ . Before TEM analysis, the sample particles were dispersed in ethanol and then loaded on carbon-coated copper grids to evaporate the solvent. Xray photoelectron spectroscopy (XPS) analysis was performed on a Kratos Axis Ultra DLD spectrometer with a monochromatized Al Ka X-ray source $(\\\\mathrm{hn} = 1486.6\\\\mathrm{eV})$ . The C 1s peak $(284.6\\\\mathrm{eV})$ was used as the reference standard for the binding energy. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,650,486,791]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The nitrogen adsorption desorption experiment was performed on BELSORP Max instrument. Before the experiment, a vacuum pretreatment was applied to the samples at $423\\\\mathrm{K}$ for $8\\\\mathrm{h}$ first and then the adsorption desorption isotherms was determined at $77\\\\mathrm{K}$ . The specific surface area and pore volume and pore size distribution were calculated according to the Brunauer-Emmett-Teller (BET) model and nonlocal density functional theory (NLDFT) method respectively. The inductively coupled plasma-optical emission spectroscopy (ICP-OES) was used to measure the actual loading of metal Cu and Ni in different catalysts on an Agilent 730 device. Before analysis, a mixture of HCl and $\\\\mathrm{HNO}_3$ with molar ratio of 3:1 was employed to dissolve the catalysts. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,792,486,908]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The $\\\\mathrm{H}_{2}$ temperature programmed reduction of the catalyst $(\\\\mathrm{H}_{2}$ TPR) was recorded on a Micromeritics Chemisorb 2750 device equipped with a thermal conductivity detector (TCD) from Micromeritics Instrument (Shanghai) Ltd. In the characterization, the samples were firstly pretreated at $350^{\\\\circ}\\\\mathrm{C}$ for $2\\\\mathrm{h}$ , and then the temperature decreased to $25^{\\\\circ}\\\\mathrm{C}$ with an argon flow of $10~\\\\mathrm{mL~min}^{-1}$ . After that, the atmosphere was switched to $10\\\\%$ hydrogen/ $90\\\\%$ argon and the reactor was heated to $800^{\\\\circ}\\\\mathrm{C}$ at a ramp rate of $10^{\\\\circ}\\\\mathrm{C~min}^{-1}$ to begin the $\\\\mathrm{H}_{2}$ temperature programmed reduction. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,75,859,88]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.4. General procedure for hydrogenation of methyl ricinoleate \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[506,100,924,138]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The catalytic activity was evaluated by the yield and selectivity toward methyl 12-hydroxystearate in the hydrogenation of methyl ricinoleate. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[506,139,926,372]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The prepared catalysts were pelleted, crushed, and screened out with 20-40 meshes. The hydrogenation reaction was performed in batch mode with a magnetically stirred $50~\\\\mathrm{mL}$ autoclave. Before the reaction, about $1\\\\mathrm{g}$ methyl ricinoleate and a certain amount of the supported catalyst were loaded in the autoclave, then the air in the reactor was expelled and pure $\\\\mathrm{H}_{2}$ was fed into the reactor to maintain a reaction pressure. Subsequently, the reactor was heated to the preset temperature to begin the reaction. After a period of reaction, the reactor was cooled to room temperature. The resulting mixture was dissolved in ethyl acetate and the solid catalyst was separated by filtration. The reused catalyst was characterization by SEM, TEM, XRD and XPS. The filtrate was analyzed by GC and GC-MS to determine the conversion of methyl ricinoleate and the yield of methyl 12-hydroxystearate as well as the composition of the crude reaction mixture respectively. To test the reusability of the supported catalyst, the catalyst recovered by filtration was washed with ethanol and dried under vacuum, and then used for next cycle. Simultaneously, the recovered catalyst was also characterized using different technique to inspect its stability in reuse. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,390,633,403]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.5. Analysis method \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[506,416,926,661]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The conversion of methyl ricinoleate and yield of products were determined by gas chromatography equipped with SH-Rtx-5 capillary column and a FID detector using biphenyl as internal standard (Shimadzu, GC-2014). The carrier gas was nitrogen, and the temperature of the injector and detector were $280^{\\\\circ}\\\\mathrm{C}$ and $300^{\\\\circ}\\\\mathrm{C}$ respectively. The temperature program was from $120^{\\\\circ}\\\\mathrm{C}$ to $280^{\\\\circ}\\\\mathrm{C}$ at a ramp of $10^{\\\\circ}\\\\mathrm{C}\\\\mathrm{min}^{-1}$ , holding $20\\\\mathrm{min}$ at $280^{\\\\circ}\\\\mathrm{C}$ . The composition of the reaction mixture after hydrogenation was identified on a GC-MS system (Shimadzu GCMS-QP2010) in the electronic impact ionization mode at $70\\\\mathrm{eV}$ and equipped with a RTX-5 MS capillary column. The temperature of the oven was programmed from $50^{\\\\circ}\\\\mathrm{C}$ to $300^{\\\\circ}\\\\mathrm{C}$ at a ramp of $20^{\\\\circ}\\\\mathrm{C}\\\\mathrm{min}^{-1}$ , and kept at $300^{\\\\circ}\\\\mathrm{C}$ for $30\\\\mathrm{min}$ . The data are given as mass units per charge $(m / z)$ . FTIR was performed on Bruker Tensor 27 FT-IR instrument spectrophotometer with KBr pellets and the wavenumber range of $4000 - 400~\\\\mathrm{cm}^{-1}$ . ${}^{1}\\\\mathrm{H}$ NMR and ${}^{13}\\\\mathrm{C}$ NMR were recorded on $400\\\\mathrm{MHz}$ and $100.6\\\\mathrm{MHz}$ spectrometers using $\\\\mathrm{CDCl}_3$ as solvent referenced to $\\\\mathrm{CDCl}_3$ (7.26 ppm for ${}^{1}\\\\mathrm{H}$ NMR and $77.00~\\\\mathrm{ppm}$ for ${}^{13}\\\\mathrm{C}$ NMR). The high resolution mass spectrometry was used to determine the molecular weight of analyte on a Varian 7.0 T FTICR-MS with ESI technique. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,676,673,687]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. Results and discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,701,679,714]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1. Catalyst characterization \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[506,727,926,908]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To investigate the surface morphology and composition of the catalysts, the XRD patterns of the as-synthesized $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite (the subscript means the molar ratio of the two metals in the catalyst), Ni/ diatomite, calcined diatomite and untreated diatomite powders were detected and depicted in Fig. 1. It can be seen that the structure of diatomite is retained in the catalyst preparation process. For the Ni/ diatomite catalyst, the characteristic peaks for metallic nickel phase (JCPDS #04-0850) at $2\\\\theta = 45^{\\\\circ}$ , $53^{\\\\circ}$ , $78^{\\\\circ}$ are observed, which reveals the existence of metallic Ni(0). After doping a certain amount of copper, the shift and attenuation of the crystal diffraction peak were observed in Fig. 1, which means that the copper-nickel bimetal alloy was formed and the formed metal particles are too small to be detected. Thus we inferred that the metal dispersion on the carrier was enhanced by doping a small amount of copper. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[71,51,140,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"X. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[712,51,926,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green Chemical Engineering 2 (2021) 187-196 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,941,508,951]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"191 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[78,77,500,334]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0297/1e7030d942db03061397d34c441dd098de3c23872e453750fdba3e93cdb2a597.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[509,76,913,337]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0033/df988beaaba3c31864d205f6f99b4ada0920aa15418a6ea7fab7ed0135b112c0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[76,335,493,597]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0537/09dc33a3d92d8b414c9cc1d8109db80a663a1b2046e7d96ac9ba40d67c238aab.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[506,337,921,600]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 6. (a) XPS survey spectra of Ni/diatomite and $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite, (b) XPS spectra for Cu 2p of $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite, (c) XPS spectra for Ni 2p of Ni/diatomite, (d) XPS spectra for Ni 2p of $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0635/75d5337d5b8a6b65ca80d4d2c0372f0bced86d379ba2271510e36e3dd33ec53c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[68,667,485,845]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The micromorphology and structures of the $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite and Ni/diatomite catalysts were determined by SEM-EDS and TEM. The SEM-EDS results in Fig. 2 and Fig. 3 showed that there were uniformly distributed nano-scale open pores in the surface of disk-like diatomite, which can endow the supported catalyst with sufficient specific surface area. For $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst, EDS mapping indicated that Cu and Ni X-ray signals were uniformly mixed together. The consistent distribution of Cu and Ni hinted a good fusion performance of Ni and Cu in the $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst, which was in consistence with the XRD results. By contrast, for the Ni/diatomite catalyst, the relative large Ni metal particles can be found on the surface of carrier, which indicated poor dispersion of metal on diatomite. Therefore, it was concluded that the dispersion of metals on the support is improved with the addition of Cu. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,848,488,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The TEM results in Fig. 4 also confirmed that Ni/Cu alloy homogeneously dispersed on the diatomite with an average particle size of $20\\\\mathrm{nm}$ . As compared with the monometallic Ni/diatomite catalyst, the Ni/Cu alloy particle was much smaller, which implies that the addition of the Cu can reduce the particle size and increase the dispersion of metals on the carrier. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[506,667,926,796]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The specific surface area, pore volume and average pore diameter of $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite and Ni/diatomite catalysts were calculated according to the nitrogen adsorption desorption results. As shown in Fig. 5, the isotherm of $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite and Ni/diatomite exhibit typical IUPAC type IV pattern with H1-type hysteresis loop, which indicates a mesoporous nature of the supported catalyst. As shown in Table 1, the specific surface area, pore volume and average pore diameter of the $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst were slightly larger than those of Ni/diatomite, which was supposed to benefit from the enhanced metal dispersion on the carrier for $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[506,796,928,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The XPS analysis was performed to obtain the detailed information on the surface chemical composition and chemical states in the reduced supported catalyst. The XPS survey spectra showed that both supported metal and $\\\\mathrm{SiO}_2$ coexist on the catalyst surface. The high resolution spectra of Ni 2p and Cu 2p photoelectron lines for $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite and Ni/diatomite were shown in Fig. 6. Two peaks can be found for the Cu $2\\\\mathrm{p}_{3/2}$ spectra of $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalysts. The peak at 932.4 eV represents metallic Cu, and the peak at 933.7 eV is associated with $\\\\mathrm{Cu}^{2+}$ in CuO. Similarly, for the Ni $2\\\\mathrm{p}_{3/2}$ spectra, two peaks at 852.7 eV and 858.9 eV were detected, which can be related to metallic Ni and $\\\\mathrm{Ni}^{2+}$ in \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[71,51,140,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"X. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[712,51,926,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green Chemical Engineering 2 (2021) 187-196 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,941,509,951]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"192 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[133,76,424,262]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 7. $\\\\\\\\mathrm{H}_2$ -TPR profiles of $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite and Ni/diatomite catalysts. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0835/f89e1a46ff0ac252c6e4c2d95e631367e7fd74e8e9378834595e74754c1dcd70.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[68,313,485,417]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"NiO, respectively. The results of XPS analysis showed that $\\\\mathrm{Ni}^0$ and $\\\\mathrm{Ni}^{2+}$ species coexist on the surface of supported Ni/diatomite and $\\\\mathrm{Ni}^0$ , $\\\\mathrm{Ni}^{2+}$ , $\\\\mathrm{Cu}^0$ and $\\\\mathrm{Cu}^{2+}$ species present on the surface of $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite. The existence of oxidized metal on the catalyst surface is ascribed to the reoxidation of reduced metal when exposed to air as well as the incomplete reduction in the tube furnace. In XRD characterization, no oxide species were detected due to the good dispersion of these species on the catalysts surface. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,418,486,560]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To detect the change of atomic environment in Ni/diatomite and $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalysts, the $\\\\mathrm{H}_2$ -TPR analysis was carried out before the reduction of catalysts and the resulting profiles are shown in Fig. 7. For Ni/diatomite, a single reduction peak between $170^{\\\\circ}\\\\mathrm{C}$ and $358^{\\\\circ}\\\\mathrm{C}$ with a reduction in the approximate temperature of $233^{\\\\circ}\\\\mathrm{C}$ was observed. For bimetallic $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst, four isolated reduction peaks were observed, which implied a complex composition on the surface of the bimetallic catalyst; presumably due to different precipitate rates between the Cu, Ni. Although different metal oxide species coexisted on the diatomite surface, the shift of main reduction peak (at $199^{\\\\circ}\\\\mathrm{C}$ ) toward low temperature meant the change of atomic environment for at least \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[508,75,926,127]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"part of Ni, which confirmed the formation of the Cu-Ni alloy. The other two minor reduction processes occurred between $140^{\\\\circ}\\\\mathrm{C} - 150^{\\\\circ}\\\\mathrm{C}$ might be ascribed to the reduction of copper oxide [29] and the reduction peak presented at $375^{\\\\circ}\\\\mathrm{C}$ , being associated with the reduction of NiO. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,141,901,155]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2. Hydrogenation of methyl ricinoleate to methyl 12-hydroxystearate \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,167,741,180]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2.1. Performances of different catalysts \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[508,180,926,464]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Having obtained the supported monometallic and bimetallic catalysts, the hydrogenation of methyl ricinoleate was performed under a relatively low pressure (2 MPa). And the results were listed in Table 2. It can be seen that in the absence of catalyst or using $\\\\mathrm{Cu}$ /diatomite as catalyst, no hydrogenation occurred (entries 1-2). The $\\\\mathrm{Ni}$ /diatomite and $\\\\mathrm{Ni} / \\\\mathrm{Cu}$ /diatomite catalyst can promote the hydrogenation. However, the usage of monometallic catalyst should be much higher than that of the bimetallic ones (entries 3-5 vs. 6-8, Table 2) to achieve comparable conversion and yield. This meant that the catalytic activity was enhanced by adding $\\\\mathrm{Cu}$ . It was also noteworthy that the disparity between the conversion of methyl ricinoleate and the yield of methyl 12-hydroxystearate can be observed for some reactions (entries 3-7), which means the by-product formation. Gratifyingly, by regulating the content of $\\\\mathrm{Cu}$ in the bimetallic catalyst, the by-product can be reduced (entries 8-11). When the $\\\\mathrm{Ni} / \\\\mathrm{Cu}$ atom ratio was 7:1, nearly equivalent conversion and up to $97\\\\%$ yield of product can be obtained. Therefore, the catalyst $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite was optimum for this reaction. The results showed that both the efficiency and selectivity of the catalyst toward methyl 12-hydroxystearate was improved by doping a small amount of $\\\\mathrm{Cu}$ . The enhanced activity and selectivity of the bimetallic catalyst may be originated from its improved ability to activate hydrogen and the specific site adsorption of the substrate on the alloy surface. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[508,464,928,567]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"With $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite as catalyst, we further studied the effect of catalyst amount on the hydrogenation reaction. It was found that both of the conversion of methyl ricinoleate and the yield of methyl 12-hydroxystearate decreased when reducing the catalyst amount (entries 8-11). Even so, $82\\\\%$ yield of product can still be obtained when the catalyst was reduced to $0.2\\\\mathrm{wt}\\\\%$ , being corroborated the high efficiency of the bimetallic catalyst. To maintain a high conversion and product yield, $1\\\\mathrm{wt}\\\\%$ $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite was used as catalyst in the following experiments. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,620,718,701]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0875/0dffbd41c35f1dddde142a7bb887adfa564171559ca843f59d4f3da824743ad6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[71,723,926,865]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0779/adf73971845a9df4c8d54bafeae5720cde2a44d7190d918ddd1b4bfe96b61969.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Entry</td><td>Catalyst</td><td>Catalyst, wt%</td><td>Conversion, %a</td><td>Yield, %a</td></tr><tr><td>1</td><td>None</td><td>-</td><td>0</td><td>0</td></tr><tr><td>2</td><td>Cu/diatomite</td><td>1</td><td>0</td><td>0</td></tr><tr><td>3</td><td>Ni/diatomite</td><td>1</td><td>47</td><td>40</td></tr><tr><td>4</td><td>Ni/diatomite</td><td>5</td><td>92</td><td>85</td></tr><tr><td>5</td><td>Ni/diatomite</td><td>8</td><td>>99</td><td>93</td></tr><tr><td>6</td><td>Ni3Cu1/diatomite</td><td>1</td><td>>99</td><td>91</td></tr><tr><td>7</td><td>Ni5Cu1/diatomite</td><td>1</td><td>>99</td><td>95</td></tr><tr><td>8</td><td>Ni7Cu1/diatomite</td><td>1</td><td>>99</td><td>97</td></tr><tr><td>9</td><td>Ni7Cu1/diatomite</td><td>0.5</td><td>88</td><td>87</td></tr><tr><td>10</td><td>Ni7Cu1/diatomite</td><td>0.3</td><td>85</td><td>83</td></tr><tr><td>11</td><td>Ni7Cu1/diatomite</td><td>0.2</td><td>83</td><td>82</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2 Catalyst screening for hydrogenation of methyl ricinoleate. \\\"]\",\n \"table_footnote\": \"[\\\"Reaction conditions: methyl ricinoleate $(3.2\\\\\\\\mathrm{mmol},1.00\\\\\\\\mathrm{g})$ $\\\\\\\\mathrm{H}_2$ 2 MPa), $130^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ 10 h. \\\",\\\"a Determined by GC with biphenyl as internal standard. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[71,51,140,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"X. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[712,51,926,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green Chemical Engineering 2 (2021) 187-196 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,941,509,951]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"193 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[230,80,803,293]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 8. Effect of reaction parameters on the hydrogenation of methyl ricinoleate. Reactions were performed with methyl ricinoleate (3.2 mmol, 1.00 g), $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite (1 wt% relative to methyl ricinoleate). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0484/fb52577cc3a97a0bc672a9cf11ceeb24cdd5024b19e3bb4d7465f666825938f0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[68,346,292,359]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2.2. Effect of the reaction parameters \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,359,485,397]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"With the selected catalyst in hand, we further optimized the other reaction conditions containing the hydrogen pressure, temperature and reaction time for the reaction. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,398,485,577]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The effect of $\\\\mathrm{H}_2$ pressure on the hydrogenation of methyl ricinoleate was investigated with the reaction temperature and reaction time set at $130^{\\\\circ}\\\\mathrm{C}$ and $9.5\\\\mathrm{h}$ . Similarly, the reaction temperature was screened by fixing the $\\\\mathrm{H}_2$ pressure and reaction time at $2\\\\mathrm{MPa}$ and $9.5\\\\mathrm{h}$ , respectively. The results in Fig. 8 showed that the reaction is sensitive to the $\\\\mathrm{H}_2$ pressure as well as the reaction temperature. When the $\\\\mathrm{H}_2$ pressure is below $1\\\\mathrm{MPa}$ and the temperature is less than $100^{\\\\circ}\\\\mathrm{C}$ , the hydrogenation of methyl ricinoleate cannot occur. Increasing the $\\\\mathrm{H}_2$ pressure and reaction temperature improved the conversion of methyl ricinoleate. However, the $\\\\mathrm{H}_2$ pressure higher than $2\\\\mathrm{MPa}$ and temperature above $130^{\\\\circ}\\\\mathrm{C}$ reduced the product selectivity. Therefore, the optimal $\\\\mathrm{H}_2$ pressure and reaction temperature were set at $2\\\\mathrm{MPa}$ and $130^{\\\\circ}\\\\mathrm{C}$ , respectively. Under these optimized conditions, up to $97\\\\%$ yield of target product can be obtained. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,579,486,630]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the subsequent investigation of reaction time, an obvious induction time was observed. After the induction time, the conversion of methyl ricinoleate and yield of methyl 12-hydroxystearate increased sharply. When the reaction time was prolonged to more than $4\\\\mathrm{h}$ , the conversion \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,670,478,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 9. Reusability of the $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite catalyst. Reaction conditions: methyl ricinoleate (3.2 mmol, $1.00\\\\\\\\mathrm{g}$ ), $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite (10 mg), $\\\\\\\\mathrm{H}_2$ (2 MPa), $130^{\\\\\\\\circ}\\\\\\\\mathrm{C}, 4\\\\\\\\mathrm{h}$ . \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0517/ade61dc009f7a009cdaa9f8dd5e794100c26e6e1e8084d66888b28388f0c80fe.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[506,346,926,488]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"remained unchanged but the product yield decreased. Simultaneously, the by-product methyl stearate was detected (the by-product has been verified by GC-MS spectra of the crude reaction mixture and the details can be found in SI). It is inferred that the induction time is the result of catalyst reactivation as the bimetallic catalyst exposed to air can be easily deactivated. Actually, in the XPS characterization of the catalyst, the oxidized Cu and Ni species was detected. After the catalyst was reactivated in the reaction system, the hydrogenation proceeded quickly and almost equivalent conversion of methyl ricinoleate can be achieved. With the increase of reaction time, side reactions occurred and the yield of target product decreased. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[508,501,846,514]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2.3. Reusability of the supported Cu/Ni bimetallic catalyst \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[506,514,926,669]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As the recyclability and reusability are the key features for the heterogeneous catalyst, the stability and reusability of the $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst was assessed for this hydrogenation reaction and the results were presented in Fig. 9. In this set of experiments, the hydrogenation reaction was conducted under the optimal conditions. When the reaction was completed, the mixture was dissolved in ethyl acetate. Then the catalyst was recovered by filtrating the reaction mixture. After appropriate treatment (as mentioned in Section 2.3), the catalyst was reused in the next run. It can be seen from Fig. 9 that after five runs of reaction, $92\\\\%$ of the catalytic activity was retained, which means that the supported bimetallic catalyst has satisfying stability and reusability. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[506,669,928,787]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To further verify the stability of the catalyst in reused, the $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst after five rounds of recycle was characterized by SEM, TEM, XRD and XPS. The results in Fig. 10 showed that the morphology and composition of the catalyst were stable during the reuse, which supported the excellent reusability of the supported bimetallic catalyst. The improved stability of this bimetallic catalyst can be attributed to the formation of $\\\\mathrm{Cu} / \\\\mathrm{Ni}$ alloy, which inhibited the migration and aggregation of Ni atom during the exothermic process and thus keep the even distribution of catalytic sites on the surface of support. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,800,609,809]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. Conclusions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[506,824,926,914]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In summary, a high efficient diatomite supported $\\\\mathrm{Cu / Ni}$ bimetallic catalyst was developed for selective hydrogenation of methyl ricinoleate to methyl 12-hydroxystearate. The results showed that the $\\\\mathrm{Cu / Ni}$ ratio of 7:1 in the supported bimetallic catalyst is optimum and the characterization results of XRD, SEM-EDS, TEM, XPS and $\\\\mathrm{H}_2$ -TPR showed that the highly dispersed $\\\\mathrm{Cu / Ni}$ alloy was formed on the surface of carrier, which might promote double bond adsorption and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[71,51,140,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"X. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[712,51,926,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green Chemical Engineering 2 (2021) 187-196 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,941,509,951]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"194 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[202,87,514,235]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"a \\\",\\\"b \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0812/c6f13b5370d5ce9890fdb9e752bfcb2d9909db382df9ade4e2927cc9c3098191.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[542,87,836,235]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0969/4698f898a460d1e8c4223dcea8cff3ccec6923aceb8c625ce0fc809da6a58cfd.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[176,254,500,472]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"c \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0060/16ef50770594cd1ec3fb526f8ee4ccdd9fd2f6a32919f8400f607dcb179ed85f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[540,254,834,471]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"d \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0214/6802893906ab0adbbf4a07a750431abd8c4b02aa7bb041d4aa1607ee958ed430.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[161,488,488,709]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"e \\\",\\\"Fig. 10. (a) SEM, (b) TEM images of reused $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite catalyst after five catalytic cycles, (c) XRD spectra of fresh and used $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite catalyst, (d) XPS survey spectra for Cu 2p and (e) Ni 2p of the reused $\\\\\\\\mathrm{Ni}_7\\\\\\\\mathrm{Cu}_1/$ diatomite catalyst after five catalytic cycles. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0757/5cc7583bfa224edf67d7b939b7f9f06cd0a304785916a576245886e956c3c90c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[68,751,488,906]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\mathrm{H}_2$ activation on the catalyst and therefore result in its superior catalytic activity and selectivity as compared with the supported Ni monometallic catalyst. Under the optimal reaction conditions, i.e. $2\\\\mathrm{MPa}$ of $\\\\mathrm{H}_2$ pressure, $130^{\\\\circ}\\\\mathrm{C}$ and $1\\\\mathrm{wt}\\\\%$ catalyst, up to $97\\\\%$ yield of methyl 12-hydroxystearate and equivalent conversion of methyl ricinoleate can be achieved in $4\\\\mathrm{h}$ . In addition, the heterogeneous $\\\\mathrm{Ni}_7\\\\mathrm{Cu}_1/$ diatomite catalyst could be easily recovered and reused without significant loss of activity. Therefore, this $\\\\mathrm{Cu} / \\\\mathrm{Ni}$ bimetallic supported catalyst proves to be efficient for commercial production of methyl 12-hydroxystearate from methyl ricinoleate. Therefore, this work will pave new avenue for developing green process for upgrading of biomass to industrial useful chemicals and materials. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,751,723,765]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Declaration of competing interest \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[508,777,926,818]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,829,635,843]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgements \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[508,855,928,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This work was financially supported by the National Program on Key Research Project (2016YFA0602900) and Nankai University Engineering Research Center for Castor and also supported by \\\"the Fundamental Research Funds for the Central Universities\\\", Nankai University (000082). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[71,51,140,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"X. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[712,51,926,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green Chemical Engineering 2 (2021) 187-196 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,941,509,951]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"195 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[71,75,143,86]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[71,100,483,434]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[1] R. 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Fu, Efficient and stable Cu-Ni/ZrO $_2$ catalysts for in situ hydrogenation and deoxygenation of oleic acid into heptadecane using methanol as a hydrogen donor, Fuel 230 (2018) 211-217. \\\"]\",\n \"page_idx\": \"9\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[71,51,140,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"X. Zhang et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[712,51,926,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green Chemical Engineering 2 (2021) 187-196 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,941,509,951]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"196 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1016/j.gce.2020.09.011"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Medicine and Health Sciences/Engineering and Manufacturing Science"},"sha256":{"kind":"string","value":"b1ea799ae8ae669c7d3abeaf19195da63e5dd4e64f78adec6913963c91fd7909"},"title":{"kind":"string","value":"Green process for hydrogenation of methyl ricinoleate to methyl 12-hydroxystearate over diatomite supported Cu/Ni bimetallic catalyst"}}},{"rowIdx":246,"cells":{"abstract":{"kind":"string","value":"Autonomous vehicles (AVs) can be equipped with Integrated sensing and communications (ISAC) devices to realize sensing and communication functions simultaneously. Time-division ISAC (TD-ISAC) is advantageous due to its ease of implementation, efficient deployment and integration into any system. TD-ISAC greatly enhances spectrum efficiency and equipment utilization and reduces system energy consumption. In this paper, we propose a communication-assisted sensing mechanism based on TD-ISAC to support multi-vehicle collaborative sensing. However, there are some challenges in applying TD-ISAC to AVs. First, AVs should allocate resources for sensing and communication in a dynamically changing environment. Second, the limited spectrum resources bring the problem of mutual interference of multi-vehicle signals. To address these issues, we construct a multi-vehicle signal interference model, formulate an optimization problem based on the partially observable Markov decision process (POMDP) framework and design a decentralized dynamic allocation scheme for multi-vehicle time–frequency resources based on a deep reinforcement learning (DRL) algorithm. Simulation results show that the proposed scheme performs better in miss detection probability and average system interference power compared to the DRQN algorithm without the communication-assisted sensing mechanism and the random algorithm without reinforcement learning. We can conclude that the proposed scheme can effectively allocate the resources of the TD-ISAC system and reduce interference between multiple vehicles."},"author":{"kind":"string","value":"Zesong Fei|Jingxuan Huang|Xinyi Wang|Yuxin Fan"},"content_list":{"kind":"list like","value":[{"bbox":"[55,121,941,184]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article Reinforcement Learning-Based Resource Allocation for Multiple Vehicles with Communication-Assisted Sensing Mechanism ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,198,534,214]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Yuxin Fan, Zesong Fei, Jingxuan Huang $\\ast \\textcircled { \\scriptsize { \\parallel } }$ and Xinyi Wang $\\textcircled{1}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,569,253,680]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Citation: Fan, Y.; Fei, Z.; Huang, J.; Wang, X. Reinforcement Learning-Based Resource Allocation for \nMultiple Vehicles with \nCommunication-Assisted Sensing Mechanism. Electronics 2024, 13, 2442. https://doi.org/10.3390/ \nelectronics13132442 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,690,247,701]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Academic Editor: Christos J. Bouras ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,712,183,765]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received: 6 May 2024 \nRevised: 17 June 2024 \nAccepted: 19 June 2024 \nPublished: 21 June 2024 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[275,240,860,278]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"School of Information and Electronics, Beijing Institute of Technology (BIT), Beijing 100081, China; fanyuxin678@163.com (Y.F.); feizesong@bit.edu.cn (Z.F.); bit_wangxy@163.com (X.W.) \\* Correspondence: jxhbit@gmail.com ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,294,941,555]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract: Autonomous vehicles (AVs) can be equipped with Integrated sensing and communications (ISAC) devices to realize sensing and communication functions simultaneously. Time-division ISAC (TD-ISAC) is advantageous due to its ease of implementation, efficient deployment and integration into any system. TD-ISAC greatly enhances spectrum efficiency and equipment utilization and reduces system energy consumption. In this paper, we propose a communication-assisted sensing mechanism based on TD-ISAC to support multi-vehicle collaborative sensing. However, there are some challenges in applying TD-ISAC to AVs. First, AVs should allocate resources for sensing and communication in a dynamically changing environment. Second, the limited spectrum resources bring the problem of mutual interference of multi-vehicle signals. To address these issues, we construct a multi-vehicle signal interference model, formulate an optimization problem based on the partially observable Markov decision process (POMDP) framework and design a decentralized dynamic allocation scheme for multi-vehicle time–frequency resources based on a deep reinforcement learning (DRL) algorithm. Simulation results show that the proposed scheme performs better in miss detection probability and average system interference power compared to the DRQN algorithm without the communication-assisted sensing mechanism and the random algorithm without reinforcement learning. We can conclude that the proposed scheme can effectively allocate the resources of the TD-ISAC system and reduce interference between multiple vehicles. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,571,937,600]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: integrated sensing and communications; communication-assisted sensing; deep reinforcement learning; time–frequency resource allocation ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,645,393,659]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[278,663,391,676]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.1. Background ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,681,941,828]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"With the development of communication technology, sensing technology, artificial intelligence and the automotive industry, the level of automotive intelligence is rapidly increasing. Autonomous vehicles (AVs), which will improve road safety and reshape the way we travel, are steering the future of transportation. Sensing and communication are two essential functions of AVs [1]. AVs have many sensors, such as LiDAR, which acquires information about the surroundings and avoids collisions by detecting the presence of obstacles [2,3]. In the meantime, AVs are equipped with wireless communication transceivers to achieve large-scale and high-capacity data exchange in vehicle-to-vehicle (V2V) or vehicle-to-infrastructure (V2I) communication. AVs’ sensing and communication functions can enhance the safety and smoothness of the transportation system. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,829,941,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Radar detection and wireless communication both transmit or obtain information through the transmission of radio waves, and in some scenarios, sensing and communication are highly coupled. First, the operating frequency bands for both sensing and communication are moving closer to the millimeter-wave frequency range [4]. Millimeter-wave radar offers advantages of extended detection range, high precision, weather independence and the ability to operate all day compared with cameras and LiDAR. Millimeter-wave communication technology, with its narrow beamwidth and large bandwidth, can significantly improve the communication capability of vehicles. In addition, the similarities between radar and communication in system design, signal processing and data processing create conditions for sharing hardware equipment, such as transceiver systems [5]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,57,285,99]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"electronics ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[57,778,154,804]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CC ? BY ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[57,966,478,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442. https://doi.org/10.3390/electronics13132442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[670,966,939,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://www.mdpi.com/journal/electronics ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[865,65,939,99]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MDPI ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[57,542,147,564]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"check for updates ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[57,809,257,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Copyright: $^ { © }$ 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[277,103,941,162]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,164,941,341]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Integrated sensing and communications (ISAC) technology aims to unify these two functions and pursue direct trade-offs and mutual performance gains [4]. Enabled by ISAC technology, AVs can simultaneously realize sensing and communication by carrying ISAC radio-frequency (RF) transceivers, which alleviates concerns for electromagnetic compatibility as well as reduces system size, weight, and energy consumption [6,7]. Currently, ISAC has five main realization methods: time division, frequency division, space division, code division and waveform sharing [1]. The time division ISAC (TD-ISAC) method is based on the fact that an RF device occupies different time resources to transmit sensing and communication signals, respectively [8]. The critical advantage of TD-ISAC is its easy implementation and seamless integration into any system [9]. Furthermore, TD-ISAC can utilize specific waveforms for sensing and communication according to their respective needs and improve system spectrum efficiency. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,342,941,431]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, AVs equipped with TD-ISAC systems face some technical challenges. First, only one function of sensing and communication can operate at a given time, leading to a trade-off in the performance of both functions, particularly in dynamic environments [10]. Second, as the number of TD-ISAC vehicles increases, it is necessary for vehicles to learn how to coordinate the use of ISAC to minimize mutual interference and improve overall performance [11]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[278,443,401,457]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.2. Related Work ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,462,941,730]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Some scholars have conducted research on time resource allocation for sensing and communication functions. The traditional time division method uses an arbitrary or fixed schedule to switch between sensing and communication. The authors in [12] use the preamble of IEEE 802.11ad standard frames for radar detection and data blocks for communication data transmission. Based on this point, Ref. [13] performs adaptive preamble design, allowing for a trade-off between radar estimation accuracy and communication rate. In addition, Refs. [14,15] study the fundamental trade-offs of radar–communication coexistence with flexible configuration. Nevertheless, the road traffic environment is dynamic and uncertain, and these solutions are fixed during the runtime and unsuitable for implementation in real-time systems. Deep reinforcement learning (DRL) has been recently introduced to find the optimal decision quickly in real time. Some studies use DRL to optimize the allocation of communication and radar time resources for individual vehicles in dynamic environments. The authors of [16–18] use the DRL algorithm to decide when to use the communication mode or the radar mode to maximize the data throughput while minimizing the miss detection probability of unexpected events given the uncertainty of the surrounding environment. The AV can quickly obtain the optimal policy without requiring any prior information about the environment. Ref. [19] jointly coordinates radar and communication and minimizes the age of information (AoI) of its communication function. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[278,731,941,909]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As the number of TD-ISAC vehicles increases, vehicles need to learn how to coordinate their use of ISAC to minimize mutual interference. In traditional radar and communication systems, interference avoidance can be used to reduce mutual interference. Interference avoidance is achieved by coordinating signal transmission in the time, frequency and space domains to reduce interference [20]. One representative method for interference avoidance in the frequency domain is spectrum allocation. The authors of [21,22] propose a centralized framework to enable multiple access to a shared spectrum among radars relying on vehicular ad hoc networking (VANET) and cellular-vehicle-to-everything (C-V2X) communication, respectively. However, centralized allocation typically involves frequent transmission of large amounts of data between vehicles and the central node, leading to increased communication costs and decision latency. Decentralized allocation, in which each AV autonomously selects its frequency sub-band, can be adopted to reduce communication costs and ensure the timeliness of spectrum resource scheduling. A direct method is random selection, which is easy to implement but cannot suppress interference [23]. In [24], the author proposes a decentralized spectrum allocation approach based on $\\scriptstyle \\mathrm { { D R L , } }$ effectively avoiding mutual interference among automotive radars. In the communication system, the issue of multi-user interference has also been studied using DRL by learning sub-band access strategies to avoid users colliding with other users in the same sub-band [25,26]. However, these studies do not use the ISAC mechanism or consider interference between communication and radar signals. Ref. [27] considers multiple vehicles based on [19] and proposes a medium access control (MAC) protocol that manages contention-free access to the communication–radar channel. However, in each time step, only one vehicle can communicate or sense. Therefore, we need a more efficient decentralized spectrum allocation method suitable for the ISAC mechanism. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,59,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,60,939,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[277,103,941,281]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[278,294,405,307]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.3. Contributions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,312,941,506]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This paper focuses on a time division integrated sensing and communication scenario in intelligent transportation systems. In this scenario, AVs on the road are equipped with both communication and sensing functions, sharing the same set of transceiver equipment and switching in a time division manner, occupying the same frequency resources. The environment in which the AVs operate is highly dynamic, with environmental conditions and communication demands constantly changing, and there is interference between signals from different AVs. In practical applications, the trained model’s ability to generalize across different road environments must be rigorously tested to ensure that AVs can make safe and reliable decisions under various circumstances. We propose an intelligent time–frequency resource allocation algorithm to mitigate multi-vehicle mutual interference in dynamic road environments. The proposed algorithm allows AVs to make decentralized decisions based on local observations to avoid significant time overheads caused by centralized scheduling. The main contributions of this paper can be summarized as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[278,511,941,780]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We propose a communication-assisted sensing mechanism based on TD-ISAC. By transmitting sensing information through communication, we can effectively reduce the number of active radars in the system. Simultaneously, by employing time division between sensing and communication, we can enhance spectrum utilization and lower the probability of multiple vehicles’ transmitted signals colliding within the same sub-band, thereby further improving system performance. \nWe construct a multi-vehicle sensing and communication interference model. Building this model contributes to a comprehensive understanding of the characteristics and sources of interference, enabling us to take appropriate measures to manage system interference. \nWe formulate a multi-vehicle optimization problem based on the partially observable Markov decision process (POMDP) framework. With the POMDP framework, vehicles can choose sensing or communication operations based on dynamic environments adaptively and select different sub-bands to reduce multi-vehicle interference. \nTo solve the optimization problem, we design a DRL algorithm using a target network and a prioritized experience replay (PER) scheme to enable multiple vehicles to better obtain the optimal strategy for time–frequency resource allocation under uncertain environmental factors. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,785,941,845]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The rest of this paper is organized as follows. We describe the problem formulation in Section 2. Section 3 builds the POMDP framework. Furthermore, in Section 4, we present a DRL algorithm. Section 5 evaluates the performance of the proposed approach. Finally, conclusions are drawn in Section 6. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,858,462,871]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. Problem Formulation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[278,873,447,888]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.1. Environment Model ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[272,891,941,922]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This paper considers a two-lane road traffic scenario in both directions with a dynamically changing environment, as shown in Figure 1. Environmental conditions are influenced by road condition, weather condition and moving object state, and the values of these factors can be obtained through a vehicle sensor system, such as a road friction sensor, weather station instrument and camera [16]. Environmental conditions are not the same for different AVs at the same time. In the following text, we provide the modeling of the relationship between environmental conditions and risk levels. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,59,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,60,939,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[277,102,941,177]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,178,941,269]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$e \\in { \\mathcal { E } }$ represents a particular environmental factor, where $\\mathcal { E } = \\{ \\rho , w , m \\} , \\rho , w$ and $m$ denote the road condition, the weather condition and the moving object state, respectively. $f \\in { \\mathcal { F } }$ represents the degree of influence of the environmental factor on the vehicle’s driving, where $\\mathcal { F } = \\{ 0 , 1 , . . . , F \\}$ . For simplicity, we can assume that ${ \\mathcal { F } } = \\{ 0 , 1 \\}$ . When $f = 0 .$ , the environmental factor is good; when $f = 1 _ { . }$ , the environmental factor is poor. $\\tau _ { f } ^ { e }$ represents the probability of the occurrence of the condition $e = f ,$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[563,280,652,312]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0075/ba3640bd22683cadac4595a59a24fc48c1e50f29d720287a62a6b7c19827a5c0.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\sum _ { f \\in \\mathcal { F } } \\tau _ { f } ^ { e } = 1 .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,317,941,365]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$p _ { f } ^ { e }$ denotes the probability of the occurrence of an unexpected event under condition $e = f$ . Using Bayes’s theorem, the average probability of an unexpected event occurring in the current environment is given by [16] ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[539,375,678,409]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0555/26dad179ff561d8dcf621633752bbf9f365bdfa043ba6d6451e52ca4b962f596.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\np _ { u } = \\sum _ { e \\in \\mathcal { E } } \\sum _ { f \\in \\mathcal { F } } \\tau _ { f } ^ { e } p _ { f } ^ { e } .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,413,941,443]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The relationship between environmental conditions and risk levels can be provided to AVs by accessing digital map databases [27]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[132,461,860,696]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 1. Multiple AVs driving in a dynamic environment. \"]","image_footnote":"[]","img_path":"images/0641/8bc3e5a9eb08e786e83234f4390380a678a9dbae3976048c4d5cdbbf5a7d5419.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,732,401,747]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.2. Signal Model ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,751,941,856]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This paper assumes that all AVs are equipped with TD-ISAC systems, i.e., RF devices occupy different time resources for sensing and communication, respectively. We propose a communication-assisted sensing mechanism. Every two adjacent vehicles in the same lane are paired through V2V communication technology, and this vehicle pair is referred to as a communication-assisted vehicle pair (CAVP). The front vehicle (FV) and the back vehicle (BV) can maintain a minimal distance (several meters or even tens of centimeters) between them by sharing speed, location, status, and other information [28]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,857,941,915]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"While driving, a CAVP can choose to sense or communicate based on the dynamic environment. The frame structure of sensing and communication for the FV and BV is illustrated in Figure 2. During the sensing frame, the FV performs forward sensing using long-range radar (LRR) while the BV awaits communication data. During the communication frame, the FV performs backward communication, and the BV receives communication data from the FV. Additionally, a specific subframe in the communication frame is allocated to the BV for backward sensing using short-range radar (SRR). The direction adjustment between sensing and communication functions is achieved through beam angle adjustment [8]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,59,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,60,939,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[275,102,941,178]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[136,192,863,428]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 2. The frame structure of sensing and communication. \"]","image_footnote":"[]","img_path":"images/0435/cd5b6783dd9b1e135a91e03f4d404999c5dc1dfd6118232b9670aaccb0b66f82.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,467,941,587]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let the set of all AVs on the road be $\\mathcal { N } = \\{ 1 , 2 , . . . , N \\}$ and the set of CAVPs be $\\mathcal { N } _ { p } = \\{ 1 , 2 , . . . , N _ { p } \\} _ { }$ , where $N = 2 N _ { p }$ . The total frequency band is divided equally into multiple orthogonal sub-bands, and the set of sub-bands is $\\mathcal { M } = \\left\\{ 1 , 2 , . . . , M \\right\\}$ [21]. A CAVP can freely select a sub-band in the sensing or communication frames. The number of AVs is rapidly increasing, while the number of sub-bands is limited, making it impossible to allocate non-reused orthogonal sub-bands for each CAVP. Multiple CAVPs will inevitably collide in the same sub-band, creating interference [21,24]. Thus, we assume that $N _ { p } \\geq M ,$ and multiple CAVPs can use the same sub-band at the same time. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,588,941,781]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Due to the proximity of paired vehicles and the relatively low importance of backward sensing, only accidents occurring in the overall front of the CAVP are considered, without considering accidents between the FV and BV or behind the BV. When the forward sensing is successful, the FV can know whether an unexpected event occurs in the environment, represented by 1 and 0, respectively, and the sensory result is stored in the data queue. However, if the FV cannot communicate with the BV in time, the sensory result will fail, which will seriously affect the safety of the BV. We use AoI [19] as a metric to characterize the timeliness of information. AoI is defined as the duration of a sensory result in the vehicle’s queue since it was acquired, denoted by $\\Delta$ . If $\\Delta$ is greater than or equal to the threshold $\\Delta _ { 0 } ,$ we consider the sensory result to have failed. The data will be removed from the queue. It is assumed that when the backward communication is successful, the FV can transmit all the non-failed sensory results. If the communication fails, all the sensory results in the queue of the FV are lost. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,794,438,808]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.3. Interference Model ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[278,813,941,870]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Different CAVPs may use the same sub-band for the sensing or communication frame, generating multi-vehicle mutual interference. Because this paper primarily focuses on reducing unexpected events occurring in front of the CAVP, we model the interference suffered by forward sensing and backward communication. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,872,941,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As shown in Figures 1 and 2, when a CAVP is in the sensing frame, the FV performs forward sensing. At this time, the radar receiver of the FV will be subjected to the same-frequency interference from the LRR signals in the opposite lane and the communication/SRR signals in the same lane. When the CAVP is in the communication frame, the FV performs backward communication. At this time, the communication receiver of the BV will be subjected to the same-frequency interference from the LRR signals in the opposite lane and the communication signals in the same lane. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,59,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,60,939,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[275,102,941,162]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[273,164,941,192]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The received interference power depends on the relative positions of CAVPs. The interference power of the LRR signal from CAVP $n$ in the opposite lane can be expressed as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[485,202,731,234]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0096/c63eebfc8cb7ea8eed2e15c62172c114e2ad0ed1f90701a22f9a66f3903a5eff.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP _ { R , I } ^ { n } = \\frac { P _ { R } G A _ { e } g } { 4 \\pi ( L ^ { 2 } + d ^ { 2 } ) } \\cdot [ p _ { a } ( \\theta ( d ) ) ] ^ { 2 } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,239,941,334]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $P _ { R }$ is the LRR transmitting power, $G$ is the antenna gain, $A _ { e }$ is the antenna effective area, $g$ is the propagation decaying factor, $p _ { a } ( \\cdot )$ is the normalized antenna beam patter [24], $L$ is the vertical distance between two lanes, $d$ is the horizontal distance between two CAVPs and $\\begin{array} { r } { \\theta ( d ) = \\arctan \\Big ( \\frac { L } { d } \\Big ) } \\end{array}$ is the radiation direction between two CAVPs. For simplicity, we assume that the power of the communication and SRR signals is the same. The interference power of the communication/SRR signal from CAVP $n$ in the same lane can be expressed as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[546,342,670,372]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0254/524ed1592d06bfa02f752670aa917650d02414311648047bc349ec9680bef0f7.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP _ { C , I } ^ { n } = { \\frac { P _ { C } G A _ { e } g } { 4 \\pi d ^ { 2 } } } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,375,705,391]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $P _ { C }$ is the communication/SRR transmitting power. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[275,392,941,420]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In conclusion, the total interference power suffered by a CAVP when it performs forward sensing or backward communication is ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[519,430,699,469]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0860/b4c2f773dde24efd7d650ffb2bc591571a6cf3ab5bc9839d14ff5ef15610f4ef.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP _ { I } = \\sum _ { n = 1 } ^ { N _ { R } } { P _ { R , I } ^ { n } } + \\sum _ { n = 1 } ^ { N _ { C } } { P _ { C , I } ^ { n } } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[275,474,941,518]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $N _ { R }$ is the number of CAVPs in the opposite lane choosing the same frequency band for the sensing frame and $N _ { C }$ is the number of CAVPs in the same lane choosing the same frequency band for the communication frame. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,519,939,548]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We use the interference-to-noise ratio (INR) to measure the level of interference to the CAVP [24]. The INR is defined as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[578,558,642,588]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0069/817d8a981adcca684dc820984990f0a164dd9adba20841851c42465344896e70.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\eta = \\frac { P _ { I } } { \\sigma ^ { 2 } } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,594,939,624]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\sigma ^ { 2 }$ is the receiver noise power. Similar to [24], if $\\eta$ is lower than the threshold $\\eta _ { 0 } ,$ , we consider the forward sensing or backward communication successful. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,636,443,650]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. Pomdp Framework ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,653,942,816]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Due to the high mobility of autonomous vehicles, there is a strict requirement for the latency of information transmission and processing to ensure the safety of autonomous driving. Each CAVP must be able to make decentralized decisions based on its local observations to avoid large time overheads caused by centralized scheduling. However, decentralized decision making leads to CAVPs having access to only the partial environmental information observed by themselves, without the ability to obtain the global information. Based on this, we model multi-agent decision problems as individual POMDP problems for each single agent [29]. A POMDP models an agent decision process in which it is assumed that the system dynamics are determined by an MDP, but the agent cannot directly observe the underlying state. In this approach, each CAVP considers the influence of other CAVPs as part of the environment and makes decisions based on its local observations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,819,941,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"During a CAVP’s driving, it continuously interacts with the dynamic environment. At each discrete time step $t ,$ each CAVP $i$ observes the local environmental state $\\mathbf { o } _ { t } ^ { i }$ . The global environmental state $\\mathbf { s } _ { t }$ of the system is a simple superposition of the local observations of the $N _ { p }$ CAVPs, i.e., $\\mathbf { \\boldsymbol { s } } _ { t } = \\left[ \\mathbf { \\boldsymbol { o } } _ { t } ^ { 1 } , \\mathbf { \\dot { o } } _ { t } ^ { \\dot { 2 } } , . . . , \\mathbf { \\boldsymbol { o } } _ { t } ^ { N _ { p } } \\right]$ . Based on the observation ${ \\mathbf { o } } _ { t } ^ { i } ,$ each CAVP takes an action $a _ { t } ^ { i }$ according to a policy $\\pi ^ { i }$ . Furthermore, the CAVP adjusts the policy $\\pi ^ { i }$ based on the environmental feedback $r _ { t } ^ { i }$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,59,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,60,939,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[277,103,436,117]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1. Observation Space ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,121,939,152]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"At each discrete time step $t ,$ a CAVP observes its surrounding environmental conditions as well as the state of the data queue: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,160,710,186]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0334/02197e08b025919386ad1912c34312b5efb57d5df9429fbabf07dd5fcd0658df.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array} { r } { \\mathbf { o } _ { t } ^ { i } = \\left[ d _ { S , t } ^ { i } , d _ { D , t } ^ { i } , \\mathbf { e } _ { t } ^ { i } , R _ { t } ^ { i } ( \\Delta _ { 0 } ) \\right] , } \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[275,193,941,299]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $d _ { S , t } ^ { i } = \\left| p _ { S , t } ^ { i } - p _ { t } ^ { i } \\right| , d _ { D , t } ^ { i } = \\sqrt { \\left( p _ { D , t } ^ { i } - p _ { t } ^ { i } \\right) ^ { 2 } + L ^ { 2 } } , p _ { t } ^ { i }$ is the position (one-dimensional coordinate) of $\\mathrm { C A V P } i ,$ and $p _ { S , t } ^ { i }$ and $p _ { D , t } ^ { i }$ are the positions of the nearest CAVPs to CAVP $i$ in the same and different lanes, respectively. CAVP $i$ obtains these values through the global navigation satellite system and camera. $\\mathbf { e } _ { t } ^ { i } = [ \\rho , w , m ] .$ ; these features are identified in Section 2 to be associated with the risk level. $R _ { t } ^ { i } ( \\Delta _ { 0 } )$ denotes the number of sensory results with $\\Delta _ { t } ^ { i } = \\Delta _ { 0 }$ in the queue, i.e., data that fail at time step $t$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,310,398,324]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2. Action Space ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,328,941,373]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"According to the system model, a CAVP can perform flexible time–frequency resource configuration according to the dynamic time-varying characteristics of the vehicle location and road environment. Therefore, the action space of CAVP $i$ at time step $t$ can be defined as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[421,382,794,407]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0158/7880f7f004def1387f50c7475ce17d27a3c6f5420a507bfdca3cee8edfa9a8a9.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\na _ { t } ^ { i } \\in \\Bigl \\{ a _ { C } ^ { < 1 > } , a _ { C } ^ { < 2 > } , . . . , a _ { C } ^ { < M > } , a _ { R } ^ { < 1 > } , a _ { R } ^ { < 2 > } , . . . , a _ { R } ^ { < M > } \\Bigr \\} ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[273,413,941,444]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $a _ { C } ^ { < m > }$ and $a _ { R } ^ { < m > }$ denote a CAVP using sub-band $m$ for the sensing frame and communication frame, respectively. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,455,428,469]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.3. Reward Function ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,474,941,638]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As described in Section 2, when a CAVP is in the communication frame, the FV performs backward communication. The total number of unexpected events at that moment is the sum of the number of unexpected events that occurred in the environment and the number of sensory results lost due to communication failures. When a CAVP is in the sensing frame, the FV performs forward sensing. The total number of unexpected events at that moment is the sum of the number of invalid sensory results in the queue and the number of unexpected events missed due to sensing failures. The reward the CAVP receives at each time step is used to balance the sensing and communication functions, encouraging the agent to minimize the number of unexpected events that are not successfully sensed or transmitted. Rewards should be negatively correlated with the total number of unexpected events. So we design the reward function of CAVP $i$ at time step $t$ as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[470,648,749,772]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0978/15d9f6efd2e96d1c27d670842c90671072412abf2b7e8091a33f154996a61897.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array} { r l } & { { r _ { t } ^ { i } } = \\left\\{ \\begin{array} { l l } { - \\omega \\Big ( u _ { C , t } ^ { i } + I _ { t } ^ { i } ( C ) \\Big ) } & { a _ { t } ^ { i } = a _ { C } , } \\\\ { - \\omega \\big ( n _ { o v e r , t } ^ { i } + I _ { t } ^ { i } ( R ) \\big ) } & { a _ { t } ^ { i } = a _ { R } , } \\end{array} \\right. } \\\\ & { \\quad \\quad \\quad I _ { t } ^ { i } ( C ) = \\left\\{ \\begin{array} { l l } { 0 } & { \\eta _ { t } ^ { i } < \\eta _ { 0 } } \\\\ { n _ { a l l , t } ^ { i } } & { \\eta _ { t } ^ { i } \\geq \\eta _ { 0 } } \\end{array} \\right. , } \\\\ & { \\quad \\quad \\quad I _ { t } ^ { i } ( R ) = \\left\\{ \\begin{array} { l l } { 0 } & { \\eta _ { t } ^ { i } < \\eta _ { 0 } } \\\\ { u _ { R , t } ^ { i } } & { \\eta _ { t } ^ { i } \\geq \\eta _ { 0 } } \\end{array} \\right. , } \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,777,941,841]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\omega$ is the weight of the reward, $u _ { C , t } ^ { i }$ and $u _ { R , t } ^ { i }$ denote the number of unexpected events in the environment when CAVP $i$ is in the sensing frame and communication frame, respectively, $n _ { a l l , t } ^ { i }$ denotes all sensory results in the queue of CAVP $i$ and $n _ { o v e r , t } ^ { i }$ denotes the number of sensory results with $\\Delta _ { t } ^ { i } = \\Delta _ { 0 }$ in CAVP $i ^ { \\prime }$ s queue. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,852,435,868]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.4. Optimal Planning ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,871,941,902]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In reinforcement learning, the merit of a policy depends on the cumulative reward obtained from performing the policy over time, and the aim of learning is to find the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,58,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,60,941,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[272,102,939,133]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"policy that maximizes the cumulative reward over time [30]. In this paper, we use the $\\gamma$ cumulative discount reward, and the optimization issue is represented as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[478,141,737,183]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0268/5511ba86bd1f3060d5c89d9dc8f25a5c6df8492d3c813594757dd4ea75ad7069.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\operatorname* { m a x } _ { \\pi ^ { i } } R \\Big ( \\pi ^ { i } \\Big ) = \\mathbb { E } \\left[ \\sum _ { t = 0 } ^ { N _ { t } } \\gamma ^ { t } r _ { t + 1 } ^ { i } \\Big ( \\pi ^ { i } \\Big ) \\right] ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[270,187,941,203]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $N _ { t }$ is the number of training steps per episode, $\\gamma$ is the discount factor and $\\gamma \\in [ 0 , 1 ]$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,214,457,229]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. Ddqn-Per Algorithm ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,233,942,441]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Even though we defined the observation space and reward function in the previous discussion, vehicles navigating in the environment cannot directly access this information. Instead, they need to learn strategies through continuous interaction with the environment. Therefore, the model-free learning algorithm of reinforcement learning should be used. In addition, each CAVP performs its decisions in a decentralized manner. Still, its strategies are influenced by the strategies of other CAVPs, leading to a non-stationary environment and difficulties in convergence. We develop an improved algorithm based on a double deep Q-network (DDQN) [31] named DDQN-PER (double deep Q-network with prioritized experience replay) to deal with the dynamics and uncertainty in a multi-agent environment. The algorithm proposed in this paper uses a deep neural network as a function approximator while using the target network and the PER [32] scheme to enable multiple CAVPs to better obtain the optimal strategy for time–frequency resource allocation under uncertain environmental factors. The algorithm flow is shown in Figure 3, and the algorithm pseudocode is shown as Algorithm 1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[282,455,820,803]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 3. The DDQN-PER algorithm flow of CAVP $i$ \"]","image_footnote":"[]","img_path":"images/0215/bcfe6288685d441afc972f1ef1eb340fd24f60717e2e70851ec61073cfe9007a.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,59,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,60,941,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[277,103,465,117]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Algorithm 1 DDQN-PER ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[290,123,941,514]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1: Inputs: \n2: $D ^ { i }$ : empty replay memory with capacity $\\left| D ^ { i } \\right|$ \n3: $\\pmb { \\theta } ^ { i }$ : initial Q-network parameters. \n4: $\\hat { \\pmb { \\theta } } ^ { i }$ : initial target Q-network parameters \n5: for episod $e = 1 : E$ do \n6: Initialize observations for all vehicles \n7: for $t = 1 : T$ do \n8: for $i = 1 : N$ do \n9: Feed observation $\\mathbf { o } _ { t } ^ { i }$ to Q-network to get $Q ^ { i }$ \n10: Choose an action $a _ { t } ^ { i }$ as (13) \n11: Get a reward $r _ { t } ^ { i }$ \n12: Obtain new observation $\\mathbf { o } _ { t + 1 } ^ { i }$ \n13: Store experience $\\left( \\mathbf { o } _ { t } ^ { i } , a _ { t } ^ { i } , r _ { t } ^ { i } , \\mathbf { o } _ { t + 1 } ^ { i } \\right)$ in $D ^ { i }$ \n14: Sample a mini-batch of experiences $\\left( \\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } , r _ { j } ^ { i } , \\mathbf { o } _ { j + 1 } ^ { i } \\right) \\mathrm { f r o m } D ^ { i }$ with prioritization \nas (15) \n15: Compute importance sampling weights $w _ { j }$ as (16) \n16: Calculate target Q-values $y _ { j } ^ { i }$ as (17) \n17: Update priorities of experiences as (14) \n18: Update Q-network parameters $\\pmb { \\theta } _ { t + 1 } ^ { i }$ as (20), $\\pmb { \\theta } _ { t } ^ { i } \\pmb { \\theta } _ { t + 1 } ^ { i }$ \n19: if $t$ mod $N _ { u } = 0$ then \n20: 1 $\\hat { \\pmb { \\theta } } _ { t } ^ { i } \\pmb { \\theta } _ { t } ^ { i }$ \n21: end if \n22: ${ \\mathbf { o } _ { t } ^ { i } \\mathbf { o } _ { t + 1 } ^ { i } }$ \n23: end for \n24: end for \n25: end for ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,526,941,617]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Each CAVP needs to learn its own policy; thus, each CAVP has a separate Q-network. The inputs of the Q-network include relative distances of neighboring CAVPs, the road condition, the weather condition, the moving object state and the data queue state. The outputs are the Q-values of sub-bands for the sensing or communication frame. At each training time step, CAVP $i$ chooses an action $a _ { t } ^ { i }$ following the $\\varepsilon$ -greedy policy when the observation is $\\mathbf { o } _ { t } ^ { i }$ . The $\\varepsilon$ -greedy policy is defined as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[477,626,742,667]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0738/1fde812813bfb003dfa530865aa447f6767ce0692e6c9971e43182663fd5623b.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\na _ { t } ^ { i } = \\left\\{ \\begin{array} { c c } { r a n d o m } & { a < \\varepsilon } \\\\ { \\arg \\operatorname* { m a x } Q ^ { i } \\left( \\mathbf { o } _ { t } ^ { i } , a ; \\mathbf { \\pmb { \\theta } } _ { t } ^ { i } \\right) } & { a \\geq \\varepsilon } \\end{array} \\right. ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[275,674,942,774]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $Q ^ { i }$ are the Q-values of the $\\mathrm { Q }$ -network of CAVP $i ,$ and ${ \\pmb { \\theta } } _ { t } ^ { i }$ are the parameters of the $\\mathrm { Q }$ -network. CAVP $i$ executes the action $a _ { t } ^ { i }$ and obtains a reward $r _ { t } ^ { i }$ and the next observation $\\mathbf { o } _ { t + 1 } ^ { i }$ . The algorithm uses an experience replay scheme to store the experience $\\xi _ { t } ^ { i } = \\left( \\mathbf { o } _ { t } ^ { i } , a _ { t } ^ { i } , \\dot { r } _ { t } ^ { i } , \\mathbf { o } _ { t + 1 } ^ { i } \\right)$ obtained from the interaction of CAVP i with the environment into the memory $D ^ { i }$ . The storage capacity of $D ^ { i }$ is $\\left| D ^ { i } \\right|$ . At each time step, CAVP $i$ randomly samples a mini-batch of experiences $\\xi _ { j } ^ { i } = \\left( \\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } , r _ { j } ^ { i } , \\mathbf { o } _ { j + 1 } ^ { i } \\right)$ from $D ^ { i }$ for training. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[275,775,942,879]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The experience replay scheme improves data utilization by breaking the correlation between data through linear storage and random sampling of experiences. However, its equal probability replay ignores the importance of experiences, resulting in valuable experiences not being used efficiently. Therefore, this paper introduces the PER scheme. PER uses the temporal difference (TD) error, which represents the difference between the current $\\mathrm { Q }$ -value and the target Q-value, to measure the importance of each experience. Express the sampling priority of the jth experience as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[557,891,660,912]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0973/a60367b61ca9396ef270979c701c0b525f4fcb3d2f5306cf9119a3b52db86f44.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\np _ { j } = \\left| \\delta _ { j } \\right| + \\mu ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[57,59,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,60,939,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"9 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[272,102,941,134]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\delta _ { j }$ is the TD-error of the jth experience, and $\\mu$ is a very small positive constant to avoid the priority being 0. The probability that the jth experience is sampled is defined as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[537,141,680,186]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0007/3762320e1163f8a67c02efd45a88807ced134f2c96204d598754caae18f3c5c3.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\np ( j ) = \\frac { p _ { j } ^ { \\alpha } } { \\sum _ { k } ^ { k \\in \\left| D ^ { i } \\right| } p _ { k } ^ { \\alpha } } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,190,941,266]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\alpha \\in [ 0 , 1 ]$ is used to regulate the priority of experience. When $\\alpha = 0$ , priority sampling will degrade to uniform sampling. Before priority sampling, it is necessary to sort the data according to their priority. However, sorting large amounts of data can be memory-intensive and have high time complexity. Therefore, PER uses a sum tree data structure for sampling to improve sampling efficiency [32]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,267,942,325]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, when sampling according to importance, the sample distribution is altered. Therefore, the bias must be compensated for according to the importance sampling weights, otherwise the model will overfit the important experiences. Express the importance sampling weights as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[532,335,685,372]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0240/4ab6b90af66eb84a6f529f1c379c760ff9f8f7875147c697f525a1b85e9d462f.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nw _ { j } = \\big ( \\frac { 1 } { \\vert D ^ { i } \\vert } \\cdot \\frac { 1 } { p ( j ) } \\big ) ^ { \\beta } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[275,376,942,420]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\beta \\in [ 0 , 1 ]$ is used to regulate the degree of compensation for bias. When $\\beta = 1$ , the bias introduced by sampling with non-uniform probability will be entirely eliminated. $\\beta$ is annealed linearly from $\\beta _ { 0 }$ to 1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[275,423,942,517]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Next, we use the sampled experience $\\xi _ { j } ^ { i } = \\left( \\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } , r _ { j } ^ { i } , \\mathbf { o } _ { j + 1 } ^ { i } \\right)$ to calculate the target $\\mathrm { Q - }$ values. To improve the stability of the algorithm, another network with the same structure and initial parameters as the original Q-network is introduced, called the target Q-network, which is specially used to compute target $\\mathrm { Q }$ -values. The parameters of the $\\mathrm { Q }$ -network are updated at each training and passed to the target $\\mathrm { Q }$ -network after $N _ { u }$ steps. The target $\\mathrm { Q }$ -value at time step $t$ is calculated as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[423,526,791,567]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0525/1c046044b01883c2be3093681f21e4f601412d69f12cb5773f044b612039d495.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\ny _ { j } ^ { i } = r _ { j } ^ { i } + \\gamma \\hat { Q } ^ { i } \\left( \\mathbf { o } _ { j + 1 } ^ { i } , \\underset { a ^ { \\prime } } { \\arg \\operatorname* { m a x } } Q ^ { i } \\left( \\mathbf { o } _ { j + 1 } ^ { i } , a ^ { \\prime } ; \\pmb { \\theta } _ { t } ^ { i } \\right) ; \\hat { \\pmb { \\theta } } _ { t } ^ { i } \\right) ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,571,942,602]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where ${ \\hat { Q } } ^ { i }$ are the Q-values of the target $\\mathrm { Q }$ -network of CAVP $i ,$ and $\\widehat { \\theta } _ { t } ^ { i }$ are the parameters of the target $\\mathrm { Q }$ -network. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,602,941,648]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The DDQN algorithm updates the Q-network parameters by minimizing the mean square error between the current $\\mathrm { Q }$ -value and the target $\\mathrm { Q }$ -value, and the loss function can be expressed as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[473,656,744,690]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0769/28407d87e5fa9e090c06372700f76fc6086f7d2634fe82da0fd4ae5e7168b136.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nL _ { t } ^ { i } \\Big ( \\pmb { \\theta } _ { t } ^ { i } \\Big ) = \\mathbb { E } \\Bigg [ \\Big ( y _ { j } ^ { i } - Q ^ { i } \\Big ( \\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } ; \\pmb { \\theta } _ { t } ^ { i } \\Big ) \\Big ) ^ { 2 } \\Bigg ] .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[314,694,573,709]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The gradient of the loss function is ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[401,719,815,745]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0667/7ee8e722dea8b53a21f6c724bd66dd8af8b5fb86958e04b6ac6ff4c1e4d8d64c.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\nabla _ { \\theta _ { t } ^ { i } } L _ { t } ^ { i } \\Big ( \\theta _ { t } ^ { i } \\Big ) = \\mathbb { E } \\Big [ \\Big ( y _ { j } ^ { i } - Q ^ { i } \\Big ( \\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } ; \\theta _ { t } ^ { i } \\Big ) \\Big ) \\nabla _ { \\theta _ { t } ^ { i } } Q ^ { i } \\Big ( \\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } ; \\theta _ { t } ^ { i } \\Big ) \\Big ] .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[273,750,941,778]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Q-network parameters are updated according to the stochastic gradient descent (SGD) algorithm: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[406,788,811,814]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0073/e1f4bb335383149402c66c26798ea5da2468bf01b43215c9734549f850ec70a0.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array} { r } { \\pmb { \\theta } _ { t + 1 } ^ { i } = \\pmb { \\theta } _ { t } ^ { i } + w _ { j } \\alpha _ { l } \\left( y _ { j } ^ { i } - Q ^ { i } \\left( \\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } ; \\pmb { \\theta } _ { t } ^ { i } \\right) \\right) \\nabla _ { \\pmb { \\theta } _ { t } ^ { i } } Q ^ { i } \\left( \\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } ; \\pmb { \\theta } _ { t } ^ { i } \\right) , } \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,819,489,833]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\alpha _ { l }$ is the learning rate. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,845,455,860]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5. Simulation Analysis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,864,941,909]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this section, we evaluate the performance of the proposed approach through simulation experiments. First, we introduce the simulation setup, performance metrics and contrasting approaches. Then, we analyze the simulation results. Simulation results show ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[894,60,941,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[57,58,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[273,103,939,133]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"that the time–frequency resource allocation problem for radar and communication in the ISAC scenario can be effectively solved within the deep Q-learning framework. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,145,428,159]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5.1. Simulation Setup ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,162,941,252]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We consider a road traffic scenario as described in Section 2. Vehicles travel at a uniform speed, and the distance $d _ { n }$ between adjacent CAVPs in the same lane follows a uniform distribution $U$ . The frame length is $T$ . We consider the spatial location and environment around the vehicle to be semi-static, i.e., not changing significantly within frame $T$ but changing dynamically over multiple frames [33]. The detailed scenario parameters are set as shown in Table 1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,285,941,470]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0531/8a3b025665386b1205306701d462eca00146abf42c41bc450288187647df2ff3.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":"<table><tr><td>Notation</td><td>Value</td></tr><tr><td>(t,ti）,e∈ε</td><td>(0.7,0.3)</td></tr><tr><td>(p,p),e∈ε</td><td>(0.01,0.1)</td></tr><tr><td>U</td><td>10 m/s</td></tr><tr><td>△0</td><td>4</td></tr><tr><td>T</td><td>0.02 s</td></tr><tr><td>PR</td><td>25 dBmW</td></tr><tr><td>Pc</td><td>15 dBmW</td></tr><tr><td>G</td><td>48 dB</td></tr><tr><td>Ae</td><td>5mm²</td></tr><tr><td>8</td><td>0.1</td></tr><tr><td>L</td><td>3m</td></tr><tr><td>n0</td><td>10</td></tr></table>","table_caption":"[\"Table 1. Scenario parameters setting. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[277,487,941,577]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The numbers of neurons in the input, hidden (two layers) and output layers of the network are set to be 6, 24, 24 and 2, respectively. The hidden layer utilizes a rectified linear unit (ReLU) as the activation function, and the output layer has no activation function. In the training, a time step equals the frame length T. Each episode contains multiple time steps. The hyperparameters used in training the $\\mathrm { Q }$ -networks are shown in Table 2. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,611,941,756]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0846/cee1ce83bfb4e143961ed61bbcd8bace18a26ed4d2b9de8e4248dcd594f4ceb9.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":"<table><tr><td>Notation</td><td>Value</td></tr><tr><td>W</td><td>200</td></tr><tr><td>m</td><td>0.9 →0.01</td></tr><tr><td>Nb</td><td>64</td></tr><tr><td>μ</td><td>0.01</td></tr><tr><td>&</td><td>0.6</td></tr><tr><td>β</td><td>0.4→1.0</td></tr><tr><td>Nu</td><td>20</td></tr><tr><td>Y</td><td>0.9</td></tr><tr><td>α1</td><td>0.0001</td></tr></table>","table_caption":"[\"Table 2. Hyperparameters Setting. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[277,771,453,784]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5.2. Performance Metrics ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[300,789,934,804]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We propose two key metrics to evaluate the performance of the proposed approach: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[280,809,939,854]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Miss detection probability: defined as the ratio of the number of unsuccessfully sensed or transmitted unexpected events to the total number of unexpected events in each episode: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[463,865,789,906]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0195/840218d8af910344f02314cdea6715b02a7075089014be7f23ebd0b48e37b119.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\np _ { m i s s } = \\sum _ { i = 1 } ^ { N _ { p } } \\sum _ { t = 0 } ^ { N _ { t } } \\frac { u _ { C , t } ^ { i } + I _ { t } ^ { i } ( C ) + n _ { o v e r , t } ^ { i } + I _ { t } ^ { i } ( R ) } { u _ { C , t } ^ { i } + u _ { R , t } ^ { i } } .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[57,59,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,60,939,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"11 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[280,102,939,133]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Average system interference power: defined as the ratio of the sum of interference power of all CAVPs per episode to the number of training steps per episode: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[547,142,705,184]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0557/72991033aff0a26ef99fadbd78cb4c3871fef46ae39e9a8f948d165a3708ff3e.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP _ { a v e } = \\frac { 1 } { N _ { t } } \\sum _ { i = 1 } ^ { N _ { p } } \\sum _ { t = 0 } ^ { N _ { t } } { P _ { I , t } ^ { i } } .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,195,473,209]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5.3. Contrasting Approaches ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[310,214,606,228]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"There are three contrasting approaches: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[275,233,941,488]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"DRQN: In [24], each vehicle performs sensing independently and does not communicate with other AVs. AVs only need to allocate sensing frequency resources. The authors in [24] introduce a long short-term memory (LSTM) network into the DQN algorithm, enabling the vehicle to learn how to select sensing sub-bands by incorporating both its current and past observations. In this case, miss detection occurs only when the vehicle does not sense successfully. Random (CAVPs): We use the random policy to allocate time–frequency resources for the sensing and communication frames of CAVPs. i.e., CAVPs randomly select an action from the action space mentioned in Equation (8) with equal probability. DDQN (CAVPs): We use the DDQN algorithm proposed in [31] to allocate time– frequency resources for the sensing and communication frames of CAVPs. DQN (single CAVP): In [16], the DQN algorithm was introduced to allocate time resources for both sensing and communication functions of a single vehicle in a dynamic environment. Nevertheless, Ref. [16] did not account for interference between vehicles, implying that both sensing and communication could be successful regardless of the chosen strategy. We apply this algorithm to CAVPs, considering it as an upper-bound performance to evaluate the effectiveness of other algorithms. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,499,425,514]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5.4. Results Analysis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[273,518,941,548]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We first verify the algorithm’s convergence by using the average system reward as a measure of convergence. The average system reward is calculated as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[534,557,684,599]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0051/2c4fd71bafde02ef3fde08cf9b3bbd0b512aa6e408136f5e499b2bb21c14a1b3.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nR _ { a v e } = \\frac { 1 } { N _ { t } } \\sum _ { i = 1 } ^ { N _ { p } } \\sum _ { t = 0 } ^ { N _ { t } } r _ { t } ^ { i } .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,602,941,676]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We selected five random seed values, namely, 10, 20, 30, 40 and 50, and calculated the average $R _ { a v e }$ of the algorithms under these five random seeds. As shown in Figure 4, the $R _ { a v e }$ of DDQN-PER gradually increases with the number of episodes and eventually stabilizes around 800 episodes. Compared with DDQN and random, DDQN-PER has better convergence performance. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[273,677,941,707]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Then, we evaluate the performance of the proposed approach and the contrasting approaches through the following four aspects: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,713,942,921]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. The number of AVs changes, other conditions are fixed: In Figure 5, as $N$ increases, $p _ { m i s s }$ and $P _ { a v e }$ increase for all algorithms except DQN. The reason is that as $N$ increases, the mutual interference between the AVs increases, while DQN is used in a single-CAVP scenario, and the effect of interference is not considered. In addition, compared with DRQN, random has a lower $P _ { a v e }$ . This is because the proposed communicationassisted sensing mechanism allows some vehicles to acquire sensory data through communication, eliminating the requirement for all vehicles to perform sensing tasks simultaneously, effectively reducing inter-vehicle interference. Nevertheless, random has a higher $p _ { m i s s }$ than DRQN. This is because the $p _ { m i s s }$ of random is not only affected by system interference but also influenced by the dynamic environment. Random cannot choose sensing or communication modes based on the environment, leading to a higher rate of $p _ { m i s s }$ . As DDQN-PER utilizes the communication-assisted sensing mechanism and adaptive time–frequency resource allocation algorithm, it can effectively control the mutual interference between vehicles and reduce the miss detection probability. Thus, compared with other algorithms, $p _ { m i s s }$ and $P _ { a v e }$ of DDQN-PER are closer to DQN, and the performance does not deteriorate significantly as $N$ increases. In conclusion, DDQN-PER proves to be more advantageous than other algorithms, particularly in scenarios with a higher volume of vehicles. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[894,60,941,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"12 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[57,59,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[315,103,941,162]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[300,177,732,419]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 4. Average system reward versus the number of episodes. \"]","image_footnote":"[]","img_path":"images/0673/44ebfb159a4654c0bd757ee58080588e2a3c288317e8e1333df6a8e5542fa85f.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[294,461,847,718]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 5. The number of AVs changes, other conditions are fixed. (a) Miss detection probability. (b) Average system interference power. \"]","image_footnote":"[]","img_path":"images/0469/fb0e1f4f3038c79aab749fd85a90dd22626bbd4dcf2f2dd2b2053e076dceca81.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,771,941,862]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. The number of sub-bands changes, other conditions are fixed: In Figure $^ { 6 , }$ as $M$ increases, $p _ { m i s s }$ and $P _ { a v e }$ decrease for all algorithms except $\\mathrm { D Q N }$ . The reason is that as $M$ increases, the probability of two signals switching to the same sub-band becomes small. Compared with other algorithms, $p _ { m i s s }$ and $P _ { a v e }$ of DDQN-PER are closer to DQN. It can be deduced that DDQN-PER holds a comparative advantage over other algorithms, especially when the number of sub-bands is limited. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,59,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,60,939,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"13 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[294,118,847,374]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 6. The number of sub-bands changes, other conditions are fixed. (a) Miss detection probability. (b) Average system interference power. \"]","image_footnote":"[]","img_path":"images/0000/5e6cd99e9a29081862457562f5a2b48b6db6d06ce96bc7912a754ee0c41695da.jpg","list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,428,942,562]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. h The interval changes, other conditions are fixed: In Figure 7, when s better performance. In addition, compared with oth $d _ { n } \\sim U ( 5 0 \\mathrm { m } , 6 0 \\mathrm { m } ) .$ $p _ { m i s s }$ of DDQN-PER is higher than DRQN. However, when $d _ { n }$ is small, DDQN-PER has better performance. In addition, compared with other algorithms, the $P _ { a v e }$ of DDQN-PER is closer to 0. This is because when the interval is small, DRQN is greatly affected by interference and cannot effectively allocate frequency resources, whileQN-PER can effectively control mutual interference and reduce the miss d DDQN-PER can effectively control mutual interference and reduce the miss detectionbability by using the communication-assisted sensing mechanism and a probability by using the communication-assisted sensing mechanism and adaptivee–frequency resource allocation algorithm. It can be concluded that DDQ time–frequency resource allocation algorithm. It can be concluded that DDQN-PER isre advantageous than other algorithms when the interval is smaller. more advantageous than other algorithms when the interval is smaller. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[280,570,778,881]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 7. Cont. \"]","image_footnote":"[]","img_path":"images/0246/1fd0d2518e78f01b1aa303377a9e0c30fb19717a18831b99e0e30fd410dffdba.jpg","list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,59,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,60,939,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"14 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[280,104,778,412]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 7. The interval changes, other conditions are fixed. (a) Miss detection probability. (b) Averagem system interference power. 1 \"]","image_footnote":"[]","img_path":"images/0463/6616058c3cb50fb3062131c7081c792bcec16a98e99bffac8632620d792323b3.jpg","list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,462,941,567]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. The R an $p _ { 1 } ^ { m }$ (i.e., the probability of the occurrence of an unexpected event under conditionDQN changes, while other algorithms are almost unchanged. This is $m = 1$ .e., the probability of the occurrence of an u) changes, other conditions are fixed: In Figure 8, as ER and DQN can adaptively allocate time–f $p _ { 1 } ^ { m }$ pected changes, quency r $p _ { m i s s }$ t under coof DDQN-rces accor = 1) changes, other conditions are fixed: In Figure 8, as pm changes, pmiss ofPER and DQN changes, while other algorithms are almost unchanged. This is becausee environment. As DDQN-PER is affected by multi-vehicle interference, R and DQN changes, while other algorithms are almost unchanged. This isDDQN-PER and DQN can adaptively allocate time–frequency resources according tom QN-PER and DQN can adaptively allocate time–frequency resourcesthe environment. As DDQN-PER is affected by multi-vehicle interference, its 1 $p _ { m i s s }$ does not continue to decrease as er algorithms, the Pave of D $p _ { 1 } ^ { m }$ increases like DQN. Furthermore, compared withN-PER is closer to 0. other algorithms, the $P _ { a v e }$ of DDQN-PER is closer to 0. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[284,576,776,883]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 8. Cont. \"]","image_footnote":"[]","img_path":"images/0640/61eee1b111d881a702b3976d99d62295fa1eccbba0265d31992f2dd4cfc44bb0.jpg","list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,59,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,60,939,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"15 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[282,105,776,418]","code_body":null,"code_caption":null,"image_caption":"[\"mFigure 8. The $p _ { 1 } ^ { m }$ changes, other conditions are fixed. (a) Miss detection probability. (b) Average 1system interference power. \"]","image_footnote":"[]","img_path":"images/0944/7c64bc220e2ce7f3f008db36f402abf66695153ad967292a0fe1f141e2abb116.jpg","list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,467,391,481]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6. Conclusions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,485,941,633]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"usionsIn this paper, we propose a communication-assisted sensing mechanism based on In this paper, we propose a communication-assisted sensing mechanism bTD-ISAC, which uses communication to transmit sensing information effectively. Moreover, we construct an interference model for multi-vehicle sensing and communication signals and formulate a multi-vehicle optimization problem based on the POMDP framework. We onstruct an interference model for multi-vehicle sensing and communicationdevelop the DDQN-PER algorithm to enable vehicles to adjust their policies adaptively for formulate a multi-vehicle optimization problem based on the POMDP framewdecentralized time–frequency resource allocation in the dynamic environment. Simulation lop the DDQN-PER algorithm to enable vehicles to adjust their policies adaptresults show that the proposed scheme can significantly reduce miss detection probability ntralized time–frequency resource allocation in the dynamic environment. Siand average system interference power. Furthermore, the method proposed in this paper also applies to the problem of multi-vehicle mutual interference where a TD-ISAC vehicle assists a radar-free vehicle. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,648,941,689]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"applies to the problem of multi-vehicle mutual interference where a TD-ISACAuthor Contributions: Methodology, Y.F.; validation and formal analysis, Z.F., J.H. and X.W.; ts a radar-free vehicle.writing—original draft preparation, Y.F.; writing—review and editing, Z.F., J.H. and X.W. All authors have read and agreed to the published version of the manuscript. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,696,941,724]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"or Contributions: Methodology, Y.F.; validation and formal analysis, Z.F., J.H. aFunding: This work was supported by the National Key R&D Program of China under Grant No. \nng—original draft preparation, Y.F.; writing—review and editing, Z.F., J.H. and X.W.2021YFB2900200 and the National Natural Science Foundation of China under Grant U20B2039. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[275,731,939,759]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"read and agreed to the published version of the manuscript.Data Availability Statement: The data and code are available from the corresponding authors upon reasonable request. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,766,709,781]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"FB2900200 and the National Natural Science FoundatiConflicts of Interest: The authors declare no conflicts of interest. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,794,142,806]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,810,942,907]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. reasonable request.Ma, D.; Shlezinger, N.; Huang, T.; Liu, Y.; Eldar, Y.C. Joint Radar-Communication Strategies for Autonomous Vehicles: Combining Two Key Automotive Technologies. IEEE Signal Process. Mag. 2020, 37, 85–97. [CrossRef] \n2. Conflicts of Interest: The authors declare no conflicts of interest.Sciuto, G.L.; Kowol, P.; Nowak, P.; Banás, W.; Coco, S.; Capizzi, G. 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V2X-communication assisted interference minimization for automotive radars. China Commun. 2019, 16, 100–111. [CrossRef] \n23. Khoury, J.; Ramanathan, R.; McCloskey, D.; Smith, R.; Campbell, T. RadarMAC: Mitigating Radar Interference in Self-Driving Cars. In Proceedings of the 13th Annual IEEE International Conference on Sensing, Communication, and Networking (SECON), London, UK, 27–30 June 2016; pp. 1–9. \n24. Liu, P.; Liu, Y.; Huang, T.; Lu, Y.; Wang, X. Decentralized Automotive Radar Spectrum Allocation to Avoid Mutual Interference Using Reinforcement Learning. IEEE Trans. Aerosp. Electron. Syst. 2021, 57, 190–205. [CrossRef] \n25. Chang, H.H.; Song, H.; Yi, Y.; Zhang, J.; He, H.; Liu, L. Distributive Dynamic Spectrum Access Through Deep Reinforcement Learning: A Reservoir Computing-Based Approach. IEEE Internet Things J. 2019, 6, 1938–1948. [CrossRef] \n26. Naparstek, O.; Cohen, K. Deep Multi-User Reinforcement Learning for Distributed Dynamic Spectrum Access. IEEE Trans. Wirel. Commun. 2019, 18, 310–323. [CrossRef] \n27. Lee, J.; Niyato, D.; Guan, Y.L.; Kim, D.I. Learning to Schedule Joint Radar-Communication with Deep Multi-Agent Reinforcement Learning. IEEE Trans. Veh. Technol. 2022, 71, 406–422. [CrossRef] \n28. Boban, M.; Kousaridas, A.; Manolakis, K.; Eichinger, J.; Xu, W. Use cases, requirements, and design considerations for 5G V2X. arXiv 2017, arXiv:1712.01754. \n29. Tampuu, A.; Matiisen, T.; Kodelja, D.; Kuzovkin, I.; Korjus, K.; Aru, J.; Aru, J.; Vicente, R. Multiagent cooperation and competition with deep reinforcement learning. PloS ONE 2017, 12, e0172395. [CrossRef] [PubMed] \n30. Sutton, R.S.; Barto, A.G. Reinforcement Learning: An Introduction; MIT Press: Cambridge, MA, USA, 2018. \n31. Van Hasselt, H.; Guez, A.; Silver, D. Deep reinforcement learning with double q-learning. In Proceedings of the 30th AAAI Conference on Artificial Intelligence, Phoenix, AZ, USA, 12–17 February 2016; Volume 30. \n32. Schaul, T.; Quan, J.; Antonoglou, I.; Silver, D. Prioritized experience replay. arXiv 2015, arXiv:1511.05952. \n33. Xing, Y.; Sun, Y.; Qiao, L.; Wang, Z.; Si, P.; Zhang, Y. Deep reinforcement learning for cooperative edge caching in vehicular networks. In Proceedings of the 13th International Conference on Communication Software and Networks (ICCSN), Chongqing, China, 4–7 June 2021; IEEE: Piscataway, NJ, USA, 2021; pp. 144–149. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,59,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,60,939,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"16 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[57,102,941,904]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,58,203,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,60,941,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"17 of 18 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[55,103,942,186]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,202,942,242]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,58,203,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electronics 2024, 13, 2442 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,60,939,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"18 of 18 ","text_format":null,"text_level":null,"type":"discarded"}],"string":"[\n {\n \"bbox\": \"[55,121,941,184]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article Reinforcement Learning-Based Resource Allocation for Multiple Vehicles with Communication-Assisted Sensing Mechanism \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,198,534,214]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Yuxin Fan, Zesong Fei, Jingxuan Huang $\\\\ast \\\\textcircled { \\\\scriptsize { \\\\parallel } }$ and Xinyi Wang $\\\\textcircled{1}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,569,253,680]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Citation: Fan, Y.; Fei, Z.; Huang, J.; Wang, X. Reinforcement Learning-Based Resource Allocation for \\nMultiple Vehicles with \\nCommunication-Assisted Sensing Mechanism. Electronics 2024, 13, 2442. https://doi.org/10.3390/ \\nelectronics13132442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,690,247,701]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Academic Editor: Christos J. Bouras \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,712,183,765]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received: 6 May 2024 \\nRevised: 17 June 2024 \\nAccepted: 19 June 2024 \\nPublished: 21 June 2024 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[275,240,860,278]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"School of Information and Electronics, Beijing Institute of Technology (BIT), Beijing 100081, China; fanyuxin678@163.com (Y.F.); feizesong@bit.edu.cn (Z.F.); bit_wangxy@163.com (X.W.) \\\\* Correspondence: jxhbit@gmail.com \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,294,941,555]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract: Autonomous vehicles (AVs) can be equipped with Integrated sensing and communications (ISAC) devices to realize sensing and communication functions simultaneously. Time-division ISAC (TD-ISAC) is advantageous due to its ease of implementation, efficient deployment and integration into any system. TD-ISAC greatly enhances spectrum efficiency and equipment utilization and reduces system energy consumption. In this paper, we propose a communication-assisted sensing mechanism based on TD-ISAC to support multi-vehicle collaborative sensing. However, there are some challenges in applying TD-ISAC to AVs. First, AVs should allocate resources for sensing and communication in a dynamically changing environment. Second, the limited spectrum resources bring the problem of mutual interference of multi-vehicle signals. To address these issues, we construct a multi-vehicle signal interference model, formulate an optimization problem based on the partially observable Markov decision process (POMDP) framework and design a decentralized dynamic allocation scheme for multi-vehicle time–frequency resources based on a deep reinforcement learning (DRL) algorithm. Simulation results show that the proposed scheme performs better in miss detection probability and average system interference power compared to the DRQN algorithm without the communication-assisted sensing mechanism and the random algorithm without reinforcement learning. We can conclude that the proposed scheme can effectively allocate the resources of the TD-ISAC system and reduce interference between multiple vehicles. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,571,937,600]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: integrated sensing and communications; communication-assisted sensing; deep reinforcement learning; time–frequency resource allocation \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,645,393,659]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,663,391,676]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.1. Background \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,681,941,828]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"With the development of communication technology, sensing technology, artificial intelligence and the automotive industry, the level of automotive intelligence is rapidly increasing. Autonomous vehicles (AVs), which will improve road safety and reshape the way we travel, are steering the future of transportation. Sensing and communication are two essential functions of AVs [1]. AVs have many sensors, such as LiDAR, which acquires information about the surroundings and avoids collisions by detecting the presence of obstacles [2,3]. In the meantime, AVs are equipped with wireless communication transceivers to achieve large-scale and high-capacity data exchange in vehicle-to-vehicle (V2V) or vehicle-to-infrastructure (V2I) communication. AVs’ sensing and communication functions can enhance the safety and smoothness of the transportation system. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,829,941,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Radar detection and wireless communication both transmit or obtain information through the transmission of radio waves, and in some scenarios, sensing and communication are highly coupled. First, the operating frequency bands for both sensing and communication are moving closer to the millimeter-wave frequency range [4]. Millimeter-wave radar offers advantages of extended detection range, high precision, weather independence and the ability to operate all day compared with cameras and LiDAR. Millimeter-wave communication technology, with its narrow beamwidth and large bandwidth, can significantly improve the communication capability of vehicles. 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Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[277,103,941,162]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,164,941,341]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Integrated sensing and communications (ISAC) technology aims to unify these two functions and pursue direct trade-offs and mutual performance gains [4]. Enabled by ISAC technology, AVs can simultaneously realize sensing and communication by carrying ISAC radio-frequency (RF) transceivers, which alleviates concerns for electromagnetic compatibility as well as reduces system size, weight, and energy consumption [6,7]. Currently, ISAC has five main realization methods: time division, frequency division, space division, code division and waveform sharing [1]. The time division ISAC (TD-ISAC) method is based on the fact that an RF device occupies different time resources to transmit sensing and communication signals, respectively [8]. The critical advantage of TD-ISAC is its easy implementation and seamless integration into any system [9]. Furthermore, TD-ISAC can utilize specific waveforms for sensing and communication according to their respective needs and improve system spectrum efficiency. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,342,941,431]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, AVs equipped with TD-ISAC systems face some technical challenges. First, only one function of sensing and communication can operate at a given time, leading to a trade-off in the performance of both functions, particularly in dynamic environments [10]. Second, as the number of TD-ISAC vehicles increases, it is necessary for vehicles to learn how to coordinate the use of ISAC to minimize mutual interference and improve overall performance [11]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,443,401,457]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.2. Related Work \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,462,941,730]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Some scholars have conducted research on time resource allocation for sensing and communication functions. The traditional time division method uses an arbitrary or fixed schedule to switch between sensing and communication. The authors in [12] use the preamble of IEEE 802.11ad standard frames for radar detection and data blocks for communication data transmission. Based on this point, Ref. [13] performs adaptive preamble design, allowing for a trade-off between radar estimation accuracy and communication rate. In addition, Refs. [14,15] study the fundamental trade-offs of radar–communication coexistence with flexible configuration. Nevertheless, the road traffic environment is dynamic and uncertain, and these solutions are fixed during the runtime and unsuitable for implementation in real-time systems. Deep reinforcement learning (DRL) has been recently introduced to find the optimal decision quickly in real time. Some studies use DRL to optimize the allocation of communication and radar time resources for individual vehicles in dynamic environments. The authors of [16–18] use the DRL algorithm to decide when to use the communication mode or the radar mode to maximize the data throughput while minimizing the miss detection probability of unexpected events given the uncertainty of the surrounding environment. The AV can quickly obtain the optimal policy without requiring any prior information about the environment. Ref. [19] jointly coordinates radar and communication and minimizes the age of information (AoI) of its communication function. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,731,941,909]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As the number of TD-ISAC vehicles increases, vehicles need to learn how to coordinate their use of ISAC to minimize mutual interference. In traditional radar and communication systems, interference avoidance can be used to reduce mutual interference. Interference avoidance is achieved by coordinating signal transmission in the time, frequency and space domains to reduce interference [20]. One representative method for interference avoidance in the frequency domain is spectrum allocation. The authors of [21,22] propose a centralized framework to enable multiple access to a shared spectrum among radars relying on vehicular ad hoc networking (VANET) and cellular-vehicle-to-everything (C-V2X) communication, respectively. However, centralized allocation typically involves frequent transmission of large amounts of data between vehicles and the central node, leading to increased communication costs and decision latency. Decentralized allocation, in which each AV autonomously selects its frequency sub-band, can be adopted to reduce communication costs and ensure the timeliness of spectrum resource scheduling. A direct method is random selection, which is easy to implement but cannot suppress interference [23]. In [24], the author proposes a decentralized spectrum allocation approach based on $\\\\scriptstyle \\\\mathrm { { D R L , } }$ effectively avoiding mutual interference among automotive radars. In the communication system, the issue of multi-user interference has also been studied using DRL by learning sub-band access strategies to avoid users colliding with other users in the same sub-band [25,26]. However, these studies do not use the ISAC mechanism or consider interference between communication and radar signals. Ref. [27] considers multiple vehicles based on [19] and proposes a medium access control (MAC) protocol that manages contention-free access to the communication–radar channel. However, in each time step, only one vehicle can communicate or sense. Therefore, we need a more efficient decentralized spectrum allocation method suitable for the ISAC mechanism. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,59,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,60,939,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[277,103,941,281]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,294,405,307]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.3. Contributions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,312,941,506]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This paper focuses on a time division integrated sensing and communication scenario in intelligent transportation systems. In this scenario, AVs on the road are equipped with both communication and sensing functions, sharing the same set of transceiver equipment and switching in a time division manner, occupying the same frequency resources. The environment in which the AVs operate is highly dynamic, with environmental conditions and communication demands constantly changing, and there is interference between signals from different AVs. In practical applications, the trained model’s ability to generalize across different road environments must be rigorously tested to ensure that AVs can make safe and reliable decisions under various circumstances. We propose an intelligent time–frequency resource allocation algorithm to mitigate multi-vehicle mutual interference in dynamic road environments. The proposed algorithm allows AVs to make decentralized decisions based on local observations to avoid significant time overheads caused by centralized scheduling. The main contributions of this paper can be summarized as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,511,941,780]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We propose a communication-assisted sensing mechanism based on TD-ISAC. By transmitting sensing information through communication, we can effectively reduce the number of active radars in the system. Simultaneously, by employing time division between sensing and communication, we can enhance spectrum utilization and lower the probability of multiple vehicles’ transmitted signals colliding within the same sub-band, thereby further improving system performance. \\nWe construct a multi-vehicle sensing and communication interference model. Building this model contributes to a comprehensive understanding of the characteristics and sources of interference, enabling us to take appropriate measures to manage system interference. \\nWe formulate a multi-vehicle optimization problem based on the partially observable Markov decision process (POMDP) framework. With the POMDP framework, vehicles can choose sensing or communication operations based on dynamic environments adaptively and select different sub-bands to reduce multi-vehicle interference. \\nTo solve the optimization problem, we design a DRL algorithm using a target network and a prioritized experience replay (PER) scheme to enable multiple vehicles to better obtain the optimal strategy for time–frequency resource allocation under uncertain environmental factors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,785,941,845]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The rest of this paper is organized as follows. We describe the problem formulation in Section 2. Section 3 builds the POMDP framework. Furthermore, in Section 4, we present a DRL algorithm. Section 5 evaluates the performance of the proposed approach. Finally, conclusions are drawn in Section 6. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,858,462,871]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. Problem Formulation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,873,447,888]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.1. Environment Model \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[272,891,941,922]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This paper considers a two-lane road traffic scenario in both directions with a dynamically changing environment, as shown in Figure 1. Environmental conditions are influenced by road condition, weather condition and moving object state, and the values of these factors can be obtained through a vehicle sensor system, such as a road friction sensor, weather station instrument and camera [16]. Environmental conditions are not the same for different AVs at the same time. In the following text, we provide the modeling of the relationship between environmental conditions and risk levels. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,59,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,60,939,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[277,102,941,177]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,178,941,269]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$e \\\\in { \\\\mathcal { E } }$ represents a particular environmental factor, where $\\\\mathcal { E } = \\\\{ \\\\rho , w , m \\\\} , \\\\rho , w$ and $m$ denote the road condition, the weather condition and the moving object state, respectively. $f \\\\in { \\\\mathcal { F } }$ represents the degree of influence of the environmental factor on the vehicle’s driving, where $\\\\mathcal { F } = \\\\{ 0 , 1 , . . . , F \\\\}$ . For simplicity, we can assume that ${ \\\\mathcal { F } } = \\\\{ 0 , 1 \\\\}$ . When $f = 0 .$ , the environmental factor is good; when $f = 1 _ { . }$ , the environmental factor is poor. $\\\\tau _ { f } ^ { e }$ represents the probability of the occurrence of the condition $e = f ,$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[563,280,652,312]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0075/ba3640bd22683cadac4595a59a24fc48c1e50f29d720287a62a6b7c19827a5c0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\sum _ { f \\\\in \\\\mathcal { F } } \\\\tau _ { f } ^ { e } = 1 .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,317,941,365]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$p _ { f } ^ { e }$ denotes the probability of the occurrence of an unexpected event under condition $e = f$ . Using Bayes’s theorem, the average probability of an unexpected event occurring in the current environment is given by [16] \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[539,375,678,409]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0555/26dad179ff561d8dcf621633752bbf9f365bdfa043ba6d6451e52ca4b962f596.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\np _ { u } = \\\\sum _ { e \\\\in \\\\mathcal { E } } \\\\sum _ { f \\\\in \\\\mathcal { F } } \\\\tau _ { f } ^ { e } p _ { f } ^ { e } .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,413,941,443]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The relationship between environmental conditions and risk levels can be provided to AVs by accessing digital map databases [27]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[132,461,860,696]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 1. Multiple AVs driving in a dynamic environment. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0641/8bc3e5a9eb08e786e83234f4390380a678a9dbae3976048c4d5cdbbf5a7d5419.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,732,401,747]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2. Signal Model \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,751,941,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This paper assumes that all AVs are equipped with TD-ISAC systems, i.e., RF devices occupy different time resources for sensing and communication, respectively. We propose a communication-assisted sensing mechanism. Every two adjacent vehicles in the same lane are paired through V2V communication technology, and this vehicle pair is referred to as a communication-assisted vehicle pair (CAVP). The front vehicle (FV) and the back vehicle (BV) can maintain a minimal distance (several meters or even tens of centimeters) between them by sharing speed, location, status, and other information [28]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,857,941,915]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"While driving, a CAVP can choose to sense or communicate based on the dynamic environment. The frame structure of sensing and communication for the FV and BV is illustrated in Figure 2. During the sensing frame, the FV performs forward sensing using long-range radar (LRR) while the BV awaits communication data. During the communication frame, the FV performs backward communication, and the BV receives communication data from the FV. Additionally, a specific subframe in the communication frame is allocated to the BV for backward sensing using short-range radar (SRR). The direction adjustment between sensing and communication functions is achieved through beam angle adjustment [8]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,59,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,60,939,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[275,102,941,178]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[136,192,863,428]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 2. The frame structure of sensing and communication. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0435/cd5b6783dd9b1e135a91e03f4d404999c5dc1dfd6118232b9670aaccb0b66f82.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,467,941,587]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let the set of all AVs on the road be $\\\\mathcal { N } = \\\\{ 1 , 2 , . . . , N \\\\}$ and the set of CAVPs be $\\\\mathcal { N } _ { p } = \\\\{ 1 , 2 , . . . , N _ { p } \\\\} _ { }$ , where $N = 2 N _ { p }$ . The total frequency band is divided equally into multiple orthogonal sub-bands, and the set of sub-bands is $\\\\mathcal { M } = \\\\left\\\\{ 1 , 2 , . . . , M \\\\right\\\\}$ [21]. A CAVP can freely select a sub-band in the sensing or communication frames. The number of AVs is rapidly increasing, while the number of sub-bands is limited, making it impossible to allocate non-reused orthogonal sub-bands for each CAVP. Multiple CAVPs will inevitably collide in the same sub-band, creating interference [21,24]. Thus, we assume that $N _ { p } \\\\geq M ,$ and multiple CAVPs can use the same sub-band at the same time. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,588,941,781]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Due to the proximity of paired vehicles and the relatively low importance of backward sensing, only accidents occurring in the overall front of the CAVP are considered, without considering accidents between the FV and BV or behind the BV. When the forward sensing is successful, the FV can know whether an unexpected event occurs in the environment, represented by 1 and 0, respectively, and the sensory result is stored in the data queue. However, if the FV cannot communicate with the BV in time, the sensory result will fail, which will seriously affect the safety of the BV. We use AoI [19] as a metric to characterize the timeliness of information. AoI is defined as the duration of a sensory result in the vehicle’s queue since it was acquired, denoted by $\\\\Delta$ . If $\\\\Delta$ is greater than or equal to the threshold $\\\\Delta _ { 0 } ,$ we consider the sensory result to have failed. The data will be removed from the queue. It is assumed that when the backward communication is successful, the FV can transmit all the non-failed sensory results. If the communication fails, all the sensory results in the queue of the FV are lost. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,794,438,808]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.3. Interference Model \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,813,941,870]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Different CAVPs may use the same sub-band for the sensing or communication frame, generating multi-vehicle mutual interference. Because this paper primarily focuses on reducing unexpected events occurring in front of the CAVP, we model the interference suffered by forward sensing and backward communication. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,872,941,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As shown in Figures 1 and 2, when a CAVP is in the sensing frame, the FV performs forward sensing. At this time, the radar receiver of the FV will be subjected to the same-frequency interference from the LRR signals in the opposite lane and the communication/SRR signals in the same lane. When the CAVP is in the communication frame, the FV performs backward communication. At this time, the communication receiver of the BV will be subjected to the same-frequency interference from the LRR signals in the opposite lane and the communication signals in the same lane. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,59,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,60,939,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[275,102,941,162]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,164,941,192]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The received interference power depends on the relative positions of CAVPs. The interference power of the LRR signal from CAVP $n$ in the opposite lane can be expressed as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[485,202,731,234]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0096/c63eebfc8cb7ea8eed2e15c62172c114e2ad0ed1f90701a22f9a66f3903a5eff.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP _ { R , I } ^ { n } = \\\\frac { P _ { R } G A _ { e } g } { 4 \\\\pi ( L ^ { 2 } + d ^ { 2 } ) } \\\\cdot [ p _ { a } ( \\\\theta ( d ) ) ] ^ { 2 } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,239,941,334]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $P _ { R }$ is the LRR transmitting power, $G$ is the antenna gain, $A _ { e }$ is the antenna effective area, $g$ is the propagation decaying factor, $p _ { a } ( \\\\cdot )$ is the normalized antenna beam patter [24], $L$ is the vertical distance between two lanes, $d$ is the horizontal distance between two CAVPs and $\\\\begin{array} { r } { \\\\theta ( d ) = \\\\arctan \\\\Big ( \\\\frac { L } { d } \\\\Big ) } \\\\end{array}$ is the radiation direction between two CAVPs. For simplicity, we assume that the power of the communication and SRR signals is the same. The interference power of the communication/SRR signal from CAVP $n$ in the same lane can be expressed as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[546,342,670,372]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0254/524ed1592d06bfa02f752670aa917650d02414311648047bc349ec9680bef0f7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP _ { C , I } ^ { n } = { \\\\frac { P _ { C } G A _ { e } g } { 4 \\\\pi d ^ { 2 } } } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,375,705,391]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $P _ { C }$ is the communication/SRR transmitting power. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[275,392,941,420]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In conclusion, the total interference power suffered by a CAVP when it performs forward sensing or backward communication is \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,430,699,469]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0860/b4c2f773dde24efd7d650ffb2bc591571a6cf3ab5bc9839d14ff5ef15610f4ef.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP _ { I } = \\\\sum _ { n = 1 } ^ { N _ { R } } { P _ { R , I } ^ { n } } + \\\\sum _ { n = 1 } ^ { N _ { C } } { P _ { C , I } ^ { n } } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[275,474,941,518]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $N _ { R }$ is the number of CAVPs in the opposite lane choosing the same frequency band for the sensing frame and $N _ { C }$ is the number of CAVPs in the same lane choosing the same frequency band for the communication frame. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,519,939,548]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We use the interference-to-noise ratio (INR) to measure the level of interference to the CAVP [24]. The INR is defined as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[578,558,642,588]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0069/817d8a981adcca684dc820984990f0a164dd9adba20841851c42465344896e70.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\eta = \\\\frac { P _ { I } } { \\\\sigma ^ { 2 } } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,594,939,624]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\sigma ^ { 2 }$ is the receiver noise power. Similar to [24], if $\\\\eta$ is lower than the threshold $\\\\eta _ { 0 } ,$ , we consider the forward sensing or backward communication successful. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,636,443,650]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. Pomdp Framework \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,653,942,816]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Due to the high mobility of autonomous vehicles, there is a strict requirement for the latency of information transmission and processing to ensure the safety of autonomous driving. Each CAVP must be able to make decentralized decisions based on its local observations to avoid large time overheads caused by centralized scheduling. However, decentralized decision making leads to CAVPs having access to only the partial environmental information observed by themselves, without the ability to obtain the global information. Based on this, we model multi-agent decision problems as individual POMDP problems for each single agent [29]. A POMDP models an agent decision process in which it is assumed that the system dynamics are determined by an MDP, but the agent cannot directly observe the underlying state. In this approach, each CAVP considers the influence of other CAVPs as part of the environment and makes decisions based on its local observations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,819,941,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"During a CAVP’s driving, it continuously interacts with the dynamic environment. At each discrete time step $t ,$ each CAVP $i$ observes the local environmental state $\\\\mathbf { o } _ { t } ^ { i }$ . The global environmental state $\\\\mathbf { s } _ { t }$ of the system is a simple superposition of the local observations of the $N _ { p }$ CAVPs, i.e., $\\\\mathbf { \\\\boldsymbol { s } } _ { t } = \\\\left[ \\\\mathbf { \\\\boldsymbol { o } } _ { t } ^ { 1 } , \\\\mathbf { \\\\dot { o } } _ { t } ^ { \\\\dot { 2 } } , . . . , \\\\mathbf { \\\\boldsymbol { o } } _ { t } ^ { N _ { p } } \\\\right]$ . Based on the observation ${ \\\\mathbf { o } } _ { t } ^ { i } ,$ each CAVP takes an action $a _ { t } ^ { i }$ according to a policy $\\\\pi ^ { i }$ . Furthermore, the CAVP adjusts the policy $\\\\pi ^ { i }$ based on the environmental feedback $r _ { t } ^ { i }$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,59,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,60,939,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[277,103,436,117]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1. Observation Space \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,121,939,152]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"At each discrete time step $t ,$ a CAVP observes its surrounding environmental conditions as well as the state of the data queue: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,160,710,186]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0334/02197e08b025919386ad1912c34312b5efb57d5df9429fbabf07dd5fcd0658df.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array} { r } { \\\\mathbf { o } _ { t } ^ { i } = \\\\left[ d _ { S , t } ^ { i } , d _ { D , t } ^ { i } , \\\\mathbf { e } _ { t } ^ { i } , R _ { t } ^ { i } ( \\\\Delta _ { 0 } ) \\\\right] , } \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[275,193,941,299]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $d _ { S , t } ^ { i } = \\\\left| p _ { S , t } ^ { i } - p _ { t } ^ { i } \\\\right| , d _ { D , t } ^ { i } = \\\\sqrt { \\\\left( p _ { D , t } ^ { i } - p _ { t } ^ { i } \\\\right) ^ { 2 } + L ^ { 2 } } , p _ { t } ^ { i }$ is the position (one-dimensional coordinate) of $\\\\mathrm { C A V P } i ,$ and $p _ { S , t } ^ { i }$ and $p _ { D , t } ^ { i }$ are the positions of the nearest CAVPs to CAVP $i$ in the same and different lanes, respectively. CAVP $i$ obtains these values through the global navigation satellite system and camera. $\\\\mathbf { e } _ { t } ^ { i } = [ \\\\rho , w , m ] .$ ; these features are identified in Section 2 to be associated with the risk level. $R _ { t } ^ { i } ( \\\\Delta _ { 0 } )$ denotes the number of sensory results with $\\\\Delta _ { t } ^ { i } = \\\\Delta _ { 0 }$ in the queue, i.e., data that fail at time step $t$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,310,398,324]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2. Action Space \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,328,941,373]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"According to the system model, a CAVP can perform flexible time–frequency resource configuration according to the dynamic time-varying characteristics of the vehicle location and road environment. Therefore, the action space of CAVP $i$ at time step $t$ can be defined as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[421,382,794,407]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0158/7880f7f004def1387f50c7475ce17d27a3c6f5420a507bfdca3cee8edfa9a8a9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\na _ { t } ^ { i } \\\\in \\\\Bigl \\\\{ a _ { C } ^ { < 1 > } , a _ { C } ^ { < 2 > } , . . . , a _ { C } ^ { < M > } , a _ { R } ^ { < 1 > } , a _ { R } ^ { < 2 > } , . . . , a _ { R } ^ { < M > } \\\\Bigr \\\\} ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[273,413,941,444]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $a _ { C } ^ { < m > }$ and $a _ { R } ^ { < m > }$ denote a CAVP using sub-band $m$ for the sensing frame and communication frame, respectively. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,455,428,469]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.3. Reward Function \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,474,941,638]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As described in Section 2, when a CAVP is in the communication frame, the FV performs backward communication. The total number of unexpected events at that moment is the sum of the number of unexpected events that occurred in the environment and the number of sensory results lost due to communication failures. When a CAVP is in the sensing frame, the FV performs forward sensing. The total number of unexpected events at that moment is the sum of the number of invalid sensory results in the queue and the number of unexpected events missed due to sensing failures. The reward the CAVP receives at each time step is used to balance the sensing and communication functions, encouraging the agent to minimize the number of unexpected events that are not successfully sensed or transmitted. Rewards should be negatively correlated with the total number of unexpected events. So we design the reward function of CAVP $i$ at time step $t$ as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[470,648,749,772]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0978/15d9f6efd2e96d1c27d670842c90671072412abf2b7e8091a33f154996a61897.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array} { r l } & { { r _ { t } ^ { i } } = \\\\left\\\\{ \\\\begin{array} { l l } { - \\\\omega \\\\Big ( u _ { C , t } ^ { i } + I _ { t } ^ { i } ( C ) \\\\Big ) } & { a _ { t } ^ { i } = a _ { C } , } \\\\\\\\ { - \\\\omega \\\\big ( n _ { o v e r , t } ^ { i } + I _ { t } ^ { i } ( R ) \\\\big ) } & { a _ { t } ^ { i } = a _ { R } , } \\\\end{array} \\\\right. } \\\\\\\\ & { \\\\quad \\\\quad \\\\quad I _ { t } ^ { i } ( C ) = \\\\left\\\\{ \\\\begin{array} { l l } { 0 } & { \\\\eta _ { t } ^ { i } < \\\\eta _ { 0 } } \\\\\\\\ { n _ { a l l , t } ^ { i } } & { \\\\eta _ { t } ^ { i } \\\\geq \\\\eta _ { 0 } } \\\\end{array} \\\\right. , } \\\\\\\\ & { \\\\quad \\\\quad \\\\quad I _ { t } ^ { i } ( R ) = \\\\left\\\\{ \\\\begin{array} { l l } { 0 } & { \\\\eta _ { t } ^ { i } < \\\\eta _ { 0 } } \\\\\\\\ { u _ { R , t } ^ { i } } & { \\\\eta _ { t } ^ { i } \\\\geq \\\\eta _ { 0 } } \\\\end{array} \\\\right. , } \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,777,941,841]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\omega$ is the weight of the reward, $u _ { C , t } ^ { i }$ and $u _ { R , t } ^ { i }$ denote the number of unexpected events in the environment when CAVP $i$ is in the sensing frame and communication frame, respectively, $n _ { a l l , t } ^ { i }$ denotes all sensory results in the queue of CAVP $i$ and $n _ { o v e r , t } ^ { i }$ denotes the number of sensory results with $\\\\Delta _ { t } ^ { i } = \\\\Delta _ { 0 }$ in CAVP $i ^ { \\\\prime }$ s queue. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,852,435,868]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.4. Optimal Planning \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,871,941,902]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In reinforcement learning, the merit of a policy depends on the cumulative reward obtained from performing the policy over time, and the aim of learning is to find the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,58,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,60,941,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[272,102,939,133]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"policy that maximizes the cumulative reward over time [30]. In this paper, we use the $\\\\gamma$ cumulative discount reward, and the optimization issue is represented as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[478,141,737,183]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0268/5511ba86bd1f3060d5c89d9dc8f25a5c6df8492d3c813594757dd4ea75ad7069.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\operatorname* { m a x } _ { \\\\pi ^ { i } } R \\\\Big ( \\\\pi ^ { i } \\\\Big ) = \\\\mathbb { E } \\\\left[ \\\\sum _ { t = 0 } ^ { N _ { t } } \\\\gamma ^ { t } r _ { t + 1 } ^ { i } \\\\Big ( \\\\pi ^ { i } \\\\Big ) \\\\right] ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[270,187,941,203]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $N _ { t }$ is the number of training steps per episode, $\\\\gamma$ is the discount factor and $\\\\gamma \\\\in [ 0 , 1 ]$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,214,457,229]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. Ddqn-Per Algorithm \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,233,942,441]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Even though we defined the observation space and reward function in the previous discussion, vehicles navigating in the environment cannot directly access this information. Instead, they need to learn strategies through continuous interaction with the environment. Therefore, the model-free learning algorithm of reinforcement learning should be used. In addition, each CAVP performs its decisions in a decentralized manner. Still, its strategies are influenced by the strategies of other CAVPs, leading to a non-stationary environment and difficulties in convergence. We develop an improved algorithm based on a double deep Q-network (DDQN) [31] named DDQN-PER (double deep Q-network with prioritized experience replay) to deal with the dynamics and uncertainty in a multi-agent environment. The algorithm proposed in this paper uses a deep neural network as a function approximator while using the target network and the PER [32] scheme to enable multiple CAVPs to better obtain the optimal strategy for time–frequency resource allocation under uncertain environmental factors. The algorithm flow is shown in Figure 3, and the algorithm pseudocode is shown as Algorithm 1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[282,455,820,803]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 3. The DDQN-PER algorithm flow of CAVP $i$ \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0215/bcfe6288685d441afc972f1ef1eb340fd24f60717e2e70851ec61073cfe9007a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,59,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,60,941,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[277,103,465,117]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Algorithm 1 DDQN-PER \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[290,123,941,514]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1: Inputs: \\n2: $D ^ { i }$ : empty replay memory with capacity $\\\\left| D ^ { i } \\\\right|$ \\n3: $\\\\pmb { \\\\theta } ^ { i }$ : initial Q-network parameters. \\n4: $\\\\hat { \\\\pmb { \\\\theta } } ^ { i }$ : initial target Q-network parameters \\n5: for episod $e = 1 : E$ do \\n6: Initialize observations for all vehicles \\n7: for $t = 1 : T$ do \\n8: for $i = 1 : N$ do \\n9: Feed observation $\\\\mathbf { o } _ { t } ^ { i }$ to Q-network to get $Q ^ { i }$ \\n10: Choose an action $a _ { t } ^ { i }$ as (13) \\n11: Get a reward $r _ { t } ^ { i }$ \\n12: Obtain new observation $\\\\mathbf { o } _ { t + 1 } ^ { i }$ \\n13: Store experience $\\\\left( \\\\mathbf { o } _ { t } ^ { i } , a _ { t } ^ { i } , r _ { t } ^ { i } , \\\\mathbf { o } _ { t + 1 } ^ { i } \\\\right)$ in $D ^ { i }$ \\n14: Sample a mini-batch of experiences $\\\\left( \\\\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } , r _ { j } ^ { i } , \\\\mathbf { o } _ { j + 1 } ^ { i } \\\\right) \\\\mathrm { f r o m } D ^ { i }$ with prioritization \\nas (15) \\n15: Compute importance sampling weights $w _ { j }$ as (16) \\n16: Calculate target Q-values $y _ { j } ^ { i }$ as (17) \\n17: Update priorities of experiences as (14) \\n18: Update Q-network parameters $\\\\pmb { \\\\theta } _ { t + 1 } ^ { i }$ as (20), $\\\\pmb { \\\\theta } _ { t } ^ { i } \\\\pmb { \\\\theta } _ { t + 1 } ^ { i }$ \\n19: if $t$ mod $N _ { u } = 0$ then \\n20: 1 $\\\\hat { \\\\pmb { \\\\theta } } _ { t } ^ { i } \\\\pmb { \\\\theta } _ { t } ^ { i }$ \\n21: end if \\n22: ${ \\\\mathbf { o } _ { t } ^ { i } \\\\mathbf { o } _ { t + 1 } ^ { i } }$ \\n23: end for \\n24: end for \\n25: end for \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,526,941,617]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Each CAVP needs to learn its own policy; thus, each CAVP has a separate Q-network. The inputs of the Q-network include relative distances of neighboring CAVPs, the road condition, the weather condition, the moving object state and the data queue state. The outputs are the Q-values of sub-bands for the sensing or communication frame. At each training time step, CAVP $i$ chooses an action $a _ { t } ^ { i }$ following the $\\\\varepsilon$ -greedy policy when the observation is $\\\\mathbf { o } _ { t } ^ { i }$ . The $\\\\varepsilon$ -greedy policy is defined as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[477,626,742,667]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0738/1fde812813bfb003dfa530865aa447f6767ce0692e6c9971e43182663fd5623b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\na _ { t } ^ { i } = \\\\left\\\\{ \\\\begin{array} { c c } { r a n d o m } & { a < \\\\varepsilon } \\\\\\\\ { \\\\arg \\\\operatorname* { m a x } Q ^ { i } \\\\left( \\\\mathbf { o } _ { t } ^ { i } , a ; \\\\mathbf { \\\\pmb { \\\\theta } } _ { t } ^ { i } \\\\right) } & { a \\\\geq \\\\varepsilon } \\\\end{array} \\\\right. ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[275,674,942,774]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $Q ^ { i }$ are the Q-values of the $\\\\mathrm { Q }$ -network of CAVP $i ,$ and ${ \\\\pmb { \\\\theta } } _ { t } ^ { i }$ are the parameters of the $\\\\mathrm { Q }$ -network. CAVP $i$ executes the action $a _ { t } ^ { i }$ and obtains a reward $r _ { t } ^ { i }$ and the next observation $\\\\mathbf { o } _ { t + 1 } ^ { i }$ . The algorithm uses an experience replay scheme to store the experience $\\\\xi _ { t } ^ { i } = \\\\left( \\\\mathbf { o } _ { t } ^ { i } , a _ { t } ^ { i } , \\\\dot { r } _ { t } ^ { i } , \\\\mathbf { o } _ { t + 1 } ^ { i } \\\\right)$ obtained from the interaction of CAVP i with the environment into the memory $D ^ { i }$ . The storage capacity of $D ^ { i }$ is $\\\\left| D ^ { i } \\\\right|$ . At each time step, CAVP $i$ randomly samples a mini-batch of experiences $\\\\xi _ { j } ^ { i } = \\\\left( \\\\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } , r _ { j } ^ { i } , \\\\mathbf { o } _ { j + 1 } ^ { i } \\\\right)$ from $D ^ { i }$ for training. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[275,775,942,879]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The experience replay scheme improves data utilization by breaking the correlation between data through linear storage and random sampling of experiences. However, its equal probability replay ignores the importance of experiences, resulting in valuable experiences not being used efficiently. Therefore, this paper introduces the PER scheme. PER uses the temporal difference (TD) error, which represents the difference between the current $\\\\mathrm { Q }$ -value and the target Q-value, to measure the importance of each experience. Express the sampling priority of the jth experience as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[557,891,660,912]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0973/a60367b61ca9396ef270979c701c0b525f4fcb3d2f5306cf9119a3b52db86f44.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\np _ { j } = \\\\left| \\\\delta _ { j } \\\\right| + \\\\mu ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[57,59,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,60,939,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"9 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[272,102,941,134]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\delta _ { j }$ is the TD-error of the jth experience, and $\\\\mu$ is a very small positive constant to avoid the priority being 0. The probability that the jth experience is sampled is defined as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[537,141,680,186]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0007/3762320e1163f8a67c02efd45a88807ced134f2c96204d598754caae18f3c5c3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\np ( j ) = \\\\frac { p _ { j } ^ { \\\\alpha } } { \\\\sum _ { k } ^ { k \\\\in \\\\left| D ^ { i } \\\\right| } p _ { k } ^ { \\\\alpha } } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,190,941,266]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\alpha \\\\in [ 0 , 1 ]$ is used to regulate the priority of experience. When $\\\\alpha = 0$ , priority sampling will degrade to uniform sampling. Before priority sampling, it is necessary to sort the data according to their priority. However, sorting large amounts of data can be memory-intensive and have high time complexity. Therefore, PER uses a sum tree data structure for sampling to improve sampling efficiency [32]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,267,942,325]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, when sampling according to importance, the sample distribution is altered. Therefore, the bias must be compensated for according to the importance sampling weights, otherwise the model will overfit the important experiences. Express the importance sampling weights as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[532,335,685,372]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0240/4ab6b90af66eb84a6f529f1c379c760ff9f8f7875147c697f525a1b85e9d462f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nw _ { j } = \\\\big ( \\\\frac { 1 } { \\\\vert D ^ { i } \\\\vert } \\\\cdot \\\\frac { 1 } { p ( j ) } \\\\big ) ^ { \\\\beta } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[275,376,942,420]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\beta \\\\in [ 0 , 1 ]$ is used to regulate the degree of compensation for bias. When $\\\\beta = 1$ , the bias introduced by sampling with non-uniform probability will be entirely eliminated. $\\\\beta$ is annealed linearly from $\\\\beta _ { 0 }$ to 1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[275,423,942,517]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Next, we use the sampled experience $\\\\xi _ { j } ^ { i } = \\\\left( \\\\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } , r _ { j } ^ { i } , \\\\mathbf { o } _ { j + 1 } ^ { i } \\\\right)$ to calculate the target $\\\\mathrm { Q - }$ values. To improve the stability of the algorithm, another network with the same structure and initial parameters as the original Q-network is introduced, called the target Q-network, which is specially used to compute target $\\\\mathrm { Q }$ -values. The parameters of the $\\\\mathrm { Q }$ -network are updated at each training and passed to the target $\\\\mathrm { Q }$ -network after $N _ { u }$ steps. The target $\\\\mathrm { Q }$ -value at time step $t$ is calculated as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[423,526,791,567]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0525/1c046044b01883c2be3093681f21e4f601412d69f12cb5773f044b612039d495.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\ny _ { j } ^ { i } = r _ { j } ^ { i } + \\\\gamma \\\\hat { Q } ^ { i } \\\\left( \\\\mathbf { o } _ { j + 1 } ^ { i } , \\\\underset { a ^ { \\\\prime } } { \\\\arg \\\\operatorname* { m a x } } Q ^ { i } \\\\left( \\\\mathbf { o } _ { j + 1 } ^ { i } , a ^ { \\\\prime } ; \\\\pmb { \\\\theta } _ { t } ^ { i } \\\\right) ; \\\\hat { \\\\pmb { \\\\theta } } _ { t } ^ { i } \\\\right) ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,571,942,602]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where ${ \\\\hat { Q } } ^ { i }$ are the Q-values of the target $\\\\mathrm { Q }$ -network of CAVP $i ,$ and $\\\\widehat { \\\\theta } _ { t } ^ { i }$ are the parameters of the target $\\\\mathrm { Q }$ -network. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,602,941,648]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The DDQN algorithm updates the Q-network parameters by minimizing the mean square error between the current $\\\\mathrm { Q }$ -value and the target $\\\\mathrm { Q }$ -value, and the loss function can be expressed as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[473,656,744,690]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0769/28407d87e5fa9e090c06372700f76fc6086f7d2634fe82da0fd4ae5e7168b136.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nL _ { t } ^ { i } \\\\Big ( \\\\pmb { \\\\theta } _ { t } ^ { i } \\\\Big ) = \\\\mathbb { E } \\\\Bigg [ \\\\Big ( y _ { j } ^ { i } - Q ^ { i } \\\\Big ( \\\\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } ; \\\\pmb { \\\\theta } _ { t } ^ { i } \\\\Big ) \\\\Big ) ^ { 2 } \\\\Bigg ] .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[314,694,573,709]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The gradient of the loss function is \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[401,719,815,745]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0667/7ee8e722dea8b53a21f6c724bd66dd8af8b5fb86958e04b6ac6ff4c1e4d8d64c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\nabla _ { \\\\theta _ { t } ^ { i } } L _ { t } ^ { i } \\\\Big ( \\\\theta _ { t } ^ { i } \\\\Big ) = \\\\mathbb { E } \\\\Big [ \\\\Big ( y _ { j } ^ { i } - Q ^ { i } \\\\Big ( \\\\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } ; \\\\theta _ { t } ^ { i } \\\\Big ) \\\\Big ) \\\\nabla _ { \\\\theta _ { t } ^ { i } } Q ^ { i } \\\\Big ( \\\\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } ; \\\\theta _ { t } ^ { i } \\\\Big ) \\\\Big ] .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[273,750,941,778]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Q-network parameters are updated according to the stochastic gradient descent (SGD) algorithm: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[406,788,811,814]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0073/e1f4bb335383149402c66c26798ea5da2468bf01b43215c9734549f850ec70a0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array} { r } { \\\\pmb { \\\\theta } _ { t + 1 } ^ { i } = \\\\pmb { \\\\theta } _ { t } ^ { i } + w _ { j } \\\\alpha _ { l } \\\\left( y _ { j } ^ { i } - Q ^ { i } \\\\left( \\\\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } ; \\\\pmb { \\\\theta } _ { t } ^ { i } \\\\right) \\\\right) \\\\nabla _ { \\\\pmb { \\\\theta } _ { t } ^ { i } } Q ^ { i } \\\\left( \\\\mathbf { o } _ { j } ^ { i } , a _ { j } ^ { i } ; \\\\pmb { \\\\theta } _ { t } ^ { i } \\\\right) , } \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,819,489,833]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\alpha _ { l }$ is the learning rate. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,845,455,860]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5. Simulation Analysis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,864,941,909]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this section, we evaluate the performance of the proposed approach through simulation experiments. First, we introduce the simulation setup, performance metrics and contrasting approaches. Then, we analyze the simulation results. Simulation results show \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[894,60,941,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[57,58,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[273,103,939,133]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"that the time–frequency resource allocation problem for radar and communication in the ISAC scenario can be effectively solved within the deep Q-learning framework. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,145,428,159]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5.1. Simulation Setup \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,162,941,252]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We consider a road traffic scenario as described in Section 2. Vehicles travel at a uniform speed, and the distance $d _ { n }$ between adjacent CAVPs in the same lane follows a uniform distribution $U$ . The frame length is $T$ . We consider the spatial location and environment around the vehicle to be semi-static, i.e., not changing significantly within frame $T$ but changing dynamically over multiple frames [33]. The detailed scenario parameters are set as shown in Table 1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,285,941,470]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0531/8a3b025665386b1205306701d462eca00146abf42c41bc450288187647df2ff3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Notation</td><td>Value</td></tr><tr><td>(t,ti）,e∈ε</td><td>(0.7,0.3)</td></tr><tr><td>(p,p),e∈ε</td><td>(0.01,0.1)</td></tr><tr><td>U</td><td>10 m/s</td></tr><tr><td>△0</td><td>4</td></tr><tr><td>T</td><td>0.02 s</td></tr><tr><td>PR</td><td>25 dBmW</td></tr><tr><td>Pc</td><td>15 dBmW</td></tr><tr><td>G</td><td>48 dB</td></tr><tr><td>Ae</td><td>5mm²</td></tr><tr><td>8</td><td>0.1</td></tr><tr><td>L</td><td>3m</td></tr><tr><td>n0</td><td>10</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. Scenario parameters setting. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[277,487,941,577]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The numbers of neurons in the input, hidden (two layers) and output layers of the network are set to be 6, 24, 24 and 2, respectively. The hidden layer utilizes a rectified linear unit (ReLU) as the activation function, and the output layer has no activation function. In the training, a time step equals the frame length T. Each episode contains multiple time steps. The hyperparameters used in training the $\\\\mathrm { Q }$ -networks are shown in Table 2. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,611,941,756]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0846/cee1ce83bfb4e143961ed61bbcd8bace18a26ed4d2b9de8e4248dcd594f4ceb9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Notation</td><td>Value</td></tr><tr><td>W</td><td>200</td></tr><tr><td>m</td><td>0.9 →0.01</td></tr><tr><td>Nb</td><td>64</td></tr><tr><td>μ</td><td>0.01</td></tr><tr><td>&</td><td>0.6</td></tr><tr><td>β</td><td>0.4→1.0</td></tr><tr><td>Nu</td><td>20</td></tr><tr><td>Y</td><td>0.9</td></tr><tr><td>α1</td><td>0.0001</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2. Hyperparameters Setting. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[277,771,453,784]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5.2. Performance Metrics \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[300,789,934,804]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We propose two key metrics to evaluate the performance of the proposed approach: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[280,809,939,854]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Miss detection probability: defined as the ratio of the number of unsuccessfully sensed or transmitted unexpected events to the total number of unexpected events in each episode: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[463,865,789,906]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0195/840218d8af910344f02314cdea6715b02a7075089014be7f23ebd0b48e37b119.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\np _ { m i s s } = \\\\sum _ { i = 1 } ^ { N _ { p } } \\\\sum _ { t = 0 } ^ { N _ { t } } \\\\frac { u _ { C , t } ^ { i } + I _ { t } ^ { i } ( C ) + n _ { o v e r , t } ^ { i } + I _ { t } ^ { i } ( R ) } { u _ { C , t } ^ { i } + u _ { R , t } ^ { i } } .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[57,59,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,60,939,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"11 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[280,102,939,133]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Average system interference power: defined as the ratio of the sum of interference power of all CAVPs per episode to the number of training steps per episode: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[547,142,705,184]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0557/72991033aff0a26ef99fadbd78cb4c3871fef46ae39e9a8f948d165a3708ff3e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP _ { a v e } = \\\\frac { 1 } { N _ { t } } \\\\sum _ { i = 1 } ^ { N _ { p } } \\\\sum _ { t = 0 } ^ { N _ { t } } { P _ { I , t } ^ { i } } .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,195,473,209]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5.3. Contrasting Approaches \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[310,214,606,228]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"There are three contrasting approaches: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[275,233,941,488]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"DRQN: In [24], each vehicle performs sensing independently and does not communicate with other AVs. AVs only need to allocate sensing frequency resources. The authors in [24] introduce a long short-term memory (LSTM) network into the DQN algorithm, enabling the vehicle to learn how to select sensing sub-bands by incorporating both its current and past observations. In this case, miss detection occurs only when the vehicle does not sense successfully. Random (CAVPs): We use the random policy to allocate time–frequency resources for the sensing and communication frames of CAVPs. i.e., CAVPs randomly select an action from the action space mentioned in Equation (8) with equal probability. DDQN (CAVPs): We use the DDQN algorithm proposed in [31] to allocate time– frequency resources for the sensing and communication frames of CAVPs. DQN (single CAVP): In [16], the DQN algorithm was introduced to allocate time resources for both sensing and communication functions of a single vehicle in a dynamic environment. Nevertheless, Ref. [16] did not account for interference between vehicles, implying that both sensing and communication could be successful regardless of the chosen strategy. We apply this algorithm to CAVPs, considering it as an upper-bound performance to evaluate the effectiveness of other algorithms. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,499,425,514]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5.4. Results Analysis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,518,941,548]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We first verify the algorithm’s convergence by using the average system reward as a measure of convergence. The average system reward is calculated as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[534,557,684,599]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0051/2c4fd71bafde02ef3fde08cf9b3bbd0b512aa6e408136f5e499b2bb21c14a1b3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nR _ { a v e } = \\\\frac { 1 } { N _ { t } } \\\\sum _ { i = 1 } ^ { N _ { p } } \\\\sum _ { t = 0 } ^ { N _ { t } } r _ { t } ^ { i } .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,602,941,676]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We selected five random seed values, namely, 10, 20, 30, 40 and 50, and calculated the average $R _ { a v e }$ of the algorithms under these five random seeds. As shown in Figure 4, the $R _ { a v e }$ of DDQN-PER gradually increases with the number of episodes and eventually stabilizes around 800 episodes. Compared with DDQN and random, DDQN-PER has better convergence performance. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,677,941,707]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Then, we evaluate the performance of the proposed approach and the contrasting approaches through the following four aspects: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,713,942,921]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. The number of AVs changes, other conditions are fixed: In Figure 5, as $N$ increases, $p _ { m i s s }$ and $P _ { a v e }$ increase for all algorithms except DQN. The reason is that as $N$ increases, the mutual interference between the AVs increases, while DQN is used in a single-CAVP scenario, and the effect of interference is not considered. In addition, compared with DRQN, random has a lower $P _ { a v e }$ . This is because the proposed communicationassisted sensing mechanism allows some vehicles to acquire sensory data through communication, eliminating the requirement for all vehicles to perform sensing tasks simultaneously, effectively reducing inter-vehicle interference. Nevertheless, random has a higher $p _ { m i s s }$ than DRQN. This is because the $p _ { m i s s }$ of random is not only affected by system interference but also influenced by the dynamic environment. Random cannot choose sensing or communication modes based on the environment, leading to a higher rate of $p _ { m i s s }$ . As DDQN-PER utilizes the communication-assisted sensing mechanism and adaptive time–frequency resource allocation algorithm, it can effectively control the mutual interference between vehicles and reduce the miss detection probability. Thus, compared with other algorithms, $p _ { m i s s }$ and $P _ { a v e }$ of DDQN-PER are closer to DQN, and the performance does not deteriorate significantly as $N$ increases. In conclusion, DDQN-PER proves to be more advantageous than other algorithms, particularly in scenarios with a higher volume of vehicles. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[894,60,941,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"12 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[57,59,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[315,103,941,162]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[300,177,732,419]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 4. Average system reward versus the number of episodes. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0673/44ebfb159a4654c0bd757ee58080588e2a3c288317e8e1333df6a8e5542fa85f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[294,461,847,718]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 5. The number of AVs changes, other conditions are fixed. (a) Miss detection probability. (b) Average system interference power. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0469/fb0e1f4f3038c79aab749fd85a90dd22626bbd4dcf2f2dd2b2053e076dceca81.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,771,941,862]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. The number of sub-bands changes, other conditions are fixed: In Figure $^ { 6 , }$ as $M$ increases, $p _ { m i s s }$ and $P _ { a v e }$ decrease for all algorithms except $\\\\mathrm { D Q N }$ . The reason is that as $M$ increases, the probability of two signals switching to the same sub-band becomes small. Compared with other algorithms, $p _ { m i s s }$ and $P _ { a v e }$ of DDQN-PER are closer to DQN. It can be deduced that DDQN-PER holds a comparative advantage over other algorithms, especially when the number of sub-bands is limited. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,59,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,60,939,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"13 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[294,118,847,374]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 6. The number of sub-bands changes, other conditions are fixed. (a) Miss detection probability. (b) Average system interference power. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0000/5e6cd99e9a29081862457562f5a2b48b6db6d06ce96bc7912a754ee0c41695da.jpg\",\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,428,942,562]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. h The interval changes, other conditions are fixed: In Figure 7, when s better performance. In addition, compared with oth $d _ { n } \\\\sim U ( 5 0 \\\\mathrm { m } , 6 0 \\\\mathrm { m } ) .$ $p _ { m i s s }$ of DDQN-PER is higher than DRQN. However, when $d _ { n }$ is small, DDQN-PER has better performance. In addition, compared with other algorithms, the $P _ { a v e }$ of DDQN-PER is closer to 0. This is because when the interval is small, DRQN is greatly affected by interference and cannot effectively allocate frequency resources, whileQN-PER can effectively control mutual interference and reduce the miss d DDQN-PER can effectively control mutual interference and reduce the miss detectionbability by using the communication-assisted sensing mechanism and a probability by using the communication-assisted sensing mechanism and adaptivee–frequency resource allocation algorithm. It can be concluded that DDQ time–frequency resource allocation algorithm. It can be concluded that DDQN-PER isre advantageous than other algorithms when the interval is smaller. more advantageous than other algorithms when the interval is smaller. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[280,570,778,881]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 7. Cont. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0246/1fd0d2518e78f01b1aa303377a9e0c30fb19717a18831b99e0e30fd410dffdba.jpg\",\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,59,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,60,939,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"14 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[280,104,778,412]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 7. The interval changes, other conditions are fixed. (a) Miss detection probability. (b) Averagem system interference power. 1 \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0463/6616058c3cb50fb3062131c7081c792bcec16a98e99bffac8632620d792323b3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,462,941,567]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. The R an $p _ { 1 } ^ { m }$ (i.e., the probability of the occurrence of an unexpected event under conditionDQN changes, while other algorithms are almost unchanged. This is $m = 1$ .e., the probability of the occurrence of an u) changes, other conditions are fixed: In Figure 8, as ER and DQN can adaptively allocate time–f $p _ { 1 } ^ { m }$ pected changes, quency r $p _ { m i s s }$ t under coof DDQN-rces accor = 1) changes, other conditions are fixed: In Figure 8, as pm changes, pmiss ofPER and DQN changes, while other algorithms are almost unchanged. This is becausee environment. As DDQN-PER is affected by multi-vehicle interference, R and DQN changes, while other algorithms are almost unchanged. This isDDQN-PER and DQN can adaptively allocate time–frequency resources according tom QN-PER and DQN can adaptively allocate time–frequency resourcesthe environment. As DDQN-PER is affected by multi-vehicle interference, its 1 $p _ { m i s s }$ does not continue to decrease as er algorithms, the Pave of D $p _ { 1 } ^ { m }$ increases like DQN. Furthermore, compared withN-PER is closer to 0. other algorithms, the $P _ { a v e }$ of DDQN-PER is closer to 0. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[284,576,776,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 8. Cont. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0640/61eee1b111d881a702b3976d99d62295fa1eccbba0265d31992f2dd4cfc44bb0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,59,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,60,939,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"15 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[282,105,776,418]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"mFigure 8. The $p _ { 1 } ^ { m }$ changes, other conditions are fixed. (a) Miss detection probability. (b) Average 1system interference power. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0944/7c64bc220e2ce7f3f008db36f402abf66695153ad967292a0fe1f141e2abb116.jpg\",\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,467,391,481]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6. Conclusions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,485,941,633]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"usionsIn this paper, we propose a communication-assisted sensing mechanism based on In this paper, we propose a communication-assisted sensing mechanism bTD-ISAC, which uses communication to transmit sensing information effectively. Moreover, we construct an interference model for multi-vehicle sensing and communication signals and formulate a multi-vehicle optimization problem based on the POMDP framework. We onstruct an interference model for multi-vehicle sensing and communicationdevelop the DDQN-PER algorithm to enable vehicles to adjust their policies adaptively for formulate a multi-vehicle optimization problem based on the POMDP framewdecentralized time–frequency resource allocation in the dynamic environment. Simulation lop the DDQN-PER algorithm to enable vehicles to adjust their policies adaptresults show that the proposed scheme can significantly reduce miss detection probability ntralized time–frequency resource allocation in the dynamic environment. Siand average system interference power. Furthermore, the method proposed in this paper also applies to the problem of multi-vehicle mutual interference where a TD-ISAC vehicle assists a radar-free vehicle. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,648,941,689]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"applies to the problem of multi-vehicle mutual interference where a TD-ISACAuthor Contributions: Methodology, Y.F.; validation and formal analysis, Z.F., J.H. and X.W.; ts a radar-free vehicle.writing—original draft preparation, Y.F.; writing—review and editing, Z.F., J.H. and X.W. All authors have read and agreed to the published version of the manuscript. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,696,941,724]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"or Contributions: Methodology, Y.F.; validation and formal analysis, Z.F., J.H. aFunding: This work was supported by the National Key R&D Program of China under Grant No. \\nng—original draft preparation, Y.F.; writing—review and editing, Z.F., J.H. and X.W.2021YFB2900200 and the National Natural Science Foundation of China under Grant U20B2039. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[275,731,939,759]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"read and agreed to the published version of the manuscript.Data Availability Statement: The data and code are available from the corresponding authors upon reasonable request. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,766,709,781]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"FB2900200 and the National Natural Science FoundatiConflicts of Interest: The authors declare no conflicts of interest. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,794,142,806]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,810,942,907]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. reasonable request.Ma, D.; Shlezinger, N.; Huang, T.; Liu, Y.; Eldar, Y.C. 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In Proceedings of the 42nd IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, USA, 5–9 March 2017; pp. 4281–4285. \\n14. Cao, N.; Chen, Y.; Gu, X.; Feng, W. Joint Bi-Static Radar and Communications Designs for Intelligent Transportation. IEEE Trans. Veh. Technol. 2020, 69, 13060–13071. [CrossRef] \\n15. Ren, P.; Munari, A.; Petrova, M. Performance Analysis of a Time-sharing Joint Radar-Communications Network. In Proceedings of the 2020 International Conference on Computing, Networking and Communications (ICNC), Big Island, HI, USA, 17–20 February 2020; pp. 908–913. \\n16. Hieu, N.Q.; Hoang, D.T.; Luong, N.C.; Niyato, D. iRDRC: An Intelligent Real-Time Dual-Functional Radar-Communication System for Automotive Vehicles. IEEE Wirel. Commun. Lett. 2020, 9, 2140–2143. [CrossRef] \\n17. Hieu, N.Q.; Hoang, D.T.; Niyato, D.; Wang, P.; Kim, D.I.; Yuen, C. 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Distributive Dynamic Spectrum Access Through Deep Reinforcement Learning: A Reservoir Computing-Based Approach. IEEE Internet Things J. 2019, 6, 1938–1948. [CrossRef] \\n26. Naparstek, O.; Cohen, K. Deep Multi-User Reinforcement Learning for Distributed Dynamic Spectrum Access. IEEE Trans. Wirel. Commun. 2019, 18, 310–323. [CrossRef] \\n27. Lee, J.; Niyato, D.; Guan, Y.L.; Kim, D.I. Learning to Schedule Joint Radar-Communication with Deep Multi-Agent Reinforcement Learning. IEEE Trans. Veh. Technol. 2022, 71, 406–422. [CrossRef] \\n28. Boban, M.; Kousaridas, A.; Manolakis, K.; Eichinger, J.; Xu, W. Use cases, requirements, and design considerations for 5G V2X. arXiv 2017, arXiv:1712.01754. \\n29. Tampuu, A.; Matiisen, T.; Kodelja, D.; Kuzovkin, I.; Korjus, K.; Aru, J.; Aru, J.; Vicente, R. Multiagent cooperation and competition with deep reinforcement learning. PloS ONE 2017, 12, e0172395. [CrossRef] [PubMed] \\n30. Sutton, R.S.; Barto, A.G. Reinforcement Learning: An Introduction; MIT Press: Cambridge, MA, USA, 2018. \\n31. Van Hasselt, H.; Guez, A.; Silver, D. Deep reinforcement learning with double q-learning. In Proceedings of the 30th AAAI Conference on Artificial Intelligence, Phoenix, AZ, USA, 12–17 February 2016; Volume 30. \\n32. Schaul, T.; Quan, J.; Antonoglou, I.; Silver, D. Prioritized experience replay. arXiv 2015, arXiv:1511.05952. \\n33. Xing, Y.; Sun, Y.; Qiao, L.; Wang, Z.; Si, P.; Zhang, Y. Deep reinforcement learning for cooperative edge caching in vehicular networks. In Proceedings of the 13th International Conference on Communication Software and Networks (ICCSN), Chongqing, China, 4–7 June 2021; IEEE: Piscataway, NJ, USA, 2021; pp. 144–149. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,59,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,60,939,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"16 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[57,102,941,904]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,58,203,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,60,941,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"17 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[55,103,942,186]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,202,942,242]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,58,203,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electronics 2024, 13, 2442 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,60,939,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"18 of 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.3390/electronics13132442"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Engineering and Manufacturing Science"},"sha256":{"kind":"string","value":"79d8b4ede5fb99216ace6a3aba1a3ed6735696d0c7cf44ac5749ed95df35120e"},"title":{"kind":"string","value":"Reinforcement Learning-Based Resource Allocation for Multiple Vehicles with Communication-Assisted Sensing Mechanism"}}},{"rowIdx":247,"cells":{"abstract":{"kind":"string","value":"The management of patients with suspected appendicitis remains a challenge in daily clinical practice, and the optimal management algorithm is still being debated. Negative appendectomy rates (NAR) continue to range between 10 and 15%. This prospective study evaluated the accuracy of a diagnostic pathway in acute appendicitis using clinical risk stratification (Alvarado score), routine ultrasonography, gynecology consult for females, and selected CT after clinical reassessment. Patients presenting with suspected appendicitis between November 2015 and September 2017 from age 18 years and above were included. Decision-making followed a clear management pathway. Patients were followed up for 6 months after discharge. The hypothesis was that the algorithm can reduce the NAR to a value of under 10%. A total of 183 patients were included. In 65 of 69 appendectomies, acute appendicitis was confirmed by histopathology, corresponding to a NAR of 5.8%. Notably, all 4 NAR appendectomies had other pathologies of the appendix. The perforation rate was 24.6%. Only 36 patients (19.7%) received a CT scan. The follow-up rate after 30 days achieved 69%, including no patients with missed appendicitis. The sensitivity and specificity of the diagnostic pathway was 100% and 96.6%, respectively. The potential saving in costs can be as much as 19.8 million €/100,000 cases presenting with the suspicion of appendicitis. The risk-stratified diagnostic algorithm yields a high diagnostic accuracy for patients with suspicion of appendicitis. Its implementation can safely reduce the NAR, simultaneously minimizing the use of CT scans and optimizing healthcare-related costs in the treatment of acute appendicitis. \n ClinicalTrials.gov\n \n Identifier: NCT02627781 (December 2015)"},"author":{"kind":"string","value":"Juliane Liese|Hanan El Youzouri|Teresa Schreckenbach|Andreas A. Schnitzbauer|Alexander Reinisch-Liese|Franziska Edmaier|Patrizia Malkomes|Wolf Otto Bechstein|Andreas M. Bucher"},"content_list":{"kind":"list like","value":[{"bbox":"[80,135,776,182]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"DIALAPP: a prospective validation of a new diagnostic algorithm for acute appendicitis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[78,200,862,232]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Patrizia Malkomes<sup>1</sup> $\\cdot$ Franziska Edmaier<sup>1</sup> $\\cdot$ Juliane Liese<sup>2</sup> $\\cdot$ Alexander Reinisch-Liese<sup>3</sup> $\\cdot$ Hanan El Youzouri<sup>1</sup> $\\cdot$ Teresa Schreckenbach<sup>1</sup> $\\cdot$ Andreas M. Bucher<sup>4</sup> $\\cdot$ Wolf Otto Bechstein<sup>1</sup> $\\cdot$ Andreas A. Schnitzbauer<sup>1</sup> ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,255,386,268]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received: 10 August 2020 / Accepted: 1 November 2020 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,269,206,281]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"© The Author(s) 2020 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,298,149,311]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[80,313,915,375]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Purpose The management of patients with suspected appendicitis remains a challenge in daily clinical practice, and the optimal management algorithm is still being debated. Negative appendectomy rates (NAR) continue to range between 10 and $15\\%$ . This prospective study evaluated the accuracy of a diagnostic pathway in acute appendicitis using clinical risk stratification (Alvarado score), routine ultrasonography, gynecology consult for females, and selected CT after clinical reassessment. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,375,915,421]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methods Patients presenting with suspected appendicitis between November 2015 and September 2017 from age 18 years and above were included. Decision-making followed a clear management pathway. Patients were followed up for 6 months after discharge. The hypothesis was that the algorithm can reduce the NAR to a value of under $10\\%$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,422,915,500]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results A total of 183 patients were included. In 65 of 69 appendectomies, acute appendicitis was confirmed by histopathology, corresponding to a NAR of $5.8\\%$ . Notably, all 4 NAR appendectomies had other pathologies of the appendix. The perforation rate was $24.6\\%$ . Only 36 patients $(19.7\\%)$ received a CT scan. The follow-up rate after 30 days achieved $69\\%$ , including no patients with missed appendicitis. The sensitivity and specificity of the diagnostic pathway was $100\\%$ and $96.6\\%$ , respectively. The potential saving in costs can be as much as 19.8 million €/100,000 cases presenting with the suspicion of appendicitis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,501,915,546]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conclusion The risk-stratified diagnostic algorithm yields a high diagnostic accuracy for patients with suspicion of appendicitis. Its implementation can safely reduce the NAR, simultaneously minimizing the use of CT scans and optimizing healthcare-related costs in the treatment of acute appendicitis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,546,608,562]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Trial registration ClinicalTrials.gov Identifier: NCT02627781 (December 2015) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,578,847,594]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords Acute appendicitis $\\cdot$ Diagnostic algorithm $\\cdot$ Risk-stratification $\\cdot$ Negative appendectomy rate $\\cdot$ Clinical trial ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,665,485,692]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Wolf Otto Bechstein and Andreas A. Schnitzbauer contributed equally to this work. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,708,267,736]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\boxtimes$ Patrizia Malkomes Patrizia.Malkomes@kgu.de ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,756,485,903]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"$^{1}$ Department of General, Visceral and Transplant Surgery, University Hospital Frankfurt, Goethe University, Theodor-Stern-Kai 7, 60590 Frankfurt am Main, Germany \",\"$^{2}$ Department of General, Abdominal, Thoracic and Transplant Surgery, University Hospital of Giessen, Giessen, Germany \",\"$^{3}$ Department of General, Visceral and Oncological Surgery, Wetzlar Clinic, Wetzlar, Germany \",\"$^{4}$ Department of Radiology, Institute for Diagnostic and Interventional Radiology, Goethe University Hospital Frankfurt, Frankfurt am Main, Germany \"]","page_idx":"0","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[509,631,626,646]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,664,915,789]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"With an incidence of 120 per 100,000 inhabitants, appendicitis is one of the most common causes of acute abdomen in Germany. The lifetime prevalence for appendicitis is approximately $7\\%$ , making appendectomy one of the most frequently performed operations with 110,000 procedures per year [1, 2]. However, the diagnosis of acute appendicitis (AA) continues to be a challenge even for experienced surgeons resulting in a mean negative appendectomy rate (NAR) of 10 to $15\\%$ [3-5]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,791,915,901]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As negative appendectomies are associated with the potential of substantial morbidity and increased healthcare-related costs, they should be reduced to a minimum [6]. Several scoring systems and modern imaging modalities have been implemented in an attempt to increase the diagnostic accuracy as they have shown to reduce NAR. Studies from the USA could reduce the NAR to $3.2\\%$ by performing a computed tomography (CT) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,39,265,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Langenbeck's Archives of Surgery ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[80,53,321,65]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1007/s00423-020-02022-7 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[90,79,223,93]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ORIGINAL ARTICLE ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,81,915,120]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Check for updates ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[80,934,300,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Published online: 19 November 2020 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[838,927,914,945]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[78,70,485,227]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"scan in each patient presenting with right-sided lower abdominal quadrant pain [7]. Nevertheless, non-selective imaging shows limited accuracy in subgroups with a low or high clinical probability of appendicitis, suggesting that improvements in diagnostic outcomes are dependent on the appropriate selective application of CT, and the integration of clinical findings with CT results [8, 9]. Moreover, several authors have criticized the widespread use of CT due to the negative impact of ionizing radiation exposure in this generally young patient population, raising concerns about cancer risk [10, 11]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,229,485,369]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In 1986, Alvarado et al. [12] devised a simple diagnostic score for the diagnosis of acute appendicitis based on the probability of clinical signs (tenderness in right lower quadrant, rebound pain, and elevated temperature $>37.5^{\\circ}\\mathrm{C}$ ), symptoms (pain migration to right lower quadrant, anorexia, and nausea/vomiting), and laboratory testing (leukocytosis and neutrophils $>75\\%$ ) for predicting appendicitis (Table 1). In subsequent studies, the Alvarado score has been validated showing a good sensitivity but a considerably low specificity of only $81\\%$ [13]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,370,487,575]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Several studies have determined the diagnostic accuracy of individual diagnostic procedures and their combinations in the diagnosis of AA [14-17]. However, there is little evidence for the application of diagnostic pathways, and none is in routine clinical use. In a study at our institution by Liese et al. [18], data from 367 patients with suspected appendicitis were retrospectively analyzed, and it was found that the overall NAR was $10.1\\%$ with a simultaneous CT rate of $35\\%$ . Patients who had received a CT scan showed a lower NAR of $5.7\\%$ in comparison with those who had not undergone imaging with a frequency of negative appendectomies of $11.7\\%$ . Thereby, CT imaging helped to reduce total hospital expenses. However only $32\\%$ of patients undergoing CT benefitted from ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,630,487,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0095/e07f3c82015249e097bdc98bdb16c8ba4ded064791494b05df614bccba2ecb4e.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":"<table><tr><td>Characteristics</td><td>Score</td></tr><tr><td>Symptoms</td><td></td></tr><tr><td>Pain migration to right lower quadrant</td><td>1</td></tr><tr><td>Anorexia</td><td>1</td></tr><tr><td>Nausea/vomiting</td><td>1</td></tr><tr><td>Clinical signs</td><td></td></tr><tr><td>Tenderness in right lower quadrant</td><td>2</td></tr><tr><td>Rebound pain</td><td>1</td></tr><tr><td>Elevated temperature > 37.5 °C</td><td>1</td></tr><tr><td>Laboratory</td><td></td></tr><tr><td>Leukocytosis</td><td>2</td></tr><tr><td>Neutrophils > 75%</td><td>1</td></tr><tr><td>Total</td><td>10</td></tr></table>","table_caption":"[\"Table 1 Alvarado scoring system for acute appendicitis \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[507,70,915,260]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"this diagnostic modality, and thus, a relevant proportion of CT scans could have been avoided [18]. Based on these retrospective findings, a clinical diagnostic algorithm was developed and implemented. The DIALAPP study (evaluation of Diagnostic ALgorithm for suspected acute APPendicitis) is a prospective observational unicentric study to evaluate the implementation and impact of the newly established diagnostic pathway in patients with suspicion of acute appendicitis. The hypothesis was that the pathway reduces the NAR to less than $10\\%$ , while simultaneously reducing the use of CT imaging. The increased quality and safety should lead to a reduction in costs and create a real value for healthcare (Fig. 1). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,289,591,306]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,322,915,402]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A clinical diagnostic algorithm was implemented at the Department for General and Visceral Surgery of the Goethe University Hospital Frankfurt starting in November 2015, which was applied to all patients over 18 years presenting with the symptoms of an acute appendicitis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,402,915,494]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Written informed consent was obtained from all patients prior to inclusion in the study in accordance with the Declaration of Helsinki and local laws and regulations. The study was approved by the institutional ethics review board (IRB-Number: 268/15) and registered at clinicaltrials.gov (NCT02627781). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,496,915,591]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"All consecutively included patients were evaluated by a resident or a consultant of the surgical department. Patients with abdominal pain due to trauma, patients under 18 years, and those who had undergone additional radiological examinations (CT or magnetic resonance imaging (MRI)) prior to surgical consultation were excluded. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,605,870,622]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Clinical diagnostic pathway and data collection ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,637,915,905]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"All patients followed a structured diagnostic algorithm including all elements of the Alvarado score (Table 1), besides other parameters. First, a clinical examination, a biochemical and hematological blood analysis, urine analysis, as well as an ultrasound by a resident and/or consultant surgeon were performed. Additionally, all female patients of childbearing age received a gynecological consultation. Thereafter, the Alvarado score was calculated for each individual patient. All clinical parameters and the management strategy were recorded on a study sheet. Patients with signs of peritonitis, positive ultrasound, or an Alvarado score of $>8$ were advised to undergo appendectomy. Patients with an Alvarado score of $<5$ and negative ultrasound were discharged to outpatient follow-up. Those with an Alvarado score between 5 and 8 were admitted to observation and clinical re-evaluation. These patients only received symptomatic therapy (infusion therapy, laxative ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[784,39,915,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Langenbecks Arch Surg ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[80,927,154,944]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[137,65,319,91]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Knowledge to practice Interpret results ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[141,103,302,116]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Establish DIALAPP-study ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[141,117,339,129]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A stratified approach combining ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[141,130,413,165]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"clinical parameters (Alvarado-score) \",\"- ultrasound \",\"- selected CT after clinical reassessment \"]","page_idx":"2","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[137,318,285,346]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data to knowledge Assembling data ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[139,356,405,370]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Liese et al., Langenbecks Arch Surg. 2014 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[139,370,534,422]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- NAR of roughly $10\\\\%$ \",\"- CT-scans in $35\\\\%$ of patients \",\"- No established algorithm for diagnosing acute appendicitis \",\"- High costs from patients without indication for appendectomy \"]","page_idx":"2","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[589,150,717,175]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Practice to data Take action ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[591,189,665,200]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data found: ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[591,202,838,291]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- NAR reduced to $5.8\\\\%$ \",\"CT-scans used in $19\\\\%$ of patients \",\"- Increased quality \",\"- Increased safety \",\"- Low costs (potential to safe 19.8 Mio. €/100.000 cases with structured algorithmic approach) \"]","page_idx":"2","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[633,307,838,439]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Formation of a learning community The negative appendectomy rate (NAR) and the rate of CT- scans in the diagnostic pathway of acute appendicitis is too high ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,472,489,525]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Fig. 1 Learning circle of the DIALAPP study. Starting with the formation of a learning community in order to minimize the rate of negative appendectomies and CT scans in the diagnosis of acute appendicitis. After the analysis of our institutional retrospective data of ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,472,915,524]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Liese et al. (data to knowledge), a diagnostic pathway was implemented and prospectively evaluated as part of the DIALAPP study (knowledge to practice). As a result, we found a reduction in the NAR and CT rate (practice to data) (NAR, negative appendectomy rate) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,572,485,837]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"measures, analgesia) but no antibiotic treatment. The clinical course was assessed within $24\\mathrm{h}$ after admission by a board-certified or consultant surgeon. Patients developing clinically suspected AA were advised to undergo appendectomy. The improvement of complaints resulted in discharge and outpatient follow-up. All patients with persistent abdominal complaints during the observation period received a CT or MRI (pregnant patients). Patients with a positive CT scan were indicated to undergo appendectomy. Those with a negative CT were discharged. Patients with alternative diagnoses on ultrasound, CT, or at the gynecological consultation received appropriate non-study specific treatment. During the application of the pathway between November 2015 and August 2017, patients were consented for prospective data collection. A telephone follow-up of all patients was undertaken after 30 days and 6 months. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,840,485,903]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The definitive diagnosis of appendicitis was determined by the final pathological report of the resected specimens. Histopathological criteria for acute appendicitis were granulocytic infiltration or ulceration of the lumen or all wall layers, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,573,914,602]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"as well as the fatty tissue. Another criterion was the presence of an intramural abscess or necrosis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,605,914,651]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The appendicitis was classified as perforated based on intraoperative findings or pathological examination of the resected organs. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,651,914,698]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A negative appendectomy was characterized by the removal of an appendix without signs of acute inflammation in the pathological examination. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,700,915,903]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"All CT scans covered the entire abdomen and pelvis, ranging from above the diaphragm to the inguinal region. Acquisition protocols were either a standard-dose abdominal and pelvic CT with primary intravenously contrast or a non-contrasted low-dose CT. All CT scans were acquired on a third-generation dual-source CT or a 64-slice multi-detector CT (Somatom Force, Somatom Definition AS+, Siemens). All scans were interpreted by two independent radiology readers and signed by senior radiology residents. CT studies were classified in a binary fashion as positive or negative for the presence of appendicitis. Patients not treated according to the algorithm and all cases with incomplete study sheets were excluded from the analysis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,39,211,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Langenbecks Arch Surg ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[838,927,912,944]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[82,70,484,132]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The primary endpoint of the study was the NAR. Secondary endpoints included accuracy of the diagnostic tools, perforation rate, duration of diagnosis, complication rate, and length of hospital stay. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,150,233,165]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Economic modeling ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[82,181,485,416]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Liese et al. [18] described the cost of appendectomies in relation to undergoing surgery with or without CT scans or avoiding surgery utilizing a CT scan. We transferred their model to our setting and calculated the costs with the same pricing to create comparability. Pricing for the treatment of appendicitis indeed did not change in Germany during the mentioned time. The costs were calculated from the ratio of patients undergoing surgery with or without CT imaging and patients having no surgery due to the utilization of a CT. Moreover, we included a model with all patients (additional those that received no CT scan and no surgery due to the algorithm) and extrapolated the numbers hypothetically obtained from the data in the publication by Liese et al. [18] to receive a narrowing estimation of the overall potential in saving expenses and costs for 100,000 cases of suspected AA. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,432,184,448]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data analysis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[82,464,485,589]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Statistical analysis was performed using BiAS (Version 11.08) and Microsoft Excel 200x (Microsoft Corporation). Values are reported as median with range or proportions. Categorical variables were compared by means of the chi-squared test or Fisher's exact test and independent variables using the Mann-Whitney $U$ -test or the Shapiro-Wilk test as appropriate. A $p$ value of $< 0.05$ was considered to be statistically significant. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,621,147,636]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[84,653,460,668]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Patient selection, decision tree, and drop-out rate ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[82,684,485,903]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A total of 266 patients were evaluated with suspected acute appendicitis during the study period. Of these, 83 patients were excluded due to severe protocol violation. Most common reasons for exclusion were missing gynecological consultation $(n = 37)$ , missing ultrasound $(n = 12)$ , missing differential blood count $(n = 10)$ or discharge with an Alvarado score of $>4$ $(n = 7)$ , observation with Alvarado score of $< 4$ $(n = 5)$ , and a CT imaging in patients with an Alvarado score of $< 5$ $(n = 6)$ . In total, 183 patients were included in the study and final analysis. Figure 2 shows a flowchart of the implementation of the standardized diagnostic pathway. Sixty-nine patients $(37.7\\%)$ underwent appendectomy based on clinical features $(n = 27; 39.1\\%)$ , the evidence of appendicitis on ultrasound $(n = 25; 36.2\\%)$ , or on a CT scan $(n = 17; 24.6\\%)$ . In 55 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,70,914,289]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"patients, the Alvarado score (5-8) and ultrasound were inconclusive. These patients were clinically observed. Of those, 21 patients recovered without operation and were discharged. Thirty-six patients with persisting abdominal complaints underwent additive CT imaging. Hereof, 17 CT scans showed signs of appendicitis, and all underwent surgery, and the diagnosis of appendicitis was confirmed in the pathology workup. In 19 patients, the CT was negative for appendicitis, and 9 CT scans determined a different diagnosis. In total, 87 patients $(47.5\\%)$ could be discharged with resolved abdominal problems, of whom only 10 $(11.4\\%)$ of the discharged and only $19.7\\%$ of all study patients) received a CT. In 27 patients, a different diagnosis than appendicitis could be determined following the diagnostic pathway. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,307,914,337]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Patient characteristics with a proven appendicitis and with no proof for appendicitis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,354,914,527]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In total, 183 were analyzed as defined per protocol. Patients with appendicitis were significantly older than patients without appendicitis (32, range 18-71 vs. 28, range 18-71; $p = 0.0004$ ). Significantly more female patients did not have appendicitis (no 69 vs. yes 22), whereas more male patients were diagnosed with appendicitis (no 49 vs. yes 43) ( $p = 0.0002$ ). The clinical parameters of white blood cell count, C-reactive protein and the median Alvarado score were significantly higher for all items in patients with AA ( $p < 0.001$ ). The hospital stay was significantly longer in patients with appendicitis (4 days vs. 3 days; $p < 0.001$ ). Data are displayed in Table 2. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,543,833,574]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Performance values of the Alvarado score, ultrasound, and the diagnostic algorithm ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,591,914,841]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The ROC (receiver operating characteristic) analysis identified a cutoff Alvarado score of 5.5 to identify patients at a high risk for AA and yielded a sensitivity of $92.4\\%$ and a specificity of $59.1\\%$ . The area under the ROC curve showed good diagnostic capacity (0.914; Fig. 3). Setting the cutoff value of the Alvarado score to $>7$ as recommended in the diagnostic algorithm, the sensitivity and specificity are $73.9\\%$ and $88.1\\%$ , respectively. The ultrasound displayed a moderate sensitivity of $58.2\\%$ and high specificity of $97.3\\%$ . In contrast, CT was equally high concerning sensitivity and specificity with $100\\%$ respectively. In summary, the whole diagnostic algorithm, consisting specifically of (1) Alvarado score, (2) gynecological consultation for females, (3) ultrasound, and (4) selective CT imaging showed a sensitivity of $100\\%$ and a specificity of $96.6\\%$ for the detection of AA. Overall performance values for the Alvarado score, ultrasound, CT, and the entire diagnostic algorithm are shown in Table 3. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,844,914,903]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In 65 of 69 patients undergoing appendectomy, an acute appendicitis could be confirmed in the histopathological examination of the resected organs. This accounts for a NAR of $5.8\\%$ , and female patients had a NAR of $4.4\\%$ , and male patients, of ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[784,40,915,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Langenbecks Arch Surg ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[84,927,154,943]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,64,917,639]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 2 Flowchart and management course of study cohort. Implementation of the proposed diagnostic algorithm in 183 patients with suspected appendicitis (AA, acute appendicitis; US, ultrasound) \"]","image_footnote":"[]","img_path":"images/0172/af5e7026a5559a039a49be2145f610ba0b9b59f88ab8947c80605351b7bb1115.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[78,684,487,891]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$6.5\\%$ . In 17 patients $(24.6\\%)$ , a perforated appendicitis was found. Table 4 shows the characteristics of patients with acute appendicitis in comparison with patients with perforated appendicitis. Patients with a perforated appendicitis were older and more often male. There was no significant difference between both groups concerning laboratory parameters, the Alvarado score, or the rate of CT-scans. The time from admission to operation was longer in patients with uncomplicated appendicitis (424 min vs. 324 min), without reaching statistical significance. Fifteen patients $(25.4\\%)$ who were operated within $12\\mathrm{h}$ after admission showed a perforation in comparison with 2 patients $(20.0\\%)$ being operated after $12\\mathrm{h}$ , indicating that the time from admission to operation had no significant ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,684,915,746]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"influence on perforation rate. Nevertheless, performing a preoperative CT scan resulted in a significantly delayed operation (599 min in patients with preoperative CT vs. 340 min in patients without CT; $p = 0.005$ ). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,748,915,889]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Patients with perforated appendicitis showed a longer hospital stay in comparison with patients with uncomplicated appendicitis. However, in our patient cohort, we could not detect a higher morbidity due to perforated appendicitis (Table 4). Sixty-eight patients underwent laparoscopic appendectomy. In one case, a conversion to open surgery was necessary $(1.5\\%)$ . One pregnant patient underwent open appendectomy simultaneously with cesarean section. Negative explorations did not occur in our cohort. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,39,211,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Langenbecks Arch Surg ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[838,927,912,945]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[78,84,915,498]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0305/1229cadfd3b679076b2b34203d4d54bf881bd9a8a7fc51f18447d6c407dd4627.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td></td><td>All (n = 183)</td><td>Appendicitis (n = 65)</td><td>No appendicitis (n = 118)</td><td>p value</td></tr><tr><td>Age (years)</td><td></td><td></td><td></td><td>0.0004</td></tr><tr><td>Median</td><td>30</td><td>32</td><td>28</td><td></td></tr><tr><td>Range</td><td>18–71</td><td>18–61</td><td>18–71</td><td></td></tr><tr><td>Sex</td><td></td><td></td><td></td><td>0.0002</td></tr><tr><td>Female</td><td>91 (49.7)</td><td>22 (33.8)</td><td>69 (58.5)</td><td></td></tr><tr><td>Male</td><td>92 (50.3)</td><td>43 (66.2)</td><td>49 (41.5)</td><td></td></tr><tr><td>BMI (kg/m2)</td><td></td><td></td><td></td><td>0.0018</td></tr><tr><td>Median</td><td>24.1</td><td>24.7</td><td>22.6</td><td></td></tr><tr><td>Range</td><td>16.8–41.2</td><td>17.4–41.2</td><td>16.8–30.1</td><td></td></tr><tr><td>Leukocytes (4.2–10/nl)</td><td></td><td></td><td></td><td><0.000001</td></tr><tr><td>Median</td><td>10.4</td><td>14.48</td><td>8.89</td><td></td></tr><tr><td>Range</td><td>2.83–24.99</td><td>2.83–24.99</td><td>2.92–23.01</td><td></td></tr><tr><td>C-reactive protein (<0.5 mg/dl)</td><td></td><td></td><td></td><td>0.000011</td></tr><tr><td>Median</td><td>0.5</td><td>1.73</td><td>0.28</td><td></td></tr><tr><td>Range</td><td>0.01–23.66</td><td>0.02–23.66</td><td>0.01–20.57</td><td></td></tr><tr><td>Alvarado score</td><td></td><td></td><td></td><td><0.000001</td></tr><tr><td>Median</td><td>5</td><td>7</td><td>4</td><td></td></tr><tr><td>Range</td><td>0–10</td><td>4–10</td><td>0–8</td><td></td></tr><tr><td>CT scan performed</td><td>36 (19.7)</td><td>17 (26.2)</td><td>19 (16.1)</td><td>0.1</td></tr><tr><td>Negative appendectomy</td><td>--</td><td>--</td><td>4 (5.8)</td><td>--</td></tr><tr><td>Length of hospital stay (days)</td><td></td><td></td><td></td><td>0.0001</td></tr><tr><td>Median</td><td>3</td><td>4</td><td>3</td><td></td></tr><tr><td>Range</td><td>1–12</td><td>3–12</td><td>1–9</td><td></td></tr></table>","table_caption":"[\"Table 2 Demographic and clinical characteristics of patients with proven appendicitis in comparison with patients without appendicitis \"]","table_footnote":"[\"Values are number of cases $(\\\\%)$ , unless otherwise indicated. For analysis of categorical variables, chi-squared test was used. Fisher's exact test was used, if appropriate. Independent variables were compared with the Mann-Whitney $U$ test or the Shapiro-Wilk test as appropriate BMI body mass index \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[78,560,485,624]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The histopathological examination of all of the four patients with negative appendectomy showed an abnormal result, including neurogenic appendicopathy $(n = 2)$ , adenoma of appendix $(n = 1)$ , and transmural fibrosis of appendix $(n = 1)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,624,485,702]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Eleven patients had postoperative complications, of whom 2 had to undergo re-do surgery. One of these patients initially received a negative appendectomy and had to be reoperated due to bowel obstruction. One patient developed an intraabdominal collection and was treated with percutaneous ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,560,914,592]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"drainage. Four patients developed surgical site infection (Table 4). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,621,850,637]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Midterm follow-up at 30 days and 6 months ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,653,915,702]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A total of $68.9\\%$ and $65.6\\%$ of all patients could be reached by telephone follow-up after 30 days and 6 months, respectively. No missed appendicitis occurred among the non-operated ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,741,915,887]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0159/0fab3fcfeaf0fdf22e9c2ab024d01056bf586057d35afc51b931077f151d818d.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td rowspan=\"2\">Measurement</td><td colspan=\"2\">Alvarado-score > 7 (n = 183)</td><td colspan=\"2\">Ultrasonography (n = 181)</td><td colspan=\"2\">CT scan (n = 36)</td><td colspan=\"2\">Diagnostic algorithm (n = 183)</td></tr><tr><td>%</td><td>95% CI</td><td>%</td><td>95% CI</td><td>%</td><td>95% CI</td><td>%</td><td>95% CI</td></tr><tr><td>Sensitivity</td><td>73.9</td><td>61–84</td><td>58.2</td><td>35–62</td><td>100</td><td>81–100</td><td>100</td><td>95–100</td></tr><tr><td>Specificity</td><td>88.1</td><td>81–93</td><td>97.3</td><td>92–99</td><td>100</td><td>82–100</td><td>96.6</td><td>92–99</td></tr><tr><td>PPV</td><td>77.4</td><td>65–87</td><td>90.0</td><td>73–98</td><td>100</td><td>81–100</td><td>94.2</td><td>86–98</td></tr><tr><td>NPV</td><td>85.9</td><td>78–92</td><td>78.9</td><td>71–85</td><td>100</td><td>82–100</td><td>100</td><td>97–100</td></tr><tr><td>Accuracy</td><td>82.3</td><td>76–87</td><td>80.9</td><td>74–87</td><td>100</td><td>92–100</td><td>97.8</td><td>95–99</td></tr></table>","table_caption":"[\"Table 3 Overall performance values for Alvarado score, ultrasound, CT, and diagnostic algorithm \"]","table_footnote":"[\"PPV positive predictive value, NPV negative predictive value \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[784,39,915,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Langenbecks Arch Surg ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[80,927,156,945]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[386,65,915,313]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.3 ROC curve. ROC (receiver operating characteristic) curve of sensitivity and specificity of the Alvarado score for diagnosis of acute appendicitis \"]","image_footnote":"[]","img_path":"images/0688/3f307b13a34726c238e73468be436b1ff01ab5f1461e72328fb3fa460e714e52.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[78,337,489,370]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"patients during the follow-up. Five patients after appendectomy were readmitted due to postoperative complications, of ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,337,915,369]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"whom one patient had to undergo re-do surgery due to intestinal obstruction. Other reasons for hospital readmission were ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,408,917,856]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0465/2857a563a384a52ac222c101c898580737ad1af44dbb747a0a61977a4645d2da.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":"<table><tr><td></td><td>All (n = 65)</td><td>No perforation (n = 48)</td><td>Perforation (n = 17)</td><td>p value</td></tr><tr><td>Age (years)</td><td></td><td></td><td></td><td>0.05</td></tr><tr><td>Median</td><td>32</td><td>32</td><td>34</td><td></td></tr><tr><td>Range</td><td>18–61</td><td>18–61</td><td>22–59</td><td></td></tr><tr><td>Sex</td><td></td><td></td><td></td><td>0.46</td></tr><tr><td>Female</td><td>22 (33.8)</td><td>15 (31.3)</td><td>7 (41.1)</td><td></td></tr><tr><td>Male</td><td>43 (66.2)</td><td>33 (68.7)</td><td>10 (58.9)</td><td></td></tr><tr><td>Leukocytes (4.2–10/ml)</td><td></td><td></td><td></td><td>0.66</td></tr><tr><td>Median</td><td>14.48</td><td>14.83</td><td>13.79</td><td></td></tr><tr><td>Range</td><td>2.83–24.99</td><td>2.83–24.37</td><td>3.2–24.99</td><td></td></tr><tr><td>C-reactive protein (<0.5 mg/dl)</td><td></td><td></td><td></td><td>0.08</td></tr><tr><td>Median</td><td>1.73</td><td>1.15</td><td>3.5</td><td></td></tr><tr><td>Range</td><td>0.02–23.66</td><td>0.02–23.66</td><td>0.06–15.4</td><td></td></tr><tr><td>Alvarado score</td><td></td><td></td><td></td><td>0.92</td></tr><tr><td>Median</td><td>7</td><td>7</td><td>7</td><td></td></tr><tr><td>Range</td><td>4–10</td><td>4–10</td><td>6–10</td><td></td></tr><tr><td>CT scan performed</td><td>17 (26.2)</td><td>12 (25.0)</td><td>5 (29.4)</td><td>0.41</td></tr><tr><td>Time to operation (min)</td><td></td><td></td><td></td><td>0.54</td></tr><tr><td>Median</td><td>404</td><td>424</td><td>357</td><td></td></tr><tr><td>Range</td><td>141–5660</td><td>141–1559</td><td>146–5660</td><td></td></tr><tr><td>Length of hospital stay (days)</td><td></td><td></td><td></td><td>0.004</td></tr><tr><td>Median</td><td>4</td><td>3</td><td>4</td><td></td></tr><tr><td>Range</td><td>3–12</td><td>3–7</td><td>3–12</td><td></td></tr><tr><td>Postoperative complications</td><td>10 (15.4)</td><td>7 (14.6)</td><td>3 (17.6)</td><td>0.55</td></tr><tr><td>Dindo-Clavien I-II</td><td>8</td><td>6</td><td>2</td><td></td></tr><tr><td>Dindo-Clavien III</td><td>2</td><td>1</td><td>1</td><td></td></tr><tr><td>Dindo-Clavien IV-V</td><td>0</td><td>0</td><td>0</td><td></td></tr></table>","table_caption":"[\"Table 4 Comparison of patients with uncomplicated and perforated appendicitis \"]","table_footnote":"[\"Values are number of cases $(\\\\%)$ , unless otherwise indicated. For analysis of categorical variables, chi-squared test was used. Fisher's exact test was used, if appropriate. Independent variables were compared with the Mann-Whitney $U$ test or the Shapiro-Wilk test as appropriate BMI body mass index \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[82,39,211,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Langenbecks Arch Surg ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[838,927,914,946]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[78,70,487,102]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"an intraabdominal abscess, a gastrointestinal motility disorder, and a myocardial infarction. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,132,480,165]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Reduction of the costs by utilizing the new DIALAPP algorithm ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[78,181,487,497]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The patients were categorized into 4 groups of costs: 1: no CT scan/surgery (1317 €), 2: CT scan/surgery (1434 €), 3: CT scan/no surgery (675 €), and 4: no CT scan/no surgery (558 € in hospital, 250 € in ambulatory setting). The groups were distributed by $52 / 59\\%$ for group 1, $17 / 19\\%$ for group 2, and $19 / 22\\%$ for group 3, resulting in 125.9 million € per 100,000 cases in the Liese et al. publication (historical patient cohort of our institution) and 119.2 million € for the present patient cohort. This accounted for a saving of 6.7 million € per 100,000 suspicious cases for AA. The extrapolated model included group 4 which was missing in the publication by Liese et al. We used the assumption that the reduction in NAR by $5\\%$ predominantly was observed in the no CT/surgery group and extrapolated the corresponding numbers accordingly: 34/ $28.4\\%$ for group 1, $12.5 / 9.2\\%$ for group 2, $5.9 / 10.3\\%$ for group 3, and 10 (ambulatory) + 37.6 (in hospital)/ $10 + 41.9\\%$ for group 4, resulting in 93.4 million € vs. 73.6 million € and a theoretic saving of 19.8 million € per 100,000 cases when applying all 4 categories. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,69,608,86]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Discussion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,102,917,497]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The prospective diagnostic pathway of diagnosing acute appendicitis combining a clinical risk scoring (Alvarado score), routine ultrasound, highly selective use of CT imaging, and clinical re-evaluation showed a high accuracy with a sensitivity and specificity of $100\\%$ and $96.6\\%$ , respectively. The implementation of the algorithm resulted in substantial improvements in surgical diagnostic accuracy when compared with our previous institutional data [18]. As shown in Table 5, the implementation led to a reduction in the rate of unnecessary operations (the NAR was reduced to $5.8\\%$ ) and an optimization of performed CT imaging (only $19\\%$ of all patients) and accelerated the access to adequate surgical treatment (mean time to operation, reduction from 684.2 to $555.6\\mathrm{min}$ ), which was considerably better than the former published experience by our group [18]. In the presented patient cohort, only four negative appendectomies occurred. Ultimately, in all four cases, histological results showed a pathological finding of the appendix, including neurogenic appendicopathy. Patients who had low clinical suspicion for appendicitis and negative ultrasound were safely discharged from the hospital, which was confirmed during the follow-up period, as we did not detect a missed appendicitis. Thus, the most important finding of the prospective single-armed interventional trial was the improvement in three surrogates of treatment quality for acute appendicitis derived from a first ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[292,525,919,875]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0009/2bc6e7e42ded6397b5196c936a18fcbfa8857bea617ead712cd5a39660a32393.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":"<table><tr><td></td><td>Pre-group (n = 367)</td><td>Pathway group (n = 183)</td></tr><tr><td>Age (years)</td><td></td><td></td></tr><tr><td>Mean</td><td>37.69</td><td>31.8</td></tr><tr><td>Range</td><td>15–91</td><td>18–71</td></tr><tr><td>Female gender (%)</td><td>158 (43.1)</td><td>91 (49.7)</td></tr><tr><td>Body mass index (kg/m2)</td><td></td><td></td></tr><tr><td>Mean</td><td>24.9</td><td>24.4</td></tr><tr><td>Range</td><td>16.3–63.8</td><td>16.8–41.2</td></tr><tr><td>Preoperative CT (%)</td><td>129/367 (35.1)</td><td>36/183 (19.7)</td></tr><tr><td>Negative appendectomy rate (%)</td><td>33/326 (10.1)</td><td>4/69 (5.8)</td></tr><tr><td>Male</td><td>10/187 (5.3%)</td><td>3/46 (6.5%)</td></tr><tr><td>Female</td><td>23/139 (16.5%)</td><td>1/23 (4.4%)</td></tr><tr><td>Appendiceal perforation rate (%)</td><td>48/293 (16.4)</td><td>17/65 (26.1)</td></tr><tr><td>Time to operation (min)</td><td></td><td></td></tr><tr><td>Mean</td><td>684.2</td><td>555.6</td></tr><tr><td>Range</td><td>52–100,004</td><td>141–5660</td></tr></table>","table_caption":"[\"Table 5 Patient demographics and clinical outcome among patients in the pre-group in comparison to the pathway group \"]","table_footnote":"[\"Pre-group, historical, retrospective patient cohort of our institution before application of the diagnostic pathway (published by Liese et al. [18]); pathway group, patient cohort during application of the diagnostic pathway \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[784,39,915,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Langenbecks Arch Surg ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[80,927,159,945]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[82,70,485,101]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"learning circle and retrospective analysis in a learning health system (Fig. 1) [18]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,102,485,510]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A number of studies describing a pathway for diagnosing patients with suspected appendicitis have been published. Only few of them have prospectively evaluated their recommended algorithm [14, 16, 17, 19]. In these studies, the implementation of a diagnostic pathway also resulted in a low rate of negative appendectomies of less than $10\\%$ . Nevertheless, the low NAR could only be achieved by a widespread use of CT scans in patients presenting with suspected appendicitis [16]. For example, Antevil [17] and co-authors observed a NAR of $4\\%$ with a simultaneous frequency of CT of $87\\%$ , probably due to a lack of clinical risk stratification before imaging. Similarly, other studies have demonstrated a decrease of NAR by an increased use of preoperative CT imaging [20-22]. Taking into account the radiation exposure, contrast-related complications, and resource consumption related to CT, some studies have implemented diagnostic pathways including clinical risk stratification before imaging in an attempt to reduce the rate of CT scans. Thus, in the STRAPPSCORE study [14], the introduction of a clinical score-based risk stratification algorithm in patients with suspicion of appendicitis resulted in less imaging and fewer admissions. But on the other hand, the algorithm did not show an effect on the proportion of negative appendectomies. Relating the number of negative appendectomies to all operated patients, the NAR was about $11\\%$ , with a maximum of $17.9\\%$ in patients with low risk for appendicitis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,512,485,668]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Comparable with the current study, Toorenvliet and colleagues [19] demonstrated a NAR of $3.3\\%$ with a minimal use of CT in only $17.9\\%$ of all patients by the implementation of a diagnostic pathway including risk stratification and regular ultrasound. However, it must be noted that in this study, the patient risk stratification was undertaken by a consultant and not according to an objective clinical scoring system. In addition, both children and adults were investigated in the study, which certainly affects the data due to the restrained use of CT imaging in children. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,670,485,903]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The results of additionally required and indicated imaging in accordance with the algorithm in the DIALAPP study were excellent. Most strikingly, CT imaging had a $100\\%$ accuracy in the diagnosis of appendicitis (no false positive and no false negative results). This corresponds to the recent literature [9, 23, 24]. Here, the use of low-dose CT protocols can reduce the radiation exposure with a comparable diagnostic accuracy with standard CT protocols [25]. These protocols could be a cost-efficient alternative to inpatient observation in patients with intermediate probability for AA. Nevertheless, not all emergency care units have 24-h availability of CT, and nonselective CT imaging is known to show lower sensitivity, mainly in patients with low or high clinical suspicion of AA [8, 26]. The results of this study indicate that most patients can be classified either in the high or the low probability group ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,70,914,353]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"following the diagnostic algorithm, and thus, the need for diagnostic imaging can be significantly reduced. Moreover, the data of accuracy of abdominal ultrasound demonstrate that CT imaging is not required in all patients to detect the correct diagnosis. The diagnostic accuracy of ultrasound here was comparable with the data from literature with a sensitivity and specificity of $58\\%$ and $97\\%$ , respectively [26, 27]. The rather low sensitivity is likely explained by the fact that members of the surgical team, as it is standard of care in Germany, performed the ultrasound and not a certified ultrasound expert. With regard to these results, ultrasound and CT should be considered as complementary techniques. Ultrasound should be the preferred primary imaging modality and enables to rule in patients with risk for appendicitis. CT imaging is needed only in cases with equivocal clinical or ultrasound examination. This means less radiation exposure for the patient and cost saving for the hospital as currently shown in a meta-analysis from the USA [28]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,355,914,651]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The literature consistently reports at least twice the NAR in women than in men [4, 20, 29-32]. Only Antevil et al. [17] achieved an equally high NAR in women and men, but performing CT scan in every female patient. The primary aim of a new diagnostic pathway should therefore be to decrease the NAR in women of childbearing potential and protect them from unnecessary radiation exposure. In the current study, by the introduction of a standardized diagnostic workflow for patients with right-sided lower abdominal quadrant pain, a relevant reduction in NAR and, here especially in women (reduction of NAR from 16.5 to $4.4\\%$ ; see Table 5) with minimal use of CT imaging was achieved. Only $20.8\\%$ of all women received a CT scan, and $18.5\\%$ , of men. This improvement can certainly also be explained by the routine gynecological consultation of all women of childbearing age as established in our diagnostic pathway. However, a routine gynecological examination is sometimes not practicable and may lead to considerable waiting times for the patient. As a result, also in our patient cohort, 37 patients were excluded due to a lack of consultation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,654,914,903]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"One of the major concerns about introducing a diagnostic pathway is an increased perforation rate due to a delay in treatment [33, 34]. At the same time, it has been shown that perforated appendicitis rates are not influenced by in-hospital delay and have not significantly changed with the increasing use of preoperative CT imaging [35, 36]. Andersson et al. [14] showed that reassessment after in-hospital observation and selective imaging in patients with an equivocal diagnosis is not associated with an increased risk for perforation and thus safe and efficient. The perforation rate in our study was $24.6\\%$ , similar to previously reported rates [19]. Neither the number of CT scans performed nor the time from admission to surgery significantly differed between patients with uncomplicated or perforated appendicitis. It is also noteworthy that the establishment of a clinical pathway accelerated the time from the first contact and interview to diagnosis in the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,40,210,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Langenbecks Arch Surg ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[840,927,912,943]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[82,70,484,164]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"DIALAPP study. As mentioned before, the time from admission to operation has been reduced in comparison with our previous institutional data [18]. This compares favorably with the results reported in the literature that the quality survey should focus on the accuracy of diagnosis rather than on its potential delay in therapeutic intervention. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,165,485,291]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A further aspect of quality improvement is the optimization of healthcare-related costs and resource utilization. Our study design does not allow a reliable statement on reduction of costs, but it allows an assessment of the potential savings. Thus, the reduction of NAR and CT scans by half at our institution has the potential for a saving of 6.7 million € per 100,000 suspicious cases for AA. Consistent implementation of the algorithm could even save up to 19.8 million € per 100,000 cases. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,292,485,384]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Similar previous studies have demonstrated that a minimization of negative appendectomies can provide financial and resource savings [37]. Scott et al. [38] showed that risk stratification and discharge of patients with low risk for appendicitis resulted in a significant reduction in admissions, preserving the availability of beds, diagnostic imaging, and financial resources. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,386,485,605]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Taken together, the simple diagnostic algorithm evaluated here showed high accuracy and the potential for an easy implementation into daily practice. The risk stratification based on objective scoring and a well-structured algorithm facilitated decision-making, particularly for the less experienced frontline surgeon who is often responsible for the initial assessment of patients. The pragmatic setup of our study represents a common clinical setting and thus increases generalizability of the study findings. We studied an unselected population of patients with acute right lower quadrant abdominal pain with a realistic sample prevalence of appendicitis. The application of the algorithm by all members of the surgical team reflects daily clinical applicability and allows scalability to other hospitals and settings. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,607,485,903]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"There was no missed appendicitis in our patient cohort, taking into account the relatively high rate of lost to follow-up. Some patients who were discharged with a very low probability of having appendicitis and who were unresponsive to telephone calls may have been readmitted and operated at another hospital. Thus, we had no absolute confirmation of the absence of AA in the non-operated patients. This limitation is also a problem and has been reported as potential bias in other studies. A further limitation of this study is that it represents only a single center's experience. Moreover, the number of exclusions was higher than expected, which increased the risk for statistical errors of the primary outcome measure \"negative appendectomies.\" This high rate of exclusion may also have led to a selection bias by the inclusion of more severe cases indicated by the high rate of perforated appendicitis and the exclusion of less severe cases indicated by a negative appendectomy rate of $15.6\\%$ in the group of excluded patients due to severe protocol violation. This high selection may have influenced the accuracy of the study. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,70,914,306]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, our institution had not implemented antibiotic treatment for cases of imaging-confirmed uncomplicated appendicitis. This might have minimized the group of early appendicitis and unnecessary appendectomies which would otherwise be resolved by antimicrobial therapy alone. Nevertheless, antibiotic therapy alone for acute appendicitis shows a treatment effectiveness of only $72.6\\%$ , resulting in an appendectomy in $26.5\\%$ of patients initially treated conservatively as shown by the meta-analysis of Harnoss et al. [39]. Moreover, the incidences of complicated appendicitis and the hospital stay are significantly increased in the antibiotic treatment group in comparison with the surgical treatment group [39]. Thus, although antibiotics may prevent some patients from appendectomies, surgery still represents the gold standard of care for acute appendicitis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,308,912,401]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The presented results support the implementation of a pathway in the diagnosis of AA. Patients with an uncertain clinical diagnosis and ultrasound result for appendicitis can safely be re-evaluated during a hospital admission. This risk-adjusted approach has the potential to reduce the number of unnecessary operation, simultaneously minimizing CT use. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,448,610,463]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conclusion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,481,912,574]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Implementation of a diagnostic algorithm combining clinical risk score, ultrasound, gynecological consultation, and selective CT imaging after re-evaluation resulted in high accuracy for the diagnosis of acute appendicitis. A low negative appendectomy rate can be achieved without increasing the risk for perforation from a delay in treatment. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,589,914,741]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Authors' contributions Patrizia Malkomes contributed to the acquisition and analysis of the data, as well as drafting of the manuscript. Franziska Edmaier was a major contributor in data acquisition and analysis. Juliane Liese and Alexander Reinisch-Liese were major contributors in the study conception and design as well as acquisition and analysis of the data. Hanan El Youzouri and Teresa Schreckenbach contributed to the acquisition and analysis of the clinical data and critically reviewed the manuscript. Andreas Bucher provided radiological data analysis and expertise. Wolf Otto Bechstein was a major contributor to the study conception and critically reviewed the manuscript. Andreas Schnitzbauer was a major contributor in interpreting the data and drafting the manuscript. All authors read and approved the final manuscript. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,758,912,770]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Funding Open Access funding enabled and organized by Projekt DEAL. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,787,912,824]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data availability The datasets generated during the current study are not publicly available due to the terms agreed with the local ethics committee. They are available from the corresponding author on reasonable request. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,841,771,856]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Compliance with ethical standards ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,872,915,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conflict of interest The authors declare that they have no conflict of interest. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[784,40,915,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Langenbecks Arch Surg ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[84,927,154,943]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,69,487,121]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Ethics approval This study was performed in line with the Declaration of Helsinki and local laws and regulations. The study was approved by the institutional ethics review board (IRB-Number: 268/15) and registered at clinicaltrials.gov (NCT02627781). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,135,485,162]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Consent to participate Written informed consent was obtained from all patients prior to inclusion in the study. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,172,485,324]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,382,181,398]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,413,487,903]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1. 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A 10-year study. Radiology 254(2):460-468. https://doi.org/10.1148/radiol.09082298 \",\"22. Naoum JJ, Mileski WJ, Daller JA, Gomez GA, Gore DC, Kimbrough TD, Ko TC, Sanford AP, Wolf SE (2002) The use of abdominal computed tomography scan decreases the frequency of misdiagnosis in cases of suspected appendicitis. Am J Surg 184(6): 587-589; discussion 589-90. https://doi.org/10.1016/s0002-9610(02)01086-3 \",\"23. Park JS, Jeong JH, Lee JI, Lee JH, Park JK, Moon HJ (2013) Accuracies of diagnostic methods for acute appendicitis. Am Surg 79(1):101-106 \",\"24. Pickhardt PJ, Lawrence EM, Pooler BD, Bruce RJ (2011) Diagnostic performance of multidetector computed tomography for suspected acute appendicitis. Ann Intern Med 154(12):789- \"]","page_idx":"10","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[82,39,211,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Langenbecks Arch Surg ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[838,927,912,944]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,69,487,551]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"796, W-291. https://doi.org/10.7326/0003-4819-154-12-201106210-00006 \",\"25. Sippola S, Virtanen J, Tammilehto V, Gronroos J, Hurme S, Niinivita H, Lietzen E, Salminen P (2020) The accuracy of low-dose computed tomography protocol in patients with suspected acute appendicitis: the OPTICAP study. Ann Surg 271(2):331-338. https://doi.org/10.1097/SLA.0000000000002976 \",\"26. van Randen A, Bipat S, Zwinderman AH, Ubbink DT, Stoker J, Boermeester MA (2008) Acute appendicitis: meta-analysis of diagnostic performance of CT and graded compression US related to prevalence of disease. Radiology 249(1):97-106. https://doi.org/10.1148/radiol.2483071652 \",\"27. Doria AS, Moineddin R, Kellenberger CJ, Epelman M, Beyene J, Schuh S, Babyn PS, Dick PT (2006) US or CT for diagnosis of appendicitis in children and adults? A meta-analysis. Radiology 241(1):83-94. https://doi.org/10.1148/radiol.2411050913 \",\"28. Parker L, Nazarian LN, Gingold EL, Palit CD, Hoey CL, Frangos AJ (2014) Cost and radiation savings of partial substitution of ultrasound for CT in appendicitis evaluation: a national projection. AJR Am J Roentgenol 202(1):124-135. https://doi.org/10.2214/AJR.12.9642 \",\"29. Andersson RE, Hugander AP, Ghazi SH, Ravn H, Offenbartl SK, Nystrom PO et al (2000) Why does the clinical diagnosis fail in suspected appendicitis? Eur J Surg 166(10):796-802. https://doi.org/10.1080/110241500447434 \",\"30. Cuschieri J, Florence M, Flum DR, Jurkovich GJ, Lin P, Steele SR et al (2008) Negative appendectomy and imaging accuracy in the Washington State Surgical Care and Outcomes Assessment Program. Ann Surg 248(4):557-563. https://doi.org/10.1097/SLA.0b013e318187aeca \",\"31. Stein GY, Rath-Wolfson L, Zeidman A, Atar E, Marcus O, Joubran S, Ram E (2012) Sex differences in the epidemiology, seasonal variation, and trends in the management of patients with acute appendicitis. Langenbeck's Arch Surg 397(7):1087-1092. https://doi.org/10.1007/s00423-012-0958-0 \",\"32. Tzovaras G, Liakou P, Baloyiannis I, Spyridakis M, Mantzos F, Tepetes K, Athanassiou E, Hatzitheofilou C (2007) Laparoscopic appendectomy: differences between male and female patients with \"]","page_idx":"11","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[510,69,915,496]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"suspected acute appendicitis. World J Surg 31(2):409-413. https://doi.org/10.1007/s00268-006-0335-7 \",\"33. Lee CC, Golub R, Singer AJ, Cantu RJR, Levinson H (2007) Routine versus selective abdominal computed tomography scan in the evaluation of right lower quadrant pain: a randomized controlled trial. Acad Emerg Med 14(2):117-122. https://doi.org/10.1197/j.aem.2006.08.007 \",\"34. Lee SL, Walsh AJ, Ho HS (2001) Computed tomography and ultrasonography do not improve and may delay the diagnosis and treatment of acute appendicitis. Arch Surg 136(5):556-562. https://doi.org/10.1001/archsurg.136.5.556 \",\"35. Guss DA, Behling CA, Munassi D (2008) Impact of abdominal helical computed tomography on the rate of negative appendicitis. J Emerg Med 34(1):7-11. https://doi.org/10.1016/j.jemermed.2007.07.062 \",\"36. Menes TS, Aufses AHJR, Rojas M, Bickell NA (2006) Increased use of computed tomography does not harm patients with acute appendicitis. Am Surg 72(4):326-329 \",\"37. Flum DR, Koepsell T (2002) The clinical and economic correlates of misdiagnosed appendicitis: nationwide analysis. Arch Surg 137(7):799-804; discussion 804. https://doi.org/10.1001/archsurg.137.7.799 \",\"38. Scott AJ, Mason SE, Arunakirinathan M, Reissis Y, Kinross JM, Smith JJ (2015) Risk stratification by the Appendicitis Inflammatory Response score to guide decision-making in patients with suspected appendicitis. Br J Surg 102(5):563-572. https://doi.org/10.1002/bjs.9773 \",\"39. Harnoss JC, Zelienka I, Probst P, Grummich K, Müller-Lantzsch C, Harnoss JM, Ulrich A, Büchler MW, Diener MK (2017) Antibiotics versus surgical therapy for uncomplicated appendicitis: systematic review and meta-analysis of controlled trials (PROSPERO 2015: CRD42015016882). Ann Surg 265(5):889-900. https://doi.org/10.1097/SLA.0000000000002039 \"]","page_idx":"11","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[509,512,915,539]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[784,39,915,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Langenbecks Arch Surg ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[82,927,100,943]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"# ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[102,930,154,944]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"}],"string":"[\n {\n \"bbox\": \"[80,135,776,182]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"DIALAPP: a prospective validation of a new diagnostic algorithm for acute appendicitis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,200,862,232]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Patrizia Malkomes<sup>1</sup> $\\\\cdot$ Franziska Edmaier<sup>1</sup> $\\\\cdot$ Juliane Liese<sup>2</sup> $\\\\cdot$ Alexander Reinisch-Liese<sup>3</sup> $\\\\cdot$ Hanan El Youzouri<sup>1</sup> $\\\\cdot$ Teresa Schreckenbach<sup>1</sup> $\\\\cdot$ Andreas M. Bucher<sup>4</sup> $\\\\cdot$ Wolf Otto Bechstein<sup>1</sup> $\\\\cdot$ Andreas A. Schnitzbauer<sup>1</sup> \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,255,386,268]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received: 10 August 2020 / Accepted: 1 November 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,269,206,281]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"© The Author(s) 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,298,149,311]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,313,915,375]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Purpose The management of patients with suspected appendicitis remains a challenge in daily clinical practice, and the optimal management algorithm is still being debated. Negative appendectomy rates (NAR) continue to range between 10 and $15\\\\%$ . This prospective study evaluated the accuracy of a diagnostic pathway in acute appendicitis using clinical risk stratification (Alvarado score), routine ultrasonography, gynecology consult for females, and selected CT after clinical reassessment. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,375,915,421]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methods Patients presenting with suspected appendicitis between November 2015 and September 2017 from age 18 years and above were included. Decision-making followed a clear management pathway. Patients were followed up for 6 months after discharge. The hypothesis was that the algorithm can reduce the NAR to a value of under $10\\\\%$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,422,915,500]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results A total of 183 patients were included. In 65 of 69 appendectomies, acute appendicitis was confirmed by histopathology, corresponding to a NAR of $5.8\\\\%$ . Notably, all 4 NAR appendectomies had other pathologies of the appendix. The perforation rate was $24.6\\\\%$ . Only 36 patients $(19.7\\\\%)$ received a CT scan. The follow-up rate after 30 days achieved $69\\\\%$ , including no patients with missed appendicitis. The sensitivity and specificity of the diagnostic pathway was $100\\\\%$ and $96.6\\\\%$ , respectively. The potential saving in costs can be as much as 19.8 million €/100,000 cases presenting with the suspicion of appendicitis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,501,915,546]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conclusion The risk-stratified diagnostic algorithm yields a high diagnostic accuracy for patients with suspicion of appendicitis. Its implementation can safely reduce the NAR, simultaneously minimizing the use of CT scans and optimizing healthcare-related costs in the treatment of acute appendicitis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,546,608,562]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Trial registration ClinicalTrials.gov Identifier: NCT02627781 (December 2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,578,847,594]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords Acute appendicitis $\\\\cdot$ Diagnostic algorithm $\\\\cdot$ Risk-stratification $\\\\cdot$ Negative appendectomy rate $\\\\cdot$ Clinical trial \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,665,485,692]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Wolf Otto Bechstein and Andreas A. Schnitzbauer contributed equally to this work. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,708,267,736]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\boxtimes$ Patrizia Malkomes Patrizia.Malkomes@kgu.de \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,756,485,903]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"$^{1}$ Department of General, Visceral and Transplant Surgery, University Hospital Frankfurt, Goethe University, Theodor-Stern-Kai 7, 60590 Frankfurt am Main, Germany \\\",\\\"$^{2}$ Department of General, Abdominal, Thoracic and Transplant Surgery, University Hospital of Giessen, Giessen, Germany \\\",\\\"$^{3}$ Department of General, Visceral and Oncological Surgery, Wetzlar Clinic, Wetzlar, Germany \\\",\\\"$^{4}$ Department of Radiology, Institute for Diagnostic and Interventional Radiology, Goethe University Hospital Frankfurt, Frankfurt am Main, Germany \\\"]\",\n \"page_idx\": \"0\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[509,631,626,646]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,664,915,789]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"With an incidence of 120 per 100,000 inhabitants, appendicitis is one of the most common causes of acute abdomen in Germany. The lifetime prevalence for appendicitis is approximately $7\\\\%$ , making appendectomy one of the most frequently performed operations with 110,000 procedures per year [1, 2]. However, the diagnosis of acute appendicitis (AA) continues to be a challenge even for experienced surgeons resulting in a mean negative appendectomy rate (NAR) of 10 to $15\\\\%$ [3-5]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,791,915,901]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As negative appendectomies are associated with the potential of substantial morbidity and increased healthcare-related costs, they should be reduced to a minimum [6]. Several scoring systems and modern imaging modalities have been implemented in an attempt to increase the diagnostic accuracy as they have shown to reduce NAR. Studies from the USA could reduce the NAR to $3.2\\\\%$ by performing a computed tomography (CT) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,39,265,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Langenbeck's Archives of Surgery \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[80,53,321,65]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1007/s00423-020-02022-7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[90,79,223,93]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ORIGINAL ARTICLE \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,81,915,120]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Check for updates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[80,934,300,948]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Published online: 19 November 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[838,927,914,945]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[78,70,485,227]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"scan in each patient presenting with right-sided lower abdominal quadrant pain [7]. Nevertheless, non-selective imaging shows limited accuracy in subgroups with a low or high clinical probability of appendicitis, suggesting that improvements in diagnostic outcomes are dependent on the appropriate selective application of CT, and the integration of clinical findings with CT results [8, 9]. Moreover, several authors have criticized the widespread use of CT due to the negative impact of ionizing radiation exposure in this generally young patient population, raising concerns about cancer risk [10, 11]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,229,485,369]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In 1986, Alvarado et al. [12] devised a simple diagnostic score for the diagnosis of acute appendicitis based on the probability of clinical signs (tenderness in right lower quadrant, rebound pain, and elevated temperature $>37.5^{\\\\circ}\\\\mathrm{C}$ ), symptoms (pain migration to right lower quadrant, anorexia, and nausea/vomiting), and laboratory testing (leukocytosis and neutrophils $>75\\\\%$ ) for predicting appendicitis (Table 1). In subsequent studies, the Alvarado score has been validated showing a good sensitivity but a considerably low specificity of only $81\\\\%$ [13]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,370,487,575]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Several studies have determined the diagnostic accuracy of individual diagnostic procedures and their combinations in the diagnosis of AA [14-17]. However, there is little evidence for the application of diagnostic pathways, and none is in routine clinical use. In a study at our institution by Liese et al. [18], data from 367 patients with suspected appendicitis were retrospectively analyzed, and it was found that the overall NAR was $10.1\\\\%$ with a simultaneous CT rate of $35\\\\%$ . Patients who had received a CT scan showed a lower NAR of $5.7\\\\%$ in comparison with those who had not undergone imaging with a frequency of negative appendectomies of $11.7\\\\%$ . Thereby, CT imaging helped to reduce total hospital expenses. However only $32\\\\%$ of patients undergoing CT benefitted from \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,630,487,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0095/e07f3c82015249e097bdc98bdb16c8ba4ded064791494b05df614bccba2ecb4e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Characteristics</td><td>Score</td></tr><tr><td>Symptoms</td><td></td></tr><tr><td>Pain migration to right lower quadrant</td><td>1</td></tr><tr><td>Anorexia</td><td>1</td></tr><tr><td>Nausea/vomiting</td><td>1</td></tr><tr><td>Clinical signs</td><td></td></tr><tr><td>Tenderness in right lower quadrant</td><td>2</td></tr><tr><td>Rebound pain</td><td>1</td></tr><tr><td>Elevated temperature > 37.5 °C</td><td>1</td></tr><tr><td>Laboratory</td><td></td></tr><tr><td>Leukocytosis</td><td>2</td></tr><tr><td>Neutrophils > 75%</td><td>1</td></tr><tr><td>Total</td><td>10</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1 Alvarado scoring system for acute appendicitis \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[507,70,915,260]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"this diagnostic modality, and thus, a relevant proportion of CT scans could have been avoided [18]. Based on these retrospective findings, a clinical diagnostic algorithm was developed and implemented. The DIALAPP study (evaluation of Diagnostic ALgorithm for suspected acute APPendicitis) is a prospective observational unicentric study to evaluate the implementation and impact of the newly established diagnostic pathway in patients with suspicion of acute appendicitis. The hypothesis was that the pathway reduces the NAR to less than $10\\\\%$ , while simultaneously reducing the use of CT imaging. The increased quality and safety should lead to a reduction in costs and create a real value for healthcare (Fig. 1). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,289,591,306]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,322,915,402]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A clinical diagnostic algorithm was implemented at the Department for General and Visceral Surgery of the Goethe University Hospital Frankfurt starting in November 2015, which was applied to all patients over 18 years presenting with the symptoms of an acute appendicitis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,402,915,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Written informed consent was obtained from all patients prior to inclusion in the study in accordance with the Declaration of Helsinki and local laws and regulations. The study was approved by the institutional ethics review board (IRB-Number: 268/15) and registered at clinicaltrials.gov (NCT02627781). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,496,915,591]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"All consecutively included patients were evaluated by a resident or a consultant of the surgical department. Patients with abdominal pain due to trauma, patients under 18 years, and those who had undergone additional radiological examinations (CT or magnetic resonance imaging (MRI)) prior to surgical consultation were excluded. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,605,870,622]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Clinical diagnostic pathway and data collection \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,637,915,905]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"All patients followed a structured diagnostic algorithm including all elements of the Alvarado score (Table 1), besides other parameters. First, a clinical examination, a biochemical and hematological blood analysis, urine analysis, as well as an ultrasound by a resident and/or consultant surgeon were performed. Additionally, all female patients of childbearing age received a gynecological consultation. Thereafter, the Alvarado score was calculated for each individual patient. All clinical parameters and the management strategy were recorded on a study sheet. Patients with signs of peritonitis, positive ultrasound, or an Alvarado score of $>8$ were advised to undergo appendectomy. Patients with an Alvarado score of $<5$ and negative ultrasound were discharged to outpatient follow-up. Those with an Alvarado score between 5 and 8 were admitted to observation and clinical re-evaluation. These patients only received symptomatic therapy (infusion therapy, laxative \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[784,39,915,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Langenbecks Arch Surg \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[80,927,154,944]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[137,65,319,91]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Knowledge to practice Interpret results \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[141,103,302,116]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Establish DIALAPP-study \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[141,117,339,129]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A stratified approach combining \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[141,130,413,165]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"clinical parameters (Alvarado-score) \\\",\\\"- ultrasound \\\",\\\"- selected CT after clinical reassessment \\\"]\",\n \"page_idx\": \"2\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[137,318,285,346]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data to knowledge Assembling data \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[139,356,405,370]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Liese et al., Langenbecks Arch Surg. 2014 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[139,370,534,422]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- NAR of roughly $10\\\\\\\\%$ \\\",\\\"- CT-scans in $35\\\\\\\\%$ of patients \\\",\\\"- No established algorithm for diagnosing acute appendicitis \\\",\\\"- High costs from patients without indication for appendectomy \\\"]\",\n \"page_idx\": \"2\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[589,150,717,175]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Practice to data Take action \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[591,189,665,200]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data found: \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[591,202,838,291]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- NAR reduced to $5.8\\\\\\\\%$ \\\",\\\"CT-scans used in $19\\\\\\\\%$ of patients \\\",\\\"- Increased quality \\\",\\\"- Increased safety \\\",\\\"- Low costs (potential to safe 19.8 Mio. €/100.000 cases with structured algorithmic approach) \\\"]\",\n \"page_idx\": \"2\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[633,307,838,439]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Formation of a learning community The negative appendectomy rate (NAR) and the rate of CT- scans in the diagnostic pathway of acute appendicitis is too high \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,472,489,525]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Fig. 1 Learning circle of the DIALAPP study. Starting with the formation of a learning community in order to minimize the rate of negative appendectomies and CT scans in the diagnosis of acute appendicitis. After the analysis of our institutional retrospective data of \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,472,915,524]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Liese et al. (data to knowledge), a diagnostic pathway was implemented and prospectively evaluated as part of the DIALAPP study (knowledge to practice). As a result, we found a reduction in the NAR and CT rate (practice to data) (NAR, negative appendectomy rate) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,572,485,837]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"measures, analgesia) but no antibiotic treatment. The clinical course was assessed within $24\\\\mathrm{h}$ after admission by a board-certified or consultant surgeon. Patients developing clinically suspected AA were advised to undergo appendectomy. The improvement of complaints resulted in discharge and outpatient follow-up. All patients with persistent abdominal complaints during the observation period received a CT or MRI (pregnant patients). Patients with a positive CT scan were indicated to undergo appendectomy. Those with a negative CT were discharged. Patients with alternative diagnoses on ultrasound, CT, or at the gynecological consultation received appropriate non-study specific treatment. During the application of the pathway between November 2015 and August 2017, patients were consented for prospective data collection. A telephone follow-up of all patients was undertaken after 30 days and 6 months. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,840,485,903]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The definitive diagnosis of appendicitis was determined by the final pathological report of the resected specimens. Histopathological criteria for acute appendicitis were granulocytic infiltration or ulceration of the lumen or all wall layers, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,573,914,602]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"as well as the fatty tissue. Another criterion was the presence of an intramural abscess or necrosis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,605,914,651]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The appendicitis was classified as perforated based on intraoperative findings or pathological examination of the resected organs. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,651,914,698]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A negative appendectomy was characterized by the removal of an appendix without signs of acute inflammation in the pathological examination. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,700,915,903]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"All CT scans covered the entire abdomen and pelvis, ranging from above the diaphragm to the inguinal region. Acquisition protocols were either a standard-dose abdominal and pelvic CT with primary intravenously contrast or a non-contrasted low-dose CT. All CT scans were acquired on a third-generation dual-source CT or a 64-slice multi-detector CT (Somatom Force, Somatom Definition AS+, Siemens). All scans were interpreted by two independent radiology readers and signed by senior radiology residents. CT studies were classified in a binary fashion as positive or negative for the presence of appendicitis. Patients not treated according to the algorithm and all cases with incomplete study sheets were excluded from the analysis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,39,211,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Langenbecks Arch Surg \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[838,927,912,944]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[82,70,484,132]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The primary endpoint of the study was the NAR. Secondary endpoints included accuracy of the diagnostic tools, perforation rate, duration of diagnosis, complication rate, and length of hospital stay. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,150,233,165]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Economic modeling \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,181,485,416]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Liese et al. [18] described the cost of appendectomies in relation to undergoing surgery with or without CT scans or avoiding surgery utilizing a CT scan. We transferred their model to our setting and calculated the costs with the same pricing to create comparability. Pricing for the treatment of appendicitis indeed did not change in Germany during the mentioned time. The costs were calculated from the ratio of patients undergoing surgery with or without CT imaging and patients having no surgery due to the utilization of a CT. Moreover, we included a model with all patients (additional those that received no CT scan and no surgery due to the algorithm) and extrapolated the numbers hypothetically obtained from the data in the publication by Liese et al. [18] to receive a narrowing estimation of the overall potential in saving expenses and costs for 100,000 cases of suspected AA. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,432,184,448]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data analysis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,464,485,589]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Statistical analysis was performed using BiAS (Version 11.08) and Microsoft Excel 200x (Microsoft Corporation). Values are reported as median with range or proportions. Categorical variables were compared by means of the chi-squared test or Fisher's exact test and independent variables using the Mann-Whitney $U$ -test or the Shapiro-Wilk test as appropriate. A $p$ value of $< 0.05$ was considered to be statistically significant. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,621,147,636]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,653,460,668]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Patient selection, decision tree, and drop-out rate \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,684,485,903]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A total of 266 patients were evaluated with suspected acute appendicitis during the study period. Of these, 83 patients were excluded due to severe protocol violation. Most common reasons for exclusion were missing gynecological consultation $(n = 37)$ , missing ultrasound $(n = 12)$ , missing differential blood count $(n = 10)$ or discharge with an Alvarado score of $>4$ $(n = 7)$ , observation with Alvarado score of $< 4$ $(n = 5)$ , and a CT imaging in patients with an Alvarado score of $< 5$ $(n = 6)$ . In total, 183 patients were included in the study and final analysis. Figure 2 shows a flowchart of the implementation of the standardized diagnostic pathway. Sixty-nine patients $(37.7\\\\%)$ underwent appendectomy based on clinical features $(n = 27; 39.1\\\\%)$ , the evidence of appendicitis on ultrasound $(n = 25; 36.2\\\\%)$ , or on a CT scan $(n = 17; 24.6\\\\%)$ . In 55 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,70,914,289]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"patients, the Alvarado score (5-8) and ultrasound were inconclusive. These patients were clinically observed. Of those, 21 patients recovered without operation and were discharged. Thirty-six patients with persisting abdominal complaints underwent additive CT imaging. Hereof, 17 CT scans showed signs of appendicitis, and all underwent surgery, and the diagnosis of appendicitis was confirmed in the pathology workup. In 19 patients, the CT was negative for appendicitis, and 9 CT scans determined a different diagnosis. In total, 87 patients $(47.5\\\\%)$ could be discharged with resolved abdominal problems, of whom only 10 $(11.4\\\\%)$ of the discharged and only $19.7\\\\%$ of all study patients) received a CT. In 27 patients, a different diagnosis than appendicitis could be determined following the diagnostic pathway. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,307,914,337]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Patient characteristics with a proven appendicitis and with no proof for appendicitis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,354,914,527]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In total, 183 were analyzed as defined per protocol. Patients with appendicitis were significantly older than patients without appendicitis (32, range 18-71 vs. 28, range 18-71; $p = 0.0004$ ). Significantly more female patients did not have appendicitis (no 69 vs. yes 22), whereas more male patients were diagnosed with appendicitis (no 49 vs. yes 43) ( $p = 0.0002$ ). The clinical parameters of white blood cell count, C-reactive protein and the median Alvarado score were significantly higher for all items in patients with AA ( $p < 0.001$ ). The hospital stay was significantly longer in patients with appendicitis (4 days vs. 3 days; $p < 0.001$ ). Data are displayed in Table 2. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,543,833,574]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Performance values of the Alvarado score, ultrasound, and the diagnostic algorithm \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,591,914,841]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The ROC (receiver operating characteristic) analysis identified a cutoff Alvarado score of 5.5 to identify patients at a high risk for AA and yielded a sensitivity of $92.4\\\\%$ and a specificity of $59.1\\\\%$ . The area under the ROC curve showed good diagnostic capacity (0.914; Fig. 3). Setting the cutoff value of the Alvarado score to $>7$ as recommended in the diagnostic algorithm, the sensitivity and specificity are $73.9\\\\%$ and $88.1\\\\%$ , respectively. The ultrasound displayed a moderate sensitivity of $58.2\\\\%$ and high specificity of $97.3\\\\%$ . In contrast, CT was equally high concerning sensitivity and specificity with $100\\\\%$ respectively. In summary, the whole diagnostic algorithm, consisting specifically of (1) Alvarado score, (2) gynecological consultation for females, (3) ultrasound, and (4) selective CT imaging showed a sensitivity of $100\\\\%$ and a specificity of $96.6\\\\%$ for the detection of AA. Overall performance values for the Alvarado score, ultrasound, CT, and the entire diagnostic algorithm are shown in Table 3. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,844,914,903]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In 65 of 69 patients undergoing appendectomy, an acute appendicitis could be confirmed in the histopathological examination of the resected organs. This accounts for a NAR of $5.8\\\\%$ , and female patients had a NAR of $4.4\\\\%$ , and male patients, of \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[784,40,915,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Langenbecks Arch Surg \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[84,927,154,943]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,64,917,639]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 2 Flowchart and management course of study cohort. Implementation of the proposed diagnostic algorithm in 183 patients with suspected appendicitis (AA, acute appendicitis; US, ultrasound) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0172/af5e7026a5559a039a49be2145f610ba0b9b59f88ab8947c80605351b7bb1115.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[78,684,487,891]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$6.5\\\\%$ . In 17 patients $(24.6\\\\%)$ , a perforated appendicitis was found. Table 4 shows the characteristics of patients with acute appendicitis in comparison with patients with perforated appendicitis. Patients with a perforated appendicitis were older and more often male. There was no significant difference between both groups concerning laboratory parameters, the Alvarado score, or the rate of CT-scans. The time from admission to operation was longer in patients with uncomplicated appendicitis (424 min vs. 324 min), without reaching statistical significance. Fifteen patients $(25.4\\\\%)$ who were operated within $12\\\\mathrm{h}$ after admission showed a perforation in comparison with 2 patients $(20.0\\\\%)$ being operated after $12\\\\mathrm{h}$ , indicating that the time from admission to operation had no significant \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,684,915,746]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"influence on perforation rate. Nevertheless, performing a preoperative CT scan resulted in a significantly delayed operation (599 min in patients with preoperative CT vs. 340 min in patients without CT; $p = 0.005$ ). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,748,915,889]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Patients with perforated appendicitis showed a longer hospital stay in comparison with patients with uncomplicated appendicitis. However, in our patient cohort, we could not detect a higher morbidity due to perforated appendicitis (Table 4). Sixty-eight patients underwent laparoscopic appendectomy. In one case, a conversion to open surgery was necessary $(1.5\\\\%)$ . One pregnant patient underwent open appendectomy simultaneously with cesarean section. Negative explorations did not occur in our cohort. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,39,211,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Langenbecks Arch Surg \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[838,927,912,945]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[78,84,915,498]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0305/1229cadfd3b679076b2b34203d4d54bf881bd9a8a7fc51f18447d6c407dd4627.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td></td><td>All (n = 183)</td><td>Appendicitis (n = 65)</td><td>No appendicitis (n = 118)</td><td>p value</td></tr><tr><td>Age (years)</td><td></td><td></td><td></td><td>0.0004</td></tr><tr><td>Median</td><td>30</td><td>32</td><td>28</td><td></td></tr><tr><td>Range</td><td>18–71</td><td>18–61</td><td>18–71</td><td></td></tr><tr><td>Sex</td><td></td><td></td><td></td><td>0.0002</td></tr><tr><td>Female</td><td>91 (49.7)</td><td>22 (33.8)</td><td>69 (58.5)</td><td></td></tr><tr><td>Male</td><td>92 (50.3)</td><td>43 (66.2)</td><td>49 (41.5)</td><td></td></tr><tr><td>BMI (kg/m2)</td><td></td><td></td><td></td><td>0.0018</td></tr><tr><td>Median</td><td>24.1</td><td>24.7</td><td>22.6</td><td></td></tr><tr><td>Range</td><td>16.8–41.2</td><td>17.4–41.2</td><td>16.8–30.1</td><td></td></tr><tr><td>Leukocytes (4.2–10/nl)</td><td></td><td></td><td></td><td><0.000001</td></tr><tr><td>Median</td><td>10.4</td><td>14.48</td><td>8.89</td><td></td></tr><tr><td>Range</td><td>2.83–24.99</td><td>2.83–24.99</td><td>2.92–23.01</td><td></td></tr><tr><td>C-reactive protein (<0.5 mg/dl)</td><td></td><td></td><td></td><td>0.000011</td></tr><tr><td>Median</td><td>0.5</td><td>1.73</td><td>0.28</td><td></td></tr><tr><td>Range</td><td>0.01–23.66</td><td>0.02–23.66</td><td>0.01–20.57</td><td></td></tr><tr><td>Alvarado score</td><td></td><td></td><td></td><td><0.000001</td></tr><tr><td>Median</td><td>5</td><td>7</td><td>4</td><td></td></tr><tr><td>Range</td><td>0–10</td><td>4–10</td><td>0–8</td><td></td></tr><tr><td>CT scan performed</td><td>36 (19.7)</td><td>17 (26.2)</td><td>19 (16.1)</td><td>0.1</td></tr><tr><td>Negative appendectomy</td><td>--</td><td>--</td><td>4 (5.8)</td><td>--</td></tr><tr><td>Length of hospital stay (days)</td><td></td><td></td><td></td><td>0.0001</td></tr><tr><td>Median</td><td>3</td><td>4</td><td>3</td><td></td></tr><tr><td>Range</td><td>1–12</td><td>3–12</td><td>1–9</td><td></td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2 Demographic and clinical characteristics of patients with proven appendicitis in comparison with patients without appendicitis \\\"]\",\n \"table_footnote\": \"[\\\"Values are number of cases $(\\\\\\\\%)$ , unless otherwise indicated. For analysis of categorical variables, chi-squared test was used. Fisher's exact test was used, if appropriate. Independent variables were compared with the Mann-Whitney $U$ test or the Shapiro-Wilk test as appropriate BMI body mass index \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[78,560,485,624]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The histopathological examination of all of the four patients with negative appendectomy showed an abnormal result, including neurogenic appendicopathy $(n = 2)$ , adenoma of appendix $(n = 1)$ , and transmural fibrosis of appendix $(n = 1)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,624,485,702]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Eleven patients had postoperative complications, of whom 2 had to undergo re-do surgery. One of these patients initially received a negative appendectomy and had to be reoperated due to bowel obstruction. One patient developed an intraabdominal collection and was treated with percutaneous \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,560,914,592]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"drainage. Four patients developed surgical site infection (Table 4). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,621,850,637]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Midterm follow-up at 30 days and 6 months \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,653,915,702]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A total of $68.9\\\\%$ and $65.6\\\\%$ of all patients could be reached by telephone follow-up after 30 days and 6 months, respectively. No missed appendicitis occurred among the non-operated \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,741,915,887]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0159/0fab3fcfeaf0fdf22e9c2ab024d01056bf586057d35afc51b931077f151d818d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=\\\"2\\\">Measurement</td><td colspan=\\\"2\\\">Alvarado-score > 7 (n = 183)</td><td colspan=\\\"2\\\">Ultrasonography (n = 181)</td><td colspan=\\\"2\\\">CT scan (n = 36)</td><td colspan=\\\"2\\\">Diagnostic algorithm (n = 183)</td></tr><tr><td>%</td><td>95% CI</td><td>%</td><td>95% CI</td><td>%</td><td>95% CI</td><td>%</td><td>95% CI</td></tr><tr><td>Sensitivity</td><td>73.9</td><td>61–84</td><td>58.2</td><td>35–62</td><td>100</td><td>81–100</td><td>100</td><td>95–100</td></tr><tr><td>Specificity</td><td>88.1</td><td>81–93</td><td>97.3</td><td>92–99</td><td>100</td><td>82–100</td><td>96.6</td><td>92–99</td></tr><tr><td>PPV</td><td>77.4</td><td>65–87</td><td>90.0</td><td>73–98</td><td>100</td><td>81–100</td><td>94.2</td><td>86–98</td></tr><tr><td>NPV</td><td>85.9</td><td>78–92</td><td>78.9</td><td>71–85</td><td>100</td><td>82–100</td><td>100</td><td>97–100</td></tr><tr><td>Accuracy</td><td>82.3</td><td>76–87</td><td>80.9</td><td>74–87</td><td>100</td><td>92–100</td><td>97.8</td><td>95–99</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 3 Overall performance values for Alvarado score, ultrasound, CT, and diagnostic algorithm \\\"]\",\n \"table_footnote\": \"[\\\"PPV positive predictive value, NPV negative predictive value \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[784,39,915,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Langenbecks Arch Surg \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[80,927,156,945]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[386,65,915,313]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.3 ROC curve. ROC (receiver operating characteristic) curve of sensitivity and specificity of the Alvarado score for diagnosis of acute appendicitis \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0688/3f307b13a34726c238e73468be436b1ff01ab5f1461e72328fb3fa460e714e52.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[78,337,489,370]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"patients during the follow-up. Five patients after appendectomy were readmitted due to postoperative complications, of \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,337,915,369]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"whom one patient had to undergo re-do surgery due to intestinal obstruction. Other reasons for hospital readmission were \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,408,917,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0465/2857a563a384a52ac222c101c898580737ad1af44dbb747a0a61977a4645d2da.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td></td><td>All (n = 65)</td><td>No perforation (n = 48)</td><td>Perforation (n = 17)</td><td>p value</td></tr><tr><td>Age (years)</td><td></td><td></td><td></td><td>0.05</td></tr><tr><td>Median</td><td>32</td><td>32</td><td>34</td><td></td></tr><tr><td>Range</td><td>18–61</td><td>18–61</td><td>22–59</td><td></td></tr><tr><td>Sex</td><td></td><td></td><td></td><td>0.46</td></tr><tr><td>Female</td><td>22 (33.8)</td><td>15 (31.3)</td><td>7 (41.1)</td><td></td></tr><tr><td>Male</td><td>43 (66.2)</td><td>33 (68.7)</td><td>10 (58.9)</td><td></td></tr><tr><td>Leukocytes (4.2–10/ml)</td><td></td><td></td><td></td><td>0.66</td></tr><tr><td>Median</td><td>14.48</td><td>14.83</td><td>13.79</td><td></td></tr><tr><td>Range</td><td>2.83–24.99</td><td>2.83–24.37</td><td>3.2–24.99</td><td></td></tr><tr><td>C-reactive protein (<0.5 mg/dl)</td><td></td><td></td><td></td><td>0.08</td></tr><tr><td>Median</td><td>1.73</td><td>1.15</td><td>3.5</td><td></td></tr><tr><td>Range</td><td>0.02–23.66</td><td>0.02–23.66</td><td>0.06–15.4</td><td></td></tr><tr><td>Alvarado score</td><td></td><td></td><td></td><td>0.92</td></tr><tr><td>Median</td><td>7</td><td>7</td><td>7</td><td></td></tr><tr><td>Range</td><td>4–10</td><td>4–10</td><td>6–10</td><td></td></tr><tr><td>CT scan performed</td><td>17 (26.2)</td><td>12 (25.0)</td><td>5 (29.4)</td><td>0.41</td></tr><tr><td>Time to operation (min)</td><td></td><td></td><td></td><td>0.54</td></tr><tr><td>Median</td><td>404</td><td>424</td><td>357</td><td></td></tr><tr><td>Range</td><td>141–5660</td><td>141–1559</td><td>146–5660</td><td></td></tr><tr><td>Length of hospital stay (days)</td><td></td><td></td><td></td><td>0.004</td></tr><tr><td>Median</td><td>4</td><td>3</td><td>4</td><td></td></tr><tr><td>Range</td><td>3–12</td><td>3–7</td><td>3–12</td><td></td></tr><tr><td>Postoperative complications</td><td>10 (15.4)</td><td>7 (14.6)</td><td>3 (17.6)</td><td>0.55</td></tr><tr><td>Dindo-Clavien I-II</td><td>8</td><td>6</td><td>2</td><td></td></tr><tr><td>Dindo-Clavien III</td><td>2</td><td>1</td><td>1</td><td></td></tr><tr><td>Dindo-Clavien IV-V</td><td>0</td><td>0</td><td>0</td><td></td></tr></table>\",\n \"table_caption\": \"[\\\"Table 4 Comparison of patients with uncomplicated and perforated appendicitis \\\"]\",\n \"table_footnote\": \"[\\\"Values are number of cases $(\\\\\\\\%)$ , unless otherwise indicated. For analysis of categorical variables, chi-squared test was used. Fisher's exact test was used, if appropriate. Independent variables were compared with the Mann-Whitney $U$ test or the Shapiro-Wilk test as appropriate BMI body mass index \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[82,39,211,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Langenbecks Arch Surg \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[838,927,914,946]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[78,70,487,102]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"an intraabdominal abscess, a gastrointestinal motility disorder, and a myocardial infarction. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,132,480,165]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Reduction of the costs by utilizing the new DIALAPP algorithm \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,181,487,497]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The patients were categorized into 4 groups of costs: 1: no CT scan/surgery (1317 €), 2: CT scan/surgery (1434 €), 3: CT scan/no surgery (675 €), and 4: no CT scan/no surgery (558 € in hospital, 250 € in ambulatory setting). The groups were distributed by $52 / 59\\\\%$ for group 1, $17 / 19\\\\%$ for group 2, and $19 / 22\\\\%$ for group 3, resulting in 125.9 million € per 100,000 cases in the Liese et al. publication (historical patient cohort of our institution) and 119.2 million € for the present patient cohort. This accounted for a saving of 6.7 million € per 100,000 suspicious cases for AA. The extrapolated model included group 4 which was missing in the publication by Liese et al. We used the assumption that the reduction in NAR by $5\\\\%$ predominantly was observed in the no CT/surgery group and extrapolated the corresponding numbers accordingly: 34/ $28.4\\\\%$ for group 1, $12.5 / 9.2\\\\%$ for group 2, $5.9 / 10.3\\\\%$ for group 3, and 10 (ambulatory) + 37.6 (in hospital)/ $10 + 41.9\\\\%$ for group 4, resulting in 93.4 million € vs. 73.6 million € and a theoretic saving of 19.8 million € per 100,000 cases when applying all 4 categories. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,69,608,86]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,102,917,497]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The prospective diagnostic pathway of diagnosing acute appendicitis combining a clinical risk scoring (Alvarado score), routine ultrasound, highly selective use of CT imaging, and clinical re-evaluation showed a high accuracy with a sensitivity and specificity of $100\\\\%$ and $96.6\\\\%$ , respectively. The implementation of the algorithm resulted in substantial improvements in surgical diagnostic accuracy when compared with our previous institutional data [18]. As shown in Table 5, the implementation led to a reduction in the rate of unnecessary operations (the NAR was reduced to $5.8\\\\%$ ) and an optimization of performed CT imaging (only $19\\\\%$ of all patients) and accelerated the access to adequate surgical treatment (mean time to operation, reduction from 684.2 to $555.6\\\\mathrm{min}$ ), which was considerably better than the former published experience by our group [18]. In the presented patient cohort, only four negative appendectomies occurred. Ultimately, in all four cases, histological results showed a pathological finding of the appendix, including neurogenic appendicopathy. Patients who had low clinical suspicion for appendicitis and negative ultrasound were safely discharged from the hospital, which was confirmed during the follow-up period, as we did not detect a missed appendicitis. Thus, the most important finding of the prospective single-armed interventional trial was the improvement in three surrogates of treatment quality for acute appendicitis derived from a first \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[292,525,919,875]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0009/2bc6e7e42ded6397b5196c936a18fcbfa8857bea617ead712cd5a39660a32393.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td></td><td>Pre-group (n = 367)</td><td>Pathway group (n = 183)</td></tr><tr><td>Age (years)</td><td></td><td></td></tr><tr><td>Mean</td><td>37.69</td><td>31.8</td></tr><tr><td>Range</td><td>15–91</td><td>18–71</td></tr><tr><td>Female gender (%)</td><td>158 (43.1)</td><td>91 (49.7)</td></tr><tr><td>Body mass index (kg/m2)</td><td></td><td></td></tr><tr><td>Mean</td><td>24.9</td><td>24.4</td></tr><tr><td>Range</td><td>16.3–63.8</td><td>16.8–41.2</td></tr><tr><td>Preoperative CT (%)</td><td>129/367 (35.1)</td><td>36/183 (19.7)</td></tr><tr><td>Negative appendectomy rate (%)</td><td>33/326 (10.1)</td><td>4/69 (5.8)</td></tr><tr><td>Male</td><td>10/187 (5.3%)</td><td>3/46 (6.5%)</td></tr><tr><td>Female</td><td>23/139 (16.5%)</td><td>1/23 (4.4%)</td></tr><tr><td>Appendiceal perforation rate (%)</td><td>48/293 (16.4)</td><td>17/65 (26.1)</td></tr><tr><td>Time to operation (min)</td><td></td><td></td></tr><tr><td>Mean</td><td>684.2</td><td>555.6</td></tr><tr><td>Range</td><td>52–100,004</td><td>141–5660</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 5 Patient demographics and clinical outcome among patients in the pre-group in comparison to the pathway group \\\"]\",\n \"table_footnote\": \"[\\\"Pre-group, historical, retrospective patient cohort of our institution before application of the diagnostic pathway (published by Liese et al. [18]); pathway group, patient cohort during application of the diagnostic pathway \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[784,39,915,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Langenbecks Arch Surg \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[80,927,159,945]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[82,70,485,101]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"learning circle and retrospective analysis in a learning health system (Fig. 1) [18]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,102,485,510]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A number of studies describing a pathway for diagnosing patients with suspected appendicitis have been published. Only few of them have prospectively evaluated their recommended algorithm [14, 16, 17, 19]. In these studies, the implementation of a diagnostic pathway also resulted in a low rate of negative appendectomies of less than $10\\\\%$ . Nevertheless, the low NAR could only be achieved by a widespread use of CT scans in patients presenting with suspected appendicitis [16]. For example, Antevil [17] and co-authors observed a NAR of $4\\\\%$ with a simultaneous frequency of CT of $87\\\\%$ , probably due to a lack of clinical risk stratification before imaging. Similarly, other studies have demonstrated a decrease of NAR by an increased use of preoperative CT imaging [20-22]. Taking into account the radiation exposure, contrast-related complications, and resource consumption related to CT, some studies have implemented diagnostic pathways including clinical risk stratification before imaging in an attempt to reduce the rate of CT scans. Thus, in the STRAPPSCORE study [14], the introduction of a clinical score-based risk stratification algorithm in patients with suspicion of appendicitis resulted in less imaging and fewer admissions. But on the other hand, the algorithm did not show an effect on the proportion of negative appendectomies. Relating the number of negative appendectomies to all operated patients, the NAR was about $11\\\\%$ , with a maximum of $17.9\\\\%$ in patients with low risk for appendicitis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,512,485,668]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Comparable with the current study, Toorenvliet and colleagues [19] demonstrated a NAR of $3.3\\\\%$ with a minimal use of CT in only $17.9\\\\%$ of all patients by the implementation of a diagnostic pathway including risk stratification and regular ultrasound. However, it must be noted that in this study, the patient risk stratification was undertaken by a consultant and not according to an objective clinical scoring system. In addition, both children and adults were investigated in the study, which certainly affects the data due to the restrained use of CT imaging in children. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,670,485,903]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The results of additionally required and indicated imaging in accordance with the algorithm in the DIALAPP study were excellent. Most strikingly, CT imaging had a $100\\\\%$ accuracy in the diagnosis of appendicitis (no false positive and no false negative results). This corresponds to the recent literature [9, 23, 24]. Here, the use of low-dose CT protocols can reduce the radiation exposure with a comparable diagnostic accuracy with standard CT protocols [25]. These protocols could be a cost-efficient alternative to inpatient observation in patients with intermediate probability for AA. Nevertheless, not all emergency care units have 24-h availability of CT, and nonselective CT imaging is known to show lower sensitivity, mainly in patients with low or high clinical suspicion of AA [8, 26]. The results of this study indicate that most patients can be classified either in the high or the low probability group \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,70,914,353]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"following the diagnostic algorithm, and thus, the need for diagnostic imaging can be significantly reduced. Moreover, the data of accuracy of abdominal ultrasound demonstrate that CT imaging is not required in all patients to detect the correct diagnosis. The diagnostic accuracy of ultrasound here was comparable with the data from literature with a sensitivity and specificity of $58\\\\%$ and $97\\\\%$ , respectively [26, 27]. The rather low sensitivity is likely explained by the fact that members of the surgical team, as it is standard of care in Germany, performed the ultrasound and not a certified ultrasound expert. With regard to these results, ultrasound and CT should be considered as complementary techniques. Ultrasound should be the preferred primary imaging modality and enables to rule in patients with risk for appendicitis. CT imaging is needed only in cases with equivocal clinical or ultrasound examination. This means less radiation exposure for the patient and cost saving for the hospital as currently shown in a meta-analysis from the USA [28]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,355,914,651]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The literature consistently reports at least twice the NAR in women than in men [4, 20, 29-32]. Only Antevil et al. [17] achieved an equally high NAR in women and men, but performing CT scan in every female patient. The primary aim of a new diagnostic pathway should therefore be to decrease the NAR in women of childbearing potential and protect them from unnecessary radiation exposure. In the current study, by the introduction of a standardized diagnostic workflow for patients with right-sided lower abdominal quadrant pain, a relevant reduction in NAR and, here especially in women (reduction of NAR from 16.5 to $4.4\\\\%$ ; see Table 5) with minimal use of CT imaging was achieved. Only $20.8\\\\%$ of all women received a CT scan, and $18.5\\\\%$ , of men. This improvement can certainly also be explained by the routine gynecological consultation of all women of childbearing age as established in our diagnostic pathway. However, a routine gynecological examination is sometimes not practicable and may lead to considerable waiting times for the patient. As a result, also in our patient cohort, 37 patients were excluded due to a lack of consultation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,654,914,903]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"One of the major concerns about introducing a diagnostic pathway is an increased perforation rate due to a delay in treatment [33, 34]. At the same time, it has been shown that perforated appendicitis rates are not influenced by in-hospital delay and have not significantly changed with the increasing use of preoperative CT imaging [35, 36]. Andersson et al. [14] showed that reassessment after in-hospital observation and selective imaging in patients with an equivocal diagnosis is not associated with an increased risk for perforation and thus safe and efficient. The perforation rate in our study was $24.6\\\\%$ , similar to previously reported rates [19]. Neither the number of CT scans performed nor the time from admission to surgery significantly differed between patients with uncomplicated or perforated appendicitis. It is also noteworthy that the establishment of a clinical pathway accelerated the time from the first contact and interview to diagnosis in the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,40,210,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Langenbecks Arch Surg \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[840,927,912,943]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[82,70,484,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"DIALAPP study. As mentioned before, the time from admission to operation has been reduced in comparison with our previous institutional data [18]. This compares favorably with the results reported in the literature that the quality survey should focus on the accuracy of diagnosis rather than on its potential delay in therapeutic intervention. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,165,485,291]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A further aspect of quality improvement is the optimization of healthcare-related costs and resource utilization. Our study design does not allow a reliable statement on reduction of costs, but it allows an assessment of the potential savings. Thus, the reduction of NAR and CT scans by half at our institution has the potential for a saving of 6.7 million € per 100,000 suspicious cases for AA. Consistent implementation of the algorithm could even save up to 19.8 million € per 100,000 cases. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,292,485,384]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Similar previous studies have demonstrated that a minimization of negative appendectomies can provide financial and resource savings [37]. Scott et al. [38] showed that risk stratification and discharge of patients with low risk for appendicitis resulted in a significant reduction in admissions, preserving the availability of beds, diagnostic imaging, and financial resources. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,386,485,605]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Taken together, the simple diagnostic algorithm evaluated here showed high accuracy and the potential for an easy implementation into daily practice. The risk stratification based on objective scoring and a well-structured algorithm facilitated decision-making, particularly for the less experienced frontline surgeon who is often responsible for the initial assessment of patients. The pragmatic setup of our study represents a common clinical setting and thus increases generalizability of the study findings. We studied an unselected population of patients with acute right lower quadrant abdominal pain with a realistic sample prevalence of appendicitis. The application of the algorithm by all members of the surgical team reflects daily clinical applicability and allows scalability to other hospitals and settings. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,607,485,903]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"There was no missed appendicitis in our patient cohort, taking into account the relatively high rate of lost to follow-up. Some patients who were discharged with a very low probability of having appendicitis and who were unresponsive to telephone calls may have been readmitted and operated at another hospital. Thus, we had no absolute confirmation of the absence of AA in the non-operated patients. This limitation is also a problem and has been reported as potential bias in other studies. A further limitation of this study is that it represents only a single center's experience. Moreover, the number of exclusions was higher than expected, which increased the risk for statistical errors of the primary outcome measure \\\"negative appendectomies.\\\" This high rate of exclusion may also have led to a selection bias by the inclusion of more severe cases indicated by the high rate of perforated appendicitis and the exclusion of less severe cases indicated by a negative appendectomy rate of $15.6\\\\%$ in the group of excluded patients due to severe protocol violation. This high selection may have influenced the accuracy of the study. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,70,914,306]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, our institution had not implemented antibiotic treatment for cases of imaging-confirmed uncomplicated appendicitis. This might have minimized the group of early appendicitis and unnecessary appendectomies which would otherwise be resolved by antimicrobial therapy alone. Nevertheless, antibiotic therapy alone for acute appendicitis shows a treatment effectiveness of only $72.6\\\\%$ , resulting in an appendectomy in $26.5\\\\%$ of patients initially treated conservatively as shown by the meta-analysis of Harnoss et al. [39]. Moreover, the incidences of complicated appendicitis and the hospital stay are significantly increased in the antibiotic treatment group in comparison with the surgical treatment group [39]. Thus, although antibiotics may prevent some patients from appendectomies, surgery still represents the gold standard of care for acute appendicitis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,308,912,401]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The presented results support the implementation of a pathway in the diagnosis of AA. Patients with an uncertain clinical diagnosis and ultrasound result for appendicitis can safely be re-evaluated during a hospital admission. This risk-adjusted approach has the potential to reduce the number of unnecessary operation, simultaneously minimizing CT use. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,448,610,463]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conclusion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,481,912,574]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Implementation of a diagnostic algorithm combining clinical risk score, ultrasound, gynecological consultation, and selective CT imaging after re-evaluation resulted in high accuracy for the diagnosis of acute appendicitis. A low negative appendectomy rate can be achieved without increasing the risk for perforation from a delay in treatment. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,589,914,741]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Authors' contributions Patrizia Malkomes contributed to the acquisition and analysis of the data, as well as drafting of the manuscript. Franziska Edmaier was a major contributor in data acquisition and analysis. Juliane Liese and Alexander Reinisch-Liese were major contributors in the study conception and design as well as acquisition and analysis of the data. Hanan El Youzouri and Teresa Schreckenbach contributed to the acquisition and analysis of the clinical data and critically reviewed the manuscript. Andreas Bucher provided radiological data analysis and expertise. Wolf Otto Bechstein was a major contributor to the study conception and critically reviewed the manuscript. Andreas Schnitzbauer was a major contributor in interpreting the data and drafting the manuscript. All authors read and approved the final manuscript. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,758,912,770]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Funding Open Access funding enabled and organized by Projekt DEAL. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,787,912,824]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data availability The datasets generated during the current study are not publicly available due to the terms agreed with the local ethics committee. They are available from the corresponding author on reasonable request. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,841,771,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Compliance with ethical standards \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,872,915,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conflict of interest The authors declare that they have no conflict of interest. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[784,40,915,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Langenbecks Arch Surg \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[84,927,154,943]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,69,487,121]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Ethics approval This study was performed in line with the Declaration of Helsinki and local laws and regulations. The study was approved by the institutional ethics review board (IRB-Number: 268/15) and registered at clinicaltrials.gov (NCT02627781). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,135,485,162]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Consent to participate Written informed consent was obtained from all patients prior to inclusion in the study. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,172,485,324]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,382,181,398]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,413,487,903]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1. Ferris M, Quan S, Kaplan BS, Molodecky N, Ball CG, Chernoff GW, Bhala N, Ghosh S, Dixon E, Ng S, Kaplan GG (2017) The global incidence of appendicitis: a systematic review of population-based studies. 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Coursey CA, Nelson RC, Patel MB, Cochran C, Dodd LG, Delong DM et al (2010) Making the diagnosis of acute appendicitis: do more preoperative CT scans mean fewer negative appendectomies? A 10-year study. Radiology 254(2):460-468. https://doi.org/10.1148/radiol.09082298 \\\",\\\"22. Naoum JJ, Mileski WJ, Daller JA, Gomez GA, Gore DC, Kimbrough TD, Ko TC, Sanford AP, Wolf SE (2002) The use of abdominal computed tomography scan decreases the frequency of misdiagnosis in cases of suspected appendicitis. Am J Surg 184(6): 587-589; discussion 589-90. https://doi.org/10.1016/s0002-9610(02)01086-3 \\\",\\\"23. Park JS, Jeong JH, Lee JI, Lee JH, Park JK, Moon HJ (2013) Accuracies of diagnostic methods for acute appendicitis. Am Surg 79(1):101-106 \\\",\\\"24. Pickhardt PJ, Lawrence EM, Pooler BD, Bruce RJ (2011) Diagnostic performance of multidetector computed tomography for suspected acute appendicitis. Ann Intern Med 154(12):789- \\\"]\",\n \"page_idx\": \"10\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[82,39,211,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Langenbecks Arch Surg \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[838,927,912,944]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,69,487,551]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"796, W-291. https://doi.org/10.7326/0003-4819-154-12-201106210-00006 \\\",\\\"25. Sippola S, Virtanen J, Tammilehto V, Gronroos J, Hurme S, Niinivita H, Lietzen E, Salminen P (2020) The accuracy of low-dose computed tomography protocol in patients with suspected acute appendicitis: the OPTICAP study. Ann Surg 271(2):331-338. https://doi.org/10.1097/SLA.0000000000002976 \\\",\\\"26. van Randen A, Bipat S, Zwinderman AH, Ubbink DT, Stoker J, Boermeester MA (2008) Acute appendicitis: meta-analysis of diagnostic performance of CT and graded compression US related to prevalence of disease. Radiology 249(1):97-106. https://doi.org/10.1148/radiol.2483071652 \\\",\\\"27. Doria AS, Moineddin R, Kellenberger CJ, Epelman M, Beyene J, Schuh S, Babyn PS, Dick PT (2006) US or CT for diagnosis of appendicitis in children and adults? A meta-analysis. Radiology 241(1):83-94. https://doi.org/10.1148/radiol.2411050913 \\\",\\\"28. Parker L, Nazarian LN, Gingold EL, Palit CD, Hoey CL, Frangos AJ (2014) Cost and radiation savings of partial substitution of ultrasound for CT in appendicitis evaluation: a national projection. AJR Am J Roentgenol 202(1):124-135. https://doi.org/10.2214/AJR.12.9642 \\\",\\\"29. Andersson RE, Hugander AP, Ghazi SH, Ravn H, Offenbartl SK, Nystrom PO et al (2000) Why does the clinical diagnosis fail in suspected appendicitis? Eur J Surg 166(10):796-802. https://doi.org/10.1080/110241500447434 \\\",\\\"30. Cuschieri J, Florence M, Flum DR, Jurkovich GJ, Lin P, Steele SR et al (2008) Negative appendectomy and imaging accuracy in the Washington State Surgical Care and Outcomes Assessment Program. Ann Surg 248(4):557-563. https://doi.org/10.1097/SLA.0b013e318187aeca \\\",\\\"31. Stein GY, Rath-Wolfson L, Zeidman A, Atar E, Marcus O, Joubran S, Ram E (2012) Sex differences in the epidemiology, seasonal variation, and trends in the management of patients with acute appendicitis. Langenbeck's Arch Surg 397(7):1087-1092. https://doi.org/10.1007/s00423-012-0958-0 \\\",\\\"32. Tzovaras G, Liakou P, Baloyiannis I, Spyridakis M, Mantzos F, Tepetes K, Athanassiou E, Hatzitheofilou C (2007) Laparoscopic appendectomy: differences between male and female patients with \\\"]\",\n \"page_idx\": \"11\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[510,69,915,496]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"suspected acute appendicitis. World J Surg 31(2):409-413. https://doi.org/10.1007/s00268-006-0335-7 \\\",\\\"33. Lee CC, Golub R, Singer AJ, Cantu RJR, Levinson H (2007) Routine versus selective abdominal computed tomography scan in the evaluation of right lower quadrant pain: a randomized controlled trial. Acad Emerg Med 14(2):117-122. https://doi.org/10.1197/j.aem.2006.08.007 \\\",\\\"34. Lee SL, Walsh AJ, Ho HS (2001) Computed tomography and ultrasonography do not improve and may delay the diagnosis and treatment of acute appendicitis. Arch Surg 136(5):556-562. https://doi.org/10.1001/archsurg.136.5.556 \\\",\\\"35. Guss DA, Behling CA, Munassi D (2008) Impact of abdominal helical computed tomography on the rate of negative appendicitis. J Emerg Med 34(1):7-11. https://doi.org/10.1016/j.jemermed.2007.07.062 \\\",\\\"36. Menes TS, Aufses AHJR, Rojas M, Bickell NA (2006) Increased use of computed tomography does not harm patients with acute appendicitis. Am Surg 72(4):326-329 \\\",\\\"37. Flum DR, Koepsell T (2002) The clinical and economic correlates of misdiagnosed appendicitis: nationwide analysis. Arch Surg 137(7):799-804; discussion 804. https://doi.org/10.1001/archsurg.137.7.799 \\\",\\\"38. Scott AJ, Mason SE, Arunakirinathan M, Reissis Y, Kinross JM, Smith JJ (2015) Risk stratification by the Appendicitis Inflammatory Response score to guide decision-making in patients with suspected appendicitis. Br J Surg 102(5):563-572. https://doi.org/10.1002/bjs.9773 \\\",\\\"39. Harnoss JC, Zelienka I, Probst P, Grummich K, Müller-Lantzsch C, Harnoss JM, Ulrich A, Büchler MW, Diener MK (2017) Antibiotics versus surgical therapy for uncomplicated appendicitis: systematic review and meta-analysis of controlled trials (PROSPERO 2015: CRD42015016882). Ann Surg 265(5):889-900. https://doi.org/10.1097/SLA.0000000000002039 \\\"]\",\n \"page_idx\": \"11\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[509,512,915,539]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[784,39,915,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Langenbecks Arch Surg \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[82,927,100,943]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"# \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[102,930,154,944]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1007/s00423-020-02022-7"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Medicine and Health Sciences"},"sha256":{"kind":"string","value":"9fa25e04caacaa8dfd0ebe9c287a1c68b6733b74ebbb15fcc63bbeb81b3b5e36"},"title":{"kind":"string","value":"DIALAPP: a prospective validation of a new diagnostic algorithm for acute appendicitis"}}},{"rowIdx":248,"cells":{"abstract":{"kind":"string","value":""},"author":{"kind":"string","value":"Wing-Fu Lai|Eric M. Huang|Wing-Tak Wong"},"content_list":{"kind":"list like","value":[{"bbox":"[105,88,240,219]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0773/3829c1b760fef12287d64c5aad438e0727efe86c6b5ee95153f1bdcba89c7674.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[258,105,848,210]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dimer-Dimer Interaction of the Bacterial Selenocysteine Synthase SelA Promotes Functional Active-Site Formation and Catalytic Specificity ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[102,242,714,279]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Yuzuru Itoh $^{1,2,3,\\dagger}$ , Markus J. Brocker $^{4,\\dagger}$ , Shun-ichi Sekine $^{1,2,5}$ , Dieter Soll $^{4,6}$ and Shigeyuki Yokoyama $^{1,2,7}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[104,292,902,424]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1 - Department of Biophysics and Biochemistry, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan \",\"2 - RIKEN Systems and Structural Biology Center, 1-7-22 Suehiro-cho, Tsurumi, Yokohama 230-0045, Japan \",\"3 - Laboratory of Membrane and Cytoskeleton Dynamics, Institute of Molecular and Cellular Biosciences, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan \",\"4 - Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT 06520-8114, USA \",\"5 - Division of Structural and Synthetic Biology, RIKEN Center for Life Science Technologies, 1-7-22 Suehiro-cho, Tsurumi, Yokohama 230-0045, Japan \",\"6 - Department of Chemistry, Yale University, New Haven, CT 06520-8114, USA \",\"7 - RIKEN Structural Biology Laboratory, 1-7-22 Suehiro-cho, Tsurumi, Yokohama 230-0045, Japan \"]","page_idx":"0","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[102,438,889,493]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Correspondence to Dieter Soll and Shigeyuki Yokoyama: D. Soll is to be contacted at: Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT 06520-8114, USA; S. Yokoyama, RIKEN Structural Biology Laboratory, 1-7-22 Suehiro, Tsurumi, Yokohama 230-0045, Japan. yokoyama@riken.jp http://dx.doi.org/10.1016/j.jmb.2014.01.003 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[105,495,242,508]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Edited by M. Guss ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[104,524,191,539]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[102,554,902,775]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The 21st amino acid, selenocysteine (Sec), is incorporated translationally into proteins and is synthesized on its specific tRNA (tRNA $^{\\text{Sec}}$ ). In Bacteria, the selenocysteine synthase SelA converts Ser-tRNA $^{\\text{Sec}}$ , formed by seryl-tRNA synthetase, to Sec-tRNA $^{\\text{Sec}}$ . SelA, a member of the fold-type-I pyridoxal $5^{\\prime}$ -phosphate-dependent enzyme superfamily, has an exceptional homodecameric quaternary structure with a molecular mass of about 500 kDa. Our previously determined crystal structures of Aquifex aeolicus SelA complexed with tRNA $^{\\text{Sec}}$ revealed that the ring-shaped decamer is composed of pentamerized SelA dimers, with two SelA dimers arranged to collaboratively interact with one Sel-tRNA $^{\\text{Sec}}$ . The SelA catalytic site is close to the dimer-dimer interface, but the significance of the dimer pentamerization in the catalytic site formation remained elusive. In the present study, we examined the quaternary interactions and demonstrated their importance for SelA activity by systematic mutagenesis. Furthermore, we determined the crystal structures of \"depentamerized\" SelA variants with mutations at the dimer-dimer interface that prevent pentamerization. These dimeric SelA variants formed a distorted and inactivated catalytic site and confirmed that the pentamer interactions are essential for productive catalytic site formation. Intriguingly, the conformation of the non-functional active site of dimeric SelA shares structural features with other fold-type-I pyridoxal $5^{\\prime}$ -phosphate-dependent enzymes with native dimer or tetramer (dimer-of-dimers) quaternary structures. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[442,776,900,791]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"© 2014 The Authors. Published by Elsevier Ltd. All rights reserved. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[104,858,225,873]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[102,883,490,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Selenocysteine (Sec) is known as the 21st amino acid incorporated translationally into proteins and is synthesized on its specific tRNA (tRNA $^{\\text{Sec}}$ ) [1]. The ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,854,904,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tRNA $^{\\text{Sec}}$ -ligated serine (Ser-tRNA $^{\\text{Sec}}$ ) generated by seryl-tRNA synthetase is converted to tRNA $^{\\text{Sec}}$ -ligated Sec (Sec-tRNA $^{\\text{Sec}}$ ), where selenophosphate, synthesized by selenophosphate synthetase, is used as a selenium donor [2]. In Eukaryotes and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[912,18,954,29]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[102,941,670,955]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"0022-2836/$ - see front matter © 2014 The Authors. Published by Elsevier Ltd. All rights reserved. ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[684,941,902,955]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.Mol.Biol.2014)426,1723-1735 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[134,108,850,435]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 1. The enzymatic reaction. Schematic views of the enzymatic reactions of SelA, SepSecS, and cystathionine $\\\\beta$ -lyase (CBL). These enzymes catalyze $\\\\alpha$ position deprotonation, followed by $\\\\beta$ position elimination, to generate tRNA-ligated or non-esterified 2-aminoacrylate intermediates, conjugated with PLP. The substrate of CBL is cystathionine, and the enzyme-substrate interaction is responsible for the $\\\\alpha$ -carboxyl group [8] (c) while SepSecS interacts with the phosphate group of its substrate Sep-tRNA[9]. However, Ser-tRNA[9], the substrate of SelA, has neither a carboxyl nor a phosphate group. Furthermore, the leaving group in the SelA-catalyzed reaction is a hydroxide ion, which is less suitable as compared to the phosphate and the deprotonated homocysteine eliminated in the SepSecS- and CBL-catalyzed reactions, respectively. \"]","image_footnote":"[]","img_path":"images/0681/157e80effbf939f8d515224685983aa04395315cf4c843894b708ba3e7168299.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[92,607,478,747]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Archaea, Ser-tRNA $^{\\text{Sec}}$ is phosphorylated by O-phosphoseryl-tRNA $^{\\text{Sec}}$ kinase (PSTK) to generate O-phosphoseryl-tRNA $^{\\text{Sec}}$ (Sep-tRNA $^{\\text{Sec}}$ ) [3], followed by Sep-to-Sec conversion catalyzed by SepSecS [4,5]. On the other hand, in Bacteria, the selenocysteine synthase SelA directly converts Ser-tRNA $^{\\text{Sec}}$ to Sec-tRNA $^{\\text{Sec}}$ , without a previous phosphorylation step [6]. Both SelA and SepSecS are pyridoxal $5^{\\prime}$ -phosphate (PLP)-dependent enzymes. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,747,482,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"SelA is a homodecameric enzyme with an overall molecular mass of about $500\\mathrm{kDa}$ . We previously determined the crystal structures of SelA with and without tRNA[Sec [7]. The SelA decamer is organized as a pentamer of intimate dimers, and it binds 10 tRNAmolecules. Residues from each of the four SelA subunits of two intimate dimers are involved in processing one Ser-tRNA[Sec] molecule, indicating that the decameric quaternary structure is essential to bind Ser-tRNA[Sec [7]. We proposed the SelA catalytic mechanism based on the co-crystal structure with thiosulfate, an analog of selenophosphate. While the tRNA-binding pocket is formed at the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,607,892,650]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"dimer-dimer interface, the significance of the formation of an $(\\alpha_{2})_{5}$ SelA structure in the generation of functional catalytic sites remained unclear. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,650,894,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The enzymes SelA and SepSecS belong to the largest PLP-dependent enzyme group, the fold-type-I superfamily, and catalyze the replacement of the amino acid $\\beta$ position ( $\\beta$ replacement) in an $\\alpha ,\\beta$ elimination reaction proceeding via a 2-aminoacrylate intermediate and a subsequent addition step (Fig.1) [6]. Although $\\beta$ replacement is a common reaction, there are two major difficulties with the Sec synthesis step. First, the precursor, Ser-tRNA<sup>Sec</sup>, lacks the $\\alpha$ -carboxyl group, which is used for the substrate-enzyme interaction in all fold-type-I PLP-dependent enzymes that work with $\\alpha$ -amino acids [10]. Second, the leaving group in the $\\beta$ elimination step is a hydroxide ion from the Ser moiety (Fig. 1) [6]. In general, a hydroxide ion is not a suitable leaving group, and no other fold-type-I members can eliminate it from the $\\beta$ position of an $\\alpha$ -amino acid. In Eukarya/Archaea, these difficulties are overcome with the assistance of PSTK. PSTK phosphorylates the Ser moiety to generate Sep-tRNA<sup>Sec</sup> [3], which is the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,71,137,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1724 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[670,71,892,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dimer-Dimer Interaction of SelA ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[144,110,378,296]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0953/124ccb7584cd84806bc13e04934d3051e4a424ffaa5d080d3fd37584c794b16b.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[386,108,643,283]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0495/fc5445f0de948b444be0a843dab1fa6119946414f53b816d02bb1f791c29fe58.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[648,110,865,279]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0153/46015ae71814435f8eb42a3ab9a3fe18576b6ad1c3d82b81dfae2a5d1279beb7.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[142,298,489,457]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0233/c5ce20c90ce5bb690e72223ad92922c74db64220305be8ae53cfae0afba08149.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[505,302,826,456]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 2. Structure of SelA. (a) Overall view of the crystal structure of decameric SelA-FL. PLPs are represented as sphere models. The N-terminal domain, the N-linker, the core domain, and the C-terminal domain of subunit A are colored cornflower blue, magenta, blue, and medium-purple, respectively, while those of subunit B are colored green-yellow, yellow, green, and aquamarine, respectively. Subunits C-J are colored gray. (b and c) Close-up views of the interactions at interfaces I (b) and II (c) between intimate dimers. Interactions between subunits A and J are shown. The colors of the ribbon diagrams are the same as in (a). (d and e) Overall views of the dimeric SelA mutants, dSelA-FL (d) and dSelA-ΔN (e). The ribbon diagrams are colored as in (a). dSelA-FL lacks PLP. \"]","image_footnote":"[]","img_path":"images/0365/7eecf4cfa949905552ef79c9fc838711bb8ef1b25f27d46f9273a072e36f2836.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[102,571,492,615]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"substrate of SepSecS (Fig. 1). The $\\beta$ elimination is thus facilitated because the phosphate is an excellent leaving group. Furthermore, the phosphate group is ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,571,905,616]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"predominantly responsible for the substrate binding to SepSecS [9]. In contrast, the bacterial system differs strikingly in that the single enzyme SelA directly ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[104,654,905,853]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0253/5d5344c51b22e7093c792b1e1953cbbd999eb8cfc57d254ed8590801c2f08f10.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":"<table><tr><td>SelA mutant</td><td>Amino acid change E. coli numbering</td><td>A. aeolicus Numbering</td><td>Function of residue</td><td>PLP occupancy (Mut10a- Mut10d) (%)</td><td>Activity in vivo</td></tr><tr><td>1</td><td>ΔGln233-Thr236</td><td>Glu222-Val225</td><td>Decamerization interface I</td><td></td><td>-</td></tr><tr><td>2</td><td>ΔGln233-Gly234</td><td>Glu222, Gly223</td><td>Decamerization interface I</td><td></td><td>-</td></tr><tr><td>3</td><td>Arg185Ala</td><td>Arg174</td><td>Decamerization interface II/III</td><td></td><td>+++</td></tr><tr><td>4</td><td>Thr202Tyr</td><td>Thr191</td><td>Decamerization interface II/III</td><td></td><td>-</td></tr><tr><td>5</td><td>Thr203Tyr</td><td>Thr192</td><td>Decamerization interface II/III</td><td></td><td>-</td></tr><tr><td>6</td><td>His207Ala</td><td>Lys196</td><td>Decamerization interface II/III</td><td></td><td>+++</td></tr><tr><td>7a</td><td>Asp210Ala</td><td>Asp199</td><td>Decamerization interface II/III</td><td></td><td>+++</td></tr><tr><td>7b</td><td>Asp210Arg</td><td>Asp199</td><td>Decamerization interface II/III</td><td></td><td>-</td></tr><tr><td>8</td><td>ΔThr203-Asn204</td><td>Thr192, Asn193</td><td>Decamerization interface II/III</td><td></td><td>-</td></tr><tr><td>9</td><td>Thr202-Arg205 = 2 × Ala</td><td>Thr191-Lys194</td><td>Decamerization interface II/III</td><td></td><td>-</td></tr><tr><td>10a</td><td>Lys295Ala</td><td>Lys285</td><td>Covalent PLP ligand</td><td>n.d.</td><td>-</td></tr><tr><td>10b</td><td>Lys295Ala, Asp294Lys</td><td>Lys285, Asp284</td><td>Covalent PLP ligand</td><td>25</td><td>-</td></tr><tr><td>10c</td><td>Lys295Ala, Leu296Lys</td><td>Lys285, Leu286</td><td>Covalent PLP ligand</td><td>37</td><td>-</td></tr><tr><td>10d</td><td>Lys295Ala, Leu297Lys</td><td>Lys285, Leu287</td><td>covalent PLP ligand</td><td>30</td><td>-</td></tr></table>","table_caption":"[\"Table 1. In vivo mutational analyses of E. coli SelA \"]","table_footnote":"[\"$+ + +$ fully active; $+$ significantly reduced activity; -, inactive; n.d., below detection limit. Mutations introduced in E. coli SelA, numbering of the corresponding residues for A. aeolicus SelA, and functions of the residues as determined from the structures and catalytic activities of the corresponding E. coli SelA variants in vivo are indicated. PLP occupancy for SelA variants 10a-10d is indicated. All SelA variants lacking catalytic activity in vivo were purified and tested for solubility to exclude the possibility that the activity loss was due to inclusion body formation. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[105,71,327,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dimer-Dimer Interaction of SelA ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[862,71,902,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1725 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[132,124,307,266]","code_body":null,"code_caption":null,"image_caption":"[\"a \"]","image_footnote":"[]","img_path":"images/0321/c414e8ef83bd545ee82fb350d336eb64de896520a11def52557cf3fb1ee3a180.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[317,124,490,264]","code_body":null,"code_caption":null,"image_caption":"[\"b \"]","image_footnote":"[]","img_path":"images/0845/2839300d104b836d516c6a6a007f01e0f77f35ed70834634112594d348d61d5f.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[497,124,672,264]","code_body":null,"code_caption":null,"image_caption":"[\"C \"]","image_footnote":"[]","img_path":"images/0058/06104589433bf48e45d62801e6200af0f2fd6f31071da69f336f80951c178d5f.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[680,124,852,264]","code_body":null,"code_caption":null,"image_caption":"[\"d \"]","image_footnote":"[]","img_path":"images/0600/e0d159f4b3f8273ca294d0798ad4a15afb4ff708292d88c4ddb68c7db50aba28.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[132,288,310,431]","code_body":null,"code_caption":null,"image_caption":"[\"e \"]","image_footnote":"[]","img_path":"images/0817/dc871f0fca304b6a86e079fab431c0b69f615d1fc41aa84ecddaf64d0af2f398.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[317,288,490,431]","code_body":null,"code_caption":null,"image_caption":"[\"f \"]","image_footnote":"[]","img_path":"images/0730/210990f6a69b83af360be996edce434f276fb392d25389339f044c1aebda1197.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[497,288,673,430]","code_body":null,"code_caption":null,"image_caption":"[\"g \"]","image_footnote":"[]","img_path":"images/0999/7016b9910beb3e3e4a2ea464910640401d83a98e3049667da0dfb1cb599cbe46.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[682,288,853,430]","code_body":null,"code_caption":null,"image_caption":"[\"h \",\"Fig. 3. Catalytic site comparison. (a–c) Catalytic site comparison between the decameric and dimeric SelAs. The $\\\\beta$ -sheet $\\\\beta6\\\\bullet\\\\beta7$ and $\\\\alpha7$ in the catalytic site also participate in the pentamerizing interaction in the decameric SelA- $\\\\Delta N$ (a). On the other hand, dSelA-FL (b) and dSelA- $\\\\Delta N$ (c) lack the $\\\\beta6\\\\bullet\\\\beta7$ sheet, and $\\\\alpha7$ changes its orientation; therefore, the catalytic site structure is disrupted. dSelA-FL also lacks PLP. Thiosulfate ions are bound in different sites among (a)-(c). Possible hydrogen bonds or ionic interactions are shown as broken lines. (d) Close-up view of the TS4- and TS5-binding sites of dSelA- $\\\\Delta N$ . The $2F_{o} - F_{c}$ electron density map at the $1.0\\\\sigma$ level is shown. (e-h) Catalytic sites of SepSecS (PDB ID: 2Z67 [11]) (e), SepCysS (PDB ID: 2E7J [12]) (f), CBL (PDB ID: 1CL1 [12]) (g), and MJ0158 (PDB ID: 2AEV [13]) (h). They lack the $\\\\beta6\\\\bullet\\\\beta7$ counterpart, and the orientations of their $\\\\alpha7$ counterparts are closer to those of $\\\\alpha7$ in depentamizerized SelA mutants. The phosphate/sulfate ions at the catalytic site are shown. The SepSecS structure 2Z67 is from the archaeon Methanococcus maripaludis. The focused Arg and Lys residues are labeled according to their numbering in human/M. maripaludis SepSecS. \"]","image_footnote":"[]","img_path":"images/0137/77e785da0f445dc75b7d785728b36013b080028b9a86924f159332fc4bb3dded.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[92,607,478,704]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"converts Ser-tRNA $^{\\text{Sec}}$ to Sec-tRNA $^{\\text{Sec}}$ , without phosphorylation. Our previous study suggested a putative binding site for the $3^{\\prime}$ -terminal A76 of tRNA $^{\\text{Sec}}$ , and the binding site could compensate for the lack of the $\\alpha$ -carboxyl group [7]. However, the mechanism that facilitates the hydroxyl-group elimination has not been elucidated. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,706,482,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this study, we have determined the structural basis for productive SelA active-site formation, which requires the cyclization of SelA dimers to a full decamer. Analyses of the structures of Aquifex aeolicus SelA and dimeric SelA variants revealed that the active-site conformations of SelA intimate dimers differ significantly from those of decameric SelA. Structural rearrangements upon decamerization generate 10 catalytically functional active sites that properly accommodate and position Ser-tRNA $^{\\text{Sec}}$ for Sec formation. Based on a comparison of SelA with phylogenetically related enzymes, we describe a refined mechanism for the direct hydroxyl-group elimination facilitated by SelA and propose an evolutionary hypothesis for the emergence of the decameric SelA architecture. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,611,737,627]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results and Discussion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[502,646,890,677]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The dimer-dimer interface in the pentamer-of-dimers structure of SelA ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,691,892,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A. aeolicus SelA is a homodecamer in which the 10 subunits, designated here as subunits A to J, form a \"pentamer of dimers\" (Fig. 2a). The \"intimate dimers\" A•B to I•J have the largest intersubunit interfaces (e.g., A•B interface, $4067\\mathring{\\mathrm{A}}^{2}$ ) on which the enzyme active sites are built. Therefore, the intimate dimer is the basal building block of SelA. In the pentamer-of-dimers quaternary structure, intimate dimers I•J and A•B, for example, interact with each other through subunits J and A. The dimer-dimer interface encompasses $1140\\mathring{\\mathrm{A}}^{2}$ and characteristically constitutes the overall decameric arrangement of SelA. The dimer-dimer interface may be divided into three parts. The first part (part I, $438\\mathring{\\mathrm{A}}^{2}$ ) has internal 2-fold symmetry and is composed of two sets of residues from Asn218 to Phe224, constituting strand $\\beta 11$ within the core domain (Fig. 2b). Strand ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,71,137,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1726 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[670,71,892,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dimer-Dimer Interaction of SelA ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[144,108,381,293]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0110/13f0109053c9f22020ee789a4eb4795b269bafcddeae95083bafa69c9c76bd9c.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[388,107,621,292]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0945/31f68c3fdb429a23ac9d97de88c6e90011f6d0f84b55cfca3e44603781820adb.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[625,110,863,279]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 4. Proposed scheme of the SelA-catalyzed reaction. (a) Docking model of the Ser-ligated terminal nucleotide (A76) of tRNA $^{\\\\text{Sec}}$ and selenophosphate (Se-P). A76 and the Ser moiety are modeled based on the mutational analyses, and their carbon atoms are colored salmon and spring green, respectively. Arg86 is located in the vicinity of Lys285 and Ser. Phe224 from subunit J and Asn218 from subunit A form the A76-binding pocket. The Ser moiety is attached covalently to PLP. Se-P occupies the TS1-binding site. (b) The reaction scheme of the protonation of the $\\\\beta$ -hydroxyl group by Lys285, which enables the elimination of the leaving group (a water molecule). Arg86 may provide the basic environment to strengthen the Lys285 protonation activity. (c) The interaction interface between the core and C-terminal domains of SelA. The N-linker (magenta) and the SelA-specific insertions I and IV (cyan) participate in the interaction between the core and C-terminal domains. The other regions are colored as in Fig. 2a. $\\\\beta1$ in the N-linker forms a $\\\\beta$ -sheet with $\\\\beta18$ in the C-terminal domain. Arg86 in the N-linker participates in the catalytic site. \"]","image_footnote":"[]","img_path":"images/0827/3c434ace1715ab553ee1e13e8b5d28637fd5e87b1679b7b32070b2cd44568d20.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[102,485,490,624]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\beta 11$ from subunit J, for example, and the corresponding strand from subunit A form an antiparallel $\\beta$ -sheet between intimate dimers I·J and A·B. The other parts, II and III (307 Ų each), are symmetrically related to each other. Parts II/III between subunits J and A comprise Arg163, Leu166, Glu168, and Arg174 (η4-loop-β6-loop-β7) from subunit J and Glu188, Thr191, Thr192, Asn193, Lys196, and Asp199 ( $\\beta 8$ -loop-β9-α8) from subunit A and vice versa (Fig. 2c). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[102,624,492,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We introduced mutations into the dimer-dimer interface by using Escherichia coli SelA (Table 1). The amino acid residues in the dimer-dimer interface are conserved between the A. aeolicus and E. coli SelAs, although the conservation in part I is relatively low (Table 1). The Mut1 and Mut2 mutations were designed to impair the antiparallel $\\beta 11\\cdot \\beta 11$ interaction in part I, by deleting residues 222-225 and 222-223, respectively (residue numbering according to A. aeolicus SelA). The enzymes bearing the Mut1 and Mut2 mutations were catalytically inactive in vivo (Table 1), indicating that the integrity of strand $\\beta 11$ and the formation of the resultant antiparallel $\\beta$ sheet are critical for the function of SelA. Mutations targeting parts II/III were also examined (Table 1). Here, the Ala mutations of individual residues in parts II/III exhibited no significant effects on the SelA activity (Mut3, Mut6, and Mut7a). In contrast, the Thr191Tyr, Thr192Tyr, and Asp199Arg mutations (Mut4, Mut5, and Mut7b), which were designed to cause steric clashes, inactivated E. coli SelA in vivo. Similarly, the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,485,902,554]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"deletion of Thr192-Asn193 (Mut8) or the replacement of four residues, Thr191-Lys194, with two Ala residues (Mut9) rendered E. coli SelA inactive in vivo. These results suggested that the integrity of parts II/III is also important for the SelA activity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,567,781,583]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Crystal structure of dimeric SelA ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,595,904,930]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The interface between the intimate dimers is much smaller than that between the subunits within the intimate dimer, suggesting weaker interactions between the dimer units. In fact, a quadruple mutation (Tyr220Pro-Asp199Arg-Thr191Tyr-Thr192Tyr) abolished the pentamerization and resulted in an inactive \"dimerized\" or \"depentamizered\" enzyme [7]. (In the following, we refer to the depentamizerized enzyme as dimeric SelA.) Importantly, dimeric SelA is stable and can be purified for crystallization. In this study, we crystallized the full-length and N-terminally truncated $(\\Delta N,$ deletion of residues 1-61) dimeric SelA proteins and determined their structures at 3.35 and $2.40\\AA$ resolutions, respectively (Fig. 2d and e). The lysine residues of the dimeric full-length SelA (dSelA-FL) were methylated for crystallization improvement, while the dimeric SelA- $\\Delta N$ (dSelA- $\\Delta N$ ) was crystallized without Lys methylation. The overall structures of dSelA-FL and dSelA- $\\Delta N$ are similar to each other and to those of the intimate dimers of decameric SelA-FL and SelA- $\\Delta N$ ,respectively. Each subunit of dSelA-FL consists of the N-terminal domain (residues 1-66), the N-linker (residues 67-89), the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[105,71,327,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dimer-Dimer Interaction of SelA ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[862,71,902,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1727 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[132,114,307,394]","code_body":null,"code_caption":null,"image_caption":"[\"a \",\"b \"]","image_footnote":"[]","img_path":"images/0098/664e234838d063ebc13441e695c4043dd14b1d6aa7697ca81075168425451d59.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[322,200,478,394]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0329/4dacf71f21dc3b5d791c4bdc1329796f1de5b377dc2b3a6f898546f067beca29.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[505,146,694,394]","code_body":null,"code_caption":null,"image_caption":"[\"C \",\"d \"]","image_footnote":"[]","img_path":"images/0286/8474d97e5724e76f8fe67fc78cb0d6d7f625e2754abdff50cb848ab4875b98e0.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[687,191,848,394]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0400/b9b1e559a50870e4db61597dcdd050a1d7b20d59a0b4c6a7b71b51345df810c4.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[132,422,305,556]","code_body":null,"code_caption":null,"image_caption":"[\"e \"]","image_footnote":"[]","img_path":"images/0996/c737a847a96c259ec2c8050da24ebd65f4154fa330049aab5b7e7605cae4233f.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[315,422,487,557]","code_body":null,"code_caption":null,"image_caption":"[\"f \"]","image_footnote":"[]","img_path":"images/0465/05ddad5b7fb470b156336d1dd24d1bc9b1ed24f685ce3b8bc50a138030bc5c73.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[497,422,673,554]","code_body":null,"code_caption":null,"image_caption":"[\"g \"]","image_footnote":"[]","img_path":"images/0938/600788169c9ceeeced0a56df4c0ef48097b4274d80172db572e445593c3a4e6c.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[682,422,852,554]","code_body":null,"code_caption":null,"image_caption":"[\"h \",\"Fig. 5. Structure comparison with other fold-type-I PLP-dependent enzymes. (a-d) Overall crystal structures of SepSecS (PDB ID: 2Z67 [8]) (a), SepCysS (PDB ID: 2E7J [11]) (b), cystathionine $\\\\beta$ -lyase (CBL) (PDB ID: 1CL1 [12]) (c), and MJ0158 (PDB ID: 2AEV [13]) (d). The N-terminal domains, the N-linkers, the core domains, and the C-terminal domains of subunits A and B are colored as in Fig. 2a. The N-terminal regions of SepCysS and MJ0158 correspond to the SelA N-linker. Like the SelA N-linker, these regions form $\\\\beta$ -sheets with their C-terminal domains. On the other hand, the N regions of the homotetrameric enzymes SepSecS and CBL participate in the interactions between the two intimate dimers, and thus, they occupy different positions from that of the SelA N-linker. The intimate dimers C-D of SepSecS and CBL are colored gray in the top panels and are not shown in the bottom panels. (e-h) Comparison of the C-terminal domain orientation with SelA. The A subunits of SepSecS (e), SepCysS (f), CBL (g), and MJ0158 (h) were superposed on the SelA subunit A, by fitting their core domains. The core and C-terminal domains of SelA are colored blue and medium-purple, respectively, as in Fig. 2a, while those of the other PLP-dependent enzymes are colored light blue and yellow, respectively. The major helices $\\\\alpha12$ and $\\\\alpha14$ , located in the core and C-terminal domains, respectively, are connected by the short helices $\\\\eta7$ and $\\\\alpha13$ in SelA. In contrast, the $\\\\alpha12$ and $\\\\alpha14$ counterparts are directly connected in SepSecS and form a continuous single helix in SepCysS and CBL. On the other hand, MJ0158 has the $\\\\alpha13$ counterparts, and the orientation of its C-terminal domain is somewhat closer to that of the SelA C-terminal domain. \"]","image_footnote":"[]","img_path":"images/0390/aae15da50fed8c00500404fa6ef748b9deb4709f2f5e47e509796e5f8eee9e94.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[92,800,480,857]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"core domain (residues 90-338), and the C-terminal domain (residues 339-452) (Fig. 2d). The $\\beta 11$ strand in part I of the dimer-dimer interface is disordered in the dSelAs. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,870,331,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Catalytic site of dimeric SelA ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,897,480,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The catalytic site is located at the subunit interface, involving the core domains and the N-linker, within ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,800,892,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the intimate dimer unit of SelA. PLP is covalently bound to Lys285, as a Schiff base. Surprisingly, the catalytic site structures of dSelA-FL and dSelA- $\\Delta N$ differ distinctly from that of the SelA decamer (Fig. 3a-c). The dimeric SelAs lack a SelA-specific $\\beta$ -sheet ( $\\beta6\\bullet\\beta7$ ), and $\\alpha7$ has a distinct orientation. These different catalytic site conformations of the dimeric mutants resemble those of other fold-type-I PLP enzymes (Fig. 3b, c, and e-h). The position of ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,71,137,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1728 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[670,71,892,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dimer-Dimer Interaction of SelA ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[107,112,489,264]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PLP in the dSelA- $\\Delta N$ catalytic site is the same as that in the SelA decamer, while dSelA-FL lacked PLP in its catalytic site. PLP may have been removed during the Lys methylation of dSelA-FL, whereas the decameric SelA-FL and SelA- $\\Delta N$ retained PLP during the methylation [7]. This indicated that the depentamerization increased the accessibility of Lys285, which probably resulted in the replacement of PLP by a methyl group, although the methyl group was not visible in the structure due to the high mobility of the Lys285 side chain. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[107,264,489,554]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The thiosulfate-binding sites also differ from those of the decameric SelA- $\\Delta N$ (Fig. 3a-c). The decameric SelA- $\\Delta N$ binds three thiosulfate ions (TS1-TS3) in each catalytic site. TS1 may mimic the substrate selenophosphate, and TS2 and TS3 may mimic the phosphate groups of the nucleotides A76 and C75 of the tRNA Sec CCA terminus [7]. In contrast, dSelA- $\\Delta N$ binds two thiosulfate ions, TS4 and TS5. TS4 may correspond to TS1, but TS5 does not correspond to any of TS1-TS3. TS1 interacts with $\\mathrm{Arg86^{A}}$ (subunit A residue) and $\\mathrm{Arg312^{B}}$ and $\\mathrm{Arg315^{B}}$ (subunit B residues), whereas TS4 interacts with Ser $172^{A}$ , $\\mathrm{Arg174^{A}}$ , $\\mathrm{Arg116^{B}}$ , and $\\mathrm{Arg315^{B}}$ (Fig. 3d). The distance between TS1 and TS4 is about $3.5\\AA$ . TS5 interacts with $\\mathrm{Arg312^{B}}$ and $\\mathrm{Arg315^{B}}$ . dSelA-FL also has two thiosulfate ions, TS5 and TS6. TS5 is the same as that in dSelA- $\\Delta N$ , whereas TS6 occupies the position of the PLP phosphate group. The difference between the thiosulfate-binding sites of dSelA- $\\Delta N$ and dSelA-FL may be caused by the lack of PLP in the catalytic sites of dSelA-FL. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[107,554,489,733]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In decameric SelA, the $\\beta 6\\bullet \\beta 7$ sheet is stabilized by the pentamerizing interactions. The main chain NH and carbonyl moieties of Glu168 in $\\beta 6$ interact with Asn193, and the Arg174 side chain forms a salt bridge with Asp199 (Fig. 3a). Since Arg174 also participates in $\\alpha 7$ , the $\\alpha 7$ orientation is dependent on the Arg174 position, which is fixed by the Arg174 Asp199 salt bridge. Although the $\\beta 6\\bullet \\beta 7$ sheet has no polar interactions with the thiosulfate ions, Gly170 in the $\\beta 6 - \\beta 7$ loop is close to TS1 and forms a van der Waals interaction (Fig. 3a). Therefore, the $\\beta 6\\bullet \\beta 7$ sheet contributes to TS1 binding and is important for catalysis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[107,733,489,844]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"These results indicated that the formation of the catalytic site structure is dependent on the pentamerization of intimate dimers and that the dimeric mutant cannot properly bind its substrates. The activity loss by the mutations introduced to the pentamerization interfaces (Table 1) should result from both the prevention of decamer-dependent tRNA $^{\\text{Sec}}$ binding and the disruption of the catalytic core structure. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[107,858,489,887]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"How does SelA eliminate the hydroxyl group from the Ser moiety? ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[107,900,489,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In general, proper binding and hydroxyl-group protonation of the substrate are essential for an ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,112,900,237]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"enzyme to eliminate a hydroxyl group. SelA has a putative binding pocket for the A76 adenine ring (Fig. 4a) [7] and can therefore accommodate the Ser moiety of Ser-tRNA $^{\\text{Sec}}$ . This binding pocket is critically important because Ser-tRNA $^{\\text{Sec}}$ lacks the $\\alpha$ -carboxyl group, which is used for the substrate-enzyme interaction in all of the fold-type-I superfamily PLP-dependent enzymes working on $\\alpha$ -amino acids [10]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,238,900,554]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To examine the mechanism of hydroxyl-group protonation, we compared SelA with other PLP-dependent enzymes. SelA is the only fold-type-I enzyme that eliminates the hydroxyl group from the substrate amino acid (or amino acid moiety). Therefore, we compared SelA with cystathionine $\\beta$ -synthase (CBS), a fold-type-II PLP-dependent enzyme that catalyzes a $\\beta$ replacement reaction. CBS eliminates the hydroxyl group from serine to generate 2-aminoacrylate and then adds homocysteine to synthesize cystathionine (Supplementary Fig. 1a). The $\\beta$ elimination step is the same as that in SelA catalysis (Fig. 1). A crystallographic study revealed that Tyr227 of CBS is responsible for the protonation of the serine hydroxyl group [14]. Interestingly, cysteine synthase (CysS), the close homolog of CBS, lacks the corresponding Tyr residue [15]. CysS catalyzes the $\\beta$ replacement reaction that eliminates an acetyl group from O-acetylserine, and it adds hydrogen sulfide to generate cysteine (Supplementary Fig. 1b). In this reaction, the leaving group is acetate, and thus, hydroxyl-group protonation is unnecessary. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,554,900,857]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"On the other hand, SelA lacks residues such as Tyr, His, and Cys that could serve as proton donors in the vicinity of the Ser-moiety-binding site, except for Lys285, which forms a Schiff base with PLP in the waiting state. Some enzymes in the sugar aminotransferase subfamily catalyze the elimination of the $\\alpha$ -hydrogen and the $\\beta$ -hydroxyl group. Here, the $\\alpha$ position indicates the position of the amino group conjugated with PLP during catalysis. The enzymes GDP-6-deoxy- $\\alpha$ -D-/lyxo-hexopyranos-4-ulose dehydratase (ColD) and CDP-6-deoxy- $\\alpha$ -D-xylo-hexopyranos-4-ulose dehydratase ( $E_1$ ) employ a His residue, which is conserved at the position of the PLP-coordinating Lys285 of SelA, to catalyze the $\\alpha,\\beta$ elimination step (Supplementary Fig. 1c and d) [16,17]. In contrast, 5-amino-3-hydroxybenzoate (AHBA) synthase, another enzyme that eliminates the $\\alpha$ -hydrogen and the $\\beta$ -hydroxyl group (Supplementary Fig. 1e), contains a conserved Lys residue, which is considered to protonate the $\\beta$ -hydroxyl group [18]. Here, the generation of a benzene ring in the product is likely to promote the $\\alpha,\\beta$ elimination reaction. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,858,900,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"These findings suggested that Lys285 in SelA can act as proton donor for the $\\beta$ -hydroxyl group (Fig. 4b). As enzymes such as ColD and $E_{1}$ utilize His, instead of Lys, to strengthen the protonation activity and AHBA generates a benzene ring to promote the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[107,73,326,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dimer-Dimer Interaction of SelA ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,71,900,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1729 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[132,108,855,638]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 6. Structure-based phylogenetic tree of the fold-type-I PLP-dependent enzymes. SelA and the crystal structures of the fold-type-I PLP enzymes, deposited in the Protein Data Bank, were analyzed. The enzyme names are colored based on their catalysis type: the enzymes that catalyze aminotransfer (AT), $\\\\alpha$ -carboxyl group replacement, $\\\\alpha$ -hydrogen replacement, reverse aldol reaction, $\\\\alpha, \\\\beta$ elimination, $\\\\beta$ replacement (type 1), $\\\\beta$ replacement (type 2), $\\\\alpha, \\\\gamma$ elimination, and $\\\\gamma$ replacement are colored dark blue, blue, sky blue, blue-violet, magenta, red, orange, spring green, and green, respectively. The enzymes with unknown functions are colored gray. The structure-based phylogenetic analysis revealed that SelA, SepSecS, and SepCysS [20] belong to distinct taxa of the fold-type-I PLP-dependent enzymes. SelA is likely to form an independent group related to the cystathionine $\\\\gamma$ -synthase (CGS) family. SepCysS is close to the cysteine desulfurase and kynureninase families, while SepSecS also forms another independent group close to the sugar aminotransferase (AT) family. \"]","image_footnote":"[]","img_path":"images/0361/d13fd3bdcefc0158438304d6c94c9a09870432e4e93be4533baf2f22ce982c45.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[92,829,480,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"protonation and elimination of the $\\beta$ -hydroxyl group, an additional auxiliary mechanism to support protonation and $\\beta$ -hydroxyl elimination might be plausible for SelA as well. Such a mechanism would involve the Arg86 residue (Fig. 4a and b). Our in vivo mutational assay revealed that Arg86 is mandatory for activity [7]. Arg86 is located in the vicinity of Lys285 (Fig. 4a), and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,829,894,930]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the positive charge of Arg86 may reinforce the protonation activity of Lys285. Arg86 is located in the N-linker between the N and core domains. The $\\beta$ -strand $\\beta 1$ in the N-linker forms a $\\beta$ -sheet with $\\beta 18$ from the C-terminal domain (Fig. 4c). Although the corresponding $\\beta$ -sheet is present in many fold-type-I PLP-dependent enzymes, the C-terminal domain ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[97,71,136,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1730 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[670,71,890,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dimer-Dimer Interaction of SelA ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[168,108,840,418]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 7. Possible steps of SelA (a) and SepSecS (b) evolution. The dimeric SelA ancestor accommodated the tRNA $^{\\\\text{Sec}}$ acceptor arm within the cleft between the core and C-terminal domains. The ancestor interacted with the substrate Sep-tRNA $^{\\\\text{Sec}}$ by binding its Sep phosphate group at the selenophosphate (Se-P)-binding site. Therefore, the Sep-to-Sec reaction and the tRNA discrimination were dependent on the Sep phosphate group. Tetramerization created the A76-binding pocket, and decamerization stabilized the interactions among intimate dimers. Finally, the acquired N-terminal domain discriminated tRNA $^{\\\\text{Sec}}$ from tRNA $^{\\\\text{Ser}}$ , by interacting with the unique D arm of tRNA $^{\\\\text{Sec}}$ . The A76-binding pocket and the tRNA $^{\\\\text{Sec}}$ discrimination enabled Ser-to-Sec conversion, and thus, SelA became independent of the Sep phosphate group. On the other hand, the dimeric SepSecS interacted with the extra arm side of the tRNA $^{\\\\text{Sec}}$ acceptor arm, since it lacks the cleft between the core and C-terminal domains. Tetramerization stabilized the tRNA $^{\\\\text{Sec}}$ binding by interacting with its T and extra arms, without recognizing the unique D arm structure. Therefore, SepSecS is unable to become independent of the Sep phosphate group of Sep-tRNA $^{\\\\text{Sec}}$ . \"]","image_footnote":"[]","img_path":"images/0309/6db4b59976575de7fbea46196895e5272489866ec1518b6d0377545377e69576.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[107,622,489,746]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"orientation in SelA differs from those of the other homologs (Fig. 5). The unique C-terminal domain orientation in SelA results in the specific positioning of the N-linker that allows participation in the catalytic site. This structural feature is the reason why the N-linker can provide Arg86 in the vicinity of Lys285. Here again, the characteristic tertiary and quaternary structures of SelA are essential for its unique catalytic activity to eliminate the hydroxyl group. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[107,747,489,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"SepSecS also possesses an Arg residue (Arg75 in human SepSecS) that occupies the space corresponding to SelA Arg86 [9]. However, Arg75 is located in the core domain of SepSecS and is not an alignment-based counterpart of SelA Arg86, which is in the N-linker. In fact, Arg75 forms an intersubunit interaction with Lys-bound PLP; that is, $\\mathrm{Arg75^{B}}$ interacts with PLP-Lys284 $^{\\text{A}}$ (Fig. 3e). In contrast, the Arg86 and PLP-Lys285 interaction is an intrasubunit one (Figs. 3a and 4a). Moreover, the PLP-ligated Lys284 in SepSecS cannot protonate the $\\beta$ -hydroxyl group of the Ser moiety; SepSecS cannot bind Ser-tRNA $^{\\text{Sec}}$ because the phosphate group of the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,622,900,650]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sep moiety is essential for the substrate Sep-tRNA Sec binding. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,664,900,691]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Why did two different pathways for Sec formation evolve? ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[517,704,900,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Considerable conservation of the translation machinery components exists among the three domains of life. However, the pathways of aminoacyl-tRNA formation evolved much more independently. For instance, the synthesis of Asn-tRNA or Gln-tRNA involves tRNA-dependent and tRNA-independent amino acid biosynthesis routes [19]. In the case of Sec, nature also designed distinct routes based on the different enzyme structures operating in Bacteria versus Archaea/Eukaryotes. Our phylogenetic analysis (Fig. 6) revealed that SelA is related to the cystathionine $\\gamma$ -synthase (CGS) family members catalyzing the $\\beta$ elimination of cysteine derivatives or the $\\gamma$ elimination and $\\gamma$ replacement of homocysteine products. Thus, the ancestor of SelA may have been an enzyme involved in sulfur metabolism. The protein ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[107,73,326,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dimer-Dimer Interaction of SelA ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,71,899,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1731 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[92,126,894,556]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0984/71bf8d9ffad96de83637d794068b326603c01d0f966389c58692d2d8012454d6.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":"<table><tr><td></td><td>dSelA-FL4KA (SeMet)</td><td>dSelA-ΔN (SeMet)</td></tr><tr><td>Lys methylation</td><td>+</td><td>-</td></tr><tr><td>Data collection</td><td></td><td></td></tr><tr><td>Beam line</td><td>SPring-8 BL41XU</td><td>SPring-8 BL41XU</td></tr><tr><td>Wavelength (Å)</td><td>0.97915</td><td>0.97915</td></tr><tr><td>Space group</td><td>I422</td><td>P21</td></tr><tr><td>Cell parameters</td><td></td><td></td></tr><tr><td>a (Å)</td><td>144.1</td><td>59.2</td></tr><tr><td>b (Å)</td><td>144.1</td><td>81.3</td></tr><tr><td>c (Å)</td><td>273.4</td><td>95.5</td></tr><tr><td>β (°)</td><td></td><td>92.2</td></tr><tr><td>Resolution (Å)</td><td>50.0–3.35 (3.47–3.35)a</td><td>50.0–2.40 (2.49–2.40)a</td></tr><tr><td>Unique reflections</td><td>21,096 (2066)a</td><td>35,457 (3520)a</td></tr><tr><td>Completeness (%)</td><td>99.7 (100.0)a</td><td>99.6 (100.0)a</td></tr><tr><td>Redundancy</td><td>6.0 (6.1)a</td><td>3.8 (3.8)a</td></tr><tr><td>Rsymb</td><td>0.102 (0.712)a</td><td>0.082 (0.561)a</td></tr><tr><td>I/σ(I)</td><td>17.2 (2.75)a</td><td>15.9 (2.40)a</td></tr><tr><td>Structure refinement</td><td></td><td></td></tr><tr><td>Working-set reflections</td><td>19,970</td><td>33,593</td></tr><tr><td>Test-set reflections</td><td>1062</td><td>1770</td></tr><tr><td>Resolution (Å)</td><td>50.0–3.35</td><td>50.0–2.40</td></tr><tr><td>Number of SelA subunits</td><td>2 (one dimer)</td><td>2 (one dimer)</td></tr><tr><td>Number of protein atoms</td><td>7035</td><td>6018</td></tr><tr><td>Number of PLP</td><td>0</td><td>2</td></tr><tr><td>Number of ions</td><td>4 (thiosulfate)</td><td>5 (thiosulfate)</td></tr><tr><td>Number of solvent molecules</td><td>0</td><td>153</td></tr><tr><td>Rwork/Rfree</td><td>0.194/0.250</td><td>0.180/0.230</td></tr><tr><td>Average B-factor (Å2)</td><td></td><td></td></tr><tr><td>Overall</td><td>144.3</td><td>64.4</td></tr><tr><td>Protein</td><td>144.2</td><td>64.6</td></tr><tr><td>PLPs</td><td>—</td><td>49.8</td></tr><tr><td>Ion</td><td>162.4</td><td>79.0</td></tr><tr><td>Solvent</td><td>—</td><td>56.7</td></tr><tr><td>RMSD bond lengths (Å)</td><td>0.009</td><td>0.008</td></tr><tr><td>RMSD bond angles (°)</td><td>1.27</td><td>1.12</td></tr></table>","table_caption":"[\"Table 2. Data collection and refinement statistics. \"]","table_footnote":"[\"a The statistics in the highest-resolution shell are given in parentheses. \",\"$R_{\\\\mathrm{sym}} = \\\\sum_{hkl}\\\\sum_l[\\\\mathcal{I}_l(hkl) - \\\\langle I(hkl)\\\\rangle ] / \\\\sum_{hkl}\\\\sum_l[I_l(hkl)]$ where $I_{\\\\ell}(hkl)$ is the intensity of the $\\\\lambda h$ measurement of $hkl$ and $\\\\langle I(hkl)\\\\rangle$ is the average value of $I_{\\\\ell}(hkl)$ for all $\\\\lambda h$ measurements. \",\"$R_{\\\\mathrm{work,free}} = \\\\sum_{hkl}(|F_0| - |f_{\\\\mathrm{c}}||) / \\\\sum_{hkl}(|F_0|),$ where $R_{\\\\mathrm{work}}$ and $R_{\\\\mathrm{free}}$ are calculated using the working-set and test-set reflections (5% of the total reflections), respectively. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[90,663,480,815]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"closest to SelA in the phylogenetic tree is the archaeal MJ0158, a homodimeric protein of unknown function that does not interact with tRNA $^{\\text{Sec}}$ (Fig. 6) [13]. Interestingly, the orientation of the C-terminal domain of MJ0158 is similar to that of the SelA C-terminal domain (Fig. 5d and h), suggesting that the change in the domain orientation occurred before SelA acquired its function. Although the N-linker of MJ0158 occupies the similar space to that of SelA, MJ0158 has a Ser residue at the corresponding position of SelA Arg86, which may reflect its functional difference from SelA. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[90,815,480,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Since the binding of the A76-Ser moiety of Ser-tRNA is impossible without the decameric assembly (the putative A76-binding site is formed at the dimer-dimer interface) [7], it is plausible that a dimeric SelA ancestor depended on the phosphate group and simply converted Sep to Sec without tRNA $^{\\text{Sec}}$ discrimination, as in the case of SepSecS (Fig. 7). In fact, the extant SelA can produce Sec-tRNA $^{\\text{Sec}}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,662,890,844]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"from Ser-tRNA $^{\\text{Sec}}$ and from Sep-tRNA $^{\\text{Sec}}$ [5], confirming that the Sec synthesis by SelA does not rely on the phosphate group of the substrate aminoacyl moiety. Like SepSecS, the SelA ancestor may have used its selenophosphate-binding site to bind the Sep phosphate moiety in order to facilitate the elimination of the phosphate group from Sep. In this case, either PSTK or an enzyme with a similar function must have existed for the phosphorylation of Ser and the discrimination of tRNA $^{\\text{Sec}}$ from tRNA $^{\\text{Ser}}$ . Alternatively, the ability of SepSecS to convert Ser to Sec was lost when PSTK evolved for more efficient Sec production. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,863,705,880]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Evolving decamerization ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[502,897,890,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In a subsequent evolutionary step, the collaboration of the two SelA dimers could have occurred to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,71,137,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1732 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[670,71,890,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dimer-Dimer Interaction of SelA ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[107,112,489,401]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"generate the A76-binding pocket at the dimer-dimer interface, thereby improving the efficiency and specificity of substrate binding. Nonetheless, in such a tetramer, only two of the four catalytic sites would have been functional (the \"half-of-the-sites\" stage). The relative orientations between the dimers could then be stabilized by acquiring decameric ring closure involving five dimers. Simultaneously, the full usage of all 10 catalytic sites was achieved (Fig. 7a). Interestingly, the non-productive catalytic site conformation of the dimeric mutant dSelA- $\\Delta N$ resembles those of the other fold-type-I members (Fig. 3b, c, and e-h) and therefore appears to be more primeval. The loop region before $\\alpha 7$ interacts with PLP in dSelA- $\\Delta N$ (Fig. 3b and c), while it forms a $\\beta$ -sheet ( $\\beta 6\\bullet \\beta 7$ ) in the SelA decamer (Fig. 3a). Hence, the catalytic site may have evolved by taking advantage of the decameric quaternary structure. The N-terminal domain was then acquired to increase its affinity for tRNA $^{\\mathrm{Sec}}$ and was further utilized for the discrimination of tRNA $^{\\mathrm{Sec}}$ from tRNA $^{\\mathrm{Ser}}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[107,428,215,443]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conclusion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[107,457,489,706]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The natural decameric arrangement of five SelA dimers allows the formation of 10 fully occupied and catalytically functional active sites. Since SelA decamerization is driven by dimer-dimer interactions, disruptive mutations at the interaction interfaces solely yield SelA dimers. In striking contrast to decameric SelA, these dimers are catalytically deficient and exhibit a distinctly distorted active-site formation that prevents productive tRNA $^{\\text{Sec}}$ coordination. In fact, the dimeric SelA conformationally resembles similar related PLP enzymes, such as the tetrameric SepSecS. The evolution of the SelA decamer may have been driven by enhanced catalytic efficiency obtained from two sources: First, the decamer allows for an active-site conformation that is optimal for direct, tRNA-dependent Ser-to-Sec conversion. Second, the 10-subunit architecture of SelA generates an N-terminal domain with the ability to discriminate tRNA $^{\\text{Sec}}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[107,738,324,752]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Materials and Methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[107,773,245,786]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Protein preparation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[107,800,489,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The genes encoding the full-length and $\\Delta N$ SelA genes from A. aeolicus were cloned into the vectors pET25b and pET22b (Novagen), respectively. The full-length SelA used for crystallization was a quadruple mutant, with the non-conserved Lys residues in the loop regions of the N-terminal domain replaced by Ala residues, Lys19Ala-Lys21Ala-Lys46Ala-Lys48Ala (SelA-FL $^{4KA}$ ). The dimerizing quadruple mutation, Tyr220Pro-Asp199Arg-Thr191Tyr-Thr192Tyr, was introduced into SelA-FL $^{4KA}$ and SelA- $\\Delta N$ by QuikChange site-directed mutagenesis (Stratagene). The E. coli strain ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[519,112,900,225]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Rosetta 2(DE3) (Stratagene) was transformed with the expression plasmids, and the native and selenomethionine (SeMet)-substituted proteins were overexpressed and purified as previously described [21]. In order to improve the crystallization efficiency, we methylated the lysine residues of dSeIA-FL $^{4\\mathrm{KA}}$ with formaldehyde and a dimethylamine-borane complex, as previously described [22]. Prior to methylation, the protein was diluted with $20~\\mathrm{mM}$ Hepes-NaOH buffer $(\\mathsf{pH}7.5)$ , containing $0.8\\mathrm{MNaCl}$ and $10~\\mathrm{mM}$ 2-mercaptoethanol. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[519,245,880,259]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Crystallization and X-ray diffraction data collection ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[519,277,900,377]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The SelA proteins were crystallized at $20^{\\circ}\\mathrm{C}$ by the sitting-drop vapor diffusion method, by mixing $0.75\\mu \\mathrm{l}$ of the sample with $0.75\\mu \\mathrm{l}$ of reservoir solutions. Prior to crystallization, dSelA-FL 4KA (SeMet substitution, Lys methylation) and dSelA-ΔN (SeMet substitution, without methylation) were dialyzed against $20\\mathrm{mM}$ Tris-HCl buffer $(\\mathsf{pH}7.5)$ , containing $200\\mathrm{mMNaCl}$ and $10\\mathrm{mM}$ 2-mercaptoethanol, and were concentrated to 9.6 and $7.8\\mathrm{mg / ml}$ , respectively. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[519,377,900,501]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Crystal Screen 2, Natrix (Hampton Research), Wizard I, and Wizard II (Emerald Bio-Science) screening kits were used for the initial screening of the crystallization conditions. The optimized reservoir solutions were $100\\mathrm{mM}$ trisodium citrate-HCl buffer $(\\mathsf{pH}5.6)$ containing $580 - 590\\mathrm{mM}$ trisodium citrate, $100\\mathrm{mM}$ L-serine, and $100\\mathrm{mMNa_2S_2O_3}$ for dSelA-FL4KA, as well as $100\\mathrm{mM}$ sodium 4-morpholineethanesulfonate HCl buffer $(\\mathsf{pH}6.5)$ containing $2.5\\%$ polyethylene glycol 4000, $150\\mathrm{mM}$ $\\mathrm{Na_2S_2O_3}$ , and $70\\mathrm{mMNaNO_3}$ for dSelA- $\\Delta \\mathsf{N}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[519,503,900,653]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The crystals thus obtained were transferred into cryoprotective solutions composed of $100\\mathrm{mM}$ trisodium citrate-HCl buffer $(\\mathsf{pH}5.6)$ , containing $1.3\\mathrm{M}$ trisodium citrate, $75\\mathrm{mM}$ L-serine, and $75\\mathrm{mMNa_2S_2O_3}$ for dSelA-FL4KA, as well as $100\\mathrm{mM}$ sodium 4-morpholineethanesulfonate HCl buffer $(\\mathsf{pH}6.5)$ , containing $30\\%$ dimethyl sulfoxide, $10\\%$ polyethylene glycol 4000, $50\\mathrm{mMNa_2S_2O_3}$ , and $70\\mathrm{mMNaNO_3}$ for dSelA- $\\Delta N_{i}$ and were flash-cooled in a cryo- $N_{2}$ stream. X-ray diffraction data were collected at $90~\\mathrm{K}$ by using synchrotron radiation at the BL41XU of SPring-8 (Harima, Japan). The data were processed with the HKL2000 program [23]. The statistics of the diffraction data collection are listed in Table 2. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[519,673,801,686]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Structure determination and refinement ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[519,699,900,814]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The structures of the dimeric SelAs, dSelA-FL $^{4KA}$ and dSelA- $\\Delta N$ , were solved by the molecular replacement method, using the Phaser program [24]. The search model was the SelA- $\\Delta N$ structure. The Coot program [25] was used for manual fitting of the models to the electron density map. The structures were refined against the diffraction data by using the CNS [26] and PHENIX [27] programs, with iterative cycles of positional and temperature factor refinements (Table 2). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[519,834,884,847]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Production and purification of E. coli SelA variants ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[519,863,900,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mutations were introduced by site-directed mutagenesis (QuikChange®; Agilent) to E. coli K12 SelA, from the ASKA E. coli K12 ORF library (GFP-minus), cloned in the pC24N vector [28]. E. coli BL21 cells were transformed with the expression plasmids. For protein overproduction, the cells ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[107,73,326,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dimer-Dimer Interaction of SelA ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[863,71,900,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1733 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[92,112,480,327]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"were grown at $25^{\\circ}\\mathrm{C}$ in LB selective medium, supplemented with $50~\\mu \\mathrm{M}$ isopropyl $\\beta$ -D-1-thiogalactopyranoside. Cells sedimented from overnight cultures were resuspended in lysis buffer (50 mM $\\mathrm{KH}_2\\mathrm{PO}_4$ pH 8,300 mM NaCl, $15\\%$ glycerol, $10\\mathrm{mM}$ imidazole) and disrupted by sonication. After centrifugation (50,000g, 45 min, $4^{\\circ}\\mathrm{C})$ the clarified lysates were subjected to immobilized metal affinity chromatography, using Ni-NTA affinity resin (Qiagen) on gravity-flow columns. The immobilized $6\\times$ His-SelA fusion proteins were washed with lysis buffer supplemented with $40~\\mathrm{mM}$ imidazole, and SelA was eluted with $240~\\mathrm{mM}$ imidazole in lysis buffer. The excess imidazole was removed by dialysis (50 mM Tris-HCl, pH 7.5, 300 mM NaCl, $15\\%$ glycerol), and the purified SelA variants were analyzed by SDS-PAGE and stored at $-80^{\\circ}C.$ The amounts of protein-bound PLP in the SelA variants were determined by UV/vis spectroscopy at $420~\\mathrm{nm}$ and in comparison to a PLP standard curve $(0 - 2\\mathrm{mM})$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,345,346,360]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"E. coli SelA in vivo activity assays ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,373,482,726]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For in vivo SelA assays, a marker-less $E$ coli SelA deletion strain was used. The initial SelA deletion strain JS1 was constructed by the replacement of the SelA gene with a kanamycin cassette in $E$ coli strain BW25113, as previously described [29], and the genomic insertion of T7 polymerase by P1 transduction [4]. The kanamycin resistance marker of $E$ coli strain JS1 was then excised by FLP recombinase-mediated homologous recombination between the FRT sites flanking the kanamycin resistance cassette, upon transformation of the JS1 strain with the plasmid pCP20 [30], resulting in the marker-less $E$ coli ΔselA strain JS2. $E$ coli ΔselA was then transformed with the plasmids encoding the $E$ coli SelA variants and grown on LB selective medium. Overnight cultures of these clones were plated on selective LB agar plates supplemented with $10~\\mu \\mathrm{M}$ isopropyl $\\beta$ -D-1-thiogalactopyranoside, $1\\mu \\mathrm{M}$ $\\mathrm{Na}_2\\mathrm{MoO}_4$ , $1\\mu \\mathrm{M}$ $\\mathrm{Na}_2\\mathrm{SeO}_3$ , and $50~\\mathrm{mM}$ sodium formate, as described previously [4], and grown anaerobically at $37^{\\circ}\\mathrm{C}$ overnight. For the oxygen-sensitive benzyl viologen assay, the plates were transferred to an anaerobic chamber (90% $\\mathbf{N}_2$ , 5% $\\mathbf{H}_2$ , 5% $\\mathbf{CO}_2$ ) and overlaid with top agar containing $1\\mathrm{mg / ml}$ benzyl viologen, $250~\\mathrm{mM}$ sodium formate, and $25\\mathrm{mM}$ $\\mathrm{KH}_2\\mathrm{PO}_4 / \\mathrm{K}_2\\mathrm{HPO}_4$ (pH 7.0). Wild-type SelA served as a positive control. The benzyl viologen assay allows the colorimetric monitoring of SelA activity by the formation of purple-colored reduced benzyl viologen. Benzyl viologen reduction is catalyzed by $\\mathrm{FDH_H}$ , which requires Sec insertion for catalytic activity. The Sec formation, finally, is dependent on the SelA activity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,747,342,762]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Structure-based phylogenetic tree ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,774,482,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The STAMP program [31] in the MultiSeq module of VMD [32] was used to superpose and calculate the structural similarity, $Q_{\\mathrm{H}}$ , among the coordinates of SelA-ΔN and the other fold-type-I PLP-dependent enzymes obtained from the Protein Data Bank. The enzymes with $>50\\%$ amino acid sequence identity were removed, and thus, the core domains of 187 coordinates, including the coordinates of both chains A and B of the heterodimeric glycine decarboxylase (PDB ID: 1WYT), were superposed. The other 185 enzymes were homooligomeric ones. The structural similarity $Q_{\\mathrm{H}}$ was calculated [33], and the neighbor-joining tree, based on the $Q_{\\mathrm{H}}$ values, was drawn using the SplitsTree program [34]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,112,653,124]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Accession numbers ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[504,139,890,165]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The coordinates and structure factors have been deposited in the Protein Data Bank (PDB IDs: 3WCN and 3WCO). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,165,890,191]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.jmb.2014.01.003. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,228,685,245]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgments ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[502,254,892,655]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We thank the staff members of SPring-8 BL41XU and the Photon Factory beam lines for assistance with our data collection. We thank T. Imada, K. Ake, and T. Nakayama for assistance with the manuscript preparation and P. O'Donoghue and M. Simonovic (University of Illinois, Chicago) for critical discussions. We are grateful to the National BioResource Project in Japan for providing the ASKA E. coli K12 ORF library. Y.I. was supported by Research Fellowships from the Japan Society for the Promotion of Science. M.J.B. holds a Feodor Lynen Postdoctoral Fellowship of the Alexander von Humboldt Foundation (Bonn, Germany). This work was supported in part by Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research (A) to S.Y. and (C) to S.S. This work was also supported in part by the Targeted Proteins Research Program, and the Platform for Drug Discovery, Informatics, and Structural Life Science from the Ministry of Education, Culture, Sports, Science, and Technology (to S.Y.). D.S. gratefully acknowledges support from the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences of the U.S. Department of Energy (DE-FG02-98ER20311; for funding the genetic experiments), from the National Institute of General Medical Sciences (GM22854), and from the Defense Advanced Research Projects Agency (contracts N66001-12-C-4020 and N66001-12-C-4211). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[695,664,890,678]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received 8 November 2013; ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[606,678,890,692]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received in revised form 9 January 2014; ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[707,693,890,706]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Accepted 12 January 2014 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[663,706,890,718]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Available online 20 January 2014 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[811,733,890,746]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[650,747,890,761]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"fold-type-I PLP-dependent enzyme; ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[742,762,890,774]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"selenium metabolism; ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[826,775,890,786]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tRNA<sup>Sec</sup>; ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[752,789,890,802]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"pentamer of dimers; ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[779,804,890,815]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"21st amino acid ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,829,890,883]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike License, which permits non-commercial use, distribution, and reproduction in any medium, provided the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[621,886,890,899]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"original author and source are credited. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[569,912,890,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y.I. and M.J.B. contributed equally to this work. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[97,71,136,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1734 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[670,71,890,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dimer-Dimer Interaction of SelA ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[344,113,490,126]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abbreviations used: ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[115,127,490,182]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"AHBA, 5-amino-3-hydroxybenzoate; CBS, cystathionine $\\beta$ -synthase; CysS, cysteine synthase; PLP, pyridoxal $5^{\\prime}$ -phosphate; PSTK, O-phosphoseryl-tRNA $^{\\text{Sec}}$ kinase; SeMet, selenomethionine. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[105,206,216,223]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[107,238,490,902]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[1] Bock A, Forchhammer K, Heider J, Leinfelder W, Sawers G, Veprek B, et al. Selenocysteine: the 21st amino acid. Mol Microbiol 1991;5:515-20. \",\"[2] Ehrenreich A, Forchhammer K, Tormay P, Veprek B, Bock A. Selenoprotein synthesis in E. coli. Purification and characterisation of the enzyme catalysing selenium activation. Eur J Biochem 1992;206:767-73. \",\"[3] Carlson BA, Xu XM, Kryukov GV, Rao M, Berry MJ, Gladyshev VN, et al. Identification and characterization of phosphoseryl-tRNA[Ser]Sec kinase. Proc Natl Acad Sci U S A 2004;101:12848-53. \",\"[4] Yuan J, Palioura S, Salazar JC, Su D, O'Donoghue P, Hohn MJ, et al. RNA-dependent conversion of phosphoserine forms selenocysteine in eukaryotes and archaea. Proc Natl Acad Sci U S A 2006;103:18923-7. \",\"[5] Xu XM, Carlson BA, Mix H, Zhang Y, Saira K, Glass RS, et al. Biosynthesis of selenocysteine on its tRNA in eukaryotes. PLoS Biol 2007;5:e4. \",\"[6] Forchhammer K, Bock A. Selenocysteine synthase from Escherichia coli. Analysis of the reaction sequence. J Biol Chem 1991;266:6324-8. \",\"[7] Itoh Y, Bröcker MJ, Sekine S, Hammond G, Suetsugu S, Söll D, et al. Decameric SelA-tRNA $^{\\\\text{Sec}}$ ring structure reveals mechanism of bacterial selenocysteine formation. Science 2013;340:75-8. \",\"[8] Clausen T, Huber R, Laber B, Pohlenz HD, Messerschmidt A. 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Structural and functional investigation of a putative archaeal selenocysteine synthase. Biochemistry 2005;44:13315-27. \",\"[14] Koutmos M, Kabil O, Smith JL, Banerjee R. Structural basis for substrate activation and regulation by cystathionine beta-synthase (CBS) domains in cystathionine $\\\\beta$ -synthase. Proc Natl Acad Sci U S A 2010;107:20958-63. \",\"[15] Burkhard P, Tai CH, Ristroph CM, Cook PF, Jansonius JN. Ligand binding induces a large conformational change in O-acetylserine sulfhydrylase from Salmonella typhimurium. J Mol Biol 1999;291:941-53. \"]","page_idx":"12","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[517,113,902,902]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[16] Cook PD, Thoden JB, Holden HM. The structure of GDP-4-keto-6-deoxy-D-mannose-3-dehydratase: a unique coenzyme B6-dependent enzyme. Protein Sci 2006;15:2093-106. \",\"[17] Chen XM, Ploux O, Liu HW. Biosynthesis of 3,6-dideoxyhexoses: in vivo and in vitro evidence for protein-protein interaction between CDP-6-deoxy-L-threo-D-glycero-4-hexulose 3-dehydrase (E1) and its reductase (E3). Biochemistry 1996;35:16412-20. \",\"[18] Eads JC, Beeby M, Scapin G, Yu TW, Floss HG. Crystal structure of 3-amino-5-hydroxybenzoic acid (AHBA) synthase. Biochemistry 1999;38:9840-9. \",\"[19] Ambrogelly A, Palioura S, Soll D. Natural expansion of the genetic code. Nat Chem Biol 2007;3:29-35. \",\"[20] Sauerwald A, Zhu W, Major TA, Roy H, Palioura S, Jahn D, et al. RNA-dependent cysteine biosynthesis in archaea. Science 2005;307:1969-72. \",\"[21] Itoh Y, Sekine S, Yokoyama S. Crystallization and preliminary X-ray crystallographic analysis of Aquifex aeolicus SelA, a bacterial selenocysteine synthase. Acta Crystallogr Sect F Struct Biol Cryst Commun 2012;68:1128-33. \",\"[22] Walter TS, Meier C, Assenberg R, Au KF, Ren J, Verma A, et al. Lysine methylation as a routine rescue strategy for protein crystallization. Structure 2006;14:1617-22. \",\"[23] Otwinowski Z, Minor W. Processing of X-ray diffraction data collected in oscillation mode. Methods Enzymol 1997;276:307-26. \",\"[24] McCoy AJ, Grosse-Kunstleve RW, Adams PD, Winn MD, Storoni LC, Read RJ. Phaser crystallographic software. J Appl Crystallogr 2007;40:658-74. \",\"[25] Emsley P, Cowtan K. Coot: model-building tools for molecular graphics. Acta Crystallogr Sect D Biol Crystallogr 2004;60:2126-32. \",\"[26] Adams PD, Pannu NS, Read RJ, Brunger AT. Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement. Proc Natl Acad Sci U S A 1997;94:5018-23. \",\"[27] Adams PD, Afonine PV, Bunkóczi G, Chen VB, Davis IW, Echols N, et al. PHENIX: a comprehensive Python-based system for macromolecular structure solution. Acta Crystallogr Sect D Biol Crystallogr 2010;66:213-21. \",\"[28] Kitagawa M, Ara T, Arifuzzaman M, Ioka-Nakamichi T, Inamoto E, Toyonaga H, et al. Complete set of ORF clones of Escherichia coli ASKA library (a complete set of $E.$ coli K-12 ORF archive): unique resources for biological research. DNA Res 2005;12:291-9. \",\"[29] Datsenko KA, Wanner BL. One-step inactivation of chromosomal genes in Escherichia coli K-12 using PCR products. Proc Natl Acad Sci U S A 2000;97:6640-5. \",\"[30] Yuan J, Hohn MJ, Sherrer RL, Palioura S, Su D, Soll D. A tRNA-dependent cysteine biosynthesis enzyme recognizes the selenocysteine-specific tRNA in Escherichia coli. FEBS Lett 2010;584:2857-61. \",\"[31] Roberts E, Eargle J, Wright D, Luthey-Schulten Z. MultiSeq: unifying sequence and structure data for evolutionary analysis. BMC Bioinformatics 2006;7:382. \",\"[32] Humphrey W, Dalke A, Schulten K. VMD: visual molecular dynamics. J Mol Graphics 1996;14:27-8. \",\"[33] O'Donoghue P, Luthey-Schulten Z. Evolutionary profiles derived from the QR factorization of multiple structural alignments gives an economy of information. J Mol Biol 2005;346:875-94. \",\"[34] Huson DH, Bryant D. Application of phylogenetic networks in evolutionary studies. Mol Biol Evol 2006;23:254-67. \"]","page_idx":"12","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[105,71,327,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dimer-Dimer Interaction of SelA ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[862,71,900,85]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1735 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[105,88,240,219]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0773/3829c1b760fef12287d64c5aad438e0727efe86c6b5ee95153f1bdcba89c7674.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[258,105,848,210]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dimer-Dimer Interaction of the Bacterial Selenocysteine Synthase SelA Promotes Functional Active-Site Formation and Catalytic Specificity \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[102,242,714,279]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Yuzuru Itoh $^{1,2,3,\\\\dagger}$ , Markus J. Brocker $^{4,\\\\dagger}$ , Shun-ichi Sekine $^{1,2,5}$ , Dieter Soll $^{4,6}$ and Shigeyuki Yokoyama $^{1,2,7}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[104,292,902,424]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1 - Department of Biophysics and Biochemistry, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan \\\",\\\"2 - RIKEN Systems and Structural Biology Center, 1-7-22 Suehiro-cho, Tsurumi, Yokohama 230-0045, Japan \\\",\\\"3 - Laboratory of Membrane and Cytoskeleton Dynamics, Institute of Molecular and Cellular Biosciences, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan \\\",\\\"4 - Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT 06520-8114, USA \\\",\\\"5 - Division of Structural and Synthetic Biology, RIKEN Center for Life Science Technologies, 1-7-22 Suehiro-cho, Tsurumi, Yokohama 230-0045, Japan \\\",\\\"6 - Department of Chemistry, Yale University, New Haven, CT 06520-8114, USA \\\",\\\"7 - RIKEN Structural Biology Laboratory, 1-7-22 Suehiro-cho, Tsurumi, Yokohama 230-0045, Japan \\\"]\",\n \"page_idx\": \"0\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[102,438,889,493]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Correspondence to Dieter Soll and Shigeyuki Yokoyama: D. Soll is to be contacted at: Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT 06520-8114, USA; S. Yokoyama, RIKEN Structural Biology Laboratory, 1-7-22 Suehiro, Tsurumi, Yokohama 230-0045, Japan. yokoyama@riken.jp http://dx.doi.org/10.1016/j.jmb.2014.01.003 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[105,495,242,508]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Edited by M. Guss \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[104,524,191,539]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[102,554,902,775]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The 21st amino acid, selenocysteine (Sec), is incorporated translationally into proteins and is synthesized on its specific tRNA (tRNA $^{\\\\text{Sec}}$ ). In Bacteria, the selenocysteine synthase SelA converts Ser-tRNA $^{\\\\text{Sec}}$ , formed by seryl-tRNA synthetase, to Sec-tRNA $^{\\\\text{Sec}}$ . SelA, a member of the fold-type-I pyridoxal $5^{\\\\prime}$ -phosphate-dependent enzyme superfamily, has an exceptional homodecameric quaternary structure with a molecular mass of about 500 kDa. Our previously determined crystal structures of Aquifex aeolicus SelA complexed with tRNA $^{\\\\text{Sec}}$ revealed that the ring-shaped decamer is composed of pentamerized SelA dimers, with two SelA dimers arranged to collaboratively interact with one Sel-tRNA $^{\\\\text{Sec}}$ . The SelA catalytic site is close to the dimer-dimer interface, but the significance of the dimer pentamerization in the catalytic site formation remained elusive. In the present study, we examined the quaternary interactions and demonstrated their importance for SelA activity by systematic mutagenesis. Furthermore, we determined the crystal structures of \\\"depentamerized\\\" SelA variants with mutations at the dimer-dimer interface that prevent pentamerization. These dimeric SelA variants formed a distorted and inactivated catalytic site and confirmed that the pentamer interactions are essential for productive catalytic site formation. Intriguingly, the conformation of the non-functional active site of dimeric SelA shares structural features with other fold-type-I pyridoxal $5^{\\\\prime}$ -phosphate-dependent enzymes with native dimer or tetramer (dimer-of-dimers) quaternary structures. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[442,776,900,791]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"© 2014 The Authors. Published by Elsevier Ltd. All rights reserved. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[104,858,225,873]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[102,883,490,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Selenocysteine (Sec) is known as the 21st amino acid incorporated translationally into proteins and is synthesized on its specific tRNA (tRNA $^{\\\\text{Sec}}$ ) [1]. The \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,854,904,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tRNA $^{\\\\text{Sec}}$ -ligated serine (Ser-tRNA $^{\\\\text{Sec}}$ ) generated by seryl-tRNA synthetase is converted to tRNA $^{\\\\text{Sec}}$ -ligated Sec (Sec-tRNA $^{\\\\text{Sec}}$ ), where selenophosphate, synthesized by selenophosphate synthetase, is used as a selenium donor [2]. In Eukaryotes and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[912,18,954,29]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[102,941,670,955]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"0022-2836/$ - see front matter © 2014 The Authors. Published by Elsevier Ltd. All rights reserved. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[684,941,902,955]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.Mol.Biol.2014)426,1723-1735 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[134,108,850,435]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 1. The enzymatic reaction. Schematic views of the enzymatic reactions of SelA, SepSecS, and cystathionine $\\\\\\\\beta$ -lyase (CBL). These enzymes catalyze $\\\\\\\\alpha$ position deprotonation, followed by $\\\\\\\\beta$ position elimination, to generate tRNA-ligated or non-esterified 2-aminoacrylate intermediates, conjugated with PLP. The substrate of CBL is cystathionine, and the enzyme-substrate interaction is responsible for the $\\\\\\\\alpha$ -carboxyl group [8] (c) while SepSecS interacts with the phosphate group of its substrate Sep-tRNA[9]. However, Ser-tRNA[9], the substrate of SelA, has neither a carboxyl nor a phosphate group. Furthermore, the leaving group in the SelA-catalyzed reaction is a hydroxide ion, which is less suitable as compared to the phosphate and the deprotonated homocysteine eliminated in the SepSecS- and CBL-catalyzed reactions, respectively. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0681/157e80effbf939f8d515224685983aa04395315cf4c843894b708ba3e7168299.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[92,607,478,747]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Archaea, Ser-tRNA $^{\\\\text{Sec}}$ is phosphorylated by O-phosphoseryl-tRNA $^{\\\\text{Sec}}$ kinase (PSTK) to generate O-phosphoseryl-tRNA $^{\\\\text{Sec}}$ (Sep-tRNA $^{\\\\text{Sec}}$ ) [3], followed by Sep-to-Sec conversion catalyzed by SepSecS [4,5]. On the other hand, in Bacteria, the selenocysteine synthase SelA directly converts Ser-tRNA $^{\\\\text{Sec}}$ to Sec-tRNA $^{\\\\text{Sec}}$ , without a previous phosphorylation step [6]. Both SelA and SepSecS are pyridoxal $5^{\\\\prime}$ -phosphate (PLP)-dependent enzymes. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,747,482,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"SelA is a homodecameric enzyme with an overall molecular mass of about $500\\\\mathrm{kDa}$ . We previously determined the crystal structures of SelA with and without tRNA[Sec [7]. The SelA decamer is organized as a pentamer of intimate dimers, and it binds 10 tRNAmolecules. Residues from each of the four SelA subunits of two intimate dimers are involved in processing one Ser-tRNA[Sec] molecule, indicating that the decameric quaternary structure is essential to bind Ser-tRNA[Sec [7]. We proposed the SelA catalytic mechanism based on the co-crystal structure with thiosulfate, an analog of selenophosphate. While the tRNA-binding pocket is formed at the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,607,892,650]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"dimer-dimer interface, the significance of the formation of an $(\\\\alpha_{2})_{5}$ SelA structure in the generation of functional catalytic sites remained unclear. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,650,894,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The enzymes SelA and SepSecS belong to the largest PLP-dependent enzyme group, the fold-type-I superfamily, and catalyze the replacement of the amino acid $\\\\beta$ position ( $\\\\beta$ replacement) in an $\\\\alpha ,\\\\beta$ elimination reaction proceeding via a 2-aminoacrylate intermediate and a subsequent addition step (Fig.1) [6]. Although $\\\\beta$ replacement is a common reaction, there are two major difficulties with the Sec synthesis step. First, the precursor, Ser-tRNA<sup>Sec</sup>, lacks the $\\\\alpha$ -carboxyl group, which is used for the substrate-enzyme interaction in all fold-type-I PLP-dependent enzymes that work with $\\\\alpha$ -amino acids [10]. Second, the leaving group in the $\\\\beta$ elimination step is a hydroxide ion from the Ser moiety (Fig. 1) [6]. In general, a hydroxide ion is not a suitable leaving group, and no other fold-type-I members can eliminate it from the $\\\\beta$ position of an $\\\\alpha$ -amino acid. In Eukarya/Archaea, these difficulties are overcome with the assistance of PSTK. PSTK phosphorylates the Ser moiety to generate Sep-tRNA<sup>Sec</sup> [3], which is the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,71,137,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1724 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[670,71,892,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dimer-Dimer Interaction of SelA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[144,110,378,296]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0953/124ccb7584cd84806bc13e04934d3051e4a424ffaa5d080d3fd37584c794b16b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[386,108,643,283]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0495/fc5445f0de948b444be0a843dab1fa6119946414f53b816d02bb1f791c29fe58.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[648,110,865,279]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0153/46015ae71814435f8eb42a3ab9a3fe18576b6ad1c3d82b81dfae2a5d1279beb7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[142,298,489,457]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0233/c5ce20c90ce5bb690e72223ad92922c74db64220305be8ae53cfae0afba08149.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[505,302,826,456]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 2. Structure of SelA. (a) Overall view of the crystal structure of decameric SelA-FL. PLPs are represented as sphere models. The N-terminal domain, the N-linker, the core domain, and the C-terminal domain of subunit A are colored cornflower blue, magenta, blue, and medium-purple, respectively, while those of subunit B are colored green-yellow, yellow, green, and aquamarine, respectively. Subunits C-J are colored gray. (b and c) Close-up views of the interactions at interfaces I (b) and II (c) between intimate dimers. Interactions between subunits A and J are shown. The colors of the ribbon diagrams are the same as in (a). (d and e) Overall views of the dimeric SelA mutants, dSelA-FL (d) and dSelA-ΔN (e). The ribbon diagrams are colored as in (a). dSelA-FL lacks PLP. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0365/7eecf4cfa949905552ef79c9fc838711bb8ef1b25f27d46f9273a072e36f2836.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[102,571,492,615]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"substrate of SepSecS (Fig. 1). The $\\\\beta$ elimination is thus facilitated because the phosphate is an excellent leaving group. Furthermore, the phosphate group is \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,571,905,616]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"predominantly responsible for the substrate binding to SepSecS [9]. In contrast, the bacterial system differs strikingly in that the single enzyme SelA directly \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[104,654,905,853]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0253/5d5344c51b22e7093c792b1e1953cbbd999eb8cfc57d254ed8590801c2f08f10.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>SelA mutant</td><td>Amino acid change E. coli numbering</td><td>A. aeolicus Numbering</td><td>Function of residue</td><td>PLP occupancy (Mut10a- Mut10d) (%)</td><td>Activity in vivo</td></tr><tr><td>1</td><td>ΔGln233-Thr236</td><td>Glu222-Val225</td><td>Decamerization interface I</td><td></td><td>-</td></tr><tr><td>2</td><td>ΔGln233-Gly234</td><td>Glu222, Gly223</td><td>Decamerization interface I</td><td></td><td>-</td></tr><tr><td>3</td><td>Arg185Ala</td><td>Arg174</td><td>Decamerization interface II/III</td><td></td><td>+++</td></tr><tr><td>4</td><td>Thr202Tyr</td><td>Thr191</td><td>Decamerization interface II/III</td><td></td><td>-</td></tr><tr><td>5</td><td>Thr203Tyr</td><td>Thr192</td><td>Decamerization interface II/III</td><td></td><td>-</td></tr><tr><td>6</td><td>His207Ala</td><td>Lys196</td><td>Decamerization interface II/III</td><td></td><td>+++</td></tr><tr><td>7a</td><td>Asp210Ala</td><td>Asp199</td><td>Decamerization interface II/III</td><td></td><td>+++</td></tr><tr><td>7b</td><td>Asp210Arg</td><td>Asp199</td><td>Decamerization interface II/III</td><td></td><td>-</td></tr><tr><td>8</td><td>ΔThr203-Asn204</td><td>Thr192, Asn193</td><td>Decamerization interface II/III</td><td></td><td>-</td></tr><tr><td>9</td><td>Thr202-Arg205 = 2 × Ala</td><td>Thr191-Lys194</td><td>Decamerization interface II/III</td><td></td><td>-</td></tr><tr><td>10a</td><td>Lys295Ala</td><td>Lys285</td><td>Covalent PLP ligand</td><td>n.d.</td><td>-</td></tr><tr><td>10b</td><td>Lys295Ala, Asp294Lys</td><td>Lys285, Asp284</td><td>Covalent PLP ligand</td><td>25</td><td>-</td></tr><tr><td>10c</td><td>Lys295Ala, Leu296Lys</td><td>Lys285, Leu286</td><td>Covalent PLP ligand</td><td>37</td><td>-</td></tr><tr><td>10d</td><td>Lys295Ala, Leu297Lys</td><td>Lys285, Leu287</td><td>covalent PLP ligand</td><td>30</td><td>-</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. In vivo mutational analyses of E. coli SelA \\\"]\",\n \"table_footnote\": \"[\\\"$+ + +$ fully active; $+$ significantly reduced activity; -, inactive; n.d., below detection limit. Mutations introduced in E. coli SelA, numbering of the corresponding residues for A. aeolicus SelA, and functions of the residues as determined from the structures and catalytic activities of the corresponding E. coli SelA variants in vivo are indicated. PLP occupancy for SelA variants 10a-10d is indicated. All SelA variants lacking catalytic activity in vivo were purified and tested for solubility to exclude the possibility that the activity loss was due to inclusion body formation. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[105,71,327,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dimer-Dimer Interaction of SelA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[862,71,902,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1725 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[132,124,307,266]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"a \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0321/c414e8ef83bd545ee82fb350d336eb64de896520a11def52557cf3fb1ee3a180.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[317,124,490,264]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"b \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0845/2839300d104b836d516c6a6a007f01e0f77f35ed70834634112594d348d61d5f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[497,124,672,264]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"C \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0058/06104589433bf48e45d62801e6200af0f2fd6f31071da69f336f80951c178d5f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[680,124,852,264]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"d \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0600/e0d159f4b3f8273ca294d0798ad4a15afb4ff708292d88c4ddb68c7db50aba28.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[132,288,310,431]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"e \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0817/dc871f0fca304b6a86e079fab431c0b69f615d1fc41aa84ecddaf64d0af2f398.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[317,288,490,431]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"f \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0730/210990f6a69b83af360be996edce434f276fb392d25389339f044c1aebda1197.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[497,288,673,430]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"g \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0999/7016b9910beb3e3e4a2ea464910640401d83a98e3049667da0dfb1cb599cbe46.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[682,288,853,430]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"h \\\",\\\"Fig. 3. Catalytic site comparison. (a–c) Catalytic site comparison between the decameric and dimeric SelAs. The $\\\\\\\\beta$ -sheet $\\\\\\\\beta6\\\\\\\\bullet\\\\\\\\beta7$ and $\\\\\\\\alpha7$ in the catalytic site also participate in the pentamerizing interaction in the decameric SelA- $\\\\\\\\Delta N$ (a). On the other hand, dSelA-FL (b) and dSelA- $\\\\\\\\Delta N$ (c) lack the $\\\\\\\\beta6\\\\\\\\bullet\\\\\\\\beta7$ sheet, and $\\\\\\\\alpha7$ changes its orientation; therefore, the catalytic site structure is disrupted. dSelA-FL also lacks PLP. Thiosulfate ions are bound in different sites among (a)-(c). Possible hydrogen bonds or ionic interactions are shown as broken lines. (d) Close-up view of the TS4- and TS5-binding sites of dSelA- $\\\\\\\\Delta N$ . The $2F_{o} - F_{c}$ electron density map at the $1.0\\\\\\\\sigma$ level is shown. (e-h) Catalytic sites of SepSecS (PDB ID: 2Z67 [11]) (e), SepCysS (PDB ID: 2E7J [12]) (f), CBL (PDB ID: 1CL1 [12]) (g), and MJ0158 (PDB ID: 2AEV [13]) (h). They lack the $\\\\\\\\beta6\\\\\\\\bullet\\\\\\\\beta7$ counterpart, and the orientations of their $\\\\\\\\alpha7$ counterparts are closer to those of $\\\\\\\\alpha7$ in depentamizerized SelA mutants. The phosphate/sulfate ions at the catalytic site are shown. The SepSecS structure 2Z67 is from the archaeon Methanococcus maripaludis. The focused Arg and Lys residues are labeled according to their numbering in human/M. maripaludis SepSecS. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0137/77e785da0f445dc75b7d785728b36013b080028b9a86924f159332fc4bb3dded.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[92,607,478,704]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"converts Ser-tRNA $^{\\\\text{Sec}}$ to Sec-tRNA $^{\\\\text{Sec}}$ , without phosphorylation. Our previous study suggested a putative binding site for the $3^{\\\\prime}$ -terminal A76 of tRNA $^{\\\\text{Sec}}$ , and the binding site could compensate for the lack of the $\\\\alpha$ -carboxyl group [7]. However, the mechanism that facilitates the hydroxyl-group elimination has not been elucidated. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,706,482,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this study, we have determined the structural basis for productive SelA active-site formation, which requires the cyclization of SelA dimers to a full decamer. Analyses of the structures of Aquifex aeolicus SelA and dimeric SelA variants revealed that the active-site conformations of SelA intimate dimers differ significantly from those of decameric SelA. Structural rearrangements upon decamerization generate 10 catalytically functional active sites that properly accommodate and position Ser-tRNA $^{\\\\text{Sec}}$ for Sec formation. Based on a comparison of SelA with phylogenetically related enzymes, we describe a refined mechanism for the direct hydroxyl-group elimination facilitated by SelA and propose an evolutionary hypothesis for the emergence of the decameric SelA architecture. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,611,737,627]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results and Discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,646,890,677]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The dimer-dimer interface in the pentamer-of-dimers structure of SelA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,691,892,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A. aeolicus SelA is a homodecamer in which the 10 subunits, designated here as subunits A to J, form a \\\"pentamer of dimers\\\" (Fig. 2a). The \\\"intimate dimers\\\" A•B to I•J have the largest intersubunit interfaces (e.g., A•B interface, $4067\\\\mathring{\\\\mathrm{A}}^{2}$ ) on which the enzyme active sites are built. Therefore, the intimate dimer is the basal building block of SelA. In the pentamer-of-dimers quaternary structure, intimate dimers I•J and A•B, for example, interact with each other through subunits J and A. The dimer-dimer interface encompasses $1140\\\\mathring{\\\\mathrm{A}}^{2}$ and characteristically constitutes the overall decameric arrangement of SelA. The dimer-dimer interface may be divided into three parts. The first part (part I, $438\\\\mathring{\\\\mathrm{A}}^{2}$ ) has internal 2-fold symmetry and is composed of two sets of residues from Asn218 to Phe224, constituting strand $\\\\beta 11$ within the core domain (Fig. 2b). Strand \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,71,137,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1726 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[670,71,892,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dimer-Dimer Interaction of SelA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[144,108,381,293]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0110/13f0109053c9f22020ee789a4eb4795b269bafcddeae95083bafa69c9c76bd9c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[388,107,621,292]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0945/31f68c3fdb429a23ac9d97de88c6e90011f6d0f84b55cfca3e44603781820adb.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[625,110,863,279]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 4. Proposed scheme of the SelA-catalyzed reaction. (a) Docking model of the Ser-ligated terminal nucleotide (A76) of tRNA $^{\\\\\\\\text{Sec}}$ and selenophosphate (Se-P). A76 and the Ser moiety are modeled based on the mutational analyses, and their carbon atoms are colored salmon and spring green, respectively. Arg86 is located in the vicinity of Lys285 and Ser. Phe224 from subunit J and Asn218 from subunit A form the A76-binding pocket. The Ser moiety is attached covalently to PLP. Se-P occupies the TS1-binding site. (b) The reaction scheme of the protonation of the $\\\\\\\\beta$ -hydroxyl group by Lys285, which enables the elimination of the leaving group (a water molecule). Arg86 may provide the basic environment to strengthen the Lys285 protonation activity. (c) The interaction interface between the core and C-terminal domains of SelA. The N-linker (magenta) and the SelA-specific insertions I and IV (cyan) participate in the interaction between the core and C-terminal domains. The other regions are colored as in Fig. 2a. $\\\\\\\\beta1$ in the N-linker forms a $\\\\\\\\beta$ -sheet with $\\\\\\\\beta18$ in the C-terminal domain. Arg86 in the N-linker participates in the catalytic site. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0827/3c434ace1715ab553ee1e13e8b5d28637fd5e87b1679b7b32070b2cd44568d20.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[102,485,490,624]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\beta 11$ from subunit J, for example, and the corresponding strand from subunit A form an antiparallel $\\\\beta$ -sheet between intimate dimers I·J and A·B. The other parts, II and III (307 Ų each), are symmetrically related to each other. Parts II/III between subunits J and A comprise Arg163, Leu166, Glu168, and Arg174 (η4-loop-β6-loop-β7) from subunit J and Glu188, Thr191, Thr192, Asn193, Lys196, and Asp199 ( $\\\\beta 8$ -loop-β9-α8) from subunit A and vice versa (Fig. 2c). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[102,624,492,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We introduced mutations into the dimer-dimer interface by using Escherichia coli SelA (Table 1). The amino acid residues in the dimer-dimer interface are conserved between the A. aeolicus and E. coli SelAs, although the conservation in part I is relatively low (Table 1). The Mut1 and Mut2 mutations were designed to impair the antiparallel $\\\\beta 11\\\\cdot \\\\beta 11$ interaction in part I, by deleting residues 222-225 and 222-223, respectively (residue numbering according to A. aeolicus SelA). The enzymes bearing the Mut1 and Mut2 mutations were catalytically inactive in vivo (Table 1), indicating that the integrity of strand $\\\\beta 11$ and the formation of the resultant antiparallel $\\\\beta$ sheet are critical for the function of SelA. Mutations targeting parts II/III were also examined (Table 1). Here, the Ala mutations of individual residues in parts II/III exhibited no significant effects on the SelA activity (Mut3, Mut6, and Mut7a). In contrast, the Thr191Tyr, Thr192Tyr, and Asp199Arg mutations (Mut4, Mut5, and Mut7b), which were designed to cause steric clashes, inactivated E. coli SelA in vivo. Similarly, the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,485,902,554]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"deletion of Thr192-Asn193 (Mut8) or the replacement of four residues, Thr191-Lys194, with two Ala residues (Mut9) rendered E. coli SelA inactive in vivo. These results suggested that the integrity of parts II/III is also important for the SelA activity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,567,781,583]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Crystal structure of dimeric SelA \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,595,904,930]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The interface between the intimate dimers is much smaller than that between the subunits within the intimate dimer, suggesting weaker interactions between the dimer units. In fact, a quadruple mutation (Tyr220Pro-Asp199Arg-Thr191Tyr-Thr192Tyr) abolished the pentamerization and resulted in an inactive \\\"dimerized\\\" or \\\"depentamizered\\\" enzyme [7]. (In the following, we refer to the depentamizerized enzyme as dimeric SelA.) Importantly, dimeric SelA is stable and can be purified for crystallization. In this study, we crystallized the full-length and N-terminally truncated $(\\\\Delta N,$ deletion of residues 1-61) dimeric SelA proteins and determined their structures at 3.35 and $2.40\\\\AA$ resolutions, respectively (Fig. 2d and e). The lysine residues of the dimeric full-length SelA (dSelA-FL) were methylated for crystallization improvement, while the dimeric SelA- $\\\\Delta N$ (dSelA- $\\\\Delta N$ ) was crystallized without Lys methylation. The overall structures of dSelA-FL and dSelA- $\\\\Delta N$ are similar to each other and to those of the intimate dimers of decameric SelA-FL and SelA- $\\\\Delta N$ ,respectively. Each subunit of dSelA-FL consists of the N-terminal domain (residues 1-66), the N-linker (residues 67-89), the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[105,71,327,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dimer-Dimer Interaction of SelA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[862,71,902,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1727 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[132,114,307,394]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"a \\\",\\\"b \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0098/664e234838d063ebc13441e695c4043dd14b1d6aa7697ca81075168425451d59.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[322,200,478,394]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0329/4dacf71f21dc3b5d791c4bdc1329796f1de5b377dc2b3a6f898546f067beca29.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[505,146,694,394]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"C \\\",\\\"d \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0286/8474d97e5724e76f8fe67fc78cb0d6d7f625e2754abdff50cb848ab4875b98e0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[687,191,848,394]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0400/b9b1e559a50870e4db61597dcdd050a1d7b20d59a0b4c6a7b71b51345df810c4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[132,422,305,556]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"e \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0996/c737a847a96c259ec2c8050da24ebd65f4154fa330049aab5b7e7605cae4233f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[315,422,487,557]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"f \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0465/05ddad5b7fb470b156336d1dd24d1bc9b1ed24f685ce3b8bc50a138030bc5c73.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[497,422,673,554]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"g \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0938/600788169c9ceeeced0a56df4c0ef48097b4274d80172db572e445593c3a4e6c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[682,422,852,554]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"h \\\",\\\"Fig. 5. Structure comparison with other fold-type-I PLP-dependent enzymes. (a-d) Overall crystal structures of SepSecS (PDB ID: 2Z67 [8]) (a), SepCysS (PDB ID: 2E7J [11]) (b), cystathionine $\\\\\\\\beta$ -lyase (CBL) (PDB ID: 1CL1 [12]) (c), and MJ0158 (PDB ID: 2AEV [13]) (d). The N-terminal domains, the N-linkers, the core domains, and the C-terminal domains of subunits A and B are colored as in Fig. 2a. The N-terminal regions of SepCysS and MJ0158 correspond to the SelA N-linker. Like the SelA N-linker, these regions form $\\\\\\\\beta$ -sheets with their C-terminal domains. On the other hand, the N regions of the homotetrameric enzymes SepSecS and CBL participate in the interactions between the two intimate dimers, and thus, they occupy different positions from that of the SelA N-linker. The intimate dimers C-D of SepSecS and CBL are colored gray in the top panels and are not shown in the bottom panels. (e-h) Comparison of the C-terminal domain orientation with SelA. The A subunits of SepSecS (e), SepCysS (f), CBL (g), and MJ0158 (h) were superposed on the SelA subunit A, by fitting their core domains. The core and C-terminal domains of SelA are colored blue and medium-purple, respectively, as in Fig. 2a, while those of the other PLP-dependent enzymes are colored light blue and yellow, respectively. The major helices $\\\\\\\\alpha12$ and $\\\\\\\\alpha14$ , located in the core and C-terminal domains, respectively, are connected by the short helices $\\\\\\\\eta7$ and $\\\\\\\\alpha13$ in SelA. In contrast, the $\\\\\\\\alpha12$ and $\\\\\\\\alpha14$ counterparts are directly connected in SepSecS and form a continuous single helix in SepCysS and CBL. On the other hand, MJ0158 has the $\\\\\\\\alpha13$ counterparts, and the orientation of its C-terminal domain is somewhat closer to that of the SelA C-terminal domain. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0390/aae15da50fed8c00500404fa6ef748b9deb4709f2f5e47e509796e5f8eee9e94.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[92,800,480,857]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"core domain (residues 90-338), and the C-terminal domain (residues 339-452) (Fig. 2d). The $\\\\beta 11$ strand in part I of the dimer-dimer interface is disordered in the dSelAs. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,870,331,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Catalytic site of dimeric SelA \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,897,480,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The catalytic site is located at the subunit interface, involving the core domains and the N-linker, within \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,800,892,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the intimate dimer unit of SelA. PLP is covalently bound to Lys285, as a Schiff base. Surprisingly, the catalytic site structures of dSelA-FL and dSelA- $\\\\Delta N$ differ distinctly from that of the SelA decamer (Fig. 3a-c). The dimeric SelAs lack a SelA-specific $\\\\beta$ -sheet ( $\\\\beta6\\\\bullet\\\\beta7$ ), and $\\\\alpha7$ has a distinct orientation. These different catalytic site conformations of the dimeric mutants resemble those of other fold-type-I PLP enzymes (Fig. 3b, c, and e-h). The position of \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,71,137,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1728 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[670,71,892,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dimer-Dimer Interaction of SelA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[107,112,489,264]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PLP in the dSelA- $\\\\Delta N$ catalytic site is the same as that in the SelA decamer, while dSelA-FL lacked PLP in its catalytic site. PLP may have been removed during the Lys methylation of dSelA-FL, whereas the decameric SelA-FL and SelA- $\\\\Delta N$ retained PLP during the methylation [7]. This indicated that the depentamerization increased the accessibility of Lys285, which probably resulted in the replacement of PLP by a methyl group, although the methyl group was not visible in the structure due to the high mobility of the Lys285 side chain. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,264,489,554]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The thiosulfate-binding sites also differ from those of the decameric SelA- $\\\\Delta N$ (Fig. 3a-c). The decameric SelA- $\\\\Delta N$ binds three thiosulfate ions (TS1-TS3) in each catalytic site. TS1 may mimic the substrate selenophosphate, and TS2 and TS3 may mimic the phosphate groups of the nucleotides A76 and C75 of the tRNA Sec CCA terminus [7]. In contrast, dSelA- $\\\\Delta N$ binds two thiosulfate ions, TS4 and TS5. TS4 may correspond to TS1, but TS5 does not correspond to any of TS1-TS3. TS1 interacts with $\\\\mathrm{Arg86^{A}}$ (subunit A residue) and $\\\\mathrm{Arg312^{B}}$ and $\\\\mathrm{Arg315^{B}}$ (subunit B residues), whereas TS4 interacts with Ser $172^{A}$ , $\\\\mathrm{Arg174^{A}}$ , $\\\\mathrm{Arg116^{B}}$ , and $\\\\mathrm{Arg315^{B}}$ (Fig. 3d). The distance between TS1 and TS4 is about $3.5\\\\AA$ . TS5 interacts with $\\\\mathrm{Arg312^{B}}$ and $\\\\mathrm{Arg315^{B}}$ . dSelA-FL also has two thiosulfate ions, TS5 and TS6. TS5 is the same as that in dSelA- $\\\\Delta N$ , whereas TS6 occupies the position of the PLP phosphate group. The difference between the thiosulfate-binding sites of dSelA- $\\\\Delta N$ and dSelA-FL may be caused by the lack of PLP in the catalytic sites of dSelA-FL. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,554,489,733]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In decameric SelA, the $\\\\beta 6\\\\bullet \\\\beta 7$ sheet is stabilized by the pentamerizing interactions. The main chain NH and carbonyl moieties of Glu168 in $\\\\beta 6$ interact with Asn193, and the Arg174 side chain forms a salt bridge with Asp199 (Fig. 3a). Since Arg174 also participates in $\\\\alpha 7$ , the $\\\\alpha 7$ orientation is dependent on the Arg174 position, which is fixed by the Arg174 Asp199 salt bridge. Although the $\\\\beta 6\\\\bullet \\\\beta 7$ sheet has no polar interactions with the thiosulfate ions, Gly170 in the $\\\\beta 6 - \\\\beta 7$ loop is close to TS1 and forms a van der Waals interaction (Fig. 3a). Therefore, the $\\\\beta 6\\\\bullet \\\\beta 7$ sheet contributes to TS1 binding and is important for catalysis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,733,489,844]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"These results indicated that the formation of the catalytic site structure is dependent on the pentamerization of intimate dimers and that the dimeric mutant cannot properly bind its substrates. The activity loss by the mutations introduced to the pentamerization interfaces (Table 1) should result from both the prevention of decamer-dependent tRNA $^{\\\\text{Sec}}$ binding and the disruption of the catalytic core structure. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,858,489,887]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"How does SelA eliminate the hydroxyl group from the Ser moiety? \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,900,489,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In general, proper binding and hydroxyl-group protonation of the substrate are essential for an \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,112,900,237]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"enzyme to eliminate a hydroxyl group. SelA has a putative binding pocket for the A76 adenine ring (Fig. 4a) [7] and can therefore accommodate the Ser moiety of Ser-tRNA $^{\\\\text{Sec}}$ . This binding pocket is critically important because Ser-tRNA $^{\\\\text{Sec}}$ lacks the $\\\\alpha$ -carboxyl group, which is used for the substrate-enzyme interaction in all of the fold-type-I superfamily PLP-dependent enzymes working on $\\\\alpha$ -amino acids [10]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,238,900,554]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To examine the mechanism of hydroxyl-group protonation, we compared SelA with other PLP-dependent enzymes. SelA is the only fold-type-I enzyme that eliminates the hydroxyl group from the substrate amino acid (or amino acid moiety). Therefore, we compared SelA with cystathionine $\\\\beta$ -synthase (CBS), a fold-type-II PLP-dependent enzyme that catalyzes a $\\\\beta$ replacement reaction. CBS eliminates the hydroxyl group from serine to generate 2-aminoacrylate and then adds homocysteine to synthesize cystathionine (Supplementary Fig. 1a). The $\\\\beta$ elimination step is the same as that in SelA catalysis (Fig. 1). A crystallographic study revealed that Tyr227 of CBS is responsible for the protonation of the serine hydroxyl group [14]. Interestingly, cysteine synthase (CysS), the close homolog of CBS, lacks the corresponding Tyr residue [15]. CysS catalyzes the $\\\\beta$ replacement reaction that eliminates an acetyl group from O-acetylserine, and it adds hydrogen sulfide to generate cysteine (Supplementary Fig. 1b). In this reaction, the leaving group is acetate, and thus, hydroxyl-group protonation is unnecessary. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,554,900,857]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"On the other hand, SelA lacks residues such as Tyr, His, and Cys that could serve as proton donors in the vicinity of the Ser-moiety-binding site, except for Lys285, which forms a Schiff base with PLP in the waiting state. Some enzymes in the sugar aminotransferase subfamily catalyze the elimination of the $\\\\alpha$ -hydrogen and the $\\\\beta$ -hydroxyl group. Here, the $\\\\alpha$ position indicates the position of the amino group conjugated with PLP during catalysis. The enzymes GDP-6-deoxy- $\\\\alpha$ -D-/lyxo-hexopyranos-4-ulose dehydratase (ColD) and CDP-6-deoxy- $\\\\alpha$ -D-xylo-hexopyranos-4-ulose dehydratase ( $E_1$ ) employ a His residue, which is conserved at the position of the PLP-coordinating Lys285 of SelA, to catalyze the $\\\\alpha,\\\\beta$ elimination step (Supplementary Fig. 1c and d) [16,17]. In contrast, 5-amino-3-hydroxybenzoate (AHBA) synthase, another enzyme that eliminates the $\\\\alpha$ -hydrogen and the $\\\\beta$ -hydroxyl group (Supplementary Fig. 1e), contains a conserved Lys residue, which is considered to protonate the $\\\\beta$ -hydroxyl group [18]. Here, the generation of a benzene ring in the product is likely to promote the $\\\\alpha,\\\\beta$ elimination reaction. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,858,900,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"These findings suggested that Lys285 in SelA can act as proton donor for the $\\\\beta$ -hydroxyl group (Fig. 4b). As enzymes such as ColD and $E_{1}$ utilize His, instead of Lys, to strengthen the protonation activity and AHBA generates a benzene ring to promote the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,73,326,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dimer-Dimer Interaction of SelA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,71,900,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1729 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[132,108,855,638]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 6. Structure-based phylogenetic tree of the fold-type-I PLP-dependent enzymes. SelA and the crystal structures of the fold-type-I PLP enzymes, deposited in the Protein Data Bank, were analyzed. The enzyme names are colored based on their catalysis type: the enzymes that catalyze aminotransfer (AT), $\\\\\\\\alpha$ -carboxyl group replacement, $\\\\\\\\alpha$ -hydrogen replacement, reverse aldol reaction, $\\\\\\\\alpha, \\\\\\\\beta$ elimination, $\\\\\\\\beta$ replacement (type 1), $\\\\\\\\beta$ replacement (type 2), $\\\\\\\\alpha, \\\\\\\\gamma$ elimination, and $\\\\\\\\gamma$ replacement are colored dark blue, blue, sky blue, blue-violet, magenta, red, orange, spring green, and green, respectively. The enzymes with unknown functions are colored gray. The structure-based phylogenetic analysis revealed that SelA, SepSecS, and SepCysS [20] belong to distinct taxa of the fold-type-I PLP-dependent enzymes. SelA is likely to form an independent group related to the cystathionine $\\\\\\\\gamma$ -synthase (CGS) family. SepCysS is close to the cysteine desulfurase and kynureninase families, while SepSecS also forms another independent group close to the sugar aminotransferase (AT) family. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0361/d13fd3bdcefc0158438304d6c94c9a09870432e4e93be4533baf2f22ce982c45.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[92,829,480,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"protonation and elimination of the $\\\\beta$ -hydroxyl group, an additional auxiliary mechanism to support protonation and $\\\\beta$ -hydroxyl elimination might be plausible for SelA as well. Such a mechanism would involve the Arg86 residue (Fig. 4a and b). Our in vivo mutational assay revealed that Arg86 is mandatory for activity [7]. Arg86 is located in the vicinity of Lys285 (Fig. 4a), and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,829,894,930]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the positive charge of Arg86 may reinforce the protonation activity of Lys285. Arg86 is located in the N-linker between the N and core domains. The $\\\\beta$ -strand $\\\\beta 1$ in the N-linker forms a $\\\\beta$ -sheet with $\\\\beta 18$ from the C-terminal domain (Fig. 4c). Although the corresponding $\\\\beta$ -sheet is present in many fold-type-I PLP-dependent enzymes, the C-terminal domain \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[97,71,136,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1730 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[670,71,890,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dimer-Dimer Interaction of SelA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[168,108,840,418]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 7. Possible steps of SelA (a) and SepSecS (b) evolution. The dimeric SelA ancestor accommodated the tRNA $^{\\\\\\\\text{Sec}}$ acceptor arm within the cleft between the core and C-terminal domains. The ancestor interacted with the substrate Sep-tRNA $^{\\\\\\\\text{Sec}}$ by binding its Sep phosphate group at the selenophosphate (Se-P)-binding site. Therefore, the Sep-to-Sec reaction and the tRNA discrimination were dependent on the Sep phosphate group. Tetramerization created the A76-binding pocket, and decamerization stabilized the interactions among intimate dimers. Finally, the acquired N-terminal domain discriminated tRNA $^{\\\\\\\\text{Sec}}$ from tRNA $^{\\\\\\\\text{Ser}}$ , by interacting with the unique D arm of tRNA $^{\\\\\\\\text{Sec}}$ . The A76-binding pocket and the tRNA $^{\\\\\\\\text{Sec}}$ discrimination enabled Ser-to-Sec conversion, and thus, SelA became independent of the Sep phosphate group. On the other hand, the dimeric SepSecS interacted with the extra arm side of the tRNA $^{\\\\\\\\text{Sec}}$ acceptor arm, since it lacks the cleft between the core and C-terminal domains. Tetramerization stabilized the tRNA $^{\\\\\\\\text{Sec}}$ binding by interacting with its T and extra arms, without recognizing the unique D arm structure. Therefore, SepSecS is unable to become independent of the Sep phosphate group of Sep-tRNA $^{\\\\\\\\text{Sec}}$ . \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0309/6db4b59976575de7fbea46196895e5272489866ec1518b6d0377545377e69576.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[107,622,489,746]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"orientation in SelA differs from those of the other homologs (Fig. 5). The unique C-terminal domain orientation in SelA results in the specific positioning of the N-linker that allows participation in the catalytic site. This structural feature is the reason why the N-linker can provide Arg86 in the vicinity of Lys285. Here again, the characteristic tertiary and quaternary structures of SelA are essential for its unique catalytic activity to eliminate the hydroxyl group. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,747,489,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"SepSecS also possesses an Arg residue (Arg75 in human SepSecS) that occupies the space corresponding to SelA Arg86 [9]. However, Arg75 is located in the core domain of SepSecS and is not an alignment-based counterpart of SelA Arg86, which is in the N-linker. In fact, Arg75 forms an intersubunit interaction with Lys-bound PLP; that is, $\\\\mathrm{Arg75^{B}}$ interacts with PLP-Lys284 $^{\\\\text{A}}$ (Fig. 3e). In contrast, the Arg86 and PLP-Lys285 interaction is an intrasubunit one (Figs. 3a and 4a). Moreover, the PLP-ligated Lys284 in SepSecS cannot protonate the $\\\\beta$ -hydroxyl group of the Ser moiety; SepSecS cannot bind Ser-tRNA $^{\\\\text{Sec}}$ because the phosphate group of the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,622,900,650]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sep moiety is essential for the substrate Sep-tRNA Sec binding. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,664,900,691]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Why did two different pathways for Sec formation evolve? \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,704,900,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Considerable conservation of the translation machinery components exists among the three domains of life. However, the pathways of aminoacyl-tRNA formation evolved much more independently. For instance, the synthesis of Asn-tRNA or Gln-tRNA involves tRNA-dependent and tRNA-independent amino acid biosynthesis routes [19]. In the case of Sec, nature also designed distinct routes based on the different enzyme structures operating in Bacteria versus Archaea/Eukaryotes. Our phylogenetic analysis (Fig. 6) revealed that SelA is related to the cystathionine $\\\\gamma$ -synthase (CGS) family members catalyzing the $\\\\beta$ elimination of cysteine derivatives or the $\\\\gamma$ elimination and $\\\\gamma$ replacement of homocysteine products. Thus, the ancestor of SelA may have been an enzyme involved in sulfur metabolism. The protein \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,73,326,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dimer-Dimer Interaction of SelA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,71,899,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1731 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[92,126,894,556]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0984/71bf8d9ffad96de83637d794068b326603c01d0f966389c58692d2d8012454d6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td></td><td>dSelA-FL4KA (SeMet)</td><td>dSelA-ΔN (SeMet)</td></tr><tr><td>Lys methylation</td><td>+</td><td>-</td></tr><tr><td>Data collection</td><td></td><td></td></tr><tr><td>Beam line</td><td>SPring-8 BL41XU</td><td>SPring-8 BL41XU</td></tr><tr><td>Wavelength (Å)</td><td>0.97915</td><td>0.97915</td></tr><tr><td>Space group</td><td>I422</td><td>P21</td></tr><tr><td>Cell parameters</td><td></td><td></td></tr><tr><td>a (Å)</td><td>144.1</td><td>59.2</td></tr><tr><td>b (Å)</td><td>144.1</td><td>81.3</td></tr><tr><td>c (Å)</td><td>273.4</td><td>95.5</td></tr><tr><td>β (°)</td><td></td><td>92.2</td></tr><tr><td>Resolution (Å)</td><td>50.0–3.35 (3.47–3.35)a</td><td>50.0–2.40 (2.49–2.40)a</td></tr><tr><td>Unique reflections</td><td>21,096 (2066)a</td><td>35,457 (3520)a</td></tr><tr><td>Completeness (%)</td><td>99.7 (100.0)a</td><td>99.6 (100.0)a</td></tr><tr><td>Redundancy</td><td>6.0 (6.1)a</td><td>3.8 (3.8)a</td></tr><tr><td>Rsymb</td><td>0.102 (0.712)a</td><td>0.082 (0.561)a</td></tr><tr><td>I/σ(I)</td><td>17.2 (2.75)a</td><td>15.9 (2.40)a</td></tr><tr><td>Structure refinement</td><td></td><td></td></tr><tr><td>Working-set reflections</td><td>19,970</td><td>33,593</td></tr><tr><td>Test-set reflections</td><td>1062</td><td>1770</td></tr><tr><td>Resolution (Å)</td><td>50.0–3.35</td><td>50.0–2.40</td></tr><tr><td>Number of SelA subunits</td><td>2 (one dimer)</td><td>2 (one dimer)</td></tr><tr><td>Number of protein atoms</td><td>7035</td><td>6018</td></tr><tr><td>Number of PLP</td><td>0</td><td>2</td></tr><tr><td>Number of ions</td><td>4 (thiosulfate)</td><td>5 (thiosulfate)</td></tr><tr><td>Number of solvent molecules</td><td>0</td><td>153</td></tr><tr><td>Rwork/Rfree</td><td>0.194/0.250</td><td>0.180/0.230</td></tr><tr><td>Average B-factor (Å2)</td><td></td><td></td></tr><tr><td>Overall</td><td>144.3</td><td>64.4</td></tr><tr><td>Protein</td><td>144.2</td><td>64.6</td></tr><tr><td>PLPs</td><td>—</td><td>49.8</td></tr><tr><td>Ion</td><td>162.4</td><td>79.0</td></tr><tr><td>Solvent</td><td>—</td><td>56.7</td></tr><tr><td>RMSD bond lengths (Å)</td><td>0.009</td><td>0.008</td></tr><tr><td>RMSD bond angles (°)</td><td>1.27</td><td>1.12</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2. Data collection and refinement statistics. \\\"]\",\n \"table_footnote\": \"[\\\"a The statistics in the highest-resolution shell are given in parentheses. \\\",\\\"$R_{\\\\\\\\mathrm{sym}} = \\\\\\\\sum_{hkl}\\\\\\\\sum_l[\\\\\\\\mathcal{I}_l(hkl) - \\\\\\\\langle I(hkl)\\\\\\\\rangle ] / \\\\\\\\sum_{hkl}\\\\\\\\sum_l[I_l(hkl)]$ where $I_{\\\\\\\\ell}(hkl)$ is the intensity of the $\\\\\\\\lambda h$ measurement of $hkl$ and $\\\\\\\\langle I(hkl)\\\\\\\\rangle$ is the average value of $I_{\\\\\\\\ell}(hkl)$ for all $\\\\\\\\lambda h$ measurements. \\\",\\\"$R_{\\\\\\\\mathrm{work,free}} = \\\\\\\\sum_{hkl}(|F_0| - |f_{\\\\\\\\mathrm{c}}||) / \\\\\\\\sum_{hkl}(|F_0|),$ where $R_{\\\\\\\\mathrm{work}}$ and $R_{\\\\\\\\mathrm{free}}$ are calculated using the working-set and test-set reflections (5% of the total reflections), respectively. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[90,663,480,815]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"closest to SelA in the phylogenetic tree is the archaeal MJ0158, a homodimeric protein of unknown function that does not interact with tRNA $^{\\\\text{Sec}}$ (Fig. 6) [13]. Interestingly, the orientation of the C-terminal domain of MJ0158 is similar to that of the SelA C-terminal domain (Fig. 5d and h), suggesting that the change in the domain orientation occurred before SelA acquired its function. Although the N-linker of MJ0158 occupies the similar space to that of SelA, MJ0158 has a Ser residue at the corresponding position of SelA Arg86, which may reflect its functional difference from SelA. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[90,815,480,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Since the binding of the A76-Ser moiety of Ser-tRNA is impossible without the decameric assembly (the putative A76-binding site is formed at the dimer-dimer interface) [7], it is plausible that a dimeric SelA ancestor depended on the phosphate group and simply converted Sep to Sec without tRNA $^{\\\\text{Sec}}$ discrimination, as in the case of SepSecS (Fig. 7). In fact, the extant SelA can produce Sec-tRNA $^{\\\\text{Sec}}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,662,890,844]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"from Ser-tRNA $^{\\\\text{Sec}}$ and from Sep-tRNA $^{\\\\text{Sec}}$ [5], confirming that the Sec synthesis by SelA does not rely on the phosphate group of the substrate aminoacyl moiety. Like SepSecS, the SelA ancestor may have used its selenophosphate-binding site to bind the Sep phosphate moiety in order to facilitate the elimination of the phosphate group from Sep. In this case, either PSTK or an enzyme with a similar function must have existed for the phosphorylation of Ser and the discrimination of tRNA $^{\\\\text{Sec}}$ from tRNA $^{\\\\text{Ser}}$ . Alternatively, the ability of SepSecS to convert Ser to Sec was lost when PSTK evolved for more efficient Sec production. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,863,705,880]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Evolving decamerization \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,897,890,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In a subsequent evolutionary step, the collaboration of the two SelA dimers could have occurred to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,71,137,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1732 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[670,71,890,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dimer-Dimer Interaction of SelA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[107,112,489,401]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"generate the A76-binding pocket at the dimer-dimer interface, thereby improving the efficiency and specificity of substrate binding. Nonetheless, in such a tetramer, only two of the four catalytic sites would have been functional (the \\\"half-of-the-sites\\\" stage). The relative orientations between the dimers could then be stabilized by acquiring decameric ring closure involving five dimers. Simultaneously, the full usage of all 10 catalytic sites was achieved (Fig. 7a). Interestingly, the non-productive catalytic site conformation of the dimeric mutant dSelA- $\\\\Delta N$ resembles those of the other fold-type-I members (Fig. 3b, c, and e-h) and therefore appears to be more primeval. The loop region before $\\\\alpha 7$ interacts with PLP in dSelA- $\\\\Delta N$ (Fig. 3b and c), while it forms a $\\\\beta$ -sheet ( $\\\\beta 6\\\\bullet \\\\beta 7$ ) in the SelA decamer (Fig. 3a). Hence, the catalytic site may have evolved by taking advantage of the decameric quaternary structure. The N-terminal domain was then acquired to increase its affinity for tRNA $^{\\\\mathrm{Sec}}$ and was further utilized for the discrimination of tRNA $^{\\\\mathrm{Sec}}$ from tRNA $^{\\\\mathrm{Ser}}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,428,215,443]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conclusion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,457,489,706]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The natural decameric arrangement of five SelA dimers allows the formation of 10 fully occupied and catalytically functional active sites. Since SelA decamerization is driven by dimer-dimer interactions, disruptive mutations at the interaction interfaces solely yield SelA dimers. In striking contrast to decameric SelA, these dimers are catalytically deficient and exhibit a distinctly distorted active-site formation that prevents productive tRNA $^{\\\\text{Sec}}$ coordination. In fact, the dimeric SelA conformationally resembles similar related PLP enzymes, such as the tetrameric SepSecS. The evolution of the SelA decamer may have been driven by enhanced catalytic efficiency obtained from two sources: First, the decamer allows for an active-site conformation that is optimal for direct, tRNA-dependent Ser-to-Sec conversion. Second, the 10-subunit architecture of SelA generates an N-terminal domain with the ability to discriminate tRNA $^{\\\\text{Sec}}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,738,324,752]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Materials and Methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,773,245,786]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Protein preparation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,800,489,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The genes encoding the full-length and $\\\\Delta N$ SelA genes from A. aeolicus were cloned into the vectors pET25b and pET22b (Novagen), respectively. The full-length SelA used for crystallization was a quadruple mutant, with the non-conserved Lys residues in the loop regions of the N-terminal domain replaced by Ala residues, Lys19Ala-Lys21Ala-Lys46Ala-Lys48Ala (SelA-FL $^{4KA}$ ). The dimerizing quadruple mutation, Tyr220Pro-Asp199Arg-Thr191Tyr-Thr192Tyr, was introduced into SelA-FL $^{4KA}$ and SelA- $\\\\Delta N$ by QuikChange site-directed mutagenesis (Stratagene). The E. coli strain \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,112,900,225]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Rosetta 2(DE3) (Stratagene) was transformed with the expression plasmids, and the native and selenomethionine (SeMet)-substituted proteins were overexpressed and purified as previously described [21]. In order to improve the crystallization efficiency, we methylated the lysine residues of dSeIA-FL $^{4\\\\mathrm{KA}}$ with formaldehyde and a dimethylamine-borane complex, as previously described [22]. Prior to methylation, the protein was diluted with $20~\\\\mathrm{mM}$ Hepes-NaOH buffer $(\\\\mathsf{pH}7.5)$ , containing $0.8\\\\mathrm{MNaCl}$ and $10~\\\\mathrm{mM}$ 2-mercaptoethanol. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,245,880,259]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Crystallization and X-ray diffraction data collection \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,277,900,377]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The SelA proteins were crystallized at $20^{\\\\circ}\\\\mathrm{C}$ by the sitting-drop vapor diffusion method, by mixing $0.75\\\\mu \\\\mathrm{l}$ of the sample with $0.75\\\\mu \\\\mathrm{l}$ of reservoir solutions. Prior to crystallization, dSelA-FL 4KA (SeMet substitution, Lys methylation) and dSelA-ΔN (SeMet substitution, without methylation) were dialyzed against $20\\\\mathrm{mM}$ Tris-HCl buffer $(\\\\mathsf{pH}7.5)$ , containing $200\\\\mathrm{mMNaCl}$ and $10\\\\mathrm{mM}$ 2-mercaptoethanol, and were concentrated to 9.6 and $7.8\\\\mathrm{mg / ml}$ , respectively. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,377,900,501]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Crystal Screen 2, Natrix (Hampton Research), Wizard I, and Wizard II (Emerald Bio-Science) screening kits were used for the initial screening of the crystallization conditions. The optimized reservoir solutions were $100\\\\mathrm{mM}$ trisodium citrate-HCl buffer $(\\\\mathsf{pH}5.6)$ containing $580 - 590\\\\mathrm{mM}$ trisodium citrate, $100\\\\mathrm{mM}$ L-serine, and $100\\\\mathrm{mMNa_2S_2O_3}$ for dSelA-FL4KA, as well as $100\\\\mathrm{mM}$ sodium 4-morpholineethanesulfonate HCl buffer $(\\\\mathsf{pH}6.5)$ containing $2.5\\\\%$ polyethylene glycol 4000, $150\\\\mathrm{mM}$ $\\\\mathrm{Na_2S_2O_3}$ , and $70\\\\mathrm{mMNaNO_3}$ for dSelA- $\\\\Delta \\\\mathsf{N}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,503,900,653]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The crystals thus obtained were transferred into cryoprotective solutions composed of $100\\\\mathrm{mM}$ trisodium citrate-HCl buffer $(\\\\mathsf{pH}5.6)$ , containing $1.3\\\\mathrm{M}$ trisodium citrate, $75\\\\mathrm{mM}$ L-serine, and $75\\\\mathrm{mMNa_2S_2O_3}$ for dSelA-FL4KA, as well as $100\\\\mathrm{mM}$ sodium 4-morpholineethanesulfonate HCl buffer $(\\\\mathsf{pH}6.5)$ , containing $30\\\\%$ dimethyl sulfoxide, $10\\\\%$ polyethylene glycol 4000, $50\\\\mathrm{mMNa_2S_2O_3}$ , and $70\\\\mathrm{mMNaNO_3}$ for dSelA- $\\\\Delta N_{i}$ and were flash-cooled in a cryo- $N_{2}$ stream. X-ray diffraction data were collected at $90~\\\\mathrm{K}$ by using synchrotron radiation at the BL41XU of SPring-8 (Harima, Japan). The data were processed with the HKL2000 program [23]. The statistics of the diffraction data collection are listed in Table 2. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,673,801,686]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Structure determination and refinement \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,699,900,814]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The structures of the dimeric SelAs, dSelA-FL $^{4KA}$ and dSelA- $\\\\Delta N$ , were solved by the molecular replacement method, using the Phaser program [24]. The search model was the SelA- $\\\\Delta N$ structure. The Coot program [25] was used for manual fitting of the models to the electron density map. The structures were refined against the diffraction data by using the CNS [26] and PHENIX [27] programs, with iterative cycles of positional and temperature factor refinements (Table 2). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,834,884,847]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Production and purification of E. coli SelA variants \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,863,900,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mutations were introduced by site-directed mutagenesis (QuikChange®; Agilent) to E. coli K12 SelA, from the ASKA E. coli K12 ORF library (GFP-minus), cloned in the pC24N vector [28]. E. coli BL21 cells were transformed with the expression plasmids. For protein overproduction, the cells \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,73,326,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dimer-Dimer Interaction of SelA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[863,71,900,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1733 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[92,112,480,327]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"were grown at $25^{\\\\circ}\\\\mathrm{C}$ in LB selective medium, supplemented with $50~\\\\mu \\\\mathrm{M}$ isopropyl $\\\\beta$ -D-1-thiogalactopyranoside. Cells sedimented from overnight cultures were resuspended in lysis buffer (50 mM $\\\\mathrm{KH}_2\\\\mathrm{PO}_4$ pH 8,300 mM NaCl, $15\\\\%$ glycerol, $10\\\\mathrm{mM}$ imidazole) and disrupted by sonication. After centrifugation (50,000g, 45 min, $4^{\\\\circ}\\\\mathrm{C})$ the clarified lysates were subjected to immobilized metal affinity chromatography, using Ni-NTA affinity resin (Qiagen) on gravity-flow columns. The immobilized $6\\\\times$ His-SelA fusion proteins were washed with lysis buffer supplemented with $40~\\\\mathrm{mM}$ imidazole, and SelA was eluted with $240~\\\\mathrm{mM}$ imidazole in lysis buffer. The excess imidazole was removed by dialysis (50 mM Tris-HCl, pH 7.5, 300 mM NaCl, $15\\\\%$ glycerol), and the purified SelA variants were analyzed by SDS-PAGE and stored at $-80^{\\\\circ}C.$ The amounts of protein-bound PLP in the SelA variants were determined by UV/vis spectroscopy at $420~\\\\mathrm{nm}$ and in comparison to a PLP standard curve $(0 - 2\\\\mathrm{mM})$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,345,346,360]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"E. coli SelA in vivo activity assays \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,373,482,726]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For in vivo SelA assays, a marker-less $E$ coli SelA deletion strain was used. The initial SelA deletion strain JS1 was constructed by the replacement of the SelA gene with a kanamycin cassette in $E$ coli strain BW25113, as previously described [29], and the genomic insertion of T7 polymerase by P1 transduction [4]. The kanamycin resistance marker of $E$ coli strain JS1 was then excised by FLP recombinase-mediated homologous recombination between the FRT sites flanking the kanamycin resistance cassette, upon transformation of the JS1 strain with the plasmid pCP20 [30], resulting in the marker-less $E$ coli ΔselA strain JS2. $E$ coli ΔselA was then transformed with the plasmids encoding the $E$ coli SelA variants and grown on LB selective medium. Overnight cultures of these clones were plated on selective LB agar plates supplemented with $10~\\\\mu \\\\mathrm{M}$ isopropyl $\\\\beta$ -D-1-thiogalactopyranoside, $1\\\\mu \\\\mathrm{M}$ $\\\\mathrm{Na}_2\\\\mathrm{MoO}_4$ , $1\\\\mu \\\\mathrm{M}$ $\\\\mathrm{Na}_2\\\\mathrm{SeO}_3$ , and $50~\\\\mathrm{mM}$ sodium formate, as described previously [4], and grown anaerobically at $37^{\\\\circ}\\\\mathrm{C}$ overnight. For the oxygen-sensitive benzyl viologen assay, the plates were transferred to an anaerobic chamber (90% $\\\\mathbf{N}_2$ , 5% $\\\\mathbf{H}_2$ , 5% $\\\\mathbf{CO}_2$ ) and overlaid with top agar containing $1\\\\mathrm{mg / ml}$ benzyl viologen, $250~\\\\mathrm{mM}$ sodium formate, and $25\\\\mathrm{mM}$ $\\\\mathrm{KH}_2\\\\mathrm{PO}_4 / \\\\mathrm{K}_2\\\\mathrm{HPO}_4$ (pH 7.0). Wild-type SelA served as a positive control. The benzyl viologen assay allows the colorimetric monitoring of SelA activity by the formation of purple-colored reduced benzyl viologen. Benzyl viologen reduction is catalyzed by $\\\\mathrm{FDH_H}$ , which requires Sec insertion for catalytic activity. The Sec formation, finally, is dependent on the SelA activity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,747,342,762]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Structure-based phylogenetic tree \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,774,482,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The STAMP program [31] in the MultiSeq module of VMD [32] was used to superpose and calculate the structural similarity, $Q_{\\\\mathrm{H}}$ , among the coordinates of SelA-ΔN and the other fold-type-I PLP-dependent enzymes obtained from the Protein Data Bank. The enzymes with $>50\\\\%$ amino acid sequence identity were removed, and thus, the core domains of 187 coordinates, including the coordinates of both chains A and B of the heterodimeric glycine decarboxylase (PDB ID: 1WYT), were superposed. The other 185 enzymes were homooligomeric ones. The structural similarity $Q_{\\\\mathrm{H}}$ was calculated [33], and the neighbor-joining tree, based on the $Q_{\\\\mathrm{H}}$ values, was drawn using the SplitsTree program [34]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,112,653,124]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Accession numbers \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,139,890,165]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The coordinates and structure factors have been deposited in the Protein Data Bank (PDB IDs: 3WCN and 3WCO). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,165,890,191]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.jmb.2014.01.003. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,228,685,245]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgments \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,254,892,655]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We thank the staff members of SPring-8 BL41XU and the Photon Factory beam lines for assistance with our data collection. We thank T. Imada, K. Ake, and T. Nakayama for assistance with the manuscript preparation and P. O'Donoghue and M. Simonovic (University of Illinois, Chicago) for critical discussions. We are grateful to the National BioResource Project in Japan for providing the ASKA E. coli K12 ORF library. Y.I. was supported by Research Fellowships from the Japan Society for the Promotion of Science. M.J.B. holds a Feodor Lynen Postdoctoral Fellowship of the Alexander von Humboldt Foundation (Bonn, Germany). This work was supported in part by Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research (A) to S.Y. and (C) to S.S. This work was also supported in part by the Targeted Proteins Research Program, and the Platform for Drug Discovery, Informatics, and Structural Life Science from the Ministry of Education, Culture, Sports, Science, and Technology (to S.Y.). D.S. gratefully acknowledges support from the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences of the U.S. Department of Energy (DE-FG02-98ER20311; for funding the genetic experiments), from the National Institute of General Medical Sciences (GM22854), and from the Defense Advanced Research Projects Agency (contracts N66001-12-C-4020 and N66001-12-C-4211). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[695,664,890,678]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received 8 November 2013; \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[606,678,890,692]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received in revised form 9 January 2014; \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[707,693,890,706]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Accepted 12 January 2014 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[663,706,890,718]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Available online 20 January 2014 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[811,733,890,746]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[650,747,890,761]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"fold-type-I PLP-dependent enzyme; \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[742,762,890,774]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"selenium metabolism; \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[826,775,890,786]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tRNA<sup>Sec</sup>; \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[752,789,890,802]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pentamer of dimers; \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[779,804,890,815]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"21st amino acid \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,829,890,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike License, which permits non-commercial use, distribution, and reproduction in any medium, provided the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[621,886,890,899]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"original author and source are credited. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[569,912,890,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y.I. and M.J.B. contributed equally to this work. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[97,71,136,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1734 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[670,71,890,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dimer-Dimer Interaction of SelA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[344,113,490,126]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abbreviations used: \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[115,127,490,182]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"AHBA, 5-amino-3-hydroxybenzoate; CBS, cystathionine $\\\\beta$ -synthase; CysS, cysteine synthase; PLP, pyridoxal $5^{\\\\prime}$ -phosphate; PSTK, O-phosphoseryl-tRNA $^{\\\\text{Sec}}$ kinase; SeMet, selenomethionine. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[105,206,216,223]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,238,490,902]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[1] Bock A, Forchhammer K, Heider J, Leinfelder W, Sawers G, Veprek B, et al. 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Proc Natl Acad Sci U S A 2009;106:16215-20. \\\",\\\"[12] Fukunaga R, Yokoyama S. Structural insights into the second step of RNA-dependent cysteine biosynthesis in archaea: crystal structure of Sep-tRNA:Cys-tRNA synthase from Archaeoglobus fulgidus. J Mol Biol 2007;370:128-41. \\\",\\\"[13] Kaiser JT, Gromadski K, Rother M, Engelhardt H, Rodnina MV, Wahl MC. Structural and functional investigation of a putative archaeal selenocysteine synthase. Biochemistry 2005;44:13315-27. \\\",\\\"[14] Koutmos M, Kabil O, Smith JL, Banerjee R. Structural basis for substrate activation and regulation by cystathionine beta-synthase (CBS) domains in cystathionine $\\\\\\\\beta$ -synthase. Proc Natl Acad Sci U S A 2010;107:20958-63. \\\",\\\"[15] Burkhard P, Tai CH, Ristroph CM, Cook PF, Jansonius JN. Ligand binding induces a large conformational change in O-acetylserine sulfhydrylase from Salmonella typhimurium. J Mol Biol 1999;291:941-53. \\\"]\",\n \"page_idx\": \"12\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[517,113,902,902]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[16] Cook PD, Thoden JB, Holden HM. The structure of GDP-4-keto-6-deoxy-D-mannose-3-dehydratase: a unique coenzyme B6-dependent enzyme. Protein Sci 2006;15:2093-106. \\\",\\\"[17] Chen XM, Ploux O, Liu HW. Biosynthesis of 3,6-dideoxyhexoses: in vivo and in vitro evidence for protein-protein interaction between CDP-6-deoxy-L-threo-D-glycero-4-hexulose 3-dehydrase (E1) and its reductase (E3). Biochemistry 1996;35:16412-20. \\\",\\\"[18] Eads JC, Beeby M, Scapin G, Yu TW, Floss HG. Crystal structure of 3-amino-5-hydroxybenzoic acid (AHBA) synthase. Biochemistry 1999;38:9840-9. \\\",\\\"[19] Ambrogelly A, Palioura S, Soll D. Natural expansion of the genetic code. Nat Chem Biol 2007;3:29-35. \\\",\\\"[20] Sauerwald A, Zhu W, Major TA, Roy H, Palioura S, Jahn D, et al. RNA-dependent cysteine biosynthesis in archaea. Science 2005;307:1969-72. \\\",\\\"[21] Itoh Y, Sekine S, Yokoyama S. Crystallization and preliminary X-ray crystallographic analysis of Aquifex aeolicus SelA, a bacterial selenocysteine synthase. Acta Crystallogr Sect F Struct Biol Cryst Commun 2012;68:1128-33. \\\",\\\"[22] Walter TS, Meier C, Assenberg R, Au KF, Ren J, Verma A, et al. Lysine methylation as a routine rescue strategy for protein crystallization. Structure 2006;14:1617-22. \\\",\\\"[23] Otwinowski Z, Minor W. Processing of X-ray diffraction data collected in oscillation mode. Methods Enzymol 1997;276:307-26. \\\",\\\"[24] McCoy AJ, Grosse-Kunstleve RW, Adams PD, Winn MD, Storoni LC, Read RJ. Phaser crystallographic software. J Appl Crystallogr 2007;40:658-74. \\\",\\\"[25] Emsley P, Cowtan K. Coot: model-building tools for molecular graphics. Acta Crystallogr Sect D Biol Crystallogr 2004;60:2126-32. \\\",\\\"[26] Adams PD, Pannu NS, Read RJ, Brunger AT. Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement. Proc Natl Acad Sci U S A 1997;94:5018-23. \\\",\\\"[27] Adams PD, Afonine PV, Bunkóczi G, Chen VB, Davis IW, Echols N, et al. PHENIX: a comprehensive Python-based system for macromolecular structure solution. Acta Crystallogr Sect D Biol Crystallogr 2010;66:213-21. \\\",\\\"[28] Kitagawa M, Ara T, Arifuzzaman M, Ioka-Nakamichi T, Inamoto E, Toyonaga H, et al. Complete set of ORF clones of Escherichia coli ASKA library (a complete set of $E.$ coli K-12 ORF archive): unique resources for biological research. DNA Res 2005;12:291-9. \\\",\\\"[29] Datsenko KA, Wanner BL. One-step inactivation of chromosomal genes in Escherichia coli K-12 using PCR products. Proc Natl Acad Sci U S A 2000;97:6640-5. \\\",\\\"[30] Yuan J, Hohn MJ, Sherrer RL, Palioura S, Su D, Soll D. A tRNA-dependent cysteine biosynthesis enzyme recognizes the selenocysteine-specific tRNA in Escherichia coli. FEBS Lett 2010;584:2857-61. \\\",\\\"[31] Roberts E, Eargle J, Wright D, Luthey-Schulten Z. MultiSeq: unifying sequence and structure data for evolutionary analysis. BMC Bioinformatics 2006;7:382. \\\",\\\"[32] Humphrey W, Dalke A, Schulten K. VMD: visual molecular dynamics. J Mol Graphics 1996;14:27-8. \\\",\\\"[33] O'Donoghue P, Luthey-Schulten Z. Evolutionary profiles derived from the QR factorization of multiple structural alignments gives an economy of information. J Mol Biol 2005;346:875-94. \\\",\\\"[34] Huson DH, Bryant D. Application of phylogenetic networks in evolutionary studies. Mol Biol Evol 2006;23:254-67. \\\"]\",\n \"page_idx\": \"12\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[105,71,327,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dimer-Dimer Interaction of SelA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[862,71,900,85]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1735 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1016/j.apmt.2020.100876"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Medicine and Health Sciences/Engineering and Manufacturing Science"},"sha256":{"kind":"string","value":"149e17a34eb69c38bf59f8ec7a90b65e73eca6b0552ea197988fe05c961687c7"},"title":{"kind":"string","value":"A gel-forming clusteroluminogenic polymer with tunable emission behavior as a sustained-release carrier enabling real-time tracking during bioactive agent delivery"}}},{"rowIdx":249,"cells":{"abstract":{"kind":"string","value":"Remote sensing has been widely used for forest monitoring. However, most forest monitoring systems largely rely on optical images that limit temporal analyses due to cloud cover, particularly in the tropics. The current study used integration of optical Landsat-8 and Sentinel-1 SAR to produce individual year land cover classification maps for Kalimantan, Indonesia that differentiate between native forest and tree plantations, such as oil palm and rubber. We applied a Bayesian network to produce a time series of land cover classification that improved accuracy of individual year land cover maps. Accuracy assessment using a confusion matrix showed that final map had overall accuracy of 90%, while user's and producer's accuracy for each land cover class was above 85%, except non–forest, which had 76% producer's accuracy due to errors in the classification between young rubber plantations and non–forest. Improved maps will support Indonesia's national forest monitoring system and sustainable forest management."},"author":{"kind":"string","value":"I. L. Sari|I. L. Sari|C. J. Weston|G. J. Newnham|L. Volkova"},"content_list":{"kind":"list like","value":[{"bbox":"[115,83,877,116]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MAPPING LAND COVER TIME SERIES USING LANDSAT-8 AND SENTINEL-1 IN SOUTH KALIMANTAN ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[319,140,675,153]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"I. L. Sari 1,2, C. J. Weston 1, G. J. Newnham 3, L. Volkova 1 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[146,165,848,227]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 School of Ecosystem and Forest Sciences, Faculty of Science, The University of Melbourne, Creswick, Australia - Weston@unimelb.edu.au, Lubav@unimelb.edu.au 2 Research Center for Remote Sensing, National Research and Innovation Agency (BRIN), Jakarta, Indonesia - inggit.lolita.sari@brin.go.id 3 CSIRO Land and Water, Clayton South, Australia - Glenn.Newnham@csiro.au ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[425,239,573,252]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Commission IV, WG 7 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,276,584,289]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"KEY WORDS: Bayesian, Time Series, Land Cover, Classification, Kalimantan. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,313,181,326]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABSTRACT: ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[94,338,904,437]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remote sensing has been widely used for forest monitoring. However, most forest monitoring systems largely rely on optical images that limit temporal analyses due to cloud cover, particularly in the tropics. The current study used integration of optical Landsat-8 and Sentinel-1 SAR to produce individual year land cover classification maps for Kalimantan, Indonesia that differentiate between native forest and tree plantations, such as oil palm and rubber. We applied a Bayesian network to produce a time series of land cover classification that improved accuracy of individual year land cover maps. Accuracy assessment using a confusion matrix showed that final map had overall accuracy of $9 0 \\%$ , while user's and producer's accuracy for each land cover class was above $8 5 \\%$ , except non– forest, which had $7 6 \\%$ producer's accuracy due to errors in the classification between young rubber plantations and non–forest. Improved maps will support Indonesia's national forest monitoring system and sustainable forest management. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[216,462,363,474]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. INTRODUCTION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[94,485,485,570]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Major deforestation in the tropics is driven by agricultural expansion, including timber logging (Hosonuma et al., 2012). Borneo island has experienced vast and rapid deforestation, with forest loss of around $6 . 0 4 \\mathrm { ~ M ~ }$ ha between 2000–2017 (Gaveau et al., 2018). Around $51 \\%$ of this forest loss was for plantation expansion, such as oil palm and rubber plantations (Gaveau et al., 2018). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,584,485,669]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remote sensing has been used for several decades to monitor forest extent and change, drawing on optical images such as those from the Landsat series of satellites (Romijn et al., 2015; Sari et al., 2021a). However, intense cloud cover limits the ability of optical images to detect temporal changes in vegetation cover and types in tropical countries (Massey et al., 2018; Sari et al., 2021a). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,682,485,756]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Synthetic Aperture Radar (SAR) systems, such as ALOS PALSAR, and Sentinel-1 offer the ability to penetrate clouds, smoke, and haze (Hoekman, Vissers, and Wielaard, 2010; Motohka et al., 2014). Furthermore, SAR data is sensitive to vegetation structure, moisture content, and ground conditions (Pohl, 2014; Miettinen, Liew, and Kwoh, 2015). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,768,485,867]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Improvement of forest monitoring may be possible by combining optical and SAR satellite sensors to reduce limitations imposed by persistent cloud cover. Integration of optical and SAR images has already been shown to improve forest classification accuracy (Sarzynski et al., 2020; Sari et al., 2022). However, employing multitemporal constraints on classification may help to further reduces the uncertainty in the land cover classification (Ban, 2016; LAPAN, 2014). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,880,485,904]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We showed that integration of Landsat-8 optical images and Sentinel-1 SAR images using a decision tree could be used to improve the classification accuracy of native forests, oil palm and rubber plantations, and non–forest areas in South Kalimantan province (Sari et al., 2022). This paper describes the use of a Bayesian network for time series classification to further refine individual year land cover maps from 2015 to 2017. The development of these improved time series of land cover maps aims to support Indonesia’s national forest monitoring program, and sustainable forest management. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,462,905,560]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[591,573,826,585]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. MATERIALS AND METHODS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,597,616,609]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.1 Study Area ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,619,904,730]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The study area is situated in the north part of South Kalimantan province, Indonesia, covering 62,500 hectares (Figure 1). Native forests, oil palm plantations, rubber plantations, and non– forest such as settlements, paddy fields, shrubs, and grasslands exist in the region. The extent of oil palm and rubber plantations increased in this province by $4 2 . 5 \\%$ over the past seventeen years, from 294,982.72 hectares in 2000 to 693,619 hectares in 2017 (BPS-Statistics Indonesia, 2000; BPS-Statistics Indonesia, 2018). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[534,738,885,895]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 1. Study area in South Kalimantan province. \"]","image_footnote":"[]","img_path":"images/0978/037ce7969f1db717cce0c28b6c40808c7276fc6ae9aef45629d7d9725458b265.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[183,948,813,971]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\circledcirc$ Author(s) 2023. CC BY 4.0 License. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[104,28,897,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLVIII-4/W6-2022 Geoinformation Week 2022 “Broadening Geospatial Science and Technology”, 14–17 November 2022, Johor Bahru, Malaysia (online) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[880,960,904,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"319 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[94,83,317,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.2 Satellite image pre-processing ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[94,107,485,156]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A time series of Landsat-8 optical and Sentinel-1 SAR images, from 2015 to 2017, were mosaiced at $2 5 ~ \\mathrm { m }$ resolution and used as the main data to produce individual year land cover map, using the decision tree approach described by Sari et al. (2022). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,169,485,255]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Landsat-8 images with less than $5 0 \\%$ cloud cover were downloaded from the USGS Earth Resources Observation and Science (EROS) Center (2019). Sentinel-1A Interferometric Wide (IW) swath mode Level-1 Ground Range Detected (GRD) images for each individual year were downloaded from the Alaska Satellite Facility Distributed Active Archive Center (2019). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,268,485,377]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Landsat-8 images pre-processing method is outlined in previous publications (LAPAN, 2014; Sari et al., 2022). The image pre-processing consists of scene selection, geometric , radiometric, terrain correction, cloud masking, and mosaicking. The annual mosaics of Landsat-8 images consist of six multispectral image bands of blue, green, red, near infrared, shortwave infrared 1, and short-wave infrared 2, and processed top of atmosphere (TOA) and bidirectional reflectance distribution function (BRDF) correction. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,390,485,464]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Sentinel-1 images pre-processing consists of applying an update of precise orbit acquisition information, radio-metric calibration, and terrain correction to remove terrain effects. The mosaic Sentinel-1A images with dual-polarization of $\\mathrm { V V + V H }$ bands were used in this study to analyse the backscatter intensity of the land cover classes. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,477,341,489]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.3 Bayesian time series classification ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,500,485,636]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Bayesian networks use prior information of land cover to predict and track past land cover changes (Lee, Cardille, and Coe, 2020). A Bayesian network was used to improve time series classification and update the certainty of land cover based on prior land cover information and plantation occurrence images. The prior land cover was the individual land cover classifications to integrate Landsat-8 and Sentinel-1 to produce four land cover classes described in Section 2.4. The plantation occurrence images for improvement of oil palm and rubber discrimination are described in Section 2.5. Thus, the steps to utilise a Bayesian network for temporal processing of these inputs were as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[122,637,485,698]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"• Create a land cover change probability matrix using individual land cover classifications from 2015 to 2017. That is, for these two years, changes in the four classes were analysed and allocated to one of 16 land cover change categories. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[146,699,484,735]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Create oil palm and rubber plantation occurrence probability maps for 2015 to 2017 (see Section 2.5). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[122,737,485,786]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"• Calculate the probability of land cover classes for the preceding year based on information from the following map for native forest and non–forest classes, using the Bayesian equation (Eq.1): ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[122,791,391,842]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0331/b6e03a0d4c72a9bdc71c6a98e05b21b64c2ccd3b15705032c6d18924ed15f80f.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array} { r l } & { \\mathrm { P } ( \\mathrm { M a p } _ { 2 0 1 6 } | \\mathrm { M a p } _ { 2 0 1 7 } ) = } \\\\ & { \\qquad \\frac { \\mathrm { P } ( \\mathrm { M a p } _ { 2 0 1 7 } | \\mathrm { M a p } _ { 2 0 1 6 } ) \\mathrm { P } ( \\mathrm { M a p } _ { 2 0 1 6 } ) } { \\mathrm { P } ( \\mathrm { M a p } _ { 2 0 1 7 } ) } , } \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[122,854,485,891]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"• Calculate the probability of land cover classes in 2016 for the rubber plantation class based on the 2017 map using the equation (Eq.2): ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[127,897,369,914]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0634/cfea4b51c7c49df4f98fa20fce972cbd3754bacd4955f9a8b350a63258a0dc29.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array} { r } { \\mathrm { P } ( \\mathrm { M a p } _ { 2 0 1 6 } | \\mathrm { M a p } _ { 2 0 1 7 } , \\mathrm { R u b b e r } _ { 2 0 1 6 } ) = } \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[554,82,852,110]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0921/3a1464459dccbb3c4f215a82b216c128f0c4384b88c36f64872258afdadc2479.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\frac { \\mathrm { P } ( \\mathrm { M a p } _ { 2 0 1 7 } , \\mathrm { R u b b e r } _ { 2 0 1 6 } | \\mathrm { M a p } _ { 2 0 1 6 } ) \\mathrm { P } ( \\mathrm { M a p } _ { 2 0 1 6 } ) } { \\mathrm { P } ( \\mathrm { M a p } _ { 2 0 1 7 } , \\mathrm { R u b b e r } _ { 2 0 1 6 } ) } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[542,135,905,172]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Land cover probability of a transition to the oil palm class was calculated based on the probability of the occurrence of oil palm (i.e., substituting rubber with oil palm in Eq. 2). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[564,174,905,359]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"• The decision if a transition should occur was based on the following rule: if the probability for stable class (similar to previous) is greater than the probability for change class then the decision will be stable (similar to previous class), and if the probability for change class is greater than the stable class then the decision class will change to a new class. Validate the oil palm and rubber plantation classes using the plantation occurrence boundary to reduce speckle class due to the pixel-based method (see Section 2.5). Apply the same Bayesian network processing in the forward time series direction to produce a final land cover map. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,373,801,384]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.4 Individual year land cover classification ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,395,905,469]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The individual year land cover classification was developed from the annual forest and non–forest maps combined with oil palm and rubber plantation algorithms developed from Landsat-8 and Sentinel-1 (LAPAN, 2014; Sari et al., 2022). The individual year land cover classification method has been outlined in Sari et al. (2022). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,481,734,494]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.5 Plantation occurrence images ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,505,905,628]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The oil palm and rubber plantations occurrence were used as additional information for assessing the plantation occurrence. The oil palm and rubber occurrence maps were created using a combination between NDVI and SWIR 1 for oil palm occurrence, and NDMI and SWIR 1 for rubber occurrence. The thresholds in the decision tree were determined from the histogram of values for training samples of oil palm and rubber. The boundary for the oil palm and rubber plantations were produced from the mosaic of the nearest year plantation occurrence image with a median filter applied. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,641,798,653]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.6 Accuracy assessment of land cover map ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,663,905,761]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A confusion matrix was used to measure the accuracy of the 2017 classification maps, including overall accuracy, producer's accuracy, and user's accuracy. The map accuracy assessment was based on stratified random sampling with 196 validation points (Sari et al., 2021b). One scene of high-resolution SPOT 6 images (resolution $1 . 5 ~ \\mathrm { m }$ ) acquired on 18 August 2018 was used as the reference images with validation based on a minimum area of 50 $\\mathrm { ~ x ~ } 5 0 \\mathrm { ~ m ~ }$ for each of 196 points. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[594,774,821,786]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. RESULTS AND DISCUSSION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,797,905,908]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The mosaic images of Landsat-8 and Sentinel-1 to develop individual land cover classification from 2015–2017 are shown in Figure 2. These Landsat-8 images are depicted in a composite of short-wave infrared 1, near infrared, and red band. While Sentinel-1 images in Figure 2 are depicted in composites of the Grey Level Co-occurrence Matrix (GLCM) variance texture of VH˗VV.Samples for decision-making using Bayesian network to produce time series classification maps for 2016 and 2017 are described in Table 1–Table 4. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[183,948,813,971]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\circledcirc$ Author(s) 2023. CC BY 4.0 License. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[880,960,904,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"320 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[100,28,899,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLVIII-4/W6-2022 Geoinformation Week 2022 “Broadening Geospatial Science and Technology”, 14–17 November 2022, Johor Bahru, Malaysia (online) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[94,97,900,479]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 2. Mosaic images of Landsat-8 and Sentinel-1 from 2015–2017. \"]","image_footnote":"[]","img_path":"images/0750/a988cc97f3e699b2a87683b4c6e37b28d59ed1b657b76580d3763a2d83718391.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[92,520,905,669]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0746/c2ab0d51860ff7cb73976a435ea7b96abb0d6b37a4e58ce5989a3df79f8621ac.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":"<table><tr><td rowspan=2 colspan=1>20172016</td><td rowspan=1 colspan=5>Land cover class</td></tr><tr><td rowspan=1 colspan=1>Native forest</td><td rowspan=1 colspan=1>Oil palm</td><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>Non-forest</td><td rowspan=1 colspan=1>Total</td></tr><tr><td rowspan=1 colspan=1>Native forest</td><td rowspan=1 colspan=1>0.223</td><td rowspan=1 colspan=1>0.010</td><td rowspan=1 colspan=1>0.013</td><td rowspan=1 colspan=1>0.008</td><td rowspan=1 colspan=1>0.254</td></tr><tr><td rowspan=1 colspan=1>Oil palm</td><td rowspan=1 colspan=1>0.009</td><td rowspan=1 colspan=1>0.110</td><td rowspan=1 colspan=1>0.004</td><td rowspan=1 colspan=1>0.003</td><td rowspan=1 colspan=1>0.126</td></tr><tr><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>0.009</td><td rowspan=1 colspan=1>0.002</td><td rowspan=1 colspan=1>0.213</td><td rowspan=1 colspan=1>0.101</td><td rowspan=1 colspan=1>0.325</td></tr><tr><td rowspan=1 colspan=1>Non-forest</td><td rowspan=1 colspan=1>0.004</td><td rowspan=1 colspan=1>0.003</td><td rowspan=1 colspan=1>0.122</td><td rowspan=1 colspan=1>0.166</td><td rowspan=1 colspan=1>0.295</td></tr><tr><td rowspan=1 colspan=1>Total</td><td rowspan=1 colspan=1>0.244</td><td rowspan=1 colspan=1>0.125</td><td rowspan=1 colspan=1>0.353</td><td rowspan=1 colspan=1>0.278</td><td rowspan=1 colspan=1>1.000</td></tr></table>","table_caption":"[\"Table 1. Land cover changes map probability for 2016–2017. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[92,700,485,849]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0482/abaf38da8113fc50485141e4829bf01ac629e9cd30a0c7734799fc94eb52c56d.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":"<table><tr><td rowspan=2 colspan=1>20172016</td><td rowspan=1 colspan=3>Land cover class</td></tr><tr><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>Non-rubber</td><td rowspan=1 colspan=1>Total</td></tr><tr><td rowspan=1 colspan=1>Native forest</td><td rowspan=1 colspan=1>0.025</td><td rowspan=1 colspan=1>0.229</td><td rowspan=1 colspan=1>0.254</td></tr><tr><td rowspan=1 colspan=1>Oil palm</td><td rowspan=1 colspan=1>0.002</td><td rowspan=1 colspan=1>0.124</td><td rowspan=1 colspan=1>0.126</td></tr><tr><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>0.200</td><td rowspan=1 colspan=1>0.125</td><td rowspan=1 colspan=1>0.325</td></tr><tr><td rowspan=1 colspan=1>Non-forest</td><td rowspan=1 colspan=1>0.070</td><td rowspan=1 colspan=1>0.224</td><td rowspan=1 colspan=1>0.295</td></tr><tr><td rowspan=1 colspan=1>Total</td><td rowspan=1 colspan=1>0.297</td><td rowspan=1 colspan=1>0.703</td><td rowspan=1 colspan=1>1.000</td></tr></table>","table_caption":"[\"Table 2. Rubber occurrence probability in 2016. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[512,700,905,849]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0104/d4147398e4f21831e2f27a4eb6cf3807b0a0f1ec508cd2f72f887ded3f29a8db.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":"<table><tr><td rowspan=2 colspan=1>20172016</td><td rowspan=1 colspan=3>Land cover class</td></tr><tr><td rowspan=1 colspan=1>Oil palm</td><td rowspan=1 colspan=1>Non-oil palm</td><td rowspan=1 colspan=1>Total</td></tr><tr><td rowspan=1 colspan=1>Native forest</td><td rowspan=1 colspan=1>0.241</td><td rowspan=1 colspan=1>0.013</td><td rowspan=1 colspan=1>0.254</td></tr><tr><td rowspan=1 colspan=1>Oil palm</td><td rowspan=1 colspan=1>0.117</td><td rowspan=1 colspan=1>0.009</td><td rowspan=1 colspan=1>0.126</td></tr><tr><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>0.314</td><td rowspan=1 colspan=1>0.012</td><td rowspan=1 colspan=1>0.325</td></tr><tr><td rowspan=1 colspan=1>Non-forest</td><td rowspan=1 colspan=1>0.190</td><td rowspan=1 colspan=1>0.104</td><td rowspan=1 colspan=1>0.295</td></tr><tr><td rowspan=1 colspan=1>Total</td><td rowspan=1 colspan=1>0.862</td><td rowspan=1 colspan=1>0.138</td><td rowspan=1 colspan=1>1.000</td></tr></table>","table_caption":"[\"Table 3. Oil palm occurrence probability in 2016. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[181,947,813,971]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\circledcirc$ Author(s) 2023. CC BY 4.0 License. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[880,960,904,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"321 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[102,28,897,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLVIII-4/W6-2022 Geoinformation Week 2022 “Broadening Geospatial Science and Technology”, 14–17 November 2022, Johor Bahru, Malaysia (online) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[92,96,905,493]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0033/e202ce4c1d413f79f5e67222a1c1cc14cb3d2fc93565c74b5ae898dc5abd03da.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":"<table><tr><td rowspan=1 colspan=1>Time seriesclass decisionLand coverchange 2016 to 2017</td><td rowspan=1 colspan=1>Probability similar to previous class</td><td rowspan=1 colspan=1>Probability to change class</td><td rowspan=1 colspan=1>Result of time series classfor map in 2016</td></tr><tr><td rowspan=1 colspan=1>Native forest to Native forest</td><td rowspan=1 colspan=1>0.905</td><td rowspan=1 colspan=1>0.095</td><td rowspan=1 colspan=1>Native forest</td></tr><tr><td rowspan=1 colspan=1>Native forest to Oil palm</td><td rowspan=1 colspan=1>0.028</td><td rowspan=1 colspan=1>0.972</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1>Native forest to Rubber</td><td rowspan=1 colspan=1>0.154</td><td rowspan=1 colspan=1>0.846</td><td rowspan=1 colspan=1>Rubber</td></tr><tr><td rowspan=1 colspan=1>Native forest to Non-forest</td><td rowspan=1 colspan=1>0.409</td><td rowspan=1 colspan=1>0.591</td><td rowspan=1 colspan=1>Non-forest</td></tr><tr><td rowspan=1 colspan=1>Oil palm to Oil palm</td><td rowspan=1 colspan=1>0.978</td><td rowspan=1 colspan=1>0.022</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1> Oil palm to Rubber</td><td rowspan=1 colspan=1>0.530</td><td rowspan=1 colspan=1>0.470</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1>Oil palm to Non-forest</td><td rowspan=1 colspan=1>0.994</td><td rowspan=1 colspan=1>0.006</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1>Oil palm to Native forest</td><td rowspan=1 colspan=1>0.994</td><td rowspan=1 colspan=1>0.006</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1>Rubber to Rubber</td><td rowspan=1 colspan=1>0.901</td><td rowspan=1 colspan=1>0.099</td><td rowspan=1 colspan=1>Rubber</td></tr><tr><td rowspan=1 colspan=1>Rubber to Non-forest</td><td rowspan=1 colspan=1>0.650</td><td rowspan=1 colspan=1>0.350</td><td rowspan=1 colspan=1>Rubber</td></tr><tr><td rowspan=1 colspan=1>Rubber to Native forest</td><td rowspan=1 colspan=1>0.848</td><td rowspan=1 colspan=1>0.152</td><td rowspan=1 colspan=1>Rubber</td></tr><tr><td rowspan=1 colspan=1>Rubber to Oil palm</td><td rowspan=1 colspan=1>0.001</td><td rowspan=1 colspan=1>0.999</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1>Non-forest to Non-forest</td><td rowspan=1 colspan=1>0.871</td><td rowspan=1 colspan=1>0.129</td><td rowspan=1 colspan=1>Non-forest</td></tr><tr><td rowspan=1 colspan=1>Non-forest to Native forest</td><td rowspan=1 colspan=1>0.085</td><td rowspan=1 colspan=1>0.915</td><td rowspan=1 colspan=1>Native forest</td></tr><tr><td rowspan=1 colspan=1>Non-forest to Oil palm</td><td rowspan=1 colspan=1>0.027</td><td rowspan=1 colspan=1>0.973</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1>Non-forest to Rubber</td><td rowspan=1 colspan=1>0.350</td><td rowspan=1 colspan=1>0.650</td><td rowspan=1 colspan=1>Rubber</td></tr></table>","table_caption":"[\"Table 4. Decision-making result for time series classification for 2016 to 2017. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[92,526,485,574]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Images of individual year land cover classification, oil palm and rubber plantation occurrence, and the Bayesian network time series classification maps from 2015 to 2017 are shown in Figure 3. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,526,905,563]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Classification accuracy for the final time series land cover map in 2017 has an overall accuracy of $9 0 \\%$ . Detailed accuracy for each land cover class is shown in Table 5. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[99,588,900,793]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0751/4169535691cb538d90117f68c30fee21957f0697f8bd39942456dc1151e274f0.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[181,947,813,971]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\circledcirc$ Author(s) 2023. CC BY 4.0 License. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[880,960,904,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"322 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[102,28,897,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLVIII-4/W6-2022 Geoinformation Week 2022 “Broadening Geospatial Science and Technology”, 14–17 November 2022, Johor Bahru, Malaysia (online) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[97,73,899,718]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 3. Individual year classification and time series classification images from 2015 to 2017 \"]","image_footnote":"[]","img_path":"images/0242/51a107acc0e5c7b75598c6c45e2c4705c9ff8e06304e8e048f52ba5568ca645f.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[92,746,907,864]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0281/315f0e57d32a2a0e592fabc8ae551aec512766c245fce18abdab4cec89e52bf9.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":"<table><tr><td rowspan=1 colspan=1>Reference data 2017Classified data 2017</td><td rowspan=1 colspan=1>Native forest</td><td rowspan=1 colspan=1> Oil palm</td><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>Non-forest</td><td rowspan=1 colspan=1>Total</td><td rowspan=1 colspan=1>User's acc. (%)</td></tr><tr><td rowspan=1 colspan=1>Native forest</td><td rowspan=1 colspan=1>38</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>41</td><td rowspan=1 colspan=1>93</td></tr><tr><td rowspan=1 colspan=1>Oil palm</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>25</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>27</td><td rowspan=1 colspan=1>93</td></tr><tr><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>85</td><td rowspan=1 colspan=1>9</td><td rowspan=1 colspan=1>95</td><td rowspan=1 colspan=1>89</td></tr><tr><td rowspan=1 colspan=1>Non-forest</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>28</td><td rowspan=1 colspan=1>33</td><td rowspan=1 colspan=1>85</td></tr><tr><td rowspan=1 colspan=1>Total</td><td rowspan=1 colspan=1>41</td><td rowspan=1 colspan=1>26</td><td rowspan=1 colspan=1>92</td><td rowspan=1 colspan=1>37</td><td rowspan=1 colspan=1>196</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>Producer's acc.(%)</td><td rowspan=1 colspan=1>93</td><td rowspan=1 colspan=1>96</td><td rowspan=1 colspan=1>92</td><td rowspan=1 colspan=1>76</td><td rowspan=1 colspan=2>Overall accuracy=90%</td></tr></table>","table_caption":"[\"Table 5. Accuracy assessment of land cover classification in 2017. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[181,947,813,971]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\circledcirc$ Author(s) 2023. CC BY 4.0 License. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[880,960,905,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"323 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[102,28,899,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLVIII-4/W6-2022 Geoinformation Week 2022 “Broadening Geospatial Science and Technology”, 14–17 November 2022, Johor Bahru, Malaysia (online) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[94,83,485,182]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Table 5 shows the Bayesian network time series classification map accuracy. User's and producer's accuracy for all land cover classes were ${ > } 8 5 \\%$ , which fulfils Indonesia’s national land cover classification accuracy benchmark to support the national forest monitoring system (Badan Informasi Geospasial, 2014). Lower producer's accuracy for the non–forest class $( 7 6 \\% )$ was primarily due to mixed classification between young rubber plantation and non–forest. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[226,202,351,214]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. CONCLUSION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,225,485,471]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A Bayesian network algorithm was used to produce a time series of land cover classification that improved accuracy of individual year land cover maps for South Kalimantan, Indonesia. A time series of Landsat-8 optical and Sentinel-1 SAR images from 2015 to 2017 were used to develop temporal maps with four land cover classes: native forest, non–forests, rubber and oil palm plantations. High-resolution SPOT images were used for the accuracy assessment of the final $2 0 1 7 \\mathrm { \\ m a p }$ . The map generated using a Bayesian network produced overall accuracy of $9 0 \\%$ . Moreover, each land cover class had a user's accuracy and producer's accuracy of ${ > } 8 5 \\%$ , except for the non–forest class which had producer's accuracy of $7 6 \\%$ due to mixed classification between young rubber plantation and non–forest. The accurate time series land cover map that differentiates between native forests and non–forests and includes two additional plantation classes will support Indonesia's national forest monitoring system and development of sustainable forest management. These maps can help to predict future plantation development, and potentially protect forests thus reducing emissions from forest degradation and deforestation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,96,905,145]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Gaveau, D.L.A.; Locatelli, B.; Salim, M.A.; Yaen, H.; Pacheco, P.; Sheil, D. Rise and fall of forest loss and industrial plantations in Borneo (2000–2017). Conserv. Lett. 2018, 12, e12622. https://doi.org/10.1111/conl.12622. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,158,905,207]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Hoekman, D.H.; Vissers, M.A.M.; Wielaard, N. PALSAR widearea mapping of Borneo: Methodology and map validation. IEEE J. Sel. Top. Appl. Earth Observ. Remote. Sens. 2010, 3, 605–617. https://doi.org/10.1109/JSTARS.2010.2070059. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,220,905,281]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Hosonuma, N.; Herold, M.; De Sy, V.; De Fries, R.S.; Brockhaus, M.; Verchot, L.; Angelsen, A.; Romijn, E. An assessment of deforestation and forest degradation drivers in developing countries. Environ. Res. Lett. 2012, 7, 044009, doi:10.1088/1748-9326/7/4/044009. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,294,905,367]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"LAPAN. The Remote Sensing Monitoring Program of Indonesia's National Carbon Accounting System: Methodology and Products, Version 1; LAPAN-IAFCP: Jakarta, Indonesia, 2014; pp. 15–78. Available online:http://incas.menlhk.go.id/methodology/incas-standardmethod-forest-cover-change/ (accessed on 4 January 2019). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,380,904,429]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lee, J.; Cardille, J.A.; Coe, M.T. Agricultural Expansion in Mato Grosso from 1986–2000: A Bayesian Time Series Approach to Tracking Past Land Cover Change. Remote Sensing 2020, 12, doi:https://doi.org/10.3390/rs12040688. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,442,904,491]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Massey, R.; Sankey, T.T.; Yadav, K.; Congalton, R.G.; Tilton, J.C. Integrating cloud-based workflows in continental-scale cropland extent classification. Remote Sens. Environ. 2018, 219, 162-179, doi:10.1016/j.rse.2018.10.013. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[201,497,378,508]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ACKNOWLEDGEMENTS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[94,520,485,568]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We thank the LCCA teams of LAPAN, the Indonesia–Australia Forest Carbon Partnership (IAFCP) for sharing data and methods. I.L.S acknowledges the Indonesian Endowment Fund for Education (LPDP) for PhD scholarship ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[238,593,339,605]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"REFERENCES ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[94,617,485,727]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Badan Informasi Geospasial. 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Assessing Accuracy of Land Cover Change Maps Derived from Automated Digital Processing and Visual Interpretation in Tropical Forests in Indonesia. Remote Sensing 2021a, 13, doi:10.3390/rs13081446. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,836,904,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sari, I.L.; Weston, C.J.; Newnham, G.J.; Volkova, L. Estimating land cover map accuracy and area uncertainty using a confusion matrix: A case study in Kalimantan, Indonesia. IOP Conference Series: Earth and Environmental Science 2021b, 914, 012025, doi:10.1088/1755-1315/914/1/012025 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[183,948,813,971]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\circledcirc$ Author(s) 2023. CC BY 4.0 License. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[880,960,904,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"324 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[97,28,899,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLVIII-4/W6-2022 Geoinformation Week 2022 “Broadening Geospatial Science and Technology”, 14–17 November 2022, Johor Bahru, Malaysia (online) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[92,83,487,133]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sari, I.L.; Weston, C.J.; Newnham, G.J.; Volkova, L. Developing Multi-Source Indices to Discriminate between Native Tropical Forests, Oil Palm and Rubber Plantations in Indonesia. Remote Sensing 2022, 14, doi:10.3390/rs14010003. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,145,487,232]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sarzynski, T.; Giam, X.; Carrasco, L.; Lee, J.S. Combining Radar and Optical Imagery to Map Oil Palm Plantations in Sumatra, Indonesia, Using the Google Earth Engine. Remote Sensing 2020, 12, doi:https://doi.org/10.3390/rs12071220. The Alaska Satellite Facility Distributed Active Archive Center (ASF DAAC). Sentinel-1. Available online:https://www.asf.alaska.edu/. (accessed on 3 July 2019). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,244,485,281]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The USGS Earth Resources Observation and Science (EROS) Center. Landsat. Available online: https://earthexplorer.usgs.gov/. (accessed on 3 July 2019). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[178,948,815,971]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\circledcirc$ Author(s) 2023. CC BY 4.0 License. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[880,960,904,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"325 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[95,28,899,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLVIII-4/W6-2022 Geoinformation Week 2022 “Broadening Geospatial Science and Technology”, 14–17 November 2022, Johor Bahru, Malaysia (online) ","text_format":null,"text_level":null,"type":"discarded"}],"string":"[\n {\n \"bbox\": \"[115,83,877,116]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MAPPING LAND COVER TIME SERIES USING LANDSAT-8 AND SENTINEL-1 IN SOUTH KALIMANTAN \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[319,140,675,153]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"I. L. Sari 1,2, C. J. Weston 1, G. J. Newnham 3, L. Volkova 1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[146,165,848,227]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 School of Ecosystem and Forest Sciences, Faculty of Science, The University of Melbourne, Creswick, Australia - Weston@unimelb.edu.au, Lubav@unimelb.edu.au 2 Research Center for Remote Sensing, National Research and Innovation Agency (BRIN), Jakarta, Indonesia - inggit.lolita.sari@brin.go.id 3 CSIRO Land and Water, Clayton South, Australia - Glenn.Newnham@csiro.au \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[425,239,573,252]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Commission IV, WG 7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,276,584,289]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"KEY WORDS: Bayesian, Time Series, Land Cover, Classification, Kalimantan. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,313,181,326]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABSTRACT: \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,338,904,437]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remote sensing has been widely used for forest monitoring. However, most forest monitoring systems largely rely on optical images that limit temporal analyses due to cloud cover, particularly in the tropics. The current study used integration of optical Landsat-8 and Sentinel-1 SAR to produce individual year land cover classification maps for Kalimantan, Indonesia that differentiate between native forest and tree plantations, such as oil palm and rubber. We applied a Bayesian network to produce a time series of land cover classification that improved accuracy of individual year land cover maps. Accuracy assessment using a confusion matrix showed that final map had overall accuracy of $9 0 \\\\%$ , while user's and producer's accuracy for each land cover class was above $8 5 \\\\%$ , except non– forest, which had $7 6 \\\\%$ producer's accuracy due to errors in the classification between young rubber plantations and non–forest. Improved maps will support Indonesia's national forest monitoring system and sustainable forest management. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[216,462,363,474]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. INTRODUCTION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,485,485,570]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Major deforestation in the tropics is driven by agricultural expansion, including timber logging (Hosonuma et al., 2012). Borneo island has experienced vast and rapid deforestation, with forest loss of around $6 . 0 4 \\\\mathrm { ~ M ~ }$ ha between 2000–2017 (Gaveau et al., 2018). Around $51 \\\\%$ of this forest loss was for plantation expansion, such as oil palm and rubber plantations (Gaveau et al., 2018). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,584,485,669]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remote sensing has been used for several decades to monitor forest extent and change, drawing on optical images such as those from the Landsat series of satellites (Romijn et al., 2015; Sari et al., 2021a). However, intense cloud cover limits the ability of optical images to detect temporal changes in vegetation cover and types in tropical countries (Massey et al., 2018; Sari et al., 2021a). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,682,485,756]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Synthetic Aperture Radar (SAR) systems, such as ALOS PALSAR, and Sentinel-1 offer the ability to penetrate clouds, smoke, and haze (Hoekman, Vissers, and Wielaard, 2010; Motohka et al., 2014). Furthermore, SAR data is sensitive to vegetation structure, moisture content, and ground conditions (Pohl, 2014; Miettinen, Liew, and Kwoh, 2015). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,768,485,867]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Improvement of forest monitoring may be possible by combining optical and SAR satellite sensors to reduce limitations imposed by persistent cloud cover. Integration of optical and SAR images has already been shown to improve forest classification accuracy (Sarzynski et al., 2020; Sari et al., 2022). However, employing multitemporal constraints on classification may help to further reduces the uncertainty in the land cover classification (Ban, 2016; LAPAN, 2014). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,880,485,904]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We showed that integration of Landsat-8 optical images and Sentinel-1 SAR images using a decision tree could be used to improve the classification accuracy of native forests, oil palm and rubber plantations, and non–forest areas in South Kalimantan province (Sari et al., 2022). This paper describes the use of a Bayesian network for time series classification to further refine individual year land cover maps from 2015 to 2017. The development of these improved time series of land cover maps aims to support Indonesia’s national forest monitoring program, and sustainable forest management. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,462,905,560]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[591,573,826,585]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. MATERIALS AND METHODS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,597,616,609]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.1 Study Area \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,619,904,730]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The study area is situated in the north part of South Kalimantan province, Indonesia, covering 62,500 hectares (Figure 1). Native forests, oil palm plantations, rubber plantations, and non– forest such as settlements, paddy fields, shrubs, and grasslands exist in the region. The extent of oil palm and rubber plantations increased in this province by $4 2 . 5 \\\\%$ over the past seventeen years, from 294,982.72 hectares in 2000 to 693,619 hectares in 2017 (BPS-Statistics Indonesia, 2000; BPS-Statistics Indonesia, 2018). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[534,738,885,895]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 1. Study area in South Kalimantan province. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0978/037ce7969f1db717cce0c28b6c40808c7276fc6ae9aef45629d7d9725458b265.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[183,948,813,971]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\\\circledcirc$ Author(s) 2023. CC BY 4.0 License. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[104,28,897,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLVIII-4/W6-2022 Geoinformation Week 2022 “Broadening Geospatial Science and Technology”, 14–17 November 2022, Johor Bahru, Malaysia (online) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[880,960,904,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"319 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[94,83,317,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2 Satellite image pre-processing \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,107,485,156]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A time series of Landsat-8 optical and Sentinel-1 SAR images, from 2015 to 2017, were mosaiced at $2 5 ~ \\\\mathrm { m }$ resolution and used as the main data to produce individual year land cover map, using the decision tree approach described by Sari et al. (2022). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,169,485,255]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Landsat-8 images with less than $5 0 \\\\%$ cloud cover were downloaded from the USGS Earth Resources Observation and Science (EROS) Center (2019). Sentinel-1A Interferometric Wide (IW) swath mode Level-1 Ground Range Detected (GRD) images for each individual year were downloaded from the Alaska Satellite Facility Distributed Active Archive Center (2019). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,268,485,377]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Landsat-8 images pre-processing method is outlined in previous publications (LAPAN, 2014; Sari et al., 2022). The image pre-processing consists of scene selection, geometric , radiometric, terrain correction, cloud masking, and mosaicking. The annual mosaics of Landsat-8 images consist of six multispectral image bands of blue, green, red, near infrared, shortwave infrared 1, and short-wave infrared 2, and processed top of atmosphere (TOA) and bidirectional reflectance distribution function (BRDF) correction. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,390,485,464]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Sentinel-1 images pre-processing consists of applying an update of precise orbit acquisition information, radio-metric calibration, and terrain correction to remove terrain effects. The mosaic Sentinel-1A images with dual-polarization of $\\\\mathrm { V V + V H }$ bands were used in this study to analyse the backscatter intensity of the land cover classes. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,477,341,489]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.3 Bayesian time series classification \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,500,485,636]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Bayesian networks use prior information of land cover to predict and track past land cover changes (Lee, Cardille, and Coe, 2020). A Bayesian network was used to improve time series classification and update the certainty of land cover based on prior land cover information and plantation occurrence images. The prior land cover was the individual land cover classifications to integrate Landsat-8 and Sentinel-1 to produce four land cover classes described in Section 2.4. The plantation occurrence images for improvement of oil palm and rubber discrimination are described in Section 2.5. Thus, the steps to utilise a Bayesian network for temporal processing of these inputs were as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[122,637,485,698]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"• Create a land cover change probability matrix using individual land cover classifications from 2015 to 2017. That is, for these two years, changes in the four classes were analysed and allocated to one of 16 land cover change categories. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[146,699,484,735]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Create oil palm and rubber plantation occurrence probability maps for 2015 to 2017 (see Section 2.5). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[122,737,485,786]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"• Calculate the probability of land cover classes for the preceding year based on information from the following map for native forest and non–forest classes, using the Bayesian equation (Eq.1): \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[122,791,391,842]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0331/b6e03a0d4c72a9bdc71c6a98e05b21b64c2ccd3b15705032c6d18924ed15f80f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array} { r l } & { \\\\mathrm { P } ( \\\\mathrm { M a p } _ { 2 0 1 6 } | \\\\mathrm { M a p } _ { 2 0 1 7 } ) = } \\\\\\\\ & { \\\\qquad \\\\frac { \\\\mathrm { P } ( \\\\mathrm { M a p } _ { 2 0 1 7 } | \\\\mathrm { M a p } _ { 2 0 1 6 } ) \\\\mathrm { P } ( \\\\mathrm { M a p } _ { 2 0 1 6 } ) } { \\\\mathrm { P } ( \\\\mathrm { M a p } _ { 2 0 1 7 } ) } , } \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[122,854,485,891]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"• Calculate the probability of land cover classes in 2016 for the rubber plantation class based on the 2017 map using the equation (Eq.2): \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[127,897,369,914]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0634/cfea4b51c7c49df4f98fa20fce972cbd3754bacd4955f9a8b350a63258a0dc29.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array} { r } { \\\\mathrm { P } ( \\\\mathrm { M a p } _ { 2 0 1 6 } | \\\\mathrm { M a p } _ { 2 0 1 7 } , \\\\mathrm { R u b b e r } _ { 2 0 1 6 } ) = } \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[554,82,852,110]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0921/3a1464459dccbb3c4f215a82b216c128f0c4384b88c36f64872258afdadc2479.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\frac { \\\\mathrm { P } ( \\\\mathrm { M a p } _ { 2 0 1 7 } , \\\\mathrm { R u b b e r } _ { 2 0 1 6 } | \\\\mathrm { M a p } _ { 2 0 1 6 } ) \\\\mathrm { P } ( \\\\mathrm { M a p } _ { 2 0 1 6 } ) } { \\\\mathrm { P } ( \\\\mathrm { M a p } _ { 2 0 1 7 } , \\\\mathrm { R u b b e r } _ { 2 0 1 6 } ) } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[542,135,905,172]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Land cover probability of a transition to the oil palm class was calculated based on the probability of the occurrence of oil palm (i.e., substituting rubber with oil palm in Eq. 2). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[564,174,905,359]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"• The decision if a transition should occur was based on the following rule: if the probability for stable class (similar to previous) is greater than the probability for change class then the decision will be stable (similar to previous class), and if the probability for change class is greater than the stable class then the decision class will change to a new class. Validate the oil palm and rubber plantation classes using the plantation occurrence boundary to reduce speckle class due to the pixel-based method (see Section 2.5). Apply the same Bayesian network processing in the forward time series direction to produce a final land cover map. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,373,801,384]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.4 Individual year land cover classification \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,395,905,469]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The individual year land cover classification was developed from the annual forest and non–forest maps combined with oil palm and rubber plantation algorithms developed from Landsat-8 and Sentinel-1 (LAPAN, 2014; Sari et al., 2022). The individual year land cover classification method has been outlined in Sari et al. (2022). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,481,734,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.5 Plantation occurrence images \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,505,905,628]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The oil palm and rubber plantations occurrence were used as additional information for assessing the plantation occurrence. The oil palm and rubber occurrence maps were created using a combination between NDVI and SWIR 1 for oil palm occurrence, and NDMI and SWIR 1 for rubber occurrence. The thresholds in the decision tree were determined from the histogram of values for training samples of oil palm and rubber. The boundary for the oil palm and rubber plantations were produced from the mosaic of the nearest year plantation occurrence image with a median filter applied. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,641,798,653]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.6 Accuracy assessment of land cover map \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,663,905,761]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A confusion matrix was used to measure the accuracy of the 2017 classification maps, including overall accuracy, producer's accuracy, and user's accuracy. The map accuracy assessment was based on stratified random sampling with 196 validation points (Sari et al., 2021b). One scene of high-resolution SPOT 6 images (resolution $1 . 5 ~ \\\\mathrm { m }$ ) acquired on 18 August 2018 was used as the reference images with validation based on a minimum area of 50 $\\\\mathrm { ~ x ~ } 5 0 \\\\mathrm { ~ m ~ }$ for each of 196 points. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[594,774,821,786]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. RESULTS AND DISCUSSION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,797,905,908]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The mosaic images of Landsat-8 and Sentinel-1 to develop individual land cover classification from 2015–2017 are shown in Figure 2. These Landsat-8 images are depicted in a composite of short-wave infrared 1, near infrared, and red band. While Sentinel-1 images in Figure 2 are depicted in composites of the Grey Level Co-occurrence Matrix (GLCM) variance texture of VH˗VV.Samples for decision-making using Bayesian network to produce time series classification maps for 2016 and 2017 are described in Table 1–Table 4. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[183,948,813,971]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\\\circledcirc$ Author(s) 2023. CC BY 4.0 License. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[880,960,904,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"320 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[100,28,899,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLVIII-4/W6-2022 Geoinformation Week 2022 “Broadening Geospatial Science and Technology”, 14–17 November 2022, Johor Bahru, Malaysia (online) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[94,97,900,479]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 2. Mosaic images of Landsat-8 and Sentinel-1 from 2015–2017. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0750/a988cc97f3e699b2a87683b4c6e37b28d59ed1b657b76580d3763a2d83718391.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[92,520,905,669]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0746/c2ab0d51860ff7cb73976a435ea7b96abb0d6b37a4e58ce5989a3df79f8621ac.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=2 colspan=1>20172016</td><td rowspan=1 colspan=5>Land cover class</td></tr><tr><td rowspan=1 colspan=1>Native forest</td><td rowspan=1 colspan=1>Oil palm</td><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>Non-forest</td><td rowspan=1 colspan=1>Total</td></tr><tr><td rowspan=1 colspan=1>Native forest</td><td rowspan=1 colspan=1>0.223</td><td rowspan=1 colspan=1>0.010</td><td rowspan=1 colspan=1>0.013</td><td rowspan=1 colspan=1>0.008</td><td rowspan=1 colspan=1>0.254</td></tr><tr><td rowspan=1 colspan=1>Oil palm</td><td rowspan=1 colspan=1>0.009</td><td rowspan=1 colspan=1>0.110</td><td rowspan=1 colspan=1>0.004</td><td rowspan=1 colspan=1>0.003</td><td rowspan=1 colspan=1>0.126</td></tr><tr><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>0.009</td><td rowspan=1 colspan=1>0.002</td><td rowspan=1 colspan=1>0.213</td><td rowspan=1 colspan=1>0.101</td><td rowspan=1 colspan=1>0.325</td></tr><tr><td rowspan=1 colspan=1>Non-forest</td><td rowspan=1 colspan=1>0.004</td><td rowspan=1 colspan=1>0.003</td><td rowspan=1 colspan=1>0.122</td><td rowspan=1 colspan=1>0.166</td><td rowspan=1 colspan=1>0.295</td></tr><tr><td rowspan=1 colspan=1>Total</td><td rowspan=1 colspan=1>0.244</td><td rowspan=1 colspan=1>0.125</td><td rowspan=1 colspan=1>0.353</td><td rowspan=1 colspan=1>0.278</td><td rowspan=1 colspan=1>1.000</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. Land cover changes map probability for 2016–2017. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[92,700,485,849]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0482/abaf38da8113fc50485141e4829bf01ac629e9cd30a0c7734799fc94eb52c56d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=2 colspan=1>20172016</td><td rowspan=1 colspan=3>Land cover class</td></tr><tr><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>Non-rubber</td><td rowspan=1 colspan=1>Total</td></tr><tr><td rowspan=1 colspan=1>Native forest</td><td rowspan=1 colspan=1>0.025</td><td rowspan=1 colspan=1>0.229</td><td rowspan=1 colspan=1>0.254</td></tr><tr><td rowspan=1 colspan=1>Oil palm</td><td rowspan=1 colspan=1>0.002</td><td rowspan=1 colspan=1>0.124</td><td rowspan=1 colspan=1>0.126</td></tr><tr><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>0.200</td><td rowspan=1 colspan=1>0.125</td><td rowspan=1 colspan=1>0.325</td></tr><tr><td rowspan=1 colspan=1>Non-forest</td><td rowspan=1 colspan=1>0.070</td><td rowspan=1 colspan=1>0.224</td><td rowspan=1 colspan=1>0.295</td></tr><tr><td rowspan=1 colspan=1>Total</td><td rowspan=1 colspan=1>0.297</td><td rowspan=1 colspan=1>0.703</td><td rowspan=1 colspan=1>1.000</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2. Rubber occurrence probability in 2016. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[512,700,905,849]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0104/d4147398e4f21831e2f27a4eb6cf3807b0a0f1ec508cd2f72f887ded3f29a8db.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=2 colspan=1>20172016</td><td rowspan=1 colspan=3>Land cover class</td></tr><tr><td rowspan=1 colspan=1>Oil palm</td><td rowspan=1 colspan=1>Non-oil palm</td><td rowspan=1 colspan=1>Total</td></tr><tr><td rowspan=1 colspan=1>Native forest</td><td rowspan=1 colspan=1>0.241</td><td rowspan=1 colspan=1>0.013</td><td rowspan=1 colspan=1>0.254</td></tr><tr><td rowspan=1 colspan=1>Oil palm</td><td rowspan=1 colspan=1>0.117</td><td rowspan=1 colspan=1>0.009</td><td rowspan=1 colspan=1>0.126</td></tr><tr><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>0.314</td><td rowspan=1 colspan=1>0.012</td><td rowspan=1 colspan=1>0.325</td></tr><tr><td rowspan=1 colspan=1>Non-forest</td><td rowspan=1 colspan=1>0.190</td><td rowspan=1 colspan=1>0.104</td><td rowspan=1 colspan=1>0.295</td></tr><tr><td rowspan=1 colspan=1>Total</td><td rowspan=1 colspan=1>0.862</td><td rowspan=1 colspan=1>0.138</td><td rowspan=1 colspan=1>1.000</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 3. Oil palm occurrence probability in 2016. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[181,947,813,971]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\\\circledcirc$ Author(s) 2023. CC BY 4.0 License. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[880,960,904,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"321 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[102,28,897,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLVIII-4/W6-2022 Geoinformation Week 2022 “Broadening Geospatial Science and Technology”, 14–17 November 2022, Johor Bahru, Malaysia (online) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[92,96,905,493]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0033/e202ce4c1d413f79f5e67222a1c1cc14cb3d2fc93565c74b5ae898dc5abd03da.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=1 colspan=1>Time seriesclass decisionLand coverchange 2016 to 2017</td><td rowspan=1 colspan=1>Probability similar to previous class</td><td rowspan=1 colspan=1>Probability to change class</td><td rowspan=1 colspan=1>Result of time series classfor map in 2016</td></tr><tr><td rowspan=1 colspan=1>Native forest to Native forest</td><td rowspan=1 colspan=1>0.905</td><td rowspan=1 colspan=1>0.095</td><td rowspan=1 colspan=1>Native forest</td></tr><tr><td rowspan=1 colspan=1>Native forest to Oil palm</td><td rowspan=1 colspan=1>0.028</td><td rowspan=1 colspan=1>0.972</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1>Native forest to Rubber</td><td rowspan=1 colspan=1>0.154</td><td rowspan=1 colspan=1>0.846</td><td rowspan=1 colspan=1>Rubber</td></tr><tr><td rowspan=1 colspan=1>Native forest to Non-forest</td><td rowspan=1 colspan=1>0.409</td><td rowspan=1 colspan=1>0.591</td><td rowspan=1 colspan=1>Non-forest</td></tr><tr><td rowspan=1 colspan=1>Oil palm to Oil palm</td><td rowspan=1 colspan=1>0.978</td><td rowspan=1 colspan=1>0.022</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1> Oil palm to Rubber</td><td rowspan=1 colspan=1>0.530</td><td rowspan=1 colspan=1>0.470</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1>Oil palm to Non-forest</td><td rowspan=1 colspan=1>0.994</td><td rowspan=1 colspan=1>0.006</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1>Oil palm to Native forest</td><td rowspan=1 colspan=1>0.994</td><td rowspan=1 colspan=1>0.006</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1>Rubber to Rubber</td><td rowspan=1 colspan=1>0.901</td><td rowspan=1 colspan=1>0.099</td><td rowspan=1 colspan=1>Rubber</td></tr><tr><td rowspan=1 colspan=1>Rubber to Non-forest</td><td rowspan=1 colspan=1>0.650</td><td rowspan=1 colspan=1>0.350</td><td rowspan=1 colspan=1>Rubber</td></tr><tr><td rowspan=1 colspan=1>Rubber to Native forest</td><td rowspan=1 colspan=1>0.848</td><td rowspan=1 colspan=1>0.152</td><td rowspan=1 colspan=1>Rubber</td></tr><tr><td rowspan=1 colspan=1>Rubber to Oil palm</td><td rowspan=1 colspan=1>0.001</td><td rowspan=1 colspan=1>0.999</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1>Non-forest to Non-forest</td><td rowspan=1 colspan=1>0.871</td><td rowspan=1 colspan=1>0.129</td><td rowspan=1 colspan=1>Non-forest</td></tr><tr><td rowspan=1 colspan=1>Non-forest to Native forest</td><td rowspan=1 colspan=1>0.085</td><td rowspan=1 colspan=1>0.915</td><td rowspan=1 colspan=1>Native forest</td></tr><tr><td rowspan=1 colspan=1>Non-forest to Oil palm</td><td rowspan=1 colspan=1>0.027</td><td rowspan=1 colspan=1>0.973</td><td rowspan=1 colspan=1>Oil palm</td></tr><tr><td rowspan=1 colspan=1>Non-forest to Rubber</td><td rowspan=1 colspan=1>0.350</td><td rowspan=1 colspan=1>0.650</td><td rowspan=1 colspan=1>Rubber</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 4. Decision-making result for time series classification for 2016 to 2017. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[92,526,485,574]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Images of individual year land cover classification, oil palm and rubber plantation occurrence, and the Bayesian network time series classification maps from 2015 to 2017 are shown in Figure 3. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,526,905,563]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Classification accuracy for the final time series land cover map in 2017 has an overall accuracy of $9 0 \\\\%$ . Detailed accuracy for each land cover class is shown in Table 5. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[99,588,900,793]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0751/4169535691cb538d90117f68c30fee21957f0697f8bd39942456dc1151e274f0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[181,947,813,971]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\\\circledcirc$ Author(s) 2023. CC BY 4.0 License. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[880,960,904,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"322 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[102,28,897,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLVIII-4/W6-2022 Geoinformation Week 2022 “Broadening Geospatial Science and Technology”, 14–17 November 2022, Johor Bahru, Malaysia (online) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[97,73,899,718]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 3. Individual year classification and time series classification images from 2015 to 2017 \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0242/51a107acc0e5c7b75598c6c45e2c4705c9ff8e06304e8e048f52ba5568ca645f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[92,746,907,864]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0281/315f0e57d32a2a0e592fabc8ae551aec512766c245fce18abdab4cec89e52bf9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=1 colspan=1>Reference data 2017Classified data 2017</td><td rowspan=1 colspan=1>Native forest</td><td rowspan=1 colspan=1> Oil palm</td><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>Non-forest</td><td rowspan=1 colspan=1>Total</td><td rowspan=1 colspan=1>User's acc. (%)</td></tr><tr><td rowspan=1 colspan=1>Native forest</td><td rowspan=1 colspan=1>38</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>41</td><td rowspan=1 colspan=1>93</td></tr><tr><td rowspan=1 colspan=1>Oil palm</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>25</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>27</td><td rowspan=1 colspan=1>93</td></tr><tr><td rowspan=1 colspan=1>Rubber</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>85</td><td rowspan=1 colspan=1>9</td><td rowspan=1 colspan=1>95</td><td rowspan=1 colspan=1>89</td></tr><tr><td rowspan=1 colspan=1>Non-forest</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>28</td><td rowspan=1 colspan=1>33</td><td rowspan=1 colspan=1>85</td></tr><tr><td rowspan=1 colspan=1>Total</td><td rowspan=1 colspan=1>41</td><td rowspan=1 colspan=1>26</td><td rowspan=1 colspan=1>92</td><td rowspan=1 colspan=1>37</td><td rowspan=1 colspan=1>196</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>Producer's acc.(%)</td><td rowspan=1 colspan=1>93</td><td rowspan=1 colspan=1>96</td><td rowspan=1 colspan=1>92</td><td rowspan=1 colspan=1>76</td><td rowspan=1 colspan=2>Overall accuracy=90%</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 5. Accuracy assessment of land cover classification in 2017. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[181,947,813,971]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\\\circledcirc$ Author(s) 2023. CC BY 4.0 License. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[880,960,905,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"323 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[102,28,899,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLVIII-4/W6-2022 Geoinformation Week 2022 “Broadening Geospatial Science and Technology”, 14–17 November 2022, Johor Bahru, Malaysia (online) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[94,83,485,182]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Table 5 shows the Bayesian network time series classification map accuracy. User's and producer's accuracy for all land cover classes were ${ > } 8 5 \\\\%$ , which fulfils Indonesia’s national land cover classification accuracy benchmark to support the national forest monitoring system (Badan Informasi Geospasial, 2014). Lower producer's accuracy for the non–forest class $( 7 6 \\\\% )$ was primarily due to mixed classification between young rubber plantation and non–forest. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[226,202,351,214]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. CONCLUSION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,225,485,471]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A Bayesian network algorithm was used to produce a time series of land cover classification that improved accuracy of individual year land cover maps for South Kalimantan, Indonesia. A time series of Landsat-8 optical and Sentinel-1 SAR images from 2015 to 2017 were used to develop temporal maps with four land cover classes: native forest, non–forests, rubber and oil palm plantations. High-resolution SPOT images were used for the accuracy assessment of the final $2 0 1 7 \\\\mathrm { \\\\ m a p }$ . The map generated using a Bayesian network produced overall accuracy of $9 0 \\\\%$ . Moreover, each land cover class had a user's accuracy and producer's accuracy of ${ > } 8 5 \\\\%$ , except for the non–forest class which had producer's accuracy of $7 6 \\\\%$ due to mixed classification between young rubber plantation and non–forest. The accurate time series land cover map that differentiates between native forests and non–forests and includes two additional plantation classes will support Indonesia's national forest monitoring system and development of sustainable forest management. These maps can help to predict future plantation development, and potentially protect forests thus reducing emissions from forest degradation and deforestation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,96,905,145]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Gaveau, D.L.A.; Locatelli, B.; Salim, M.A.; Yaen, H.; Pacheco, P.; Sheil, D. Rise and fall of forest loss and industrial plantations in Borneo (2000–2017). Conserv. Lett. 2018, 12, e12622. https://doi.org/10.1111/conl.12622. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,158,905,207]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Hoekman, D.H.; Vissers, M.A.M.; Wielaard, N. PALSAR widearea mapping of Borneo: Methodology and map validation. IEEE J. Sel. Top. Appl. Earth Observ. Remote. Sens. 2010, 3, 605–617. https://doi.org/10.1109/JSTARS.2010.2070059. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,220,905,281]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Hosonuma, N.; Herold, M.; De Sy, V.; De Fries, R.S.; Brockhaus, M.; Verchot, L.; Angelsen, A.; Romijn, E. An assessment of deforestation and forest degradation drivers in developing countries. Environ. Res. Lett. 2012, 7, 044009, doi:10.1088/1748-9326/7/4/044009. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,294,905,367]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"LAPAN. The Remote Sensing Monitoring Program of Indonesia's National Carbon Accounting System: Methodology and Products, Version 1; LAPAN-IAFCP: Jakarta, Indonesia, 2014; pp. 15–78. Available online:http://incas.menlhk.go.id/methodology/incas-standardmethod-forest-cover-change/ (accessed on 4 January 2019). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,380,904,429]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lee, J.; Cardille, J.A.; Coe, M.T. Agricultural Expansion in Mato Grosso from 1986–2000: A Bayesian Time Series Approach to Tracking Past Land Cover Change. Remote Sensing 2020, 12, doi:https://doi.org/10.3390/rs12040688. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,442,904,491]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Massey, R.; Sankey, T.T.; Yadav, K.; Congalton, R.G.; Tilton, J.C. Integrating cloud-based workflows in continental-scale cropland extent classification. Remote Sens. Environ. 2018, 219, 162-179, doi:10.1016/j.rse.2018.10.013. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[201,497,378,508]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ACKNOWLEDGEMENTS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,520,485,568]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We thank the LCCA teams of LAPAN, the Indonesia–Australia Forest Carbon Partnership (IAFCP) for sharing data and methods. I.L.S acknowledges the Indonesian Endowment Fund for Education (LPDP) for PhD scholarship \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[238,593,339,605]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"REFERENCES \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,617,485,727]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Badan Informasi Geospasial. 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In Proceedings of IOP Conference Series: Earth and Environmental Science; p. 012012. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,688,904,749]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Romijn, E.; Lantican, C.B.; Herold, M.; Lindquist, E.; Ochieng, R.; Wijaya, A.; Murdiyarso, D.; Verchot, L. Assessing change in national forest monitoring capacities of 99 tropical countries. Forest Ecology and Management 2015, 352, 109-123, doi:10.1016/j.foreco.2015.06.003. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,762,904,823]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sari, I.L.; Weston, C.J.; Newnham, G.J.; Volkova, L. Assessing Accuracy of Land Cover Change Maps Derived from Automated Digital Processing and Visual Interpretation in Tropical Forests in Indonesia. Remote Sensing 2021a, 13, doi:10.3390/rs13081446. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,836,904,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sari, I.L.; Weston, C.J.; Newnham, G.J.; Volkova, L. Estimating land cover map accuracy and area uncertainty using a confusion matrix: A case study in Kalimantan, Indonesia. IOP Conference Series: Earth and Environmental Science 2021b, 914, 012025, doi:10.1088/1755-1315/914/1/012025 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[183,948,813,971]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\\\circledcirc$ Author(s) 2023. 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Developing Multi-Source Indices to Discriminate between Native Tropical Forests, Oil Palm and Rubber Plantations in Indonesia. Remote Sensing 2022, 14, doi:10.3390/rs14010003. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,145,487,232]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sarzynski, T.; Giam, X.; Carrasco, L.; Lee, J.S. Combining Radar and Optical Imagery to Map Oil Palm Plantations in Sumatra, Indonesia, Using the Google Earth Engine. Remote Sensing 2020, 12, doi:https://doi.org/10.3390/rs12071220. The Alaska Satellite Facility Distributed Active Archive Center (ASF DAAC). Sentinel-1. Available online:https://www.asf.alaska.edu/. (accessed on 3 July 2019). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,244,485,281]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The USGS Earth Resources Observation and Science (EROS) Center. Landsat. Available online: https://earthexplorer.usgs.gov/. (accessed on 3 July 2019). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[178,948,815,971]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLVIII-4-W6-2022-319-2023 | $\\\\circledcirc$ Author(s) 2023. 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We discuss the relevance and concerns of ChatGPT and other GAI tools in environmental psychology research. We propose three use categories for GAI tools: integrated and contextualized understanding, practical and flexible implementation, and two-way external communication. These categories are exemplified by topics such as the health benefits of green space, theory building, visual simulation, and identifying practical relevance. However, we also highlight the balance of productivity with ethical issues, as well as the need for ethical guidelines, professional training, and changes in the academic performance evaluation systems. We hope this perspective can foster constructive dialogue and responsible practice of GAI tools."},"author":{"kind":"string","value":"Fu Li|Muhammad Mainuddin Patwary|Olivia McAnirlin|Aaron Reuben|Mondira Bardhan|Shuai Yuan|Matthew H. E. M. 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","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,455,228,464]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Front. Psychol. 15:1295275. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,464,260,475]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"doi: 10.3389/fpsyg.2024.1295275 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,483,134,491]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"COPYRIGHT","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,492,324,630]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"© 2024 Yuan, Li, Browning, Bardhan, Zhang, McAnirlin, Patwary and Reuben. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[366,143,915,292]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Leveraging and exercising caution with ChatGPT and other generative artificial intelligence tools in environmental psychology research ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[366,305,784,322]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Shuai Yuan $^{1*}$ , Fu Li $^{1}$ , Matthew H. E. M. Browning $^{1}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[366,324,806,340]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mondira Bardhan<sup>1</sup>, Kuiran Zhang<sup>1</sup>, Olivia McAnirlin<sup>1</sup>, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[368,342,831,357]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Muhammad Mainuddin Patwary $^{2,3}$ and Aaron Reuben $^{4}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[366,363,910,418]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"<sup>1</sup>Virtual Reality and Nature Lab, Department of Parks, Recreation and Tourism Management, Clemson University, Clemson, SC, United States, <sup>2</sup>Environment and Sustainability Research Initiative, Khulna, Bangladesh, <sup>3</sup>Environmental Science Discipline, Life Science School, Khulna University, Khulna, Bangladesh, <sup>4</sup>Department of Psychology and Neuroscience, Duke University, Durham, NC, United States ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[364,439,917,611]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Generative Artificial Intelligence (GAI) is an emerging and disruptive technology that has attracted considerable interest from researchers and educators across various disciplines. We discuss the relevance and concerns of ChatGPT and other GAI tools in environmental psychology research. We propose three use categories for GAI tools: integrated and contextualized understanding, practical and flexible implementation, and two-way external communication. These categories are exemplified by topics such as the health benefits of green space, theory building, visual simulation, and identifying practical relevance. However, we also highlight the balance of productivity with ethical issues, as well as the need for ethical guidelines, professional training, and changes in the academic performance evaluation systems. We hope this perspective can foster constructive dialogue and responsible practice of GAI tools. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[366,629,423,638]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"KEYWORDS ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[366,644,868,670]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"environmental psychology, generative artificial intelligence, ChatGPT, research methods, research ethics ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[366,731,521,747]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[364,763,917,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Generative Artificial Intelligence (GAI) has sparked enthusiasm and concern in how we conceive knowledge creation (Nature Editorials, 2023; Stokel-Walker and Van Noorden, 2023). Generated content includes language and text but also images, audio, video, and 3D objects (Supplementary Table S1). Their applications in higher education have raised interest and concerns from educators (Chen et al., 2020), including the UNESCO (Sabzalieva and Valentini, 2023). The applications in scientific writing (Lund et al., 2023) and various scientific domains such as healthcare research (Dahmen et al., 2023; Sallam, 2023), environmental research (Agathokleous et al., 2023; Zhu et al., 2023), and environmental planning and design (Fernberg and Chamberlain, 2023; Wang et al., 2023) have also been discussed. As with all powerful tools, GAI offers opportunities and poses risks depending on the user's knowledge and choices when using the tool (Dwivedi et al., 2023). For example, ChatGPT's responses can ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,39,102,58]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"# ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[105,42,194,57]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"frontiers ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[215,43,381,58]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Frontiers in Psychology ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[736,39,828,48]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"TYPE Perspective ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[737,49,870,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PUBLISHED 08 April 2024 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[737,60,917,70]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"DOI 10.3389/fpsyg.2024.1295275 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[80,948,210,959]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Frontiers in Psychology ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[490,948,505,958]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"01 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[835,948,915,959]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"frontiersin.org ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[77,93,490,165]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"sound plausible for a research paper but may not match the expected precise and accuracy level for scientific discourse. Therefore, it is time to ask what role GAI can play in environmental psychology. This article aims to prepare the field of environmental psychology to take advantage of GAI while, ideally, avoiding the pitfalls. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,165,490,548]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Environmental psychology investigates the interaction between human and socio-physical environments, with a practical orientation to solving community-environmental problems using psychological research tools and insights (Stokols, 1978). Given this focus, the field has several challenges that GAI tools might assist. First, human environmental experience depends on the person and the physical, social, and situational contexts (Lazarus and Launier, 1978; Altman and Rogoff, 1987; Hartig, 1993; Wapner and Demick, 2002). Due to the field's preference for generalized, objective knowledge (Seamon, 1982; Franck, 1987), and researchers' reliance on existing literature instead of learning from real-life experiences and communities, it struggles to cater to diverse human experiences. Second, environmental psychology's interdisciplinary nature leads to knowledge gaps for researchers trained in specific disciplines. Researchers may miss advancements in related fields or be unaware of older literature, creating barriers to fully informed research and application (Rapoport, 1997). Third, there can be a lack of alignment between empirical research and practice, especially in environmental planning and design. This may be due to communication gaps (Franck, 1987), lack of integrated perspectives (Hillier et al., 1972), and the complex interactions between factors in practice contexts (Alexander, 1964; Altman and Rogoff, 1987). Fourth, researchers face constraints from the techniques and technologies they can access for applying the appropriate method to a research question. Mastering multiple techniques can be overwhelming and cost-prohibitive, and the opportunity to collaborate, practice, and get feedback from others is not always available. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,549,489,791]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The issues above reflect the limited capacity of human researchers and institutional research structures. We suggest that GAI tools may help fill the various gaps, as they can connect board knowledge to specific contexts, foster interdisciplinary learning through interactive conversations, and assist with various procedures and techniques. To illustrate how GAI can be used to advance environmental psychology as a field, we propose three areas in the research process where GAI tools can be beneficial: (1) integrated and contextualized understanding, (2) effective and flexible implementation, and (3) two-way communication between researchers and external audiences (Figure 1). These three areas cover the various research activities in the research process, such as idea generation, planning and decision support, development of stimuli, data analysis, and communication of findings. To illustrate how these GAI applications could be put into practice, we provide specific examples of our interactions with ChatGPT (see Supplementary material 1-6). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,816,418,848]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 Integrated and contextualized understanding ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[77,863,490,921]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Environmental psychology researchers benefit from continual learning, building, and expanding integrated and contextualized understanding of human-environment interaction. Large language models can assist with this pursuit throughout the research process, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,90,915,355]","code_body":null,"code_caption":null,"image_caption":"[\"FIGURE 1 Categories of generative artificial intelligence (GAI) applications for advancing environmental psychology research. \"]","image_footnote":"[]","img_path":"images/0156/92acb782af6ec5f778431ec55732510b685df4065629281a7be71e0c8fa04cc1.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[505,435,917,464]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"from brainstorming research ideas, evaluating potential research factors, collecting examples, and interpreting research findings. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,489,831,507]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.1 Research question formulation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[504,521,919,777]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Generative Artificial Intelligence can accelerate the idea-generation process by connecting a loosely described phenomenon or assumption to a list of scientific concepts and theories across different fields. GAI can also help researchers better initiate a study from the perspective of helping to build a knowledge map comprehensively. For example, ChatGPT could assist a researcher interested in human-nature connections by framing questions from the relevant perspectives of psychology, social science, environment, tourism, education, planning, and health science (Ives et al., 2017; Hallsworth et al., 2023). In addition, ChatGPT can provide a matched level of competence to explore unfocused areas (i.e., helping partitioners and researchers to learn other research areas). Therefore, researchers may more likely to identify important but understudied factors and relationships (Supplementary material 1). For example, extreme heat may limit or dissolve how well green space supports healthy behaviors and psychological restoration, though the prevailing modeling has focused on mitigating urban heat islands outside of heat waves (Li et al., 2023). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,803,692,821]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.2 Theory building ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[505,834,917,920]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ChatGPT can help perform three theory-building processes described by Walker and Avant (2014), which are derivation (making an analogy and borrowing a concept), synthesis (combining information into a concept), and analysis (breaking down a concept). These processes are more effective when ChatGPT also generates examples and scenarios as hypothetical empirical materials. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,38,137,48]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Yuan et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[759,38,917,49]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10.3389/fpsyg.2024.1295275 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[78,948,211,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Frontiers in Psychology ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[489,948,507,958]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"02 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[835,948,915,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"frontiersin.org ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,93,489,434]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Researchers can flexibly use ChatGPT's capacities, including the three strategies we described here. One is an inductive approach, where researchers use ChatGPT to generate examples with social, physical, situational contexts and/or personal factors and abstract and synthesize those examples. This is particularly useful for an initial phase or when empirical data is unavailable. For example, Stokols (2000) has emphasized the research gap in identifying high-impact social-physical circumstances that enhance or constrain human stress coping and functioning. Researchers can use ChatGPT to generate many examples instantly and identify the key factors or groups (Supplementary material 2). Another deductive strategy can be refining and breaking down an existing concept and using hypothetical examples to test the tentative subconcepts. For example, breaking down the concept of compatibility in attention restoration theory (Kaplan, 1995) may help connect it to various environments and human goals (Supplementary material 2). Third but not least, many theory-building approaches involve purposive sample collection to extend or corroborate a theory (i.e., theoretical sampling; Eisenhardt and Graebner, 2007; Corbin and Strauss, 2015). Environmental psychology is often about and can be challenged by everyday experiences. One can use ChatGPT to deliberately collect hypothetical everyday environmental experiences that may contradict a theory. Such counterexamples can be abstracted or synthesized to identify boundary conditions or new mediators and moderators. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,461,452,476]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.3 Development of measurement tools ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[80,492,489,776]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Generative Artificial Intelligence tools can ease the item pool generation of psychometric scales and environmental audit tools. One can use ChatGPT to generate items or indicators for a concept or phenomenon that is described broadly or precisely. Alternatively, one can first explore the potential construct structure using the inductive and deductive approaches described in theory building, and generate the item pool based on the dimensions. ChatGPT's large knowledge base and ability to generate many items may help improve content validity. For specific populations or environments (e.g., children, neighborhoods, and urban parks), ChatGPT can also help identify specific factors, assess the suitability of general or related measurement tools, and identify gaps or mismatches. This might improve the relevance of the measurements for the participants and environments. Moreover, ChatGPT's ability to apply general knowledge and logical reasoning can help explore the potential dimensions of a construct from a list of indicators (Supplementary material 3). By repeating this action, items often categorized into different categories over time may be less valid. Although this cannot replace expert review, it can provide a low-cost check of the quality of ongoing work or existing measurement tools developed using a rational or theoretical approach. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,802,317,833]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 Effective and flexible implementation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[80,848,487,932]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Implementation plays an important role in environmental psychology, but technical issues are a major barrier for researchers implementing their research ideas. GAI can mitigate such barriers and allow researchers to focus more on the research itself. In addition to the implementation aspects common to the social and behavioral sciences, such as institutional review boards (IRBs), recruitment, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,93,917,134]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"surveys, interviews, and statistics, environmental psychology has a strong focus on field observation and the creation of environmental stimuli. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,161,769,178]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1 Visual stimuli generation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,193,917,419]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Manipulating factors of interest and controlling confounders is crucial for experiment validity. However, learning the required design knowledge and media creation skills can be prohibitive for researchers with non-environmental design backgrounds (Stamps, 2016). Image generators such as DALLE-2, Midjourney, and Stable Diffusion enable rapid generation and modification of imagery to align with the research question (i.e., varying an independent variable in the environment). For example, a Stable Diffusion-based tool, Skybox AI, could generate a VR environment within seconds with a short prompt (Figure 2). Stable Diffusion can also enable style transformation, such as changing the season, time, architectural style and elements while keeping the spatial layout. 3D content generators such as Point E and Shape E can help build virtual 3D Objects. ChatGPT and GitHub Copilot can further help with computer programming tasks in developing virtual scenes in game engines (e.g., Unity 3D or Unreal) for advanced and interactive simulation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,447,776,463]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2 Verbal stimuli generation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,478,917,762]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Large language models like ChatGPT can create high-quality verbal stimuli with specific contents or factors, communication purposes, and rhetoric considerations. Several research areas, such as decision-making and information-seeking in travel, health, and pro-environmental behavior, could require more complex stimuli beyond visual perception. In this case, researchers can use text generators to create voiceover scripts in the intervention that require specific tones, inclusive languages, and clear narratives. For example, translating scripts for non-native English speakers can lead to misunderstandings and measurement errors when the local dialect is ignored (Solano-Flores, 2006), which could be assisted by GAI. These tools can also create a series of text-based scenarios (vignettes) for priming, contextualizing, and incorporating different parameters for complex conditions (Aguinis and Bradley, 2014). This technique is frequently employed for forecasted scenarios and recreation behavior, pro-environmental behavior, and acceptance of sustainable design (Jaung, 2022; Hu and Shealy, 2023; Urban et al., 2023). For audio narration, advanced text-to-speech tools such as Vall E can mimic tones and emotions for languages, which can be used to test narration scripts, in intervention materials, or as experiment instructions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,789,912,819]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.3 Internal communication with participants and institutional review boards ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,834,915,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Large language models can help edit language in materials presented to participants. For example, ChatGPT can be used to develop engaging and easily understandable recruitment materials and easy-to-understand experimental instructions. Such language models can also reduce issues such as uncommon or obsolete words, non-inclusive language, and leading questions in existing survey batteries. In verbal-based communication, those tools may improve communication with special ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,39,136,48]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Yuan et al. 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Prompts are (A) \\\"a summer scene outside a lovely house, realistic\\\"; (B) \\\"a fall scene outside a lovely house with leave fall on the ground, realistic\\\"; (C) \\\"a winter scene outside a lovely house, with less light and a clear night sky, realistic\\\"; and (D) \\\"a space scene outside a lovely house on the moon, Earth in the distance, Sci-Fi.\\\" All variants used the \\\"Mixed Mode\\\" option, which will generate a new image based on the image of the first prompt. Retrieved from Skybox AI, version beta 0.4.2. on May 31, 2023. \"]","image_footnote":"[]","img_path":"images/0116/d8728df5c6fb08076dd4f8f9af291b940f1ddbda834c2069e444bf4bcc503c93.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[77,478,489,620]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"populations, such as children, elderly individuals, and people with disabilities and mental health conditions, ensuring understanding, inclusiveness, and compliance. IRB-related documents and materials require specific structures, tones, and an understanding of ethical issues. AI tools might also explain ethical concerns and present potential solutions. It can transfer existing materials into new structures and formats, after cross-checking with specific institutional policies. See Supplementary material 4 for using ChatGPT transferring a description of the procedure from a citation into a training manual, an IRB application, and a consent form. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,646,287,663]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.4 Basic data analysis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[77,677,489,863]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Generative Artificial Intelligence tools can facilitate basic quantitative methods such as the use of R in data cleaning, regression, and factor analysis. ChatGPT can interpret statistical software outputs or model results and suggest visualization options. These tools can assist researchers with qualitative or environmental backgrounds in conducting quantitative or mixed-methods research. Qualitative analysis may benefit less from GAI tools because most qualitative approaches need researchers' knowledge and experience to interpret data meaning and significance (Creswell and Poth, 2017). However, GAI tools may perform minor roles such as suggesting codes to merge, checking code abstraction levels, and interpreting ambiguous sentences. Also, qualitative data analysis software such as MAXQDA provides a GAI tool<sup>1</sup> for defining codes based on related quotations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,478,917,535]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"QDA software may also offer an auto-coding function based on regular expression, which is suitable for the exploration of data or more descriptive research. ChatGPT can be used to generate regular expressions to identify objects or features in different texts. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,561,774,579]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.5 Computer programming ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[505,592,919,820]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In addition, computational thinking and programming are trending skills for researchers to effectively and flexibly implement data-driven methods and analysis (Chen and Wojcik, 2016). Environmental psychology researchers may increasingly feel they need to learn and apply \"advanced\" data analysis skill sets, including image, spatial and spatial-temporal data, network data, natural language, or physiological data, in their research. GAI tools excel in assisting the process of program learning and analysis with natural and instant interaction. For example, ChatGPT and GitHub Copilot could help explain code, generate queries, identify relevant coding libraries and functions, explain errors, assisting debug, or write prototype coding for future studies in almost every coding language, such as R, Python, Matlab, etc. (Biswas, 2023; Feng et al., 2023; Rahman and Watanobe, 2023). These capabilities help researchers with both limited and massive coding experience to speed up the research data cleaning, analysis, and visualization process. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,846,828,864]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.6 Planning and decision support ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[505,877,917,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Successful study implementation requires careful planning, effective problem-solving, and informed decision-making. While support from colleagues, committee members, and advisors is ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,38,137,48]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Yuan et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[759,38,917,49]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10.3389/fpsyg.2024.1295275 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[78,907,339,917]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 https://www.maxqda.com/products/ai-assist ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[80,948,211,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Frontiers in Psychology ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[489,948,507,958]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"04 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[835,948,915,959]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"frontiersin.org ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[77,93,492,380]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"invaluable, such mentors have limited availability. GAI tools' knowledge base and planning capacities (Wu et al., 2023) can help researchers evaluate methodological choices and trade-offs between them. For example, an environmental psychologist could prompt ChatGPT to generate approaches with higher vs. lower levels of experimental control and ecological validity in a healthcare facility wayfinding study using virtual reality (Joseph et al., 2020). When used in dealing with planning and problem-solving, ChatGPT can facilitate describing an entire procedure and adding details, analyzing the cause of problems, and planning for worst-case scenarios. This can be applied to a large variety of data collection procedures, such as experimental sessions, equipment use, and focus groups. Another example is field observation in urban public spaces (Sussman, 2016). We found that ChatGPT could describe potential iterations in refining observational protocol (Supplementary material 5). It also identified potential issues such as public space being unexpectedly closed, equipment malfunctions or being stolen, failure to adequately familiarize with the site, and notes or data being damaged in transportation. Then one can use ChatGPT to draft a comprehensive logistical checklist and preparation action list. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,403,473,435]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 Two-way communication between researchers and external audiences ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[77,450,489,634]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Communicating science with practitioners, policymakers, and the general public requires unique skill sets. This is especially true in environmental psychology, where from its beginnings, this field of research has had an applied emphasis that would benefit from collaboration with practitioners (Wohlwill, 1970; Stokols, 1978, 1995; Devlin, 2018). Communication requires advanced knowledge of external audiences and is not a one-directional stream of information (Ham, 1992). Multi-perspective thinking helps ensure messages are received as intended, and that feedback is considered (Blythe, 2010). GAI tools can assist with this through their large knowledge base that encompasses scientific, professional, and everyday content in addition to the ability to explain audience characteristics, identify relevant scientific concepts, and demonstrate practical relevance. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,661,398,690]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.1 Learning about audiences and stakeholders ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[77,706,492,906]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Generative Artificial Intelligence tools can suggest possible expectations and needs of diverse external audiences. Environmental psychology can have implications for designers, planners, healthcare professionals, business owners, residents, land managers, and many other fields. Researchers may be familiar with select professions and communities but are unlikely to consider and know all relevant stakeholders. For example, scholars familiar with speaking with conservation biologists may use an entirely different lexicon about urban greening than scholars trained in public and environmental policy (Vogt, 2018). ChatGPT can be used to identify new stakeholders for research studies, recommend how to communicate with these audiences, learn about their needs and concerns, and provide nuanced \"pitches\" to capture and maintain stakeholders' interest (Supplementary material 6). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,91,823,108]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.2 Evaluating practical relevance ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[505,121,919,307]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The broad base of procedure knowledge in GAI tools can facilitate identifying relevant practical actions that emerge from research findings. These actions can be useful in suggesting practical implications in scientific publications and practical guidelines. The broad knowledge base can also help assess the feasibility and requirements for a proposed action/approach, provide alternatives, and discuss alignment with practitioner needs, resources, and constraints. These tools can also be used to generate ideas to discuss directly with practitioners. For example, natural sounds may have clear applicability to environmental psychologists interested in restorative landscapes but also have wider applicability—though perhaps less known to these environmental psychologists—for measuring biodiversity and urban ecology (Fleming et al., 2023). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,332,843,349]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.3 Communication with the media ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[505,363,919,577]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In addition to the uses of GAI tools to assist with scientific writing (Buriak et al., 2023; Dwivedi et al., 2023; Lund et al., 2023), these tools can translate scientific writing to social media posts, blogs, storyboards for short videos, technical reports, conference abstracts, and many other content types (Supplementary material 7). The complex concepts and technical language in the original text can be simplified; GAI tools create examples, analogies, and real-world case studies to explain concepts and engage audiences. These tools can also articulate the procedures and steps to implement practical guidance and takeaways from research findings. The text from ChatGPT can emphasize the important implications and limitations for practitioners, policymakers, and other stakeholders and can translate the language into the appropriate tone for a specific audience. For a practical guide on ChatGPT and social media content creation, see Stone (2023). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,602,885,634]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 Responsible use of GAI in environmental psychology research ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[505,649,919,904]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Generative Artificial Intelligence tools can have many benefits, but some uses can reduce these benefits or even threaten the value of their research applications. Relying on ChatGPT and other language models for research ideas or a conceptual understanding may compromise originality and critical thinking, or even lead to false information and plagiarism (Beerbaum, 2023; Polonsky and Rotman, 2023; Rahimi and Talebi Bezmin Abadi, 2023; Xames and Shefa, 2023). ChatGPT's responses can be influenced by how prompts are formulated, such as language ambiguity, complexity level, and clarity of user's intentions. It is also susceptible to leading questions and can generate misinformation with questions beyond its knowledge base, for example, questions about underrepresented countries and regions. Such complexities of this tool operation can limit the tool's value. Also, ChatGPT is trained on publicly available datasets. It may copy phrases from the trained documents without giving credit, thus leading to plagiarism. Approximately half of the citations provided by ChatGPT are fabricated, depending on the model version and the type of reference (Bhattacharyya et al., 2023; Walters and Wilder, 2023). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,38,137,48]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Yuan et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[759,38,917,49]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10.3389/fpsyg.2024.1295275 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[80,948,211,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Frontiers in Psychology ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[489,948,507,958]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"05 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[835,948,917,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"frontiersin.org ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,93,487,177]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Therefore, researchers should always evaluate and fact-check the output to avoid misinformation or plagiarism (Kitamura, 2023). In addition, reliance on GAI in literature searches and idea generation without other sources may constrain creativity (Dwivedi et al., 2023) or impede scholars from developing a foundational knowledge base of a research area. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,179,487,376]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Reliance on GAI tools to enhance productivity in research can also compromise research validity and the value of research findings. When motivated to publish and seek grants, researchers may use GAI to accelerate their productivity at the expense of originality and professional growth (Dwivedi et al., 2023). While using GAI undeniably boosts productivity, it can bias topic and methodology selection toward those it can assist. These could, in turn, decrease the validity and reliability of research findings, and undercut the benefit of effective and flexible implementation from GAI tools. Furthermore, increased use of GAI for productivity may entrench competition between researchers or institutions regarding publication output, increasing the share of \"fast food\" publications (van Dalen and Henkens, 2012) with less contribution and significance for understanding human-environment problems. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,378,487,662]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Therefore, we support the many calls to action from scholars and publishers to create ethical guidelines for GAI use (Dwivedi et al., 2023; Graf and Bernardi, 2023; Liebrenz et al., 2023; Lund et al., 2023; Rahimi and Talebi Bezmin Abadi, 2023). To maintain research originality and significance, it is important to incorporate diverse sources and find a balance between GAI automation and researchers' thinking. We can refer to the conceptual model of levels and stages of automation from human factor psychology (Parasuraman et al., 2000; Parasuraman and Wickens, 2008), which includes a continuum of automation levels and four automation stages from information-related (information acquisition and information analysis) to action-related (decision selection and action implementation). We recommend using GAI tools for limited stages and at a lower level of automation for the information-related stages. For example, one may select an existing perspective or technique and have ChatGPT facilitate application to new topics (information analysis) or have ChatGPT suggest programming codes and manually test the codes (decision selection). By contrast, using ChatGPT to write a paragraph with references compromises originality (high automation at multiple stages). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,663,487,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Institutions should integrate GAI into professional training. For example, the book by An (2023) provides beginner-friendly guidance on ChatGPT for environmental and health behavior research. Training may also cover advanced skills of GAI, such as prompt engineering, retrieval from files, and fine-tuning. Prompt engineering has been recommended as the initial attempt to obtain a more accurate output (OpenAI, 2024c). It involves improving prompts by providing context, defining expected results, and using intermediate steps for complex tasks (Nori et al., 2023; Wei et al., 2023; White et al., 2023; OpenAI, 2024d). Supplementary material 1, for example, explored the impacts of heat events on greenspace health benefits with an interest in comprehensive, design-oriented answers. Therefore, it set the context of \"public health and environmental design\" and the expected result structure of \"physical, social, and personal contexts.\" In addition, uploading files allows the model to retrieve relevant contextual information from a data source outside its training dataset (Retrieval Augmented Generation; OpenAI, 2024a,b,e), which is supported by GPT-4 and the OpenAI API. For example, reference measurement ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,93,915,249]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tools may be uploaded in the measurement tool creation example (Supplementary material 3), and a related research proposal can be uploaded for creating field observation protocols (Supplementary material 5). Fine-tuning adapts a model for focused and specialized tasks such as rating, sentiment analysis, FAQs, or generating structured results (Google, 2024; OpenAI, 2024c). This process involves a simplified training process (\"tuning\") with specific input and output examples, rather than just supplying instructions (prompt engineering) or unstructured data (retrieval). Thus, it offers the largest level of customization but requires the researcher's technical capabilities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,250,915,449]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We also argue that institutions need to update their policies to promote ethical GAI practices and maintaining academic integrity. Without highlighting the ethical GAI use, scholars and committees involved with tenure and promotion might associate GAI with neutral or negative connotations (i.e., hallucinating false information and biases in training data) instead of their tremendous values to promote scholarship and produce knowledge. Additionally, it is important to recognize topics and methods that are less likely to be promoted by GAI, such as qualitative approaches seeking to deeply understand the lived experiences of individuals and groups. Correspondingly, we see an urgency to modify performance evaluation systems related to publications, funding, and career advancement to protect researchers who use GAI tools in pursuit of increasing the quality and transparency of their research, not only the quantity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,475,786,492]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data availability statement ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,506,915,548]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,574,729,590]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Author contributions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,606,915,733]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"SY: Conceptualization, Investigation, Project administration, Visualization, Writing - original draft, Writing - review & editing. FL: Conceptualization, Investigation, Visualization, Writing - original draft, Writing - review & editing. MBr: Conceptualization, Investigation, Project administration, Writing - original draft, Writing - review & editing. MBA: Conceptualization, Investigation, Writing - review & editing. KZ: Conceptualization, Writing - review & editing. OM: Writing - review & editing. MP: Writing - review & editing. AR: Writing - review & editing. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,759,594,777]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Funding ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,791,915,819]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,845,707,860]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conflict of interest ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,877,915,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. 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This had no impact on the peer review process and the final decision. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,161,250,177]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Publisher's note ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[78,193,489,235]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. 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(1970). The emerging discipline of environmental psychology. Am. Psychol. 25, 303-312. doi: 10.1037/h0029448 \",\"Wu, T., He, S., Liu, J., Sun, S., Liu, K., Han, Q.-L., et al. (2023). A brief overview of ChatGPT: the history, status quo and potential future futurity. IEEE/CAA J. Automat. Sin. 10, 1122-1136. doi: 10.1109/JAS.2023.123618 \",\"Xames, M. D., and Shefa, J. (2023). ChatGPT for research and publication: opportunities and challenges. J. Appl. Learn. Teach. 6. doi: 10.2139/ssrn.4381803 \",\"Zhu, J.-J., Jiang, J., Yang, M., and Ren, Z. J. (2023). ChatGPT and Environmental Research. Environ. Sci. Technol. 57, 17667-17670. doi: 10.1021/acs.est.3c01818 \"]","page_idx":"7","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[80,39,137,48]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Yuan et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[759,38,917,49]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10.3389/fpsyg.2024.1295275 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[80,948,210,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Frontiers in Psychology ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[489,948,507,959]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"08 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[836,948,915,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"frontiersin.org ","text_format":null,"text_level":null,"type":"footer"}],"string":"[\n {\n \"bbox\": \"[80,148,104,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0920/d8b4d32ab9bffb2c99a22fa41ba0308584e62a37ab77934d63edae54ae19fa48.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[109,151,201,162]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Check for updates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,187,163,197]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"OPEN ACCESS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,205,129,214]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"EDITED BY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,216,169,225]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Paola Passafaro, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,225,263,236]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sapienza University of Rome, Italy \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,243,142,252]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"REVIEWED BY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,254,183,263]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Kathryn E. 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\"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Shuai Yuan \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,325,220,334]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"syuan2@g.clemson.edu \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,341,233,350]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"RECEIVED 15 September 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,351,213,361]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ACCEPTED 01 March 2024 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,362,206,370]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PUBLISHED 08 April 2024 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": 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null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Zhang K, McAnirlin O, Patwary MM and Reuben A (2024) Leveraging and exercising caution with ChatGPT and other generative artificial intelligence tools in environmental psychology research. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,455,228,464]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Front. Psychol. 15:1295275. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,464,260,475]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"doi: 10.3389/fpsyg.2024.1295275 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,483,134,491]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"COPYRIGHT\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,492,324,630]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"© 2024 Yuan, Li, Browning, Bardhan, Zhang, McAnirlin, Patwary and Reuben. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[366,143,915,292]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Leveraging and exercising caution with ChatGPT and other generative artificial intelligence tools in environmental psychology research \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[366,305,784,322]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Shuai Yuan $^{1*}$ , Fu Li $^{1}$ , Matthew H. E. M. Browning $^{1}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[366,324,806,340]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mondira Bardhan<sup>1</sup>, Kuiran Zhang<sup>1</sup>, Olivia McAnirlin<sup>1</sup>, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[368,342,831,357]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Muhammad Mainuddin Patwary $^{2,3}$ and Aaron Reuben $^{4}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[366,363,910,418]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"<sup>1</sup>Virtual Reality and Nature Lab, Department of Parks, Recreation and Tourism Management, Clemson University, Clemson, SC, United States, <sup>2</sup>Environment and Sustainability Research Initiative, Khulna, Bangladesh, <sup>3</sup>Environmental Science Discipline, Life Science School, Khulna University, Khulna, Bangladesh, <sup>4</sup>Department of Psychology and Neuroscience, Duke University, Durham, NC, United States \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[364,439,917,611]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Generative Artificial Intelligence (GAI) is an emerging and disruptive technology that has attracted considerable interest from researchers and educators across various disciplines. We discuss the relevance and concerns of ChatGPT and other GAI tools in environmental psychology research. We propose three use categories for GAI tools: integrated and contextualized understanding, practical and flexible implementation, and two-way external communication. These categories are exemplified by topics such as the health benefits of green space, theory building, visual simulation, and identifying practical relevance. However, we also highlight the balance of productivity with ethical issues, as well as the need for ethical guidelines, professional training, and changes in the academic performance evaluation systems. We hope this perspective can foster constructive dialogue and responsible practice of GAI tools. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[366,629,423,638]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"KEYWORDS \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[366,644,868,670]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"environmental psychology, generative artificial intelligence, ChatGPT, research methods, research ethics \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[366,731,521,747]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[364,763,917,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Generative Artificial Intelligence (GAI) has sparked enthusiasm and concern in how we conceive knowledge creation (Nature Editorials, 2023; Stokel-Walker and Van Noorden, 2023). Generated content includes language and text but also images, audio, video, and 3D objects (Supplementary Table S1). Their applications in higher education have raised interest and concerns from educators (Chen et al., 2020), including the UNESCO (Sabzalieva and Valentini, 2023). The applications in scientific writing (Lund et al., 2023) and various scientific domains such as healthcare research (Dahmen et al., 2023; Sallam, 2023), environmental research (Agathokleous et al., 2023; Zhu et al., 2023), and environmental planning and design (Fernberg and Chamberlain, 2023; Wang et al., 2023) have also been discussed. As with all powerful tools, GAI offers opportunities and poses risks depending on the user's knowledge and choices when using the tool (Dwivedi et al., 2023). For example, ChatGPT's responses can \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,39,102,58]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"# \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[105,42,194,57]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"frontiers \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[215,43,381,58]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Frontiers in Psychology \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[736,39,828,48]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"TYPE Perspective \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[737,49,870,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PUBLISHED 08 April 2024 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[737,60,917,70]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"DOI 10.3389/fpsyg.2024.1295275 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[80,948,210,959]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Frontiers in Psychology \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[490,948,505,958]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"01 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[835,948,915,959]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"frontiersin.org \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[77,93,490,165]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"sound plausible for a research paper but may not match the expected precise and accuracy level for scientific discourse. Therefore, it is time to ask what role GAI can play in environmental psychology. This article aims to prepare the field of environmental psychology to take advantage of GAI while, ideally, avoiding the pitfalls. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,165,490,548]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Environmental psychology investigates the interaction between human and socio-physical environments, with a practical orientation to solving community-environmental problems using psychological research tools and insights (Stokols, 1978). Given this focus, the field has several challenges that GAI tools might assist. First, human environmental experience depends on the person and the physical, social, and situational contexts (Lazarus and Launier, 1978; Altman and Rogoff, 1987; Hartig, 1993; Wapner and Demick, 2002). Due to the field's preference for generalized, objective knowledge (Seamon, 1982; Franck, 1987), and researchers' reliance on existing literature instead of learning from real-life experiences and communities, it struggles to cater to diverse human experiences. Second, environmental psychology's interdisciplinary nature leads to knowledge gaps for researchers trained in specific disciplines. Researchers may miss advancements in related fields or be unaware of older literature, creating barriers to fully informed research and application (Rapoport, 1997). Third, there can be a lack of alignment between empirical research and practice, especially in environmental planning and design. This may be due to communication gaps (Franck, 1987), lack of integrated perspectives (Hillier et al., 1972), and the complex interactions between factors in practice contexts (Alexander, 1964; Altman and Rogoff, 1987). Fourth, researchers face constraints from the techniques and technologies they can access for applying the appropriate method to a research question. Mastering multiple techniques can be overwhelming and cost-prohibitive, and the opportunity to collaborate, practice, and get feedback from others is not always available. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,549,489,791]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The issues above reflect the limited capacity of human researchers and institutional research structures. We suggest that GAI tools may help fill the various gaps, as they can connect board knowledge to specific contexts, foster interdisciplinary learning through interactive conversations, and assist with various procedures and techniques. To illustrate how GAI can be used to advance environmental psychology as a field, we propose three areas in the research process where GAI tools can be beneficial: (1) integrated and contextualized understanding, (2) effective and flexible implementation, and (3) two-way communication between researchers and external audiences (Figure 1). These three areas cover the various research activities in the research process, such as idea generation, planning and decision support, development of stimuli, data analysis, and communication of findings. To illustrate how these GAI applications could be put into practice, we provide specific examples of our interactions with ChatGPT (see Supplementary material 1-6). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,816,418,848]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 Integrated and contextualized understanding \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,863,490,921]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Environmental psychology researchers benefit from continual learning, building, and expanding integrated and contextualized understanding of human-environment interaction. Large language models can assist with this pursuit throughout the research process, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,90,915,355]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"FIGURE 1 Categories of generative artificial intelligence (GAI) applications for advancing environmental psychology research. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0156/92acb782af6ec5f778431ec55732510b685df4065629281a7be71e0c8fa04cc1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[505,435,917,464]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"from brainstorming research ideas, evaluating potential research factors, collecting examples, and interpreting research findings. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,489,831,507]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.1 Research question formulation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,521,919,777]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Generative Artificial Intelligence can accelerate the idea-generation process by connecting a loosely described phenomenon or assumption to a list of scientific concepts and theories across different fields. GAI can also help researchers better initiate a study from the perspective of helping to build a knowledge map comprehensively. For example, ChatGPT could assist a researcher interested in human-nature connections by framing questions from the relevant perspectives of psychology, social science, environment, tourism, education, planning, and health science (Ives et al., 2017; Hallsworth et al., 2023). In addition, ChatGPT can provide a matched level of competence to explore unfocused areas (i.e., helping partitioners and researchers to learn other research areas). Therefore, researchers may more likely to identify important but understudied factors and relationships (Supplementary material 1). For example, extreme heat may limit or dissolve how well green space supports healthy behaviors and psychological restoration, though the prevailing modeling has focused on mitigating urban heat islands outside of heat waves (Li et al., 2023). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,803,692,821]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2 Theory building \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,834,917,920]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ChatGPT can help perform three theory-building processes described by Walker and Avant (2014), which are derivation (making an analogy and borrowing a concept), synthesis (combining information into a concept), and analysis (breaking down a concept). These processes are more effective when ChatGPT also generates examples and scenarios as hypothetical empirical materials. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,38,137,48]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Yuan et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[759,38,917,49]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10.3389/fpsyg.2024.1295275 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[78,948,211,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Frontiers in Psychology \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[489,948,507,958]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"02 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[835,948,915,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"frontiersin.org \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,93,489,434]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Researchers can flexibly use ChatGPT's capacities, including the three strategies we described here. One is an inductive approach, where researchers use ChatGPT to generate examples with social, physical, situational contexts and/or personal factors and abstract and synthesize those examples. This is particularly useful for an initial phase or when empirical data is unavailable. For example, Stokols (2000) has emphasized the research gap in identifying high-impact social-physical circumstances that enhance or constrain human stress coping and functioning. Researchers can use ChatGPT to generate many examples instantly and identify the key factors or groups (Supplementary material 2). Another deductive strategy can be refining and breaking down an existing concept and using hypothetical examples to test the tentative subconcepts. For example, breaking down the concept of compatibility in attention restoration theory (Kaplan, 1995) may help connect it to various environments and human goals (Supplementary material 2). Third but not least, many theory-building approaches involve purposive sample collection to extend or corroborate a theory (i.e., theoretical sampling; Eisenhardt and Graebner, 2007; Corbin and Strauss, 2015). Environmental psychology is often about and can be challenged by everyday experiences. One can use ChatGPT to deliberately collect hypothetical everyday environmental experiences that may contradict a theory. Such counterexamples can be abstracted or synthesized to identify boundary conditions or new mediators and moderators. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,461,452,476]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.3 Development of measurement tools \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,492,489,776]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Generative Artificial Intelligence tools can ease the item pool generation of psychometric scales and environmental audit tools. One can use ChatGPT to generate items or indicators for a concept or phenomenon that is described broadly or precisely. Alternatively, one can first explore the potential construct structure using the inductive and deductive approaches described in theory building, and generate the item pool based on the dimensions. ChatGPT's large knowledge base and ability to generate many items may help improve content validity. For specific populations or environments (e.g., children, neighborhoods, and urban parks), ChatGPT can also help identify specific factors, assess the suitability of general or related measurement tools, and identify gaps or mismatches. This might improve the relevance of the measurements for the participants and environments. Moreover, ChatGPT's ability to apply general knowledge and logical reasoning can help explore the potential dimensions of a construct from a list of indicators (Supplementary material 3). By repeating this action, items often categorized into different categories over time may be less valid. Although this cannot replace expert review, it can provide a low-cost check of the quality of ongoing work or existing measurement tools developed using a rational or theoretical approach. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,802,317,833]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 Effective and flexible implementation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,848,487,932]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Implementation plays an important role in environmental psychology, but technical issues are a major barrier for researchers implementing their research ideas. GAI can mitigate such barriers and allow researchers to focus more on the research itself. In addition to the implementation aspects common to the social and behavioral sciences, such as institutional review boards (IRBs), recruitment, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,93,917,134]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"surveys, interviews, and statistics, environmental psychology has a strong focus on field observation and the creation of environmental stimuli. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,161,769,178]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1 Visual stimuli generation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,193,917,419]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Manipulating factors of interest and controlling confounders is crucial for experiment validity. However, learning the required design knowledge and media creation skills can be prohibitive for researchers with non-environmental design backgrounds (Stamps, 2016). Image generators such as DALLE-2, Midjourney, and Stable Diffusion enable rapid generation and modification of imagery to align with the research question (i.e., varying an independent variable in the environment). For example, a Stable Diffusion-based tool, Skybox AI, could generate a VR environment within seconds with a short prompt (Figure 2). Stable Diffusion can also enable style transformation, such as changing the season, time, architectural style and elements while keeping the spatial layout. 3D content generators such as Point E and Shape E can help build virtual 3D Objects. ChatGPT and GitHub Copilot can further help with computer programming tasks in developing virtual scenes in game engines (e.g., Unity 3D or Unreal) for advanced and interactive simulation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,447,776,463]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2 Verbal stimuli generation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,478,917,762]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Large language models like ChatGPT can create high-quality verbal stimuli with specific contents or factors, communication purposes, and rhetoric considerations. Several research areas, such as decision-making and information-seeking in travel, health, and pro-environmental behavior, could require more complex stimuli beyond visual perception. In this case, researchers can use text generators to create voiceover scripts in the intervention that require specific tones, inclusive languages, and clear narratives. For example, translating scripts for non-native English speakers can lead to misunderstandings and measurement errors when the local dialect is ignored (Solano-Flores, 2006), which could be assisted by GAI. These tools can also create a series of text-based scenarios (vignettes) for priming, contextualizing, and incorporating different parameters for complex conditions (Aguinis and Bradley, 2014). This technique is frequently employed for forecasted scenarios and recreation behavior, pro-environmental behavior, and acceptance of sustainable design (Jaung, 2022; Hu and Shealy, 2023; Urban et al., 2023). For audio narration, advanced text-to-speech tools such as Vall E can mimic tones and emotions for languages, which can be used to test narration scripts, in intervention materials, or as experiment instructions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,789,912,819]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.3 Internal communication with participants and institutional review boards \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,834,915,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Large language models can help edit language in materials presented to participants. For example, ChatGPT can be used to develop engaging and easily understandable recruitment materials and easy-to-understand experimental instructions. Such language models can also reduce issues such as uncommon or obsolete words, non-inclusive language, and leading questions in existing survey batteries. In verbal-based communication, those tools may improve communication with special \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,39,136,48]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Yuan et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[761,38,915,49]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10.3389/fpsyg.2024.1295275 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[80,948,210,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Frontiers in Psychology \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[490,948,505,959]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"03 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[836,948,915,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"frontiersin.org \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[156,118,504,241]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"A \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0785/b57b3bdc80674b5463c586842eb321df77d08354bac70871f4c92f7ab5382216.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[507,118,855,242]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"B \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0517/99b4bc06334f0a6188801ee0fab001cc4ca680415e065517a6751de7f1b405db.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[154,250,504,375]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"C \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0440/8ff71c0d10bd6d1215f00af27e4c345505ac236597688587a26262ca06e6bd9a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[507,250,855,374]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"D \\\",\\\"FIGURE 2 Example of Al generated virtual reality environment form the same structure. Prompts are (A) \\\\\\\"a summer scene outside a lovely house, realistic\\\\\\\"; (B) \\\\\\\"a fall scene outside a lovely house with leave fall on the ground, realistic\\\\\\\"; (C) \\\\\\\"a winter scene outside a lovely house, with less light and a clear night sky, realistic\\\\\\\"; and (D) \\\\\\\"a space scene outside a lovely house on the moon, Earth in the distance, Sci-Fi.\\\\\\\" All variants used the \\\\\\\"Mixed Mode\\\\\\\" option, which will generate a new image based on the image of the first prompt. Retrieved from Skybox AI, version beta 0.4.2. on May 31, 2023. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0116/d8728df5c6fb08076dd4f8f9af291b940f1ddbda834c2069e444bf4bcc503c93.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[77,478,489,620]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"populations, such as children, elderly individuals, and people with disabilities and mental health conditions, ensuring understanding, inclusiveness, and compliance. IRB-related documents and materials require specific structures, tones, and an understanding of ethical issues. AI tools might also explain ethical concerns and present potential solutions. It can transfer existing materials into new structures and formats, after cross-checking with specific institutional policies. See Supplementary material 4 for using ChatGPT transferring a description of the procedure from a citation into a training manual, an IRB application, and a consent form. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,646,287,663]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.4 Basic data analysis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,677,489,863]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Generative Artificial Intelligence tools can facilitate basic quantitative methods such as the use of R in data cleaning, regression, and factor analysis. ChatGPT can interpret statistical software outputs or model results and suggest visualization options. These tools can assist researchers with qualitative or environmental backgrounds in conducting quantitative or mixed-methods research. Qualitative analysis may benefit less from GAI tools because most qualitative approaches need researchers' knowledge and experience to interpret data meaning and significance (Creswell and Poth, 2017). However, GAI tools may perform minor roles such as suggesting codes to merge, checking code abstraction levels, and interpreting ambiguous sentences. Also, qualitative data analysis software such as MAXQDA provides a GAI tool<sup>1</sup> for defining codes based on related quotations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,478,917,535]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"QDA software may also offer an auto-coding function based on regular expression, which is suitable for the exploration of data or more descriptive research. ChatGPT can be used to generate regular expressions to identify objects or features in different texts. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,561,774,579]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.5 Computer programming \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,592,919,820]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In addition, computational thinking and programming are trending skills for researchers to effectively and flexibly implement data-driven methods and analysis (Chen and Wojcik, 2016). Environmental psychology researchers may increasingly feel they need to learn and apply \\\"advanced\\\" data analysis skill sets, including image, spatial and spatial-temporal data, network data, natural language, or physiological data, in their research. GAI tools excel in assisting the process of program learning and analysis with natural and instant interaction. For example, ChatGPT and GitHub Copilot could help explain code, generate queries, identify relevant coding libraries and functions, explain errors, assisting debug, or write prototype coding for future studies in almost every coding language, such as R, Python, Matlab, etc. (Biswas, 2023; Feng et al., 2023; Rahman and Watanobe, 2023). These capabilities help researchers with both limited and massive coding experience to speed up the research data cleaning, analysis, and visualization process. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,846,828,864]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.6 Planning and decision support \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,877,917,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Successful study implementation requires careful planning, effective problem-solving, and informed decision-making. While support from colleagues, committee members, and advisors is \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,38,137,48]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Yuan et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[759,38,917,49]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10.3389/fpsyg.2024.1295275 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[78,907,339,917]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 https://www.maxqda.com/products/ai-assist \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[80,948,211,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Frontiers in Psychology \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[489,948,507,958]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"04 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[835,948,915,959]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"frontiersin.org \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[77,93,492,380]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"invaluable, such mentors have limited availability. GAI tools' knowledge base and planning capacities (Wu et al., 2023) can help researchers evaluate methodological choices and trade-offs between them. For example, an environmental psychologist could prompt ChatGPT to generate approaches with higher vs. lower levels of experimental control and ecological validity in a healthcare facility wayfinding study using virtual reality (Joseph et al., 2020). When used in dealing with planning and problem-solving, ChatGPT can facilitate describing an entire procedure and adding details, analyzing the cause of problems, and planning for worst-case scenarios. This can be applied to a large variety of data collection procedures, such as experimental sessions, equipment use, and focus groups. Another example is field observation in urban public spaces (Sussman, 2016). We found that ChatGPT could describe potential iterations in refining observational protocol (Supplementary material 5). It also identified potential issues such as public space being unexpectedly closed, equipment malfunctions or being stolen, failure to adequately familiarize with the site, and notes or data being damaged in transportation. Then one can use ChatGPT to draft a comprehensive logistical checklist and preparation action list. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,403,473,435]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 Two-way communication between researchers and external audiences \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,450,489,634]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Communicating science with practitioners, policymakers, and the general public requires unique skill sets. This is especially true in environmental psychology, where from its beginnings, this field of research has had an applied emphasis that would benefit from collaboration with practitioners (Wohlwill, 1970; Stokols, 1978, 1995; Devlin, 2018). Communication requires advanced knowledge of external audiences and is not a one-directional stream of information (Ham, 1992). Multi-perspective thinking helps ensure messages are received as intended, and that feedback is considered (Blythe, 2010). GAI tools can assist with this through their large knowledge base that encompasses scientific, professional, and everyday content in addition to the ability to explain audience characteristics, identify relevant scientific concepts, and demonstrate practical relevance. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,661,398,690]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.1 Learning about audiences and stakeholders \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,706,492,906]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Generative Artificial Intelligence tools can suggest possible expectations and needs of diverse external audiences. Environmental psychology can have implications for designers, planners, healthcare professionals, business owners, residents, land managers, and many other fields. Researchers may be familiar with select professions and communities but are unlikely to consider and know all relevant stakeholders. For example, scholars familiar with speaking with conservation biologists may use an entirely different lexicon about urban greening than scholars trained in public and environmental policy (Vogt, 2018). ChatGPT can be used to identify new stakeholders for research studies, recommend how to communicate with these audiences, learn about their needs and concerns, and provide nuanced \\\"pitches\\\" to capture and maintain stakeholders' interest (Supplementary material 6). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,91,823,108]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.2 Evaluating practical relevance \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,121,919,307]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The broad base of procedure knowledge in GAI tools can facilitate identifying relevant practical actions that emerge from research findings. These actions can be useful in suggesting practical implications in scientific publications and practical guidelines. The broad knowledge base can also help assess the feasibility and requirements for a proposed action/approach, provide alternatives, and discuss alignment with practitioner needs, resources, and constraints. These tools can also be used to generate ideas to discuss directly with practitioners. For example, natural sounds may have clear applicability to environmental psychologists interested in restorative landscapes but also have wider applicability—though perhaps less known to these environmental psychologists—for measuring biodiversity and urban ecology (Fleming et al., 2023). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,332,843,349]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.3 Communication with the media \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,363,919,577]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In addition to the uses of GAI tools to assist with scientific writing (Buriak et al., 2023; Dwivedi et al., 2023; Lund et al., 2023), these tools can translate scientific writing to social media posts, blogs, storyboards for short videos, technical reports, conference abstracts, and many other content types (Supplementary material 7). The complex concepts and technical language in the original text can be simplified; GAI tools create examples, analogies, and real-world case studies to explain concepts and engage audiences. These tools can also articulate the procedures and steps to implement practical guidance and takeaways from research findings. The text from ChatGPT can emphasize the important implications and limitations for practitioners, policymakers, and other stakeholders and can translate the language into the appropriate tone for a specific audience. For a practical guide on ChatGPT and social media content creation, see Stone (2023). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,602,885,634]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 Responsible use of GAI in environmental psychology research \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,649,919,904]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Generative Artificial Intelligence tools can have many benefits, but some uses can reduce these benefits or even threaten the value of their research applications. Relying on ChatGPT and other language models for research ideas or a conceptual understanding may compromise originality and critical thinking, or even lead to false information and plagiarism (Beerbaum, 2023; Polonsky and Rotman, 2023; Rahimi and Talebi Bezmin Abadi, 2023; Xames and Shefa, 2023). ChatGPT's responses can be influenced by how prompts are formulated, such as language ambiguity, complexity level, and clarity of user's intentions. It is also susceptible to leading questions and can generate misinformation with questions beyond its knowledge base, for example, questions about underrepresented countries and regions. Such complexities of this tool operation can limit the tool's value. Also, ChatGPT is trained on publicly available datasets. It may copy phrases from the trained documents without giving credit, thus leading to plagiarism. Approximately half of the citations provided by ChatGPT are fabricated, depending on the model version and the type of reference (Bhattacharyya et al., 2023; Walters and Wilder, 2023). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,38,137,48]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Yuan et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[759,38,917,49]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10.3389/fpsyg.2024.1295275 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[80,948,211,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Frontiers in Psychology \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[489,948,507,958]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"05 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[835,948,917,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"frontiersin.org \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,93,487,177]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Therefore, researchers should always evaluate and fact-check the output to avoid misinformation or plagiarism (Kitamura, 2023). In addition, reliance on GAI in literature searches and idea generation without other sources may constrain creativity (Dwivedi et al., 2023) or impede scholars from developing a foundational knowledge base of a research area. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,179,487,376]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Reliance on GAI tools to enhance productivity in research can also compromise research validity and the value of research findings. When motivated to publish and seek grants, researchers may use GAI to accelerate their productivity at the expense of originality and professional growth (Dwivedi et al., 2023). While using GAI undeniably boosts productivity, it can bias topic and methodology selection toward those it can assist. These could, in turn, decrease the validity and reliability of research findings, and undercut the benefit of effective and flexible implementation from GAI tools. Furthermore, increased use of GAI for productivity may entrench competition between researchers or institutions regarding publication output, increasing the share of \\\"fast food\\\" publications (van Dalen and Henkens, 2012) with less contribution and significance for understanding human-environment problems. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,378,487,662]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Therefore, we support the many calls to action from scholars and publishers to create ethical guidelines for GAI use (Dwivedi et al., 2023; Graf and Bernardi, 2023; Liebrenz et al., 2023; Lund et al., 2023; Rahimi and Talebi Bezmin Abadi, 2023). To maintain research originality and significance, it is important to incorporate diverse sources and find a balance between GAI automation and researchers' thinking. We can refer to the conceptual model of levels and stages of automation from human factor psychology (Parasuraman et al., 2000; Parasuraman and Wickens, 2008), which includes a continuum of automation levels and four automation stages from information-related (information acquisition and information analysis) to action-related (decision selection and action implementation). We recommend using GAI tools for limited stages and at a lower level of automation for the information-related stages. For example, one may select an existing perspective or technique and have ChatGPT facilitate application to new topics (information analysis) or have ChatGPT suggest programming codes and manually test the codes (decision selection). By contrast, using ChatGPT to write a paragraph with references compromises originality (high automation at multiple stages). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,663,487,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Institutions should integrate GAI into professional training. For example, the book by An (2023) provides beginner-friendly guidance on ChatGPT for environmental and health behavior research. Training may also cover advanced skills of GAI, such as prompt engineering, retrieval from files, and fine-tuning. Prompt engineering has been recommended as the initial attempt to obtain a more accurate output (OpenAI, 2024c). It involves improving prompts by providing context, defining expected results, and using intermediate steps for complex tasks (Nori et al., 2023; Wei et al., 2023; White et al., 2023; OpenAI, 2024d). Supplementary material 1, for example, explored the impacts of heat events on greenspace health benefits with an interest in comprehensive, design-oriented answers. Therefore, it set the context of \\\"public health and environmental design\\\" and the expected result structure of \\\"physical, social, and personal contexts.\\\" In addition, uploading files allows the model to retrieve relevant contextual information from a data source outside its training dataset (Retrieval Augmented Generation; OpenAI, 2024a,b,e), which is supported by GPT-4 and the OpenAI API. For example, reference measurement \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,93,915,249]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tools may be uploaded in the measurement tool creation example (Supplementary material 3), and a related research proposal can be uploaded for creating field observation protocols (Supplementary material 5). Fine-tuning adapts a model for focused and specialized tasks such as rating, sentiment analysis, FAQs, or generating structured results (Google, 2024; OpenAI, 2024c). This process involves a simplified training process (\\\"tuning\\\") with specific input and output examples, rather than just supplying instructions (prompt engineering) or unstructured data (retrieval). Thus, it offers the largest level of customization but requires the researcher's technical capabilities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,250,915,449]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We also argue that institutions need to update their policies to promote ethical GAI practices and maintaining academic integrity. Without highlighting the ethical GAI use, scholars and committees involved with tenure and promotion might associate GAI with neutral or negative connotations (i.e., hallucinating false information and biases in training data) instead of their tremendous values to promote scholarship and produce knowledge. Additionally, it is important to recognize topics and methods that are less likely to be promoted by GAI, such as qualitative approaches seeking to deeply understand the lived experiences of individuals and groups. Correspondingly, we see an urgency to modify performance evaluation systems related to publications, funding, and career advancement to protect researchers who use GAI tools in pursuit of increasing the quality and transparency of their research, not only the quantity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,475,786,492]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data availability statement \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,506,915,548]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,574,729,590]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Author contributions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,606,915,733]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"SY: Conceptualization, Investigation, Project administration, Visualization, Writing - original draft, Writing - review & editing. FL: Conceptualization, Investigation, Visualization, Writing - original draft, Writing - review & editing. MBr: Conceptualization, Investigation, Project administration, Writing - original draft, Writing - review & editing. MBA: Conceptualization, Investigation, Writing - review & editing. KZ: Conceptualization, Writing - review & editing. OM: Writing - review & editing. MP: Writing - review & editing. AR: Writing - review & editing. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,759,594,777]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Funding \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,791,915,819]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,845,707,860]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conflict of interest \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,877,915,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,39,137,48]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Yuan et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[761,38,915,49]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10.3389/fpsyg.2024.1295275 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[80,948,210,959]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Frontiers in Psychology \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[490,948,507,958]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"06 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[836,948,915,959]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"frontiersin.org \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[78,93,489,135]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The author(s) declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,161,250,177]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Publisher's note \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,193,489,235]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,261,200,277]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,288,487,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Agathokleous, E., Saitanis, C. J., Fang, C., and Yu, Z. (2023). Use of ChatGPT: What does it mean for biology and environmental science? Sci. Total Environ. 888:164154. doi: 10.1016/j.scitotenv.2023.164154 \\\",\\\"Aguinis, H., and Bradley, K. J. (2014). 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People Nat. 5, 742-757. doi:10.1002/pan3.10454 \\\"]\",\n \"page_idx\": \"6\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[505,93,917,135]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,161,763,179]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Supplementary material \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,193,917,235]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Supplementary material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fpsyg.2024.1295275/full#supplementary-material \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,288,917,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Franck, K. 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Received YYY; in original form ZZZ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,237,151,249]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABSTRACT ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[67,253,922,425]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Matched filters are routinely used in cosmology in order to detect galaxy clusters from mm observations through their thermal Sunyaev-Zeldovich (tSZ) signature. In addition, they naturally provide an observable, the detection signal-to-noise or significance, which can be used as a mass proxy in number counts analyses of tSZ-selected cluster samples. In this work, we show that this observable is, in general, non-Gaussian, and that it suffers from a positive bias, which we refer to as optimisation bias. Both aspects arise from the fact that the signal-to-noise is constructed through an optimisation operation on noisy data, and hold even if the cluster signal is modelled perfectly well, no foregrounds are present, and the noise is Gaussian. After reviewing the general mathematical formalism underlying matched filters, we study the statistics of the signal-to-noise with a set Monte Carlo mock observations, finding it to be well-described by a unit-variance Gaussian for signal-to-noise values of 6 and above, and quantify the magnitude of the optimisation bias, for which we give an approximate expression that may be used in practice. We also consider the impact of the bias on the cluster number counts of Planck and the Simons Observatory (SO), finding it to be negligible for the former and potentially significant for the latter. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[72,434,721,450]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Key words: galaxies: clusters: general – cosmology: observations – cosmology: diffuse radiation ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,497,205,510]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 INTRODUCTION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,519,478,713]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"First proposed in the galaxy cluster context more than two decades ago (Haehnelt & Tegmark 1996; Herranz et al. 2002; Melin et al. 2006), matched filters have become a standard tool with which to detect and characterise galaxy clusters from CMB observations via their thermal Sunyaev-Zeldovich (tSZ) signature. Indeed, matched filters have been used in the construction of the cluster catalogues derived from SPT, ACT, and Planck data (e.g., Vanderlinde et al. 2010; Hasselfield et al. 2013; Planck 2013 results XXIX 2014; Bleem et al. 2015; Planck 2015 results XXVII 2016; Hilton et al. 2021; Melin et al. 2021), and as a result they have also played an important role in the cosmological analyses based on these cluster samples (e.g., Vanderlinde et al. 2010; Hasselfield et al. 2013; Planck 2013 results XX 2014; Bleem et al. 2015; Planck 2015 results XXIV 2016; Bocquet et al. 2019; Zubeldia & Challinor 2019). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,716,478,895]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Matched filters provide a natural quantity, the detection significance or signal-to-noise, that can be used to construct cluster samples by selecting the clusters whose signal-to-noise falls above a certain threshold (e.g., Planck 2015 results XXVII 2016; Hilton et al. 2021). The signal-to-noise can also be employed as a mass proxy in a cluster number counts analysis, in which the cluster abundance across a number of observables (usually, redshift and one or more ‘mass proxies’, that is, observables that scale with cluster mass) is used to constrain cosmology (e.g., Planck 2015 results XXIV 2016; Bocquet et al. 2019; Zubeldia & Challinor 2019; see Allen et al. 2011 for a review). Essential for the success of such analyses is the accurate determination of the mass–observable(s) scaling relation(s), which allows to link the predicted cluster abundance across mass and redshift, as given by the halo mass function, to the observed abundance. At present, this constitutes the main source of systematic uncertainty in cluster number counts analyses, and, as such, a lot of effort is being devoted to the calibration of mass–observable relations (e.g., Nicola et al. 2020; Zubeldia & Challinor 2020; Andrade-Santos et al. 2021; see Pratt et al. 2019 for a review). Any significant biases in any of the mass–observable relation could lead to biased cosmological constraints. Thus, if the matched filter signal-to-noise is to be used as a mass observable in a number counts analysis, its relation to cluster mass and redshift must be well understood. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,497,921,635]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,641,921,864]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Relating the cluster mass and redshift to the observed signal-tonoise is usually thought of as a two-step process (see, e.g., Planck 2015 results XXIV 2016 and Bocquet et al. 2019). First, the cluster mass and redshift are related to some mean signal-to-noise via a set of scaling relations, which after the addition of some ‘intrinsic scatter’ (due to cluster triaxiality, deviations from the mean profile, etc.) one obtains the ‘true’ signal-to-noise of a cluster, i.e., the signalto-noise that would be measured after ensemble averaging over what is understood as noise in the matched filtering process. Then, a layer of additive ‘noise’ or ‘observational scatter’ connects the true signalto-noise with the observed one. This observational scatter is typically assumed to be Gaussian-distributed and to have a standard deviation equal to unity and a mean equal to either the true-signal-to-noise (Planck and ACT; see, e.g., Hasselfield et al. 2013; Planck 2015 results XXIV 2016) or a corrected version of it (SPT; see, e.g., Bocquet et al. 2019). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,870,921,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this work we focus on this second layer of the scatter, which is comparatively much less studied than the intrinsic scatter. In order to do this, we first review the matched filter formalism, deriving the matched filter using a maximum-likelihood approach. We show that, as opposed to what is typically assumed, the observational scatter is, in general, non-Gaussian. We also show that the observed signal-to-noise is, in general, biased high with respect to the true signal-to-noise. Both the non-Gaussianity and the bias are a result of the signal-to-noise being obtained through an optimisation process on noisy data. As a consequence, they hold even if the signal is modelled perfectly, no foregrounds are present, and the noise in the data is Gaussian, which is indeed the case we consider. After presenting these theoretical considerations, we then use a set of Monte Carlo (MC) mock observations in order to quantify the non-Gaussianity of the observational scatter, its variance, and the magnitude of the optimisation bias. We find that for signal-to-noise values of $\\gtrsim 6$ , the scatter can taken to be approximately Gaussian and with a variance equal to unity. We also find that, for a similar signal-to-noise range, the optimisation bias can be described accurately with a simple approximate expression. This expression is the same as the correction used in the SPT analyses (Bocquet et al. 2019), which was originally introduced in Vanderlinde et al. (2010) and justified with a rather heuristic argument. Here, we provide further insight into its origin and a more detailed study of its validity in the Gaussian noise regime. Finally, we quantify the impact of the optimisation bias in the cluster number counts of Planck and the Simons Observatory (SO; Simons Observatory Collaboration 2019), finding it to be negligible for the former and potentially significant for the latter. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,928,309,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"★ E-mail: inigo.zubeldia@manchester.ac.uk ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[673,39,922,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Compiled using MNRAS LATEX style file v3.0 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,38,215,49]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MNRAS 000, 1–13 (2015) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,955,181,966]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$©$ 2015 The Authors ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[478,38,591,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Preprint 8 June 2021 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[26,244,62,732]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"arXiv:2106.03718v1 [astro-ph.CO] 7 Jun 2021 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,67,480,390]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,391,478,613]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This paper is organised as follows. In Section 2 we review the matched filter formalism, deriving the matched filter from a maximum likelihood point of view (Section 2.1) and noting the biases that arise from this process, both in the retrieved parameter estimates (Section 2.2) and in the signal-to-noise (the ‘optimisation bias’; Sections 2.3 and 2.4). Then, after a brief review of how matched filters are used in practice in the tSZ context (Section 3.1), in Section 3.2 we use a set of MC mock observations in order to study the statistics of the observational scatter of the signal-to-noise, quantifying its departure from Gaussianity, its variance, and its mean (the latter as quantified through the optimisation bias). We also comment briefly on other possible biases in the signal-to-noise, such as that arising from estimating the noise covariance from the data in a naive way (Section 3.3). Next, in Section 3.4 we consider the impact of the optimisation bias on the cluster number counts of Planck and SO, and finally conclude in Section 4. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[67,639,462,653]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 MATCHED FILTERING: A LIKELIHOOD APPROACH ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,662,433,676]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.1 Matched filtering as maximum likelihood estimation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,684,478,767]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Consider a data vector $\\mathbf { \\Delta } \\mathbf { d }$ . This can be, e.g., a map of the Compton-$y$ parameter, a map of the lensing convergence, or a set of intensity maps across several frequencies. In the first two cases, the data vector dimension is equal to the number of pixels, $n$ , whereas in the third it is equal to the number of pixels times the number of frequency channels. Let us assume that this data vector can be written as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[223,790,322,805]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0225/24be079ad03a077dc789ebacb1d4465a8934154440154f8cd5d7c0658bdfefa2.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\pmb { d } = s _ { 0 } \\pmb { s } ( \\pmb { \\theta } ) + \\pmb { n } .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[68,813,478,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Here, $s _ { 0 } \\pmb { s } ( \\pmb \\theta )$ is the signal that is present in the data (e.g., the Compton-$y$ signal due to a galaxy cluster), which we assume that can be written as an amplitude, or normalisation, parameter $s _ { 0 }$ times a template function $\\pmb { s } ( \\pmb { \\theta } )$ , which depends upon a number of $f$ additional parameters $\\pmb \\theta$ . This set of parameters can include, for example, a size parameter (e.g., $\\theta _ { 5 0 0 }$ for a galaxy cluster), as well as location parameters specifying the position of the peak of the signal in the map. In addition, our data vector has some additive noise, $\\pmb { n }$ , which we will assume to be Gaussian distributed and with zero mean. In practice, this noise term needs not be instrumental noise alone: it can also include the signal from one, or several, foregrounds, as long as it is Gaussian distributed and has zero mean. The logarithm of the likelihood (hereafter, the log-likelihood) of our data can then be written as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,67,922,136]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[563,153,867,213]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0453/543153ed692abd38877db3ede5117e35353f16c8682b920778c5455fa0b29168.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array} { c } { \\displaystyle \\ln \\mathcal { L } ( s _ { 0 } , \\theta ) = - \\frac { 1 } { 2 } \\left[ d - s _ { 0 } s ( \\theta ) \\right] ^ { T } \\mathbf { C } ^ { - 1 } [ d - s _ { 0 } s ( \\theta ) ] } \\\\ { \\displaystyle - \\frac { 1 } { 2 } \\ln \\left[ ( 2 \\pi ) ^ { n } \\mathrm { d e t } ( \\mathbf { C } ) \\right] , } \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[510,216,922,257]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where C is the noise covariance, which we assume to be known. The second term of this likelihood is independent from the parameters, and so we will ignore it in the following. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,259,921,300]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let us now consider the set of parameter values that maximises the log-likelihood, $\\big \\{ \\hat { s } _ { 0 } , \\hat { \\pmb \\theta } \\big \\}$ . We first optimise the log-likelihood with respect to $s _ { 0 }$ . Imposing $\\partial \\ln \\mathcal { L } / \\partial s _ { 0 } = 0$ yields ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[640,317,791,351]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0805/36e6c3bf567dc65ad082a548741f45b8b427458ac4df4aeb003d6307d955dce1.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\hat { s } _ { 0 } ( \\pmb { \\theta } ) = \\frac { s ( \\pmb { \\theta } ) ^ { T } \\pmb { \\mathsf { c } } ^ { - 1 } \\pmb { d } } { s ( \\pmb { \\theta } ) ^ { T } \\pmb { \\mathsf { c } } ^ { - 1 } s ( \\pmb { \\theta } ) } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,356,922,383]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"which is the well-known matched filter estimate of $s _ { 0 }$ at a given value of $\\pmb \\theta$ , and which has an associated standard deviation $\\sigma _ { s _ { 0 } }$ given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[616,400,816,429]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0370/9959fce8aec22509139599df61f5dbed997310c7867f3c23493ce0879e03a7df.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\boldsymbol { \\sigma } _ { s _ { 0 } } ( \\pmb { \\theta } ) = \\left[ s ( \\pmb { \\theta } ) ^ { T } \\mathbb { c } ^ { - 1 } s ( \\pmb { \\theta } ) \\right] ^ { - 1 / 2 } .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[510,433,889,447]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We can then define the signal-to-noise ratio of the detection as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[594,464,836,503]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0058/2bc36d6395615e8d0f77447b2b933441351564814cebd45c407c262f8ea20dd7.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nq ( \\pmb \\theta ) \\equiv \\frac { \\hat { s } _ { 0 } ( \\pmb \\theta ) } { \\sigma _ { s _ { 0 } } ( \\pmb \\theta ) } = \\frac { \\pmb { s } ( \\pmb \\theta ) ^ { T } \\pmb \\subset ^ { - 1 } \\pmb d } { \\left[ \\pmb { s } ( \\pmb \\theta ) ^ { T } \\pmb { \\mathbb C } ^ { - 1 } \\pmb { s } ( \\pmb \\theta ) \\right] ^ { 1 / 2 } } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[510,508,910,521]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where we have stressed its dependence on $\\pmb \\theta$ by leaving it explicit. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,524,922,549]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"By substituting the expression for $\\hat { s } _ { 0 }$ of Eq. (3) into Eq. (2), the log-likelihood can be rewritten as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[611,566,820,595]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0892/4634b07a8d36645ef7084a1a2ffef6969a0587ba609e64601badaa534b3f3a5b.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\ln \\mathcal { L } ( \\pmb { \\theta } ) = - \\frac { 1 } { 2 } \\pmb { d } ^ { T } \\mathbf { C } ^ { - 1 } \\pmb { d } + \\frac { 1 } { 2 } \\pmb { q } ( \\pmb { \\theta } ) ^ { 2 } .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[510,599,922,712]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We note that the likelihood no longer depends on $s _ { 0 }$ , as this parameter has already been maximised over, and we recall that we have dropped the second, parameter-independent term. From Eq. (6) it follows that the set of parameter values $\\pmb \\theta$ that maximises the loglikelihood is equal to that which maximises the signal-to-noise $q$ . That is, the maximum likelihood solution is equal to the value of $\\pmb \\theta$ that maximises the matched filter signal-to-noise, along with the corresponding matched filter amplitude estimate, $\\hat { s } _ { 0 } ( \\hat { \\pmb { \\theta } } )$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,712,922,809]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"When matched filters are used in practice, it is customary to maximise the signal-to-noise with respect to $\\pmb \\theta$ (e.g., Melin et al. 2006). Here, we have shown that this matched filter solution is equal to the maximum likelihood solution. In brief, matched filtering with signal-to-noise maximisation can be understood as maximum likelihood estimation for a Gaussian likelihood and a model which can be written as an amplitude parameter times a template function. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,833,715,847]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.2 Matched filter solution bias ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,855,922,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"By identifying the matched filter solution with the maximum likelihood solution, $\\left\\{ \\hat { s } _ { 0 } , \\hat { \\pmb \\theta } \\right\\}$ , it follows that the matched filter estimates of $s _ { 0 }$ and $\\pmb \\theta$ are, in general, biased, as they are in general maximum likelihood estimators. We thus warn against using matched filter solutions without proper consideration of this bias. As we illustrate numerically in Section 3.2.5, the magnitude of the bias typically decreases with the signal-to-noise, being arbitrarily small for arbitrarily large values of signal-to-noise (i.e., for arbitrarily low noise). Care should be taken, however, when conducting inference from the combination of the matched filter solutions of a set of different observations, i.e., a set of $m$ data vectors $\\pmb { d }$ . In this case, the overall signal-to-noise, which will set the precision of the inference, will be larger than the signal-to-noise of the individual measurements, increasing as $\\sqrt { m }$ , but the bias will not decrease accordingly. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,955,215,966]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MNRAS 000, 1–13 (2015) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,34,242,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 Í. Zubeldia et al. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,67,480,180]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,180,478,333]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We also note that the bias is parametrisation-dependent. As an illustration, consider, for example, that $\\pmb \\theta$ includes two location parameters, $\\theta _ { x }$ and $\\theta _ { \\mathrm { y } }$ , which specify the Cartesian coordinates of the peak of the signal. By symmetry, their matched filter solution, ${ \\hat { \\theta } } _ { X }$ and $\\hat { \\theta } _ { y }$ , cannot be biased, i.e., $\\left. { \\hat { \\theta } } _ { x } \\right. = \\theta _ { x } ^ { \\mathrm { { t r u e } } }$ and $\\left. \\hat { \\theta } _ { y } \\right. = \\theta _ { y } ^ { \\mathrm { t r u e } }$ , where angular brackets denote ensemble averaging over noise realisations. Consider now an alternative and fully equivalent parametrisation, $\\theta = ( \\theta _ { x } ^ { 2 } + \\theta _ { y } ^ { 2 } ) ^ { 1 / 2 }$ and $\\phi = \\tan ^ { - 1 } ( \\theta _ { y } / \\theta _ { x } )$ . It should be apparent that the matched filter solution for $\\theta$ is biased, as its expected value receives contributions from the second-order moments of ${ \\hat { \\theta } } _ { x }$ and $\\hat { \\theta } _ { y }$ . We illustrate this point numerically in Section 3.2.5. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,369,341,383]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.3 Using the optimal $q$ : optimisation bias ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,391,478,586]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In some applications of matched filtering (e.g., galaxy cluster detection in tSZ surveys, see Section 3), the main quantity of interest is the signal-to-noise ratio, $q$ , and, more specifically, its maximum value, that is, the value that it takes at the maximum likelihood solution, $q ( { \\hat { \\pmb { \\theta } } } )$ . We refer to this quantity as the ‘optimal signal-to-noise’ and denote it with $q _ { \\mathrm { o p t } }$ . In order to be able to infer information from a measured value of $q _ { \\mathrm { o p t } }$ , one needs to be able to relate this quantity to the true mean signal-to-noise ratio, which is given by ensemble-averaging Eq. (5) over noise realisations at the true parameter values, and which we denote with $\\bar { q } _ { \\mathrm { t } }$ . That is, one needs to determine $P ( q _ { \\mathrm { o p t } } | \\bar { q } _ { \\mathrm { t } } )$ . This is usually known as ‘observational scatter’ or ‘noise’ (e.g., Zubeldia $\\&$ Challinor 2019), as opposed to the intrinsic scatter due to triaxiality, inhomogeneities, etc., which we ignore in this work. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[67,588,478,643]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For a given noise realisation $\\pmb { n }$ , $P ( q _ { \\mathrm { o p t } } | \\bar { q } _ { \\mathrm { t } } , \\pmb { n } )$ is a $\\delta$ function centred at $q ( \\widehat { \\pmb { \\theta } } ( \\pmb { \\theta } _ { \\mathrm { t } } , \\pmb { n } ) , \\pmb { n } )$ , where we have written explicitly the dependence of the matched filter solution $\\hat { \\pmb { \\theta } }$ on the true parameter values and on the noise. Hence, we can write ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[115,663,431,693]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0385/79450176c5369dd0b47a661d0cf4fde2e79515fc5d3ad8e501f19c6f2b062624.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP ( q _ { \\mathrm { o p t } } | \\bar { q } _ { \\mathrm { t } } ) = \\int \\delta \\left[ q _ { \\mathrm { o p t } } - q ( \\hat { \\pmb \\theta } ( \\pmb \\theta _ { \\mathrm { t } } , \\pmb n ) , \\pmb n ) \\right] P ( \\pmb n ) d ^ { n } \\pmb { n } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[68,700,480,813]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $P ( \\pmb { n } )$ is the noise probability density function, which, if the noise is Gaussian, as we assume, is a multi-variate Gaussian. This is, in general, a non-Gaussian distribution, reflecting the fact that optimisation is a non-linear operation. Intuitively, to the Gaussian variation due to the noise one should add the variation due to evaluating Eq. (5) at different values of $\\pmb \\theta$ (for each measurement, its matched filter solution $\\hat { \\pmb { \\theta } }$ ). The $m$ -th moment of this distribution can be written as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[164,832,383,863]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0959/84a65218cde5406e04b3cd6e91206f6ee644636c4bf6dac159e71f44407ef92a.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\langle q _ { \\mathrm { o p t } } ^ { m } \\rangle = \\int q ( \\hat { \\pmb { \\theta } } ( \\pmb { \\theta } _ { \\mathrm { t } } , \\pmb { n } ) ) ^ { m } P ( \\pmb { n } ) d ^ { n } \\pmb { n } .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[68,869,480,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This is a set of high-dimensional integrals which are difficult to compute in practice. However, their values can be estimated in a fast way with Monte Carlo (MC) simulations, as we do in Section 3 for $m = 1 , \\ldots , 4$ in the context of galaxy cluster tSZ observations. Nevertheless, further insight into the value of the first moment, the mean, which we denote with $\\bar { q } _ { \\mathrm { o p t } }$ , can be gained with the following argument. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,67,922,95]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,95,922,194]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Consider the value of $- 2 \\ln \\mathcal { L }$ , i.e., of the sum of the residuals. If we evaluate it at the true value of $\\theta , \\theta _ { \\mathrm { t } }$ , and at the corresponding matched filter value of $s _ { 0 }$ , $\\hat { s } _ { 0 } ( \\pmb { \\theta } _ { \\mathrm { t } } )$ , there is only one fitting parameter, $s _ { 0 }$ , the model being linear in it. Thus, in this case $- 2 \\ln \\mathcal { L }$ is $\\chi ^ { 2 }$ - distributed with $n - 1$ degrees of freedom, where we recall that $n$ is the dimension of our data vector (e.g., Andrae et al. 2010). Using Eq. (6), its expected value can be written as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[546,212,884,231]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0574/a247350353679814a2f15fc398ed3086e638eb692bfbe1e6dfba45b9bbca9316.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array} { r } { \\langle - 2 \\ln \\mathcal { L } ( \\hat { s } _ { 0 } ( \\theta _ { \\mathrm { t } } ) , \\theta _ { \\mathrm { t } } ) \\rangle = t ^ { T } { \\bf C } ^ { - 1 } t + n - \\langle q ( \\theta _ { \\mathrm { t } } ) ^ { 2 } \\rangle = n - 1 , } \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,237,921,294]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $t$ it the true signal (i.e., the model evaluated at the true parameter values), and where we have ignored the second, parameterindependent term. Since $\\left. q ( \\pmb { \\theta } _ { \\mathrm { t } } ) \\right. = \\bar { q } _ { \\mathrm { t } }$ , and since $q ( \\pmb \\theta _ { \\mathrm { t } } )$ has unit variance, it follows that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[623,313,805,331]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0066/42643de0547e0cb887f8abf7825957332a741b6a8b5ac2c8736dd6e1696bd925.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nt ^ { T } { \\bf C } ^ { - 1 } t + n - 1 - \\bar { q } _ { \\mathrm { t } } ^ { 2 } = n - 1 .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[510,337,922,492]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"On the other hand, $- 2 \\ln \\mathcal { L }$ is not $\\chi ^ { 2 }$ -distributed if we evaluate it for the matched filter solution, in which $f$ additional parameters are fitted, as now the model is, in general, non-linear in the parameters (see, e.g., Andrae et al. 2010). Equivalently, this can be seen as a consequence of $q _ { \\mathrm { o p t } }$ being non-Gaussian. This means, in particular, that we cannot compute its expected value by invoking the number of degrees of freedom in the fit, as we did in the previous case. However, this is still a well-defined quantity, which we write as $n - 1 - f _ { \\mathrm { e f f } }$ , where we have introduced $f _ { \\mathrm { e f f } }$ as the ‘effective number of additional fitting parameters’. The value of $f _ { \\mathrm { e f f } }$ cannot be determined a priori, but it is clear that $f _ { \\mathrm { e f f } } \\geq 0$ . We can now write ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[526,511,880,531]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0478/26668c7e77bd1fe077007c7c4756d409155008a4e2eefebcb55f5f97853afbaf.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left. - 2 \\ln \\mathcal { L } ( \\hat { s } _ { 0 } ( \\hat { \\pmb { \\theta } } ) , \\hat { \\pmb { \\theta } } ) \\right. = { t } ^ { T } { \\bf C } ^ { - 1 } { \\pmb { t } } + n - \\langle q _ { \\mathrm { o p t } } ^ { 2 } \\rangle = n - 1 - f _ { \\mathrm { e f f } } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[510,538,552,549]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and so ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[591,570,836,589]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0772/ddd7bb1c4ae8024743c3dd164a1a28b6da62038717c01b5624bb40912a7fb3d2.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nt ^ { T } \\mathsf { C } ^ { - 1 } t + n - \\sigma _ { \\mathrm { o p t } } ^ { 2 } - \\bar { q } _ { \\mathrm { o p t } } ^ { 2 } = n - 1 - f _ { \\mathrm { e f f } } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,594,922,636]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\sigma _ { \\mathrm { o p t } }$ denotes the standard deviation of $q _ { \\mathrm { o p t } }$ , which need not be equal to unity, as in the Gaussian case. Subtracting Eq. (10) from Eq. (12) and rearranging, we find ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[636,654,794,679]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0886/a066c40fc6dfb338895a3912282e955f56d8333b8b12ab57485609496e90b9e4.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\bar { q } _ { \\mathrm { o p t } } = \\sqrt { \\bar { q } _ { \\mathrm { t } } ^ { 2 } + f _ { \\mathrm { e f f } } + \\Delta \\sigma ^ { 2 } } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[510,686,652,702]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\Delta \\sigma ^ { 2 } \\equiv 1 - \\sigma _ { \\mathrm { o p t } } ^ { 2 }$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,703,922,799]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Thus, $\\bar { q } _ { \\mathrm { o p t } }$ is biased with respect to ${ \\bar { q } } _ { \\mathfrak { t } }$ . We refer to this bias as optimisation bias, and note that it is a positive bias, with $\\bar { q } _ { \\mathrm { o p t } } > \\bar { q } _ { \\mathrm { t } }$ . This can in fact be deduced from a simple argument: for any noise realisation, $q _ { \\mathrm { o p t } } > q ( \\pmb \\theta _ { \\mathrm { t } } )$ by construction (except in the case in which $\\widehat { \\pmb { \\theta } } = \\pmb { \\theta } _ { 1 }$ , which happens with formally zero probability), and thus $\\bar { q } _ { \\mathrm { o p t } } > \\bar { q } _ { \\mathrm { t } }$ . Intuitively: by allowing for additional freedom in the fit, the signal-to-noise is boosted, as one is effectively fitting noise. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,800,922,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In summary, $P ( q _ { \\mathrm { o p t } } | \\bar { q } _ { \\mathrm { t } } )$ is a non-Gaussian distribution with moments given by Eq. (8) and whose mean can be also written as in Eq. (13). In order for a set of $q _ { \\mathrm { o p t } }$ measurements to be used in practice, one has to determine how much $P ( q _ { \\mathrm { o p t } } | \\bar { q } _ { \\mathrm { t } } )$ deviates from Gaussianity, as well as the values of $f _ { \\mathrm { e f f } }$ and $\\sigma _ { \\mathrm { o p t } }$ , both of which can be a function of $\\bar { q } _ { \\mathrm { t } }$ . In Section 3 we do so using MC simulations for the case in which the signal to be extracted is the tSZ signal from a galaxy cluster, finding that, for sufficiently large values of $\\bar { q } _ { \\mathrm { t } }$ $( \\simeq 6 )$ , $P ( q _ { \\mathrm { o p t } } | \\bar { q } _ { \\mathrm { t } } )$ approaches a unit-variance Gaussian and $f _ { \\mathrm { e f f } }$ approaches the actual number of additional fitting parameters, $f$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[561,35,921,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Matched filters for precision cosmology 3 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[776,955,921,966]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MNRAS 000, 1–13 (2015) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,67,225,81]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.4 Partial optimisation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[70,89,478,299]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Thus far we have assumed that the optimisation procedure finds the true signal-to-noise maximum, i.e., that the true maximum likelihood solution is obtained. In some applications of matched filtering, however, the signal-to-noise is evaluated on a given parameter grid, with the ‘matched filter solution’ and its associated signal-to-noise, $q _ { \\mathrm { o p t } }$ , now being the grid coordinates at which the signal-to-noise is maximised and the corresponding signal-to-noise value, respectively. As we will see in Section 3, this partial optimisation can have an impact on the statistics of $q _ { \\mathrm { o p t } }$ . In general, a dependency on the grid chosen is introduced, with the statistics of the partially-optimised $q _ { \\mathrm { o p t } }$ being obviously expected to approach those of the true $q _ { \\mathrm { o p t } }$ as the grid spacing is decreased. As we illustrate in Section 3, the impact of this partial optimisation must be carefully considered if unbiased information is to be extracted from partially-optimised $q _ { \\mathrm { o p t } }$ measurements. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,335,465,361]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 A PRACTICAL APPLICATION: SZ GALAXY CLUSTER DETECTION AND NUMBER COUNTS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[67,370,391,384]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1 Matched filtering in the galaxy cluster context ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,393,480,742]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As noted in the Introduction, matched filters are now routinely used in order to detect and characterise galaxy clusters from mm data. They have indeed been used in experiments such as SPT, ACT, and Planck (Vanderlinde et al. 2010; Hasselfield et al. 2013; Planck 2013 results XXIX 2014; Bleem et al. 2015; Planck 2015 results XXVII 2016; Hilton et al. 2021; Melin et al. 2021), and will also continue to be used in upcoming experiments such as SO and CMB-S4 (Abazajian et al. 2016; Simons Observatory Collaboration 2019). In these works, galaxy clusters are detected following, roughly, the same general procedure. First, the cluster search sky area is divided into a set of patches, which allows for local noise estimation. Then, a model for the cluster tSZ signal is assumed. This model is parametrised as our signal in Eq. (1), with an overall amplitude parameter and a template function, which is typically taken to depend on two sky location parameters and on an angular size parameter. For each of the patches, this template is used to construct a matched filter, for which the signal-to-noise (in our notation, $q$ ) is evaluated across a number of sky locations (usually, for each pixel) and angular sizes. We note that if observations at more than one frequency channel are used, the matched filter operates across the maps at the different frequencies considered, and is usually referred to as a multifrequency matched filter (MMF). If we put the frequency and spatial indices on the same footing, however, an MMF can be seen as a ‘singlefrequency’ matched filter, which means that the formalism and the insights presented in Section 2 remain entirely valid. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,744,478,938]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For each patch, the sky locations of the cluster candidates in it are then obtained from the local peaks in the signal-to-noise map, with the specific procedure varying from analysis to analysis, but being in essence a maximisation of the signal-to-noise over sky location (a ‘partial’ maximisation, however; see Section 2.4). The characterisation of the cluster signal, nonetheless, depends more significantly on the analysis considered. In Planck and SPT, the signal-to-noise (partially) maximised over sky location and angular size is used $\\scriptstyle \\mathbf { \\bar { \\varphi } } _ { q _ { 0 } { \\mathrm { p t } } }$ in our notation; e.g., Vanderlinde et al. 2010; Planck 2013 results XXIX 2014). In ACT, on the other hand, the signal-to-noise is maximised only to assign a sky location, the matched filter being only used at a single fixed angular size, at which the signal amplitude ( $\\hat { s } _ { 0 }$ in our notation) is computed and used as the cluster observable. In the likelihood, however, this $\\hat { s } _ { 0 }$ measurement has as associated standard deviation the corresponding matched filter standard deviation (given by Eq. 4), so using $\\hat { s } _ { 0 }$ at a fixed angular scale as an observable is equivalent to using the corresponding $q$ measurement. There is an obvious loss of statistical power due to fixing the angular scale, but, as argued in Hasselfield et al. (2013) and Hilton et al. (2021), doing this should partially mitigate against what we understand is the optimisation bias. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,67,921,164]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,166,921,491]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In short, as the cluster tSZ observable, SPT and Planck use $q _ { \\mathrm { o p t } }$ with (partial) optimisation over sky location and angular size, whereas ACT effectively uses $q _ { \\mathrm { o p t } }$ with only (partial) optimisation over sky location, fixing the angular size to a fiducial value. In the associated cosmological analyses, these tSZ observables are modelled differently. All three sets of analyses assume that $q _ { \\mathrm { o p t } }$ follows a unit-variance Gaussian distribution. The mean it is assigned, however, differs from analysis to analysis. The SPT cluster number counts analyses (Vanderlinde et al. 2010; Bleem et al. 2015; Bocquet et al. 2019) account for the optimisation bias at the likelihood level, using as the expected value of $q _ { \\mathrm { o p t } }$ (their ‘biased significance’, $\\xi ,$ ) $\\bar { q } _ { \\mathrm { o p t } } = ( \\bar { q } _ { \\mathrm { t } } ^ { 2 } + 3 ) ^ { 1 / 2 }$ . This corresponds to our formula for $\\bar { q } _ { \\mathrm { o p t } }$ , given in Eq. (13), if we set $\\Delta \\sigma ^ { 2 } = 0$ and $f _ { \\mathrm { e f f } } = f$ ; a rather heuristic justification for this prescription is given in Vanderlinde et al. (2010). The Planck cluster number counts analyses (Planck 2013 results XX 2014; Planck 2015 results XXIV 2016), despite using $q _ { \\mathrm { o p t } }$ as an observable, do not account for the optimisation bias at all, as neither does the reanalysis with CMB lensing mass calibration of Zubeldia & Challinor (2019). Finally, the ACT analysis (Hasselfield et al. 2013), which uses $q _ { \\mathrm { o p t } }$ at a fixed angular scale in order to mitigate against the optimisation bias, does not account for optimisation over sky location, which means that in principle it suffers from the bias, although from a somewhat smaller one. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,492,921,617]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Thanks to the insights gained in Section 2, it should be clear that if the signal-to-noise is maximised over some set of parameters, the consequences of doing so (non-Gaussianity, standard deviation different from unity, and optimisation bias) should be carefully quantified and, if deemed non-negligible, properly accounted for. As an illustration of how this can be done, as well as of the general theoretical arguments presented in Section 2, in the next section we quantify these effects for an idealised SZ experiment using a set of MC mock observations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,664,890,679]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2 Quantifying the statistics of $q _ { \\mathrm { o p t } }$ with MC observations ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,686,690,699]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2.1 Production of MC data ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,708,921,890]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this section, we quantify the statistics of $q _ { \\mathrm { o p t } }$ for a set of idealised tSZ observations produced with MC simulations. As our signal we take the Compton- $y$ map due to a set of galaxy clusters of some given masses $M _ { 5 0 0 }$ (defined, as customary, as the mass within $R _ { 5 0 0 }$ the radius within which the mean enclosed density is 500 times the critical density at the cluster’s redshift) and at some redshift $z$ . We take our clusters to be at $z = 0 . 3$ and consider a set of 16 masses such that the mean signal-to-noise $\\bar { q } _ { \\mathrm { t } }$ , as given by Eq. (5) after ensemble averaging over noise realisations, is logarithmically spaced between $\\bar { q } _ { \\mathrm { t } } = 3$ and $\\bar { q } _ { \\mathrm { t } } = 3 0$ (see our assumed experimental specifications below). We assume that our clusters have the pressure profile of Arnaud et al. (2010) (used, e.g., in the Planck analyses), from which the Compton- $y$ signal at a given sky location can be computed, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[657,911,773,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0767/a4f0669dd3b9ac500e469f2a746c51907f182a1370d7e3046f215738f3618cbd.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\ny = \\frac { \\sigma _ { \\mathrm { T } } } { m _ { \\mathrm { e } } c ^ { 2 } } \\int P d l ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[68,955,215,966]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MNRAS 000, 1–13 (2015) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,34,242,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 Í. Zubeldia et al. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,67,478,136]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $P$ is the cluster electron pressure, $\\sigma _ { \\mathrm { T } }$ is the electron Thomson scattering cross-section, $m _ { \\mathrm { e } }$ is the electron mass, and $d l$ is the proper distance element along the line of sight. Following the Planck analyses, we fix the concentration to $c = 1 . 1 7 7$ (e.g., Planck 2013 results $\\mathrm { X X } 2 0 1 4 )$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,139,478,299]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Adopting this cluster model, our signal vector $s _ { 0 } \\pmb { s }$ is the cluster Compton- $y$ parameter map, as given by Eq. (14), convolved with a Gaussian beam with a FWHM of 5 arcmin and evaluated on a square map of $1 2 8 \\times 1 2 8$ pixels. We use a pixel size of 1.7 arcmin and place the cluster at the centre of the map. We then add Gaussian white noise with a standard deviation per pixel of $\\sigma _ { \\mathrm { p i x e l } } = 8 . 8 3 \\times 1 0 ^ { - 7 }$ , which corresponds to a noise level of $\\sigma _ { n } = 1 . 5 \\times 1 0 ^ { - 6 }$ arcmin. That is, our noise covariance matrix C is diagonal, with all diagonal elements equal to ??2pixel. This procedure generates a simulated data vector ?? within the formalism of Section 2. We generate $1 0 ^ { 5 }$ such mock data vectors for each of our 16 values of $\\bar { q } _ { \\mathfrak { t } }$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,300,480,732]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We then use our signal, $s _ { 0 } \\pmb { s }$ , in order to construct a matched filter template, $\\pmb { s }$ , using as the amplitude (or normalisation) parameter $s _ { 0 }$ the value of the signal at $R _ { 5 0 0 }$ . We regard this template as a function of three parameters $\\pmb \\theta$ : the cluster angular size, $\\theta _ { 5 0 0 }$ , defined as $R _ { 5 0 0 } / d _ { A }$ , where $d _ { A }$ is the angular diameter distance to the cluster, and the two angular coordinates of its centre with respect to the centre of the map (i.e., with respect to the true cluster centre), $\\theta _ { x }$ and $\\theta _ { y }$ . That is, within the theoretical framework of Section 2, the number of additional fitting parameters (or ‘template parameters’) is $f = 3$ . Throughout this section we assume the noise covariance to be known; in Section 3.3, however, we consider the impact of noise covariance estimation. Using the matched filter constructed this way, for each of our mock data vectors we make a signal-to-noise measurement at the true parameter values $( \\theta _ { 5 0 0 } = \\theta _ { 5 0 0 } ^ { \\mathrm { t r u e } }$ and $\\theta _ { x } = \\theta _ { y } = 0 \\mathrm { \\Omega }$ ), $q _ { \\mathrm { t } }$ , an optimal signal-to-noise $q _ { \\mathrm { o p t } }$ , obtained by maximising the signal-to-noise over the three template parameters, and a partially-optimal signal-to-noise $q _ { \\mathrm { p - o p t } }$ , obtained by evaluating the signal-to-noise on a parameter grid and picking the maximum value. For this last set of measurements we use the parameter grid spanned by 80 values of $\\theta _ { 5 0 0 }$ logarithmically spaced between $\\theta _ { 5 0 0 } = 0 . 9 4$ arcmin and $\\theta _ { 5 0 0 } = 1 0 1 . 5 7$ arcmin and the angular coordinates of the centres of each pixel. This procedure generates a set of $q _ { \\mathrm { t } }$ , $q _ { \\mathrm { o p t } }$ and $q _ { \\mathrm { p - o p t } }$ mock measurements generated according to the formalism of Section 2. For each data vector we also compute $- 2 \\ln \\mathcal { L }$ for four different cases: (i) at the true value of the template parameters $\\pmb \\theta$ and of the amplitude parameter $s _ { 0 }$ , i.e., for the true model (the ‘true case’), (ii) at the true value of $\\pmb \\theta$ and the matched filter estimate of $s _ { 0 }$ at that value of $\\pmb \\theta$ , $\\hat { s } _ { 0 } ( \\pmb { \\theta } ^ { \\mathrm { t r u e } } )$ (the ‘fixed case’), (iii) at the matched filter solution for $\\theta , \\hat { \\pmb \\theta }$ , and its corresponding matched filter estimate of $s _ { 0 }$ , $\\hat { s } _ { 0 } ( \\hat { \\pmb { \\theta } } )$ (the ‘optimal case’), and (iv), at the partially-optimised parameter values and the corresponding matched filter estimate (the ‘partially optimal’ case). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,734,478,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We note that our setup may not seem equivalent to what is usually done in practice in order to detect and characterise galaxy clusters in mm surveys, which is to use multi-frequency matched filters (MMF) that operate directly on the experiment frequency maps, rather than on an estimated Compton-?? map (e.g., Planck 2013 results XX 2014). In Appendix A, however, we show that if the Compton- $\\boldsymbol { \\cdot } \\boldsymbol { y }$ map is obtained through an Internal Linear Combination (ILC; see, e.g., Delabrouille & Cardoso 2007), these two approaches are mathematically equivalent. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,890,351,904]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2.2 Standard deviation and non-Gaussianity ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,911,478,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We first investigate the standard deviation of $q _ { \\mathrm { o p t } }$ and $q _ { \\mathrm { p - o p t } }$ and the extent of their departure from Gaussianity. Fig. 1 shows the standard deviation $\\sigma _ { q }$ , reduced skewness $\\lambda _ { 3 , q }$ , and reduced kurtosis $\\lambda _ { 4 , q }$ of the distribution of $q _ { \\mathrm { o p t } }$ (orange error bars) and of $q _ { \\mathrm { p - o p t } }$ (red error bars) as a function of true mean signal-to-noise $\\bar { q } _ { \\mathrm { t } }$ , as estimated with our set of mock measurements. We note that the error bars of the estimates of the standard deviation have been increased by a factor of 10 to allow for better visualisation. It can be seen that these three statistics are essentially the same for both $q _ { \\mathrm { o p t } }$ and $q _ { \\mathrm { p - o p t } }$ . Both $q _ { \\mathrm { o p t } }$ and $q _ { \\mathrm { p - o p t } }$ become progressively more Gaussian as ${ \\bar { q } } _ { \\mathfrak { t } }$ is increased, their skewness and kurtosis being driven to zero. In addition, their standard deviation approaches unity with increasing $\\bar { q } _ { \\mathrm { t } }$ . Roughly, for values of $\\bar { q } _ { \\mathrm { t } }$ greater than $\\simeq 6$ , $q _ { \\mathrm { o p t } }$ can be approximately taken to follow a unit-variance Gaussian distribution. For comparison, the standard deviation, skewness, and kurtosis of $q _ { \\mathrm { t } }$ , as estimated from our mock measurements, are also shown. As expected, the standard deviation is consistent with unity throughout, as are the skewness and kurtosis with zero. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[529,120,895,516]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 1. Standard deviation (top panel), reduced skewness (middle panel), and reduced kurtosis (bottom panel) of $q _ { \\\\mathrm { o p t } }$ (orange error bars), $q _ { \\\\mathrm { p - o p t } }$ (red error bars), and $q _ { \\\\mathrm { t } }$ (blue error bars) as a function of true mean signal-to-noise, $\\\\bar { q } _ { \\\\mathrm { t } }$ , as estimated with our set of mock observations. The reference values of $\\\\sigma _ { q } = 1$ , $\\\\lambda _ { 3 , q } = 0$ , $\\\\lambda _ { 4 , q } = 0$ , and $\\\\bar { q } _ { \\\\mathrm { t } } = 6$ are shown as straight lines. We note that the error bars have been increased by a factor of 10 for better visualisation. \"]","image_footnote":"[]","img_path":"images/0193/cc9acfcab1224780019a1514f3d4b0f048590906b0ccc6c605f93f2709ff76b3.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[512,716,922,938]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[561,35,921,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Matched filters for precision cosmology 5 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[776,955,921,966]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MNRAS 000, 1–13 (2015) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,69,470,81]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2.3 Effective number of fitting parameters and optimisation bias ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,85,480,640]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We now quantify, as a function of the mean signal-to-noise, the effective number of additional fitting parameters $f _ { \\mathrm { e f f } }$ associated with optimising the signal-to-noise over our three template parameters. We do so with our measured values of $- 2 \\ln \\mathcal { L }$ . The top panel of Fig. 2 shows the empirical mean of this quantity as a function of $\\bar { q } _ { \\mathrm { t } }$ for the four cases for which we have computed it: the ‘true case’ (green error bars), the ‘fixed case’ (blue error bars), the optimal case (orange error bars), and the partially optimal case (red error bars). For the true case, for which $- 2 \\ln \\mathcal { L }$ is $\\chi ^ { 2 }$ -distributed with $n$ degrees of freedom, where $n$ is the number of data points, the estimated mean is consistent with $1 6 3 8 4 = 1 2 8 ^ { 2 }$ throughout, as expected. Similarly, for the fixed case, for which $- 2 \\ln \\mathcal { L }$ is also $\\chi ^ { 2 }$ -distributed, though with $n - 1$ degrees of freedom, the estimated mean is consistent with $1 2 8 ^ { 2 } - 1$ , also as expected. However, for the optimal and partially optimal cases, the situation is different, as a result of $- 2 \\ln \\mathcal { L }$ no longer being $\\chi ^ { 2 }$ - distributed. For the optimal case, the estimated mean of $- 2 \\ln \\mathcal { L }$ is consistent with $1 2 8 ^ { 2 } - 4 = 1 6 3 8 0$ for large values of $\\bar { q } _ { \\mathfrak { t } }$ (roughly, for $\\bar { q } _ { \\mathrm { t } } > 6$ ), as it would be naively (and wrongly) expected for three additional fitting parameters, but it drops to lower values for small values of $\\bar { q } _ { \\mathrm { t } }$ : at the low signal-to-noise end, our model ‘fits the data better’ than a linear model would. For the partially optimal case, the estimated mean of $- 2 \\ln \\mathcal { L }$ is consistent with $1 2 8 ^ { 2 } - 2 = 1 6 3 8 0$ for large values of $\\bar { q } _ { \\mathrm { t } }$ , dropping to lower values for smaller values of $\\bar { q } _ { \\mathrm { t } }$ , as in the optimal case. The high signal-to-noise behaviour, indicative of just one additional fitting parameter, can be explained by the fact that, at high signal-to-noise, the true central pixel is almost always chosen in the grid optimisation process, and therefore no overfitting arising from location can take place. Effectively, there is just one additional fitting parameter, the cluster angular size. We note that this is a feature of our true signal being placed in the centre of a pixel, which allows for the possibility of the grid optimisation algorithm matching the sky location perfectly. This will obviously not be the case in a real experimental setting, in which there will always be an offset between the centre of the chosen pixel and the true cluster sky location. This implies that, in a real setting, the fit will be worse, and $- 2 \\ln \\mathcal { L }$ will not converge to $n ^ { 2 } - 2$ , but will take larger values. We note that true optimisation does not suffer from this artefact, which means that our results in that instance are applicable to a real experimental setting in which the cluster may not be centred in the centre of a pixel. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,641,480,754]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the bottom panel of Fig. 2 we rephrase the problem in terms of the effective number of additional fitting parameters, $f _ { \\mathrm { e f f } }$ , where we recall that $\\langle - 2 \\ln \\mathcal { L } \\rangle = n - 1 - f _ { \\mathrm { e f f } }$ . As expected from the top panel, for the fixed case, $f _ { \\mathrm { e f f } }$ is consistent with zero throughout; for the optimal case, $f _ { \\mathrm { e f f } } \\simeq 3$ for large values of $\\bar { q } _ { \\mathrm { t } }$ (roughly, for $\\bar { q } _ { \\mathrm { t } } > 6$ ), progressively taking larger values for smaller values of ${ \\bar { q } } _ { \\mathfrak { t } }$ ; and for the partially optimal case, $f _ { \\mathrm { e f f } } \\simeq 1$ for large values of $\\bar { q } _ { \\mathrm { t } }$ , similarly taking larger values with decreasing $\\bar { q } _ { \\mathrm { t } }$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,757,478,938]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Now that we have determined the standard deviation of $q _ { \\mathrm { o p t } }$ and $f _ { \\mathrm { e f f } }$ as a function of $\\bar { q } _ { \\mathrm { t } }$ , we are in a position to compute $\\bar { q } _ { \\mathrm { o p t } }$ using Eq. (13). We do so by interpolating over our values of $\\sigma _ { q }$ and $f _ { \\mathrm { e f f } }$ . Fig. 3 shows such prediction (shown as $\\bar { q } _ { \\mathrm { o p t } } / \\bar { q } _ { \\mathrm { t } } )$ as a function of ${ \\bar { q } } _ { \\mathfrak { t } }$ (solid orange curve), along with the associated direct estimates of $\\bar { q } _ { \\mathrm { o p t } }$ obtained by ensemble averaging over our $q _ { \\mathrm { o p t } }$ measurements (orange error bars). To illustrate the relative importance of accounting for the deviation form unity in the variance and for the change in $f _ { \\mathrm { e f f } }$ from the ‘naive’ value of $f = 3$ , we also show the curve that is obtained if we ignore the change in the variance and set $f _ { \\mathrm { e f f } } = f = 3$ , which we refer to as the $f$ correction (dotted orange curve), and the one that is obtained if we ignore the change in the variance but use the MC-estimated value of $f _ { \\mathrm { e f f } }$ (dashed orange curve). It can be seen that for, roughly, $\\bar { q } _ { \\mathrm { o p t } } > 6$ , $\\bar { q } _ { \\mathrm { o p t } }$ is essentially given by $\\bar { q } _ { \\mathrm { o p t } } \\simeq ( \\bar { q } _ { \\mathrm { t } } ^ { 2 } + f ) ^ { 1 / 2 }$ , i.e., by the $f$ correction alone. This was to be expected from our MC measurements of $\\sigma _ { q }$ and of $f _ { \\mathrm { e f f } }$ , which we recall converge to 1 and to $f$ , respectively, by $\\bar { q } _ { \\mathrm { o p t } } \\simeq 6$ . This constitutes a remarkable result, as it means that for signal-to-noise values similar to those typically used as selection thresholds in cosmological tSZ catalogues (e.g., in Planck, a threshold of $q _ { \\mathrm { o p t } } = 6$ was chosen), as well as for higher values, $\\bar { q } _ { \\mathrm { o p t } }$ can be computed accurately (e.g., in a likelihood) in a straightforward way without the need to resort to MC data. If a more accurate expression at low values of $\\bar { q } _ { \\mathrm { o p t } }$ is needed (e.g., if a lower selection threshold is used in an analysis), one could interpolate over the numerical results, either over $f _ { \\mathrm { e f f } }$ and $\\sigma _ { q }$ , or directly over $\\bar { q } _ { \\mathrm { o p t } }$ ; alternatively, one could fit a function (e.g., a polynomial) to them. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[521,93,895,304]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 2. Top panel: Expected value of $- 2 \\\\ln$ $\\\\mathcal { L }$ for the true, fixed, optimal, and partially optimal cases (green, blue, orange, and red error bars, respectively) as a function of the mean true signal-to-noise, $\\\\bar { q } _ { \\\\mathrm { t } }$ , as estimated with our mock observations, shown along their associated reference values of 16384, 16383, 16382, and 16380, respectively. Bottom panel: Effective number of additional fitting parameters, $f _ { \\\\mathrm { e f f } }$ , for the fixed, optimal, and partially optimal cases (blue, orange, and red error bars, respectively) as a function of $\\\\bar { q } _ { \\\\mathrm { t } }$ , as estimated with our mock observations, shown along their reference values of 0, 1 and 3. The reference value of $\\\\bar { q } _ { \\\\mathrm { t } } = 6$ is also shown. \"]","image_footnote":"[]","img_path":"images/0634/092f14ccfaf6b20fb9ed099555dc0651da607cdef2041dc96aa3d36e100a0a1e.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[510,471,922,653]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,656,922,822]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We remark that we have obtained our numerical results for the case in which three parameters (one angular size parameter and two sky coordinates) are optimised over. This was the case of the Planck and SPT analyses (e.g., Planck 2015 results XXVII 2016; Bocquet et al. 2019), and we thus expect our results to be relevant for them. In ACT, on the other hand, the signal-to-noise over was optimised only over two sky coordinates (e.g, Hilton et al. 2021). Since this involves less parameters than the case considered here, and since these are the same as two of our three parameters, we expect our results to also be relevant for ACT. In particular, the $f$ correction should be accurate in a similar, if not broader, signal-to-noise range, noting that, in this case, $f = 2$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,847,635,861]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2.4 Gridding bias ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,870,921,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Fig. 3 also shows the empirical means of our $q _ { \\mathrm { p - o p t } }$ and $q _ { \\mathrm { t } }$ measurements as a function of ${ \\bar { q } } _ { \\mathfrak { t } }$ , shown, too, normalised by $\\bar { q } _ { \\mathrm { t } }$ (red and blue error bars, respectively). As expected, the mean of the $q _ { \\mathrm { t } }$ measurements is consistent with $\\bar { q } _ { \\mathrm { t } }$ and the mean of $q _ { \\mathrm { p - o p t } }$ is always below that of $q _ { \\mathrm { o p t } }$ , as, due to gridding, there is less ‘overfitting’. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,955,215,966]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MNRAS 000, 1–13 (2015) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,34,242,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 Í. Zubeldia et al. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[70,67,478,277]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This can be understood as a ‘gridding bias’ acting in the direction opposite to the optimisation bias (in the context of just sky location, this would be the usual miscentering bias). We remark that this bias depends on the grid chosen: a coarser grid would lead to a larger gridding bias, which could even lead to an overall negative bias, whereas a grid with infinitesimal cells would yield a vanishingly small gridding bias, $q _ { \\mathrm { p - o p t } }$ being equal to $q _ { \\mathrm { o p t } }$ . Due to the presence of this additional bias, which does not exist for true optimisation, and to the fact that for true optimisation the optimisation bias can be accurately modelled with the simple $f$ correction for reasonably large values of signal-to-noise, we advocate for the use of the ‘true’ optimal signal-to-noise, $q _ { \\mathrm { o p t } }$ , as a cluster observable, in detriment to the commonly-used partially-optimal signal-to-noise. In practice, this can be realised, if not with an optimisation algorithm, with the use of an appropriately finely-spaced grid. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,280,478,418]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Regarding the spatial gridding, we should note that in our mock observations, each pixel receives an independent noise realisation; as a consequence, the ‘optimal limit’ is not reached by evaluating the signal-to-noise at the centre of each pixel, as there is structure in the data down to the pixel level. This is not typically the case in real maps, which tend to be well oversampled: the ‘optimal limit’ in the angular coordinates may therefore be reached by just evaluating the signal-to-noise at the centre of each pixel. Care should still be taken, however, with the grid optimisation of the angular scale parameter (and of any other additional parameters). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[72,507,368,520]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2.5 Parameter estimates: $\\theta _ { 5 0 0 }$ and sky position ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,530,478,753]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Although the signal-to-noise is usually the main quantity of interest in tSZ galaxy cluster studies, maximising the matched filter signalto-noise over a set of parameters $\\pmb \\theta$ also yields an estimator for $\\mathbf { \\hat { \\theta } } , \\hat { \\pmb { \\theta } }$ , which we refer to as the matched filter solution. As shown in Section 2, this matched filter solution is equal to the maximum-likelihood estimator for $\\pmb \\theta$ , and therefore it is, in general, biased (see Section 2.2). As an illustration of this point, Fig. 4 shows the empirical means of the matched filter solutions of two of our parameters, $\\theta _ { 5 0 0 }$ (upper panel) and $\\theta _ { x }$ (middle panel), as a function of ${ \\bar { q } } _ { \\mathrm { t } }$ , as obtained with our mock measurements for true optimisation (orange error bars) and partial optimisation (red error bars). (The results for $\\theta _ { y }$ are analogous to those of $\\theta _ { x }$ and hence not shown.) It can be observed that the matched filter estimates of $\\theta _ { 5 0 0 }$ are biased high for both true and partial optimisation, the bias decreasing with increasing signalto-noise. The estimates of $\\theta _ { x }$ , on the other hand, are not biased, as expected from the symmetry of the problem. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,755,478,938]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In order to illustrate the point made in Section 2.2 that the extent, and even the existence, of a bias in the parameter estimates is entirely parametrisation-dependent, the bottom panel of Fig. 4 shows the empirical means of the parameter $\\theta _ { r } \\equiv \\mathbf { \\dot { \\Gamma } } ( \\theta _ { x } ^ { 2 } + \\theta _ { y } ^ { 2 } ) ^ { 1 / 2 }$ , which along with $\\phi \\equiv \\tan ^ { - 1 } ( \\theta _ { y } / \\theta _ { x } )$ constitute a fully equivalent parametrisation to $\\theta _ { x }$ and $\\theta _ { y }$ . As expected, the estimates of $\\theta _ { r }$ are biased high, as they receives contributions from the second-order moments of $\\theta _ { x }$ and $\\theta _ { y }$ . We note that for the partially-optimised case, the bias disappears at high signal-to-noise. This is an artefact of our simulated clusters being centred at the centre of a pixel, which allows, at the high signal-to-noise end, for the true location to be chosen perfectly by the grid optimisation algorithm. This will of course not happen in a real experimental setting (see Section 3.2.3 for a similar discussion). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,67,811,81]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2.6 Dependence on redshift and on noise levels ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,89,921,327]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The results presented in the previous sections were obtained as a function of mean true signal-to-noise, $\\bar { q } _ { \\mathfrak { t } }$ , by fixing the cluster redshift at $z = 0 . 3$ and varying the cluster mass $M _ { 5 0 0 }$ . There is, of course, a perfect degeneracy in $\\bar { q } _ { \\mathrm { t } }$ , whereby a given value of ${ \\bar { q } } _ { \\mathfrak { t } }$ can be obtained by moving along some curve in the $M _ { 5 0 0 } – z$ plane. However, although $\\bar { q } _ { \\mathrm { t } }$ may be perfectly degenerate along this curve, the actual observation (the Compton-?? map) will not be so. As a consequence, the statistics of $q _ { \\mathrm { o p t } }$ and, in particular, the magnitude of the optimisation bias are not guaranteed to depend exclusively on $\\bar { q } _ { \\mathrm { t } }$ , but should in general be regarded as a function of both $M _ { 5 0 0 }$ and $z$ . One can also regard them as dependent on the assumed observational specifications, e.g., the white noise levels, under which $\\bar { q } _ { \\mathrm { t } }$ is also perfectly degenerate, with the data not being so either. This poses the question of to what extent can our results, especially the magnitude of the optimisation bias, be regarded as a function of only $\\bar { q } _ { \\mathrm { t } }$ , i.e., whether the higherdimensional dependency on $M _ { 5 0 0 }$ , ??, noise levels, etc. can be safely condensed into a dependency on just $\\bar { q } _ { \\mathrm { t } }$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,328,922,494]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In order to address this question, we produce a new set of mock observations following exactly the same procedure as the one detailed in Section 3.2.1, but for a set of 16 points lying in the curve of the $M _ { 5 0 0 } – z$ plane defined by $\\bar { q } _ { \\mathrm { t } } ( M _ { 5 0 0 } , z ) = 6$ . Specifically, we consider 16 values of $z$ linearly spaced between $z = 0 . 1$ and $z = 0 . 8$ and compute the corresponding value of $M _ { 5 0 0 }$ that yields $\\bar { q } _ { \\mathrm { t } } = 6$ . We produce $1 0 ^ { 4 }$ mock data vectors for each point along this curve, and we do so for three different white noise levels: $\\sigma _ { n } = 1 . 5 { \\times } 1 0 ^ { - 6 }$ arcmin (the same as used for the mock data of the previous sections), $\\sigma _ { n } =$ $3 \\times 1 0 ^ { - 6 }$ arcmin, and $\\sigma _ { n } = 0 . 7 5 \\times 1 0 ^ { - 6 }$ arcmin. Here we consider only true optimisation, computing the value of $q _ { \\mathrm { o p t } }$ for each mock data vector. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,497,921,750]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Fig. 5 shows the empirical mean (upper panel) and standard deviation (lower panel) of these $q _ { \\mathrm { o p t } }$ measurements as a function of $M _ { 5 0 0 }$ for the the three instances of noise levels (blue, orange, and red error bars). The upper panel also shows as straight lines the reference values of $q = 6$ , which is the value of ${ \\bar { q } } _ { \\mathrm { t } }$ for all the measurements (blue line), and that of $\\bar { q } _ { \\mathrm { o p t } }$ computed with only the $f$ correction, i.e., $\\bar { q } _ { \\mathrm { o p t } } = ( \\bar { q } _ { \\mathrm { t } } ^ { 2 } + f ) ^ { 1 / 2 }$ with $f = 3$ , which we know is an accurate approximation for $\\bar { q } _ { \\mathrm { o p t } }$ at $\\bar { q } _ { \\mathrm { t } } = 6$ (orange line). On the other hand, the lower panel also shows the reference value of unity standard deviation (blue line). It can be seen that any variation of $\\bar { q } _ { \\mathrm { o p t } }$ and $\\sigma _ { q }$ across the curve $\\bar { q } _ { \\mathrm { t } } ( M _ { 5 0 0 } , z ) = 6$ is clearly subdominant with respect to the overall differences with respect to $\\bar { q } _ { \\mathrm { t } } = 6$ and $\\sigma _ { q } = 1$ , respectively, and that this is true for the three noise levels that we have considered. We expect this to also be the case for $\\bar { q } _ { \\mathrm { t } } > 6$ , as with increasing $\\bar { q } _ { \\mathrm { t } }$ the $f$ correction becomes progressively more accurate and $\\sigma _ { q }$ gets closer to unity. In brief, within the mass–redshift and noise levels range that we have considered, the optimisation bias and $\\sigma _ { q }$ can be safely regarded as just a function of ${ \\bar { q } } _ { \\mathfrak { t } }$ for, at least, $\\bar { q } _ { \\mathrm { t } } > 6$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,777,825,791]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.3 Noise covariance estimation and other biases ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,799,921,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Throughout this paper we have assumed the noise covariance to be perfectly known. In a real setting, however, the noise covariance is typically estimated from the data itself. If the signal to be extracted is small enough, it can be taken to be equal to the total data covariance. This was the case, e.g., of the Planck analysis, in which the noise covariance was taken to be the empirically-estimated data covariance (Planck 2015 results XXVII 2016). While this is a good approximation at the low signal-to-noise end, it is no longer so for larger signalto-noise values, where the signal becomes comparable to the noise, potentially leading to a bias in the retrieved signal. This is illustrated in Figure 6, which shows the empirical mean and standard deviation of two sets of $q _ { \\mathrm { o p t } }$ mock measurements as a function of $\\bar { q } _ { \\mathrm { t } }$ (1000 data points for each value of ${ \\bar { q } } _ { \\mathrm { t } }$ each). In order to generate these two data sets, we produced mock data vectors (Compton-?? maps) with the same specifications as used in Section 3.2 and we then applied a matched filter on each of them, maximising the signal-to-noise over angular size and sky location. For one of the data sets (orange error bars), the noise covariance used to construct the matched filter was the true noise covariance (i.e., this mock data set is equivalent to that analysed throughout Section 3.2). For the other data set (green error bars), the noise covariance was taken to be equal to the data covariance, which was estimated empirically from the data vector by taking its standard deviation (that is, assuming the noise to be white). Is is apparent that while the empirical means of these two sets are essentially the same at low signal-to-noise, where noise is dominant, they deviate at the high signal-to-noise end, with noise estimation biasing $q _ { \\mathrm { o p t } }$ low. This negative bias has a simple explanation (see, e.g., Eq. 5): as the noise covariance is overestimated, the signal-tonoise is underestimated. The standard deviation is also affected at the high signal-to-noise end, although less so. Approaches in which an estimate of the signal is subtracted from the data, allowing for better noise covariance estimation (something that can be done, e.g., iteratively), can be followed to mitigate against this bias. An assessment of these approaches is, however, beyond the scope of this paper. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[776,955,921,966]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MNRAS 000, 1–13 (2015) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[561,35,921,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Matched filters for precision cosmology 7 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[176,111,766,445]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 3. Empirical means of our $q _ { \\\\mathrm { o p t } }$ , $q _ { \\\\mathrm { p - o p t } }$ , and $q _ { \\\\mathrm { t } }$ measurements (orange, red, and blue error bars, respectively), shown along with three predictions for the mean of $q _ { \\\\mathrm { o p t } }$ , $\\\\bar { q } _ { \\\\mathrm { o p t } }$ : the full prediction given by Eq. 13 (solid orange curve), that given by Eq. 13 neglecting the variance change term (i.e., $\\\\bar { \\\\Delta } \\\\sigma ^ { 2 } = 0$ ) (dashed orange curve), and that given by the simple $f$ correction, with $f _ { \\\\mathrm { e f f } } = f = 3$ (dotted orange curve). All the error bars have been multiplied by a factor of 10 to allow for better visualisation, and the reference value of $\\\\bar { q } _ { \\\\mathrm { t } } = 6$ is shown as a vertical dashed line. As noted in Section 3.2.3, the $f$ correction is the most significant contribution to $\\\\bar { q } _ { \\\\mathrm { o p t } }$ for $\\\\bar { q } _ { \\\\mathrm { t } } \\\\gtrsim 6$ . \"]","image_footnote":"[]","img_path":"images/0574/73e47882dc991663c68dc7160327efb7e4667da194da66f8ce22e00491ad8e6d.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[80,583,455,795]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 4. Matched filter estimates of $\\\\pmb { \\\\theta } _ { 5 0 0 }$ , $\\\\theta _ { x }$ , and $\\\\theta _ { r }$ , as obtained from our mock data for both true and partial optimisation (orange and red error bars, respectively). \"]","image_footnote":"[]","img_path":"images/0642/c84b0d94a793c31b8a43492787172a4481dc118078f6542747fc7c3929245fad.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[67,897,478,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[529,583,897,795]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 5. Empirical mean (upper panel) and standard deviation (lower panel) of our $q _ { \\\\mathrm { o p t } }$ measurements produced along the $\\\\bar { q } _ { \\\\mathrm { t } } ( M _ { 5 0 0 } , z ) = 6$ curve for three different noise levels (blue, orange, and red error bars). In the upper panel, the reference values of $q = 6$ and $q = ( 6 ^ { 2 } + 3 ) ^ { 1 / 2 }$ are shown as straight lines (blue and orange lines, respectively), as is $\\\\sigma _ { q } = 1$ in the lower panel (blue line). \"]","image_footnote":"[]","img_path":"images/0539/e14a72e30efe57496b47668aa5b421af5c80d75ff097066e90ab0e8d527318b3.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[68,955,215,966]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MNRAS 000, 1–13 (2015) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,35,242,49]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 Í. Zubeldia et al. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[87,93,453,304]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 6. Empirical mean and standard deviation of our $q _ { \\\\mathrm { o p t } }$ measurements produced using the true noise covariance (orange error bars) and estimating it from the data (green error bars). \"]","image_footnote":"[]","img_path":"images/0346/891a3f955adcbb3e2420c89e79a2b5b08f07d511d7346ccc68737080e4dab222.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[68,398,480,693]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,694,478,833]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Other potential sources of bias include, but are not limited to, the wrong modelling of the signal to be extracted, i.e., the matched filter not matching the true cluster tSZ signal, both spatially and spectrally, the latter possible if the relativistic SZ effect (e.g., Sazonov & Sunyaev 1998; Challinor & Lasenby 1998; Chluba et al. 2012) is non-negligible, and the presence of other, ‘foreground’ signals such as the CMB, the kSZ effect, radio emission from the cluster’s galaxies, and point sources (see, e.g., Mroczkowski et al. 2019; Erler et al. 2019). Any assessment of these potential sources of systematics is beyond the scope of this paper. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,863,462,888]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.4 Impact of optimisation on cluster number counts: Planck and the Simons Observatory ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,898,478,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We now shift our attention to the impact of the effects of optimisation that were described theoretically in Section 2 and illustrated numerically in Section 3.2 may have on cluster number counts analyses that use $q _ { \\mathrm { o p t } }$ as an observable. We will focus solely on the optimisation bias, as indeed the non-Gaussianity of $q _ { \\mathrm { o p t } }$ and the deviation of its standard deviation from unity are small for signal-to-noise values of about 6 and above, which is the typical selection threshold in such analyses. In particular, we will determine whether the optimisation bias can be safely neglected in the analysis of cluster samples from Planck and the Simons Observatory (SO; Simons Observatory Collaboration 2019), or whether doing so may lead to biased cosmological constraints. To do so, we will compute the cluster abundances to be detected by these experiments both if the optimisation bias is neglected and if it is accounted for, comparing them appropriately. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,67,921,222]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,246,660,259]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.4.1 Experiment model ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,267,921,519]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We model our cluster number counts analysis as follows. We assume that an Internal Linear Combination (ILC; see, e.g., Delabrouille & Cardoso 2007) is applied on its temperature frequency maps in order to produce a Compton- $\\boldsymbol { \\cdot } \\boldsymbol { y }$ map covering a fraction $f _ { \\mathrm { s k y } }$ of the sky. For Planck we take $f _ { \\mathrm { s k y } } = 0 . 6 2$ (e.g., Planck 2015 results XXIV 2016), whereas for SO we take $f _ { \\mathrm { s k y } } = 0 . 4$ (Simons Observatory Collaboration 2019). We then assume that galaxy clusters are detected by applying a matched filter on this Compton- $\\boldsymbol { \\cdot } \\boldsymbol { y }$ map, which is previously subdivided appropriately into a number of tiles, maximising the signal-to-noise over angular size and sky location (i.e., three parameters) and imposing a selection threshold $q _ { \\mathrm { t h } }$ . For Planck we take a selection threshold of $q _ { \\mathrm { t h } } = 6$ , which is equal to that used to construct the MMF3 cosmology sample used in the Planck baseline analysis (Planck 2015 results XXIV 2016), whereas for SO we consider two selection thresholds, $q _ { \\mathrm { t h } } = 5$ and $q _ { \\mathrm { t h } } = 6$ . We note that, as we show in Appendix A, this $\\mathrm { I I } C +$ matched filter approach is equivalent to a multi-frequency matched filter approach, which was followed, e.g., in the real Planck analysis (see, e.g., Planck 2013 results XX 2014). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,520,922,745]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Construction of the matched filter requires as input a model for the signal to be detected, that is, a model for the cluster Compton- $y$ signal in our case, as well as the noise covariance. As the cluster model we assume the Arnaud et al. (2010) universal pressure profile, which integrated along the line-of-sight (see Eq. 14) gives the cluster Compton- $y$ signal at given mass $( 1 - b ) M _ { 5 0 0 }$ and redshift $z$ , where $1 - b$ is the so-called ‘hydrostatic’ mass bias. We use the best-fit parameters of Arnaud et al. (2010) and a mass bias of $1 - b \\ =$ 0.62 (taken from Planck 2018 results I 2020). We write our model as $y _ { \\mathrm { c } } ( M _ { 5 0 0 } , z ) = y _ { 0 } y _ { \\mathrm { t } } ( \\theta _ { 5 0 0 } ( M _ { 5 0 0 } , z ) )$ , where $y _ { 0 }$ is an amplitude parameter defined as the value of $\\boldsymbol { y } _ { \\mathbf { c } }$ at $R _ { 5 0 0 }$ , and $y _ { \\mathrm { t } }$ is an angular function that depends on mass and redshift only through the cluster’s angular size, $\\theta _ { 5 0 0 } = \\mathrm { \\Delta } R _ { 5 0 0 } / d _ { \\mathrm { A } }$ , where $d _ { \\mathrm { A } }$ is the angular diameter distance to the cluster. Assuming this model for the cluster signal and the noise covariance, the matched filter noise at a given angular size $\\theta _ { 5 0 0 }$ is then given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[593,760,836,797]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"1003/1af8084f19f54245dc8f1d1d55112da19cf2182d4f7446370fd709adb4399771.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\sigma ( \\theta _ { 5 0 0 } ) = \\left[ \\int d ^ { 2 } l \\frac { | y _ { \\mathrm { t } } ( \\theta _ { 5 0 0 } ; l ) | ^ { 2 } } { N ( l ) } \\right] ^ { - 1 / 2 } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[510,803,921,901]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $N ( l )$ is the noise power spectrum. For Planck, we take $N ( l )$ to be the power spectrum of the Full Mission NILC Compton- $y$ map, which we estimate directly from the map, which is publicly available in the Planck Legacy Archive1. This estimated power spectrum includes the tSZ signal of galaxy clusters: this is analogous to what was done in the actual Planck analysis, in which the clusters’ tSZ signal was not subtracted from the frequency maps when estimating their power spectra. For SO, we take it to be the sum of the forecast baseline tSZ reconstruction noise power spectrum of Simons Observatory Collaboration (2019) (namely, the solid orange curve of Fig. 36 of this paper) and the Compton- $y$ power spectrum due to halos up to masses of $M _ { 5 0 0 } = 1 0 ^ { 1 4 } \\tilde { M _ { \\odot } }$ , which we compute with the pubicly-available code pysz2. This assumes that that the tSZ signal due to more massive halos will be identified and removed for noise estimation purposes. The mean signal-to-noise at given mass $M _ { 5 0 0 }$ and redshift $z$ is then given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[776,955,921,966]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MNRAS 000, 1–13 (2015) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[561,35,922,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Matched filters for precision cosmology 9 9 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[510,927,636,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 pla.esac.esa.int ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,67,478,194]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[173,213,374,244]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"1017/5874aea9729bf5181bd21315c1031566e1cd293b51088abced24c7abcb5f02e7.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\bar { q } ( M _ { 5 0 0 } , z ) = \\frac { y _ { 0 } ( M _ { 5 0 0 } , z ) } { \\sigma ( \\theta _ { 5 0 0 } ( M _ { 5 0 0 } , z ) ) } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[68,250,478,318]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where the dependency on the mass bias is left implicit. Note that Eq. (15) is simply a Fourier space, cluster-specific version of Eq. (4). In order to evaluate the matched filter integral, we assume flat sky tiles of $1 0 2 4 \\times 1 0 2 4$ pixels, with a pixel size of 0.8 arcmin for Planck and of 0.2 arcmin for SO. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,319,480,446]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In order to link the mean signal-to-noise, given by Eq. (16), to $q _ { \\mathrm { o p t } }$ , we first assume a layer of log-normal intrinsic scatter. This introduces the variable $\\ln q _ { \\mathrm { t } }$ , which is given by a Gaussian centred on $\\ln \\bar { q } ( M _ { 5 0 0 } , z )$ and with a standard deviation of $\\sigma _ { \\ln \\mathrm { q } } ~ = ~ 0 . 1 7 3$ (taken from Planck 2015 results XXIV 2016). We then consider a layer of ‘observational scatter’ due to what is understood as noise in the matched filtering process, finally linking $q _ { \\mathrm { t } }$ to $q _ { \\mathrm { o p t } }$ . Motivated by our numerical results of Section 3.2, we take this scatter to be Gaussian-distributed with unit variance and with a mean equal to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[216,465,331,491]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0490/55888c7d9d014724918fdc6374f7c7a6b9c9163385aad849d86825b610e33ef3.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\bar { q } _ { \\mathrm { o p t } } = \\sqrt { q _ { \\mathrm { t } } ^ { 2 } + f _ { \\mathrm { e f f } } } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[68,496,480,594]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $f _ { \\mathrm { e f f } }$ is the effective number of fitting parameters, and where we note that we have neglected the contribution due to the change in the variance (compare with Eq. 17), as it is small for $q \\gtrsim 5$ (see Figure 3). As discussed in Section 3.2, for $q \\gtrsim 6$ , $f _ { \\mathrm { e f f } } \\simeq f = 3$ . Thus, we take $f _ { \\mathrm { e f f } } = 3$ when accounting for the bias; we take $f _ { \\mathrm { e f f } } = 0$ when ignoring it. The differential mean number of clusters to be detected as a function of $q _ { \\mathrm { o p t } }$ is then given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,612,472,647]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0429/1a2876e0349b39327c52eaf910484d5f80b8df10e1285fdb650a93d8bee5000e.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\frac { d \\bar { N } } { d q _ { \\mathrm { o p t } } } = 4 \\pi f _ { \\mathrm { s k y } } \\int P ( q _ { \\mathrm { o p t } } | M _ { 5 0 0 } , z ) \\frac { d ^ { 4 } N } { d ^ { 3 } V d M _ { 5 0 0 } } \\frac { d ^ { 3 } V } { d z d ^ { 2 } \\Omega } d M _ { 5 0 0 } d z .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[68,657,478,728]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Here, $d ^ { 4 } N / ( d ^ { 3 } V d M _ { 5 0 0 } )$ is the halo mass function, which we take to be that of Tinker et al. (2008), $d ^ { 3 } V / ( d z d ^ { 2 } \\Omega )$ is the differential volume element, and $P ( q _ { \\mathrm { o p t } } | M _ { 5 0 0 } , z )$ is the probability for a cluster of mass $M _ { 5 0 0 }$ and redshift $z$ to have an optimal signal-to-noise $q _ { \\mathrm { o p t } }$ , which is given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[99,746,423,777]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0895/8b15a0406e872fcabf464a817bc3086323e83e7418fc897049eabfd3d436c35b.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP ( q _ { \\mathrm { o p t } } | M _ { 5 0 0 } , z ) = \\int _ { 0 } ^ { \\infty } P ( q _ { \\mathrm { o p t } } | q _ { \\mathrm { t } } ) P ( q _ { \\mathrm { t } } | M _ { 5 0 0 } , z ) d q _ { \\mathrm { t } } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[67,783,478,841]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where the first factor of the integrand is the Gaussian describing observational scatter, and the second one is the log-normal distribution accounting for intrinsic scatter. The mean number of clusters with $q _ { \\mathrm { o p t } }$ between $q _ { \\mathrm { m i n } }$ and $q _ { \\mathrm { m a x } }$ is then given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[196,859,351,892]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0069/39d404a53dc6b7f85f75a994ac96107047eb6a58deace430992ace9da51c3278.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\bar { N } = \\int _ { q _ { \\mathrm { m i n } } } ^ { q _ { \\mathrm { m a x } } } \\frac { d \\bar { N } } { d q _ { \\mathrm { o p t } } } d q _ { \\mathrm { o p t } } .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[510,67,921,108]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We perform our calculations fixing all the cosmological parameters to their Planck 2018 TT,TE,EE+lowE+lensing best-fit values (Planck 2018 results VI 2020). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,136,685,149]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.4.2 Results and discussion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,158,922,326]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 7 shows the mean number of clusters as a function of $q _ { \\mathrm { o p t } }$ for our reference Planck and SO-like experiments both if the optimisation bias is taken into account (‘corrected’ orange bars) and if it is ignored by setting $f _ { \\mathrm { e f f } } = 0$ (‘uncorrected’ blue bars). Specifically, for each experiment, the mean number of clusters is computed using Eq. (20) for 14 logarithmically-spaced bins between $q _ { \\mathrm { o p t } } = 6$ and $q _ { \\mathrm { o p t } } = 2 5$ . As expected, in any bin more clusters are found if the optimisation bias is accounted for, since the cluster abundance decreases with $q _ { \\mathrm { o p t } }$ and the optimisation bias boosts the signal-tonoise at given mass and redshift. Also as expected, the effect of the optimisation bias on the number counts is most significant at low signal-to-noise, quickly decreasing with increasing signal-to-noise. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,327,922,493]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 7 also shows, as black error bars, the Poisson errors associated with the corrected number counts, which for each bin are given by $\\Delta \\bar { N } _ { \\mathrm { P o i s s o n } } = \\bar { N } ^ { 1 / 2 }$ . They provide a measure of the change in the number counts that the analysis is sensitive to: if the change due to neglecting the optimisation bias is much smaller than the Poisson error, then it can be safely neglected, whereas if it is larger, it may have to be taken into account in order to avoid biasing the inference. It can be seen how for Planck this change is smaller than the Poisson error across all the bins, whereas for SO it is larger for the lowest signal-to-noise bins. This implies that the impact of neglecting the optimisation bias in Planck is probably negligible, but that this may not the case for SO. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,494,922,690]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Table 1 shows the total mean number of clusters detected by each experiment, which is given by Eq. (20) by setting its lower and upper integration limits to $q _ { \\mathrm { t h } }$ and infinity, respectively. For Planck we have imposed a selection threshold of $q _ { \\mathrm { t h } } = 6$ (as in the real baseline analysis, see Planck 2015 results XXIV 2016), whereas for SO we have considered two selection thresholds, $q _ { \\mathrm { t h } } = 6$ and $q _ { \\mathrm { t h } } = 5$ . As with Figure 7, the number counts are given both if the optimisation bias is accounted for and if it is neglected; their difference and the associated Poisson errors are also shown. As expected from Figure 7, while the change in the number counts for Planck is well within the Poisson error, this is not the case for SO, especially if the selection threshold is lowered to $q _ { \\mathrm { t h } } = 5$ . This again implies that the optimisation bias probably has to be taken into account in SO, especially if a selection threshold as low as $q _ { \\mathrm { t h } } = 5$ is chosen. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,691,922,872]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The number counts in Figure 7 and in Table 1 were computed at fixed cosmological and scaling relation parameters. The uncertainty in the scaling relation parameters inherent to any real analysis means that the changes in the number counts shown in both Figure 7 and Table 1 can thus be interpreted as an upper limit on the change that is discernible by the analysis and that can be (wrongly) attributed to cosmology. Indeed, if the tSZ-mass scaling relation is given enough freedom, the optimisation bias may be calibrated away to some extent3. Quantifying the extent to which this can happen is beyond the scope of this paper. It could be done by generating a set of mock cluster samples (e.g., by sampling from the halo mass function and adding the appropriate scatter) and analysing them with a number counts likelihood (e.g., with the one used in Zubeldia & Challinor ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,900,922,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 While the optimisation bias is not completely degenerate with a power law tSZ–mass scaling relation (the form that is usually assumed), as it does not have a power law behaviour, some degeneracy is expected. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,955,215,966]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MNRAS 000, 1–13 (2015) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[70,34,252,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10 Í. Zubeldia et al. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,927,260,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 github.com/ryumakiya/pysz ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[84,107,455,414]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 7. Cluster abundances as a function of optimal signal-to-noise, $q _ { \\\\mathrm { o p t } }$ for Planck (upper panel) and SO (lower panel), both if the optimisation bias is neglected (blue bars) and if it is accounted for (orange bars, shown along the associated Poisson errors). \"]","image_footnote":"[]","img_path":"images/0241/6d9c6c073adaa8ea58c077690d7257b6bec403ac49b770b46650b82a7c5d5628.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[97,590,448,658]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0391/2920ce6ade57c5ac792844d8cd6a689abb7c6736846edeb57984b360ed5fe887.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":"<table><tr><td>Experiment</td><td>N (corr.)</td><td>N (uncorr.)</td><td>AN</td><td>△NPoisson</td></tr><tr><td>Planck</td><td>334.0</td><td>320.7</td><td>13.3</td><td>18.3</td></tr><tr><td>SO (qth = 6)</td><td>9400.9</td><td>9116.9</td><td>284.0</td><td>97.0</td></tr><tr><td>SO (qth = 5)</td><td>14837.6</td><td>14090.8</td><td>746.8</td><td>121.8</td></tr></table>","table_caption":"[\"Table 1. Mean number of clusters to be detected by our Planck and SO-like experiments, with and without optimisation bias taken into account (first and second columns, respectively). Their difference is also shown (third column), along with the corresponding Poisson error (fourth column). \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[68,675,478,855]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2019) with and without the optimisation bias taken into account. One could then look at the differences in the derived constraints on the relevant cosmological parameters (e.g., $\\Omega _ { \\mathrm { m } }$ and $\\sigma _ { 8 }$ ). We have decided not to pursue this avenue, as our conclusions would be dependent on how well the tSZ-mass scaling relation is calibrated, which is yet to be determined for SO, the experiment for which this full analysis would be interesting to perform. Furthermore, since the optimisation bias can be accounted for, and, indeed, implemented numerically in a very simple way (to lowest order, at least), we do not find it necessary to analyse its impact on our idealised experiments in any more detail. We simply recommend it to be considered in any future number counts analysis that makes use of $q _ { \\mathrm { o p t } }$ , or any equivalent quantity, as an observable. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,890,186,904]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 CONCLUSION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[67,911,480,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this paper, we have studied in detail the statistical properties of the matched filter optimal signal-to-noise, $q _ { \\mathrm { o p t } }$ , in the context of galaxy cluster tSZ detection and characterisation. In particular, we have shown that $q _ { \\mathrm { o p t } }$ is, in general, a non-Gaussian variable with a standard deviation different from unity and an expected value that is biased high with respect to the true mean signal-to-noise, a bias that we have referred to as optimisation bias. We have shown that this bias arises from the fact that $q _ { \\mathrm { o p t } }$ is obtained from an optimisation procedure on noisy data. As such, it is present even if the signal is modelled perfectly, no foregrounds are present, and the noise in the data is Gaussian. After presenting these arguments in a general way in Section 2, we have then used a set of MC mock observations in order to study numerically these effects of optimisation in the tSZ galaxy cluster context. We have found that, if optimisation is carried out over three parameters (an angular size and two location parameters), $q _ { \\mathrm { o p t } }$ can be taken to be approximately Gaussian-distributed and with a standard deviation approximately equal to unity for $q _ { \\mathrm { o p t } } ~ \\gtrsim ~ 6$ Similarly, for $q _ { \\mathrm { o p t } } \\gtrsim 6$ , the optimisation bias can be accounted for with a simple expression, $\\bar { q } _ { \\mathrm { o p t } } = ( q _ { \\mathrm { t } } ^ { 2 } + f ) ^ { 1 / 2 }$ , where $\\bar { q } _ { \\mathrm { o p t } }$ is the expected value of $q _ { \\mathrm { o p t } }$ , $\\bar { q } _ { \\mathrm { t } }$ is the expected value of the true signal-tonoise, and $f$ is the number of fitting parameters (three in our case). We stress that this correction, which we have refer to as the $\\cdot _ { f }$ correction’, is accurate if ‘true’ optimisation is achieved: if the signal-to-noise is only partially optimised by evaluating it on a coarse parameter grid, an additional, grid-dependent negative bias on the retrieved signal-to-noise will be induced (see Section 3.2.4). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,69,921,405]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,414,922,622]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In addition, we note that if in a given context the $f$ correction may be suspected not be accurate enough, or the standard deviation of $q _ { \\mathrm { o p t } }$ may be significantly different from unity, this paper offers a route through which these aspects can be quantified, namely through the generation and analysis of a set of mock $q _ { \\mathrm { o p t } }$ observations. This may be the case if low signal-to-noise clusters are considered, or if the parameters over which the optimisation is carried out are different from the ones we have considered, either in nature and/or in number. Indeed, while in this paper we have considered optimisation of the signal-to-noise over three parameters, in future experiments additional parameters could be considered, e.g., including extensions in the modelling of the cluster atmosphere (e.g., Moser et al. 2021), or the cluster temperature (Remazeilles et al. 2019; Remazeilles & Chluba 2020) in experiments sensitive to the relativistic SZ effect such as PICO (Hanany et al. 2019). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,630,921,938]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Our results have implications for any cluster number counts analysis that may use $q _ { \\mathrm { o p t } }$ as a mass observable. In these analyses, a signal-to-noise threshold of around 6 is typically used as the selection criterion for the construction of the cluster sample. Thus, our results suggest that, while the non-Gaussianity of $q _ { \\mathrm { o p t } }$ and the deviation of its standard deviation from unity are small and probably negligible, the optimisation bias, which is a $\\sim 5 \\%$ effect at signalto-noise of 6, may have a significant impact. In the past, analyses using both Planck and ACT clusters have ignored this bias, even if optimisation over a number of parameters was carried out (three parameters in Planck and two in ACT; Hasselfield et al. 2013; Planck 2013 results XX 2014; Planck 2015 results XXIV 2016; Zubeldia & Challinor 2019). Only the SPT analyses, in which the signal-to-noise was optimised over three parameters, have properly accounted for it using a correction equal to ours (Vanderlinde et al. 2010; Bleem et al. 2015; Bocquet et al. 2019), offering a rather heuristic justification for its use (Vanderlinde et al. 2010). Here we have quantified the relevance of the bias in Planck and SO by computing its effect on the expected number counts across signal-to-noise. We have found it to be negligible for Planck and potentially significant for SO, the latter being especially true if a precise mass–observable tSZ scaling relation is used in the analysis. We also expect the bias to be relevant for CMB-S4, which is forecast to find about an order of magnitude more clusters than SO (Abazajian et al. 2016). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[776,955,921,966]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MNRAS 000, 1–13 (2015) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[551,35,919,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Matched filters for precision cosmology 11 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,67,478,94]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,97,478,249]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This paper highlights the well-known fact that, though galaxy clusters are and will continue to be a very powerful cosmological probe from a statistical point of view, accurately determining the mass-observable relation is crucial for this statistical power to be realised in practice. For the specific case considered here, that of SZ surveys using matched filters, we have evidenced that, for upcoming surveys, accurately calibrating the mass– $\\cdot q _ { \\mathrm { o p t } }$ relation will probably require proper modelling of the optimisation bias. Here we have shown that this can be done in a numerically straightforward way. We thus encourage that the bias is duly accounted for in any future analysis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,251,480,585]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, although in this work we have focused on tSZ detection and characterisation of galaxy clusters, matched filters can also be used for cluster detection in photometric surveys (e.g., Bellagamba et al. 2018) and using jointly mm and X-ray observations (Tarrío et al. 2018), as well as for the confirmation of X-ray detected clusters using optical photometric data (Klein et al. 2018). They also have a variety of other applications, such as the detection of the CMB lensing signal of galaxy clusters (Melin & Bartlett 2015; Horowitz et al. 2019; Zubeldia & Challinor 2019) and voids (Raghunathan et al. 2020), of the moving lens effect (Hotinli et al. 2021), of line intensity mapping sources (Schaan & White 2021), of large-scale structures such as voids in $2 1 \\mathrm { c m }$ data (White & Padmanabhan 2017), and of the ISW signal of large-scale structures (Nadathur & Crittenden 2016). They are also widely used for gravitational wave detection (see, e.g., Pitkin et al. 2011 for a review). All the theoretical insights of Section 2, including the non-Gaussianity of the signal-to-noise and the existence of a positive optimisation bias, are completely general and hold in any other applications of matched filters. We expect the general numerical trends presented in Section 3 (e.g., the non-Gaussianity and the optimisation bias both decreasing with increasing signal-tonoise) to apply in other contexts as well. Considering other uses of matched filters in any detail is beyond the scope of this paper, but we hope that the insights and results presented here may find useful applications in some of these other areas too. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,625,245,638]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ACKNOWLEDGEMENTS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,647,478,702]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This work was supported by the ERC Consolidator Grant CMBSPEC (No. 725456). JC was furthermore supported by the Royal Society as a Royal Society University Research Fellow at the University of Manchester, UK. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,740,223,754]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"DATA AVAILABILITY ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,763,478,790]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The data underlying this article will be shared on reasonable request to the corresponding author. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,828,171,841]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"REFERENCES ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[68,850,478,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abazajian K. N., et al., 2016, preprint, (arXiv:1610.02743) \nAllen S. W., Evrard A. E., Mantz A. B., 2011, ARA&A, 49, 409 \nAndrade-Santos F., et al., 2021, arXiv e-prints, p. arXiv:2103.07545 \nAndrae R., Schulze-Hartung T., Melchior P., 2010, arXiv e-prints, p. arXiv:1012.3754 \nArnaud M., Pratt G. W., Piffaretti R., Böhringer H., Croston J. 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V., Klypin A., Abazajian K., Warren M., Yepes G., Gottlöber S., Holz D. E., 2008, ApJ, 688, 709 \nVanderlinde K., Crawford T. M., de Haan T., Dudley J. P., Shaw L., et al., 2010, ApJ, 722, 1180 \nWhite M., Padmanabhan N., 2017, MNRAS, 471, 1167 \nZubeldia Í., Challinor A., 2019, MNRAS, 489, 401 \nZubeldia Í., Challinor A., 2020, MNRAS, 497, 5326 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,63,924,753]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,777,885,805]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"APPENDIX A: EQUIVALENCE BETWEEN MMF AND $\\mathbf { I L C { + } M F }$ ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,813,921,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"When multi-frequency mm data is available, galaxy clusters are typically detected using a multi-frequency matched filter (MMF), which operates directly on the frequency maps (Melin et al. 2006; for an application on real data, see, e.g., Planck 2015 results XXVII 2016). Throughout this paper, however, we have considered a ‘singlefrequency’ matched filter acting on a Compton-?? map. In this appendix, we show that these two approaches are mathematically equivalent if the Compton-?? map is produced with an Internal Linear Combination (ILC; see, e.g., Delabrouille & Cardoso 2007). Thus, the results presented in this work are also applicable to multi-frequency matched filters. We restrict our proof to the case in which the noise covariance is isotropic. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,34,252,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"12 Í. Zubeldia et al. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,955,215,966]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MNRAS 000, 1–13 (2015) ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[67,67,478,109]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[67,109,478,166]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Consider a set of beam-deconvolved intensity maps at different frequencies, $\\pmb { d } ( \\pmb { x } )$ , where the vector dimension of $\\mathbf { \\Delta } \\mathbf { d }$ is equal to the number of frequency channels and where $\\boldsymbol { x }$ denotes angular position. We assume that $\\pmb { d } ( \\pmb { x } )$ can be written as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[205,186,341,203]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0355/7446ee7e8a0c266ad3187e203705ed2fb2ff032d031d0c355fc7a77d0e2e196a.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\pmb { d } ( \\pmb { x } ) = \\pmb { j } _ { \\nu } \\pmb { y } ( \\pmb { x } ) + \\pmb { n } ( \\pmb { x } ) ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[68,209,480,306]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $j _ { \\nu }$ is the frequency dependency of the signal of interest (the tSZ effect in our case), $y ( \\pmb { x } )$ is its spatial variation (the Compton-$y$ map in our case), and $\\pmb { n } ( \\pmb { x } )$ is some additive ‘noise’, which also includes all other signals different from the component of interest (in our case, the CMB, the kSZ signal, etc.). Assuming the covariance of the noise to be isotropic, a Fourier-space ILC estimate of $y ( x )$ can be written as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[206,323,341,360]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0214/2d6b370cf2b0849de7a9e30aba48306c47e17e5bcdcda511d88a3b875e702bd0.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\hat { y } ( l ) = \\frac { j _ { \\nu } ^ { T } \\mathsf { N } ^ { - 1 } ( l ) d ( l ) } { j _ { \\nu } ^ { T } \\mathsf { N } ^ { - 1 } ( l ) j _ { \\nu } } ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[68,364,478,392]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where ${ \\pmb { \\mathsf { N } } } ( l )$ is the noise covariance matrix, and which has an associated variance equal to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[196,409,351,437]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0854/72fdd8784b6db935626a47e93b686e236ac56b4491c6a9bbcbbcfd881ef075b1.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nN ( l ) = \\left[ j _ { \\nu } ^ { T } \\mathsf { N } ^ { - 1 } ( l ) j _ { \\nu } \\right] ^ { - 1 } .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[68,442,478,484]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If we then assume that the signal $y ( l )$ can be written as $y ( l ) = y _ { 0 } y _ { \\mathrm { t } } ( l )$ , where $y _ { 0 }$ is an amplitude parameter and $y _ { \\mathrm { t } } ( l )$ is a spatial template, a matched filter estimate for $y _ { 0 }$ can then be written as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[142,489,403,525]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0407/c9f10113a42d741223e34fe8e28f8919a062be84d497440c1ca65049b68c065e.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\hat { y } _ { 0 } = \\left[ \\int d ^ { 2 } { l } \\frac { | y _ { \\mathrm { t } } ( l ) | ^ { 2 } } { N ( l ) } \\right] ^ { - 1 } \\int d ^ { 2 } { l } \\frac { y _ { \\mathrm { t } } ^ { \\ast } ( l ) \\hat { y } ( l ) } { N ( l ) } .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[67,530,478,571]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This is the ‘single-frequency’ matched filter that we have considered in this work. If we now substitute the ILC expression for $\\hat { y } ( I )$ of Eq. (A2), we find ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,588,470,624]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0734/90f683090988e4c1b155c4c76f9a26d62e7c0635af905177657395dad5759e36.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\hat { y } _ { 0 } = \\left[ \\int d ^ { 2 } l y _ { \\mathrm { t } } ^ { * } ( l ) j _ { \\nu } ^ { T } { \\bf N } ^ { - 1 } ( l ) j _ { \\nu } y _ { \\mathrm { t } } ( l ) \\right] ^ { - 1 } \\int d ^ { 2 } l y _ { \\mathrm { t } } ^ { * } ( l ) j _ { \\nu } ^ { T } { \\bf N } ^ { - 1 } ( l ) d ( l ) .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[67,634,480,690]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This is a multi-frequency matched filter, acting directly on the frequency maps $\\pmb { d } ( l )$ (for comparison, see, e.g., Melin et al. 2006). Thus, it is equivalent to a ‘single-frequency’ matched filter operating on an ILC estimate of the Compton- $y$ map. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[67,708,465,721]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This paper has been typeset from a $\\mathrm { T e X / I A T _ { E } X }$ file prepared by the author. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[549,35,922,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Matched filters for precision cosmology 13 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[774,955,922,966]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MNRAS 000, 1–13 (2015) ","text_format":null,"text_level":null,"type":"discarded"}],"string":"[\n {\n \"bbox\": \"[67,93,695,116]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Understanding matched filters for precision cosmology \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[72,135,611,166]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Íñigo Zubeldia,1★ Aditya Rotti,1 Jens Chluba1 and Richard Battye1 1Jodrell Bank Centre for Astrophysics, University of Manchester, Manchester M13 9PL UK \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,196,359,208]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Accepted XXX. Received YYY; in original form ZZZ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,237,151,249]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABSTRACT \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[67,253,922,425]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Matched filters are routinely used in cosmology in order to detect galaxy clusters from mm observations through their thermal Sunyaev-Zeldovich (tSZ) signature. In addition, they naturally provide an observable, the detection signal-to-noise or significance, which can be used as a mass proxy in number counts analyses of tSZ-selected cluster samples. In this work, we show that this observable is, in general, non-Gaussian, and that it suffers from a positive bias, which we refer to as optimisation bias. Both aspects arise from the fact that the signal-to-noise is constructed through an optimisation operation on noisy data, and hold even if the cluster signal is modelled perfectly well, no foregrounds are present, and the noise is Gaussian. After reviewing the general mathematical formalism underlying matched filters, we study the statistics of the signal-to-noise with a set Monte Carlo mock observations, finding it to be well-described by a unit-variance Gaussian for signal-to-noise values of 6 and above, and quantify the magnitude of the optimisation bias, for which we give an approximate expression that may be used in practice. We also consider the impact of the bias on the cluster number counts of Planck and the Simons Observatory (SO), finding it to be negligible for the former and potentially significant for the latter. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[72,434,721,450]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Key words: galaxies: clusters: general – cosmology: observations – cosmology: diffuse radiation \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,497,205,510]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 INTRODUCTION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,519,478,713]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"First proposed in the galaxy cluster context more than two decades ago (Haehnelt & Tegmark 1996; Herranz et al. 2002; Melin et al. 2006), matched filters have become a standard tool with which to detect and characterise galaxy clusters from CMB observations via their thermal Sunyaev-Zeldovich (tSZ) signature. Indeed, matched filters have been used in the construction of the cluster catalogues derived from SPT, ACT, and Planck data (e.g., Vanderlinde et al. 2010; Hasselfield et al. 2013; Planck 2013 results XXIX 2014; Bleem et al. 2015; Planck 2015 results XXVII 2016; Hilton et al. 2021; Melin et al. 2021), and as a result they have also played an important role in the cosmological analyses based on these cluster samples (e.g., Vanderlinde et al. 2010; Hasselfield et al. 2013; Planck 2013 results XX 2014; Bleem et al. 2015; Planck 2015 results XXIV 2016; Bocquet et al. 2019; Zubeldia & Challinor 2019). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,716,478,895]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Matched filters provide a natural quantity, the detection significance or signal-to-noise, that can be used to construct cluster samples by selecting the clusters whose signal-to-noise falls above a certain threshold (e.g., Planck 2015 results XXVII 2016; Hilton et al. 2021). The signal-to-noise can also be employed as a mass proxy in a cluster number counts analysis, in which the cluster abundance across a number of observables (usually, redshift and one or more ‘mass proxies’, that is, observables that scale with cluster mass) is used to constrain cosmology (e.g., Planck 2015 results XXIV 2016; Bocquet et al. 2019; Zubeldia & Challinor 2019; see Allen et al. 2011 for a review). Essential for the success of such analyses is the accurate determination of the mass–observable(s) scaling relation(s), which allows to link the predicted cluster abundance across mass and redshift, as given by the halo mass function, to the observed abundance. At present, this constitutes the main source of systematic uncertainty in cluster number counts analyses, and, as such, a lot of effort is being devoted to the calibration of mass–observable relations (e.g., Nicola et al. 2020; Zubeldia & Challinor 2020; Andrade-Santos et al. 2021; see Pratt et al. 2019 for a review). Any significant biases in any of the mass–observable relation could lead to biased cosmological constraints. Thus, if the matched filter signal-to-noise is to be used as a mass observable in a number counts analysis, its relation to cluster mass and redshift must be well understood. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,497,921,635]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,641,921,864]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Relating the cluster mass and redshift to the observed signal-tonoise is usually thought of as a two-step process (see, e.g., Planck 2015 results XXIV 2016 and Bocquet et al. 2019). First, the cluster mass and redshift are related to some mean signal-to-noise via a set of scaling relations, which after the addition of some ‘intrinsic scatter’ (due to cluster triaxiality, deviations from the mean profile, etc.) one obtains the ‘true’ signal-to-noise of a cluster, i.e., the signalto-noise that would be measured after ensemble averaging over what is understood as noise in the matched filtering process. Then, a layer of additive ‘noise’ or ‘observational scatter’ connects the true signalto-noise with the observed one. This observational scatter is typically assumed to be Gaussian-distributed and to have a standard deviation equal to unity and a mean equal to either the true-signal-to-noise (Planck and ACT; see, e.g., Hasselfield et al. 2013; Planck 2015 results XXIV 2016) or a corrected version of it (SPT; see, e.g., Bocquet et al. 2019). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,870,921,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this work we focus on this second layer of the scatter, which is comparatively much less studied than the intrinsic scatter. In order to do this, we first review the matched filter formalism, deriving the matched filter using a maximum-likelihood approach. We show that, as opposed to what is typically assumed, the observational scatter is, in general, non-Gaussian. We also show that the observed signal-to-noise is, in general, biased high with respect to the true signal-to-noise. Both the non-Gaussianity and the bias are a result of the signal-to-noise being obtained through an optimisation process on noisy data. As a consequence, they hold even if the signal is modelled perfectly, no foregrounds are present, and the noise in the data is Gaussian, which is indeed the case we consider. After presenting these theoretical considerations, we then use a set of Monte Carlo (MC) mock observations in order to quantify the non-Gaussianity of the observational scatter, its variance, and the magnitude of the optimisation bias. We find that for signal-to-noise values of $\\\\gtrsim 6$ , the scatter can taken to be approximately Gaussian and with a variance equal to unity. We also find that, for a similar signal-to-noise range, the optimisation bias can be described accurately with a simple approximate expression. This expression is the same as the correction used in the SPT analyses (Bocquet et al. 2019), which was originally introduced in Vanderlinde et al. (2010) and justified with a rather heuristic argument. Here, we provide further insight into its origin and a more detailed study of its validity in the Gaussian noise regime. Finally, we quantify the impact of the optimisation bias in the cluster number counts of Planck and the Simons Observatory (SO; Simons Observatory Collaboration 2019), finding it to be negligible for the former and potentially significant for the latter. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,928,309,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"★ E-mail: inigo.zubeldia@manchester.ac.uk \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[673,39,922,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Compiled using MNRAS LATEX style file v3.0 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,38,215,49]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MNRAS 000, 1–13 (2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,955,181,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$©$ 2015 The Authors \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[478,38,591,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Preprint 8 June 2021 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[26,244,62,732]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"arXiv:2106.03718v1 [astro-ph.CO] 7 Jun 2021 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,67,480,390]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,391,478,613]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This paper is organised as follows. In Section 2 we review the matched filter formalism, deriving the matched filter from a maximum likelihood point of view (Section 2.1) and noting the biases that arise from this process, both in the retrieved parameter estimates (Section 2.2) and in the signal-to-noise (the ‘optimisation bias’; Sections 2.3 and 2.4). Then, after a brief review of how matched filters are used in practice in the tSZ context (Section 3.1), in Section 3.2 we use a set of MC mock observations in order to study the statistics of the observational scatter of the signal-to-noise, quantifying its departure from Gaussianity, its variance, and its mean (the latter as quantified through the optimisation bias). We also comment briefly on other possible biases in the signal-to-noise, such as that arising from estimating the noise covariance from the data in a naive way (Section 3.3). Next, in Section 3.4 we consider the impact of the optimisation bias on the cluster number counts of Planck and SO, and finally conclude in Section 4. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[67,639,462,653]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 MATCHED FILTERING: A LIKELIHOOD APPROACH \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,662,433,676]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.1 Matched filtering as maximum likelihood estimation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,684,478,767]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Consider a data vector $\\\\mathbf { \\\\Delta } \\\\mathbf { d }$ . This can be, e.g., a map of the Compton-$y$ parameter, a map of the lensing convergence, or a set of intensity maps across several frequencies. In the first two cases, the data vector dimension is equal to the number of pixels, $n$ , whereas in the third it is equal to the number of pixels times the number of frequency channels. Let us assume that this data vector can be written as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[223,790,322,805]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0225/24be079ad03a077dc789ebacb1d4465a8934154440154f8cd5d7c0658bdfefa2.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\pmb { d } = s _ { 0 } \\\\pmb { s } ( \\\\pmb { \\\\theta } ) + \\\\pmb { n } .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[68,813,478,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Here, $s _ { 0 } \\\\pmb { s } ( \\\\pmb \\\\theta )$ is the signal that is present in the data (e.g., the Compton-$y$ signal due to a galaxy cluster), which we assume that can be written as an amplitude, or normalisation, parameter $s _ { 0 }$ times a template function $\\\\pmb { s } ( \\\\pmb { \\\\theta } )$ , which depends upon a number of $f$ additional parameters $\\\\pmb \\\\theta$ . This set of parameters can include, for example, a size parameter (e.g., $\\\\theta _ { 5 0 0 }$ for a galaxy cluster), as well as location parameters specifying the position of the peak of the signal in the map. In addition, our data vector has some additive noise, $\\\\pmb { n }$ , which we will assume to be Gaussian distributed and with zero mean. In practice, this noise term needs not be instrumental noise alone: it can also include the signal from one, or several, foregrounds, as long as it is Gaussian distributed and has zero mean. The logarithm of the likelihood (hereafter, the log-likelihood) of our data can then be written as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,67,922,136]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[563,153,867,213]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0453/543153ed692abd38877db3ede5117e35353f16c8682b920778c5455fa0b29168.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array} { c } { \\\\displaystyle \\\\ln \\\\mathcal { L } ( s _ { 0 } , \\\\theta ) = - \\\\frac { 1 } { 2 } \\\\left[ d - s _ { 0 } s ( \\\\theta ) \\\\right] ^ { T } \\\\mathbf { C } ^ { - 1 } [ d - s _ { 0 } s ( \\\\theta ) ] } \\\\\\\\ { \\\\displaystyle - \\\\frac { 1 } { 2 } \\\\ln \\\\left[ ( 2 \\\\pi ) ^ { n } \\\\mathrm { d e t } ( \\\\mathbf { C } ) \\\\right] , } \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[510,216,922,257]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where C is the noise covariance, which we assume to be known. The second term of this likelihood is independent from the parameters, and so we will ignore it in the following. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,259,921,300]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let us now consider the set of parameter values that maximises the log-likelihood, $\\\\big \\\\{ \\\\hat { s } _ { 0 } , \\\\hat { \\\\pmb \\\\theta } \\\\big \\\\}$ . We first optimise the log-likelihood with respect to $s _ { 0 }$ . Imposing $\\\\partial \\\\ln \\\\mathcal { L } / \\\\partial s _ { 0 } = 0$ yields \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[640,317,791,351]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0805/36e6c3bf567dc65ad082a548741f45b8b427458ac4df4aeb003d6307d955dce1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\hat { s } _ { 0 } ( \\\\pmb { \\\\theta } ) = \\\\frac { s ( \\\\pmb { \\\\theta } ) ^ { T } \\\\pmb { \\\\mathsf { c } } ^ { - 1 } \\\\pmb { d } } { s ( \\\\pmb { \\\\theta } ) ^ { T } \\\\pmb { \\\\mathsf { c } } ^ { - 1 } s ( \\\\pmb { \\\\theta } ) } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,356,922,383]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"which is the well-known matched filter estimate of $s _ { 0 }$ at a given value of $\\\\pmb \\\\theta$ , and which has an associated standard deviation $\\\\sigma _ { s _ { 0 } }$ given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[616,400,816,429]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0370/9959fce8aec22509139599df61f5dbed997310c7867f3c23493ce0879e03a7df.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\boldsymbol { \\\\sigma } _ { s _ { 0 } } ( \\\\pmb { \\\\theta } ) = \\\\left[ s ( \\\\pmb { \\\\theta } ) ^ { T } \\\\mathbb { c } ^ { - 1 } s ( \\\\pmb { \\\\theta } ) \\\\right] ^ { - 1 / 2 } .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[510,433,889,447]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We can then define the signal-to-noise ratio of the detection as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[594,464,836,503]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0058/2bc36d6395615e8d0f77447b2b933441351564814cebd45c407c262f8ea20dd7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nq ( \\\\pmb \\\\theta ) \\\\equiv \\\\frac { \\\\hat { s } _ { 0 } ( \\\\pmb \\\\theta ) } { \\\\sigma _ { s _ { 0 } } ( \\\\pmb \\\\theta ) } = \\\\frac { \\\\pmb { s } ( \\\\pmb \\\\theta ) ^ { T } \\\\pmb \\\\subset ^ { - 1 } \\\\pmb d } { \\\\left[ \\\\pmb { s } ( \\\\pmb \\\\theta ) ^ { T } \\\\pmb { \\\\mathbb C } ^ { - 1 } \\\\pmb { s } ( \\\\pmb \\\\theta ) \\\\right] ^ { 1 / 2 } } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[510,508,910,521]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where we have stressed its dependence on $\\\\pmb \\\\theta$ by leaving it explicit. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,524,922,549]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"By substituting the expression for $\\\\hat { s } _ { 0 }$ of Eq. (3) into Eq. (2), the log-likelihood can be rewritten as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[611,566,820,595]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0892/4634b07a8d36645ef7084a1a2ffef6969a0587ba609e64601badaa534b3f3a5b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\ln \\\\mathcal { L } ( \\\\pmb { \\\\theta } ) = - \\\\frac { 1 } { 2 } \\\\pmb { d } ^ { T } \\\\mathbf { C } ^ { - 1 } \\\\pmb { d } + \\\\frac { 1 } { 2 } \\\\pmb { q } ( \\\\pmb { \\\\theta } ) ^ { 2 } .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[510,599,922,712]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We note that the likelihood no longer depends on $s _ { 0 }$ , as this parameter has already been maximised over, and we recall that we have dropped the second, parameter-independent term. From Eq. (6) it follows that the set of parameter values $\\\\pmb \\\\theta$ that maximises the loglikelihood is equal to that which maximises the signal-to-noise $q$ . That is, the maximum likelihood solution is equal to the value of $\\\\pmb \\\\theta$ that maximises the matched filter signal-to-noise, along with the corresponding matched filter amplitude estimate, $\\\\hat { s } _ { 0 } ( \\\\hat { \\\\pmb { \\\\theta } } )$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,712,922,809]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"When matched filters are used in practice, it is customary to maximise the signal-to-noise with respect to $\\\\pmb \\\\theta$ (e.g., Melin et al. 2006). Here, we have shown that this matched filter solution is equal to the maximum likelihood solution. In brief, matched filtering with signal-to-noise maximisation can be understood as maximum likelihood estimation for a Gaussian likelihood and a model which can be written as an amplitude parameter times a template function. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,833,715,847]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2 Matched filter solution bias \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,855,922,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"By identifying the matched filter solution with the maximum likelihood solution, $\\\\left\\\\{ \\\\hat { s } _ { 0 } , \\\\hat { \\\\pmb \\\\theta } \\\\right\\\\}$ , it follows that the matched filter estimates of $s _ { 0 }$ and $\\\\pmb \\\\theta$ are, in general, biased, as they are in general maximum likelihood estimators. We thus warn against using matched filter solutions without proper consideration of this bias. As we illustrate numerically in Section 3.2.5, the magnitude of the bias typically decreases with the signal-to-noise, being arbitrarily small for arbitrarily large values of signal-to-noise (i.e., for arbitrarily low noise). Care should be taken, however, when conducting inference from the combination of the matched filter solutions of a set of different observations, i.e., a set of $m$ data vectors $\\\\pmb { d }$ . In this case, the overall signal-to-noise, which will set the precision of the inference, will be larger than the signal-to-noise of the individual measurements, increasing as $\\\\sqrt { m }$ , but the bias will not decrease accordingly. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,955,215,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MNRAS 000, 1–13 (2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,34,242,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 Í. Zubeldia et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,67,480,180]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,180,478,333]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We also note that the bias is parametrisation-dependent. As an illustration, consider, for example, that $\\\\pmb \\\\theta$ includes two location parameters, $\\\\theta _ { x }$ and $\\\\theta _ { \\\\mathrm { y } }$ , which specify the Cartesian coordinates of the peak of the signal. By symmetry, their matched filter solution, ${ \\\\hat { \\\\theta } } _ { X }$ and $\\\\hat { \\\\theta } _ { y }$ , cannot be biased, i.e., $\\\\left. { \\\\hat { \\\\theta } } _ { x } \\\\right. = \\\\theta _ { x } ^ { \\\\mathrm { { t r u e } } }$ and $\\\\left. \\\\hat { \\\\theta } _ { y } \\\\right. = \\\\theta _ { y } ^ { \\\\mathrm { t r u e } }$ , where angular brackets denote ensemble averaging over noise realisations. Consider now an alternative and fully equivalent parametrisation, $\\\\theta = ( \\\\theta _ { x } ^ { 2 } + \\\\theta _ { y } ^ { 2 } ) ^ { 1 / 2 }$ and $\\\\phi = \\\\tan ^ { - 1 } ( \\\\theta _ { y } / \\\\theta _ { x } )$ . It should be apparent that the matched filter solution for $\\\\theta$ is biased, as its expected value receives contributions from the second-order moments of ${ \\\\hat { \\\\theta } } _ { x }$ and $\\\\hat { \\\\theta } _ { y }$ . We illustrate this point numerically in Section 3.2.5. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,369,341,383]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.3 Using the optimal $q$ : optimisation bias \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,391,478,586]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In some applications of matched filtering (e.g., galaxy cluster detection in tSZ surveys, see Section 3), the main quantity of interest is the signal-to-noise ratio, $q$ , and, more specifically, its maximum value, that is, the value that it takes at the maximum likelihood solution, $q ( { \\\\hat { \\\\pmb { \\\\theta } } } )$ . We refer to this quantity as the ‘optimal signal-to-noise’ and denote it with $q _ { \\\\mathrm { o p t } }$ . In order to be able to infer information from a measured value of $q _ { \\\\mathrm { o p t } }$ , one needs to be able to relate this quantity to the true mean signal-to-noise ratio, which is given by ensemble-averaging Eq. (5) over noise realisations at the true parameter values, and which we denote with $\\\\bar { q } _ { \\\\mathrm { t } }$ . That is, one needs to determine $P ( q _ { \\\\mathrm { o p t } } | \\\\bar { q } _ { \\\\mathrm { t } } )$ . This is usually known as ‘observational scatter’ or ‘noise’ (e.g., Zubeldia $\\\\&$ Challinor 2019), as opposed to the intrinsic scatter due to triaxiality, inhomogeneities, etc., which we ignore in this work. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[67,588,478,643]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For a given noise realisation $\\\\pmb { n }$ , $P ( q _ { \\\\mathrm { o p t } } | \\\\bar { q } _ { \\\\mathrm { t } } , \\\\pmb { n } )$ is a $\\\\delta$ function centred at $q ( \\\\widehat { \\\\pmb { \\\\theta } } ( \\\\pmb { \\\\theta } _ { \\\\mathrm { t } } , \\\\pmb { n } ) , \\\\pmb { n } )$ , where we have written explicitly the dependence of the matched filter solution $\\\\hat { \\\\pmb { \\\\theta } }$ on the true parameter values and on the noise. Hence, we can write \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[115,663,431,693]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0385/79450176c5369dd0b47a661d0cf4fde2e79515fc5d3ad8e501f19c6f2b062624.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP ( q _ { \\\\mathrm { o p t } } | \\\\bar { q } _ { \\\\mathrm { t } } ) = \\\\int \\\\delta \\\\left[ q _ { \\\\mathrm { o p t } } - q ( \\\\hat { \\\\pmb \\\\theta } ( \\\\pmb \\\\theta _ { \\\\mathrm { t } } , \\\\pmb n ) , \\\\pmb n ) \\\\right] P ( \\\\pmb n ) d ^ { n } \\\\pmb { n } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[68,700,480,813]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $P ( \\\\pmb { n } )$ is the noise probability density function, which, if the noise is Gaussian, as we assume, is a multi-variate Gaussian. This is, in general, a non-Gaussian distribution, reflecting the fact that optimisation is a non-linear operation. Intuitively, to the Gaussian variation due to the noise one should add the variation due to evaluating Eq. (5) at different values of $\\\\pmb \\\\theta$ (for each measurement, its matched filter solution $\\\\hat { \\\\pmb { \\\\theta } }$ ). The $m$ -th moment of this distribution can be written as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[164,832,383,863]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0959/84a65218cde5406e04b3cd6e91206f6ee644636c4bf6dac159e71f44407ef92a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\langle q _ { \\\\mathrm { o p t } } ^ { m } \\\\rangle = \\\\int q ( \\\\hat { \\\\pmb { \\\\theta } } ( \\\\pmb { \\\\theta } _ { \\\\mathrm { t } } , \\\\pmb { n } ) ) ^ { m } P ( \\\\pmb { n } ) d ^ { n } \\\\pmb { n } .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[68,869,480,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This is a set of high-dimensional integrals which are difficult to compute in practice. However, their values can be estimated in a fast way with Monte Carlo (MC) simulations, as we do in Section 3 for $m = 1 , \\\\ldots , 4$ in the context of galaxy cluster tSZ observations. Nevertheless, further insight into the value of the first moment, the mean, which we denote with $\\\\bar { q } _ { \\\\mathrm { o p t } }$ , can be gained with the following argument. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,67,922,95]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,95,922,194]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Consider the value of $- 2 \\\\ln \\\\mathcal { L }$ , i.e., of the sum of the residuals. If we evaluate it at the true value of $\\\\theta , \\\\theta _ { \\\\mathrm { t } }$ , and at the corresponding matched filter value of $s _ { 0 }$ , $\\\\hat { s } _ { 0 } ( \\\\pmb { \\\\theta } _ { \\\\mathrm { t } } )$ , there is only one fitting parameter, $s _ { 0 }$ , the model being linear in it. Thus, in this case $- 2 \\\\ln \\\\mathcal { L }$ is $\\\\chi ^ { 2 }$ - distributed with $n - 1$ degrees of freedom, where we recall that $n$ is the dimension of our data vector (e.g., Andrae et al. 2010). Using Eq. (6), its expected value can be written as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[546,212,884,231]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0574/a247350353679814a2f15fc398ed3086e638eb692bfbe1e6dfba45b9bbca9316.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array} { r } { \\\\langle - 2 \\\\ln \\\\mathcal { L } ( \\\\hat { s } _ { 0 } ( \\\\theta _ { \\\\mathrm { t } } ) , \\\\theta _ { \\\\mathrm { t } } ) \\\\rangle = t ^ { T } { \\\\bf C } ^ { - 1 } t + n - \\\\langle q ( \\\\theta _ { \\\\mathrm { t } } ) ^ { 2 } \\\\rangle = n - 1 , } \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,237,921,294]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $t$ it the true signal (i.e., the model evaluated at the true parameter values), and where we have ignored the second, parameterindependent term. Since $\\\\left. q ( \\\\pmb { \\\\theta } _ { \\\\mathrm { t } } ) \\\\right. = \\\\bar { q } _ { \\\\mathrm { t } }$ , and since $q ( \\\\pmb \\\\theta _ { \\\\mathrm { t } } )$ has unit variance, it follows that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[623,313,805,331]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0066/42643de0547e0cb887f8abf7825957332a741b6a8b5ac2c8736dd6e1696bd925.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nt ^ { T } { \\\\bf C } ^ { - 1 } t + n - 1 - \\\\bar { q } _ { \\\\mathrm { t } } ^ { 2 } = n - 1 .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[510,337,922,492]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"On the other hand, $- 2 \\\\ln \\\\mathcal { L }$ is not $\\\\chi ^ { 2 }$ -distributed if we evaluate it for the matched filter solution, in which $f$ additional parameters are fitted, as now the model is, in general, non-linear in the parameters (see, e.g., Andrae et al. 2010). Equivalently, this can be seen as a consequence of $q _ { \\\\mathrm { o p t } }$ being non-Gaussian. This means, in particular, that we cannot compute its expected value by invoking the number of degrees of freedom in the fit, as we did in the previous case. However, this is still a well-defined quantity, which we write as $n - 1 - f _ { \\\\mathrm { e f f } }$ , where we have introduced $f _ { \\\\mathrm { e f f } }$ as the ‘effective number of additional fitting parameters’. The value of $f _ { \\\\mathrm { e f f } }$ cannot be determined a priori, but it is clear that $f _ { \\\\mathrm { e f f } } \\\\geq 0$ . We can now write \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,511,880,531]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0478/26668c7e77bd1fe077007c7c4756d409155008a4e2eefebcb55f5f97853afbaf.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left. - 2 \\\\ln \\\\mathcal { L } ( \\\\hat { s } _ { 0 } ( \\\\hat { \\\\pmb { \\\\theta } } ) , \\\\hat { \\\\pmb { \\\\theta } } ) \\\\right. = { t } ^ { T } { \\\\bf C } ^ { - 1 } { \\\\pmb { t } } + n - \\\\langle q _ { \\\\mathrm { o p t } } ^ { 2 } \\\\rangle = n - 1 - f _ { \\\\mathrm { e f f } } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[510,538,552,549]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and so \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[591,570,836,589]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0772/ddd7bb1c4ae8024743c3dd164a1a28b6da62038717c01b5624bb40912a7fb3d2.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nt ^ { T } \\\\mathsf { C } ^ { - 1 } t + n - \\\\sigma _ { \\\\mathrm { o p t } } ^ { 2 } - \\\\bar { q } _ { \\\\mathrm { o p t } } ^ { 2 } = n - 1 - f _ { \\\\mathrm { e f f } } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,594,922,636]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\sigma _ { \\\\mathrm { o p t } }$ denotes the standard deviation of $q _ { \\\\mathrm { o p t } }$ , which need not be equal to unity, as in the Gaussian case. Subtracting Eq. (10) from Eq. (12) and rearranging, we find \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[636,654,794,679]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0886/a066c40fc6dfb338895a3912282e955f56d8333b8b12ab57485609496e90b9e4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\bar { q } _ { \\\\mathrm { o p t } } = \\\\sqrt { \\\\bar { q } _ { \\\\mathrm { t } } ^ { 2 } + f _ { \\\\mathrm { e f f } } + \\\\Delta \\\\sigma ^ { 2 } } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[510,686,652,702]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\Delta \\\\sigma ^ { 2 } \\\\equiv 1 - \\\\sigma _ { \\\\mathrm { o p t } } ^ { 2 }$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,703,922,799]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Thus, $\\\\bar { q } _ { \\\\mathrm { o p t } }$ is biased with respect to ${ \\\\bar { q } } _ { \\\\mathfrak { t } }$ . We refer to this bias as optimisation bias, and note that it is a positive bias, with $\\\\bar { q } _ { \\\\mathrm { o p t } } > \\\\bar { q } _ { \\\\mathrm { t } }$ . This can in fact be deduced from a simple argument: for any noise realisation, $q _ { \\\\mathrm { o p t } } > q ( \\\\pmb \\\\theta _ { \\\\mathrm { t } } )$ by construction (except in the case in which $\\\\widehat { \\\\pmb { \\\\theta } } = \\\\pmb { \\\\theta } _ { 1 }$ , which happens with formally zero probability), and thus $\\\\bar { q } _ { \\\\mathrm { o p t } } > \\\\bar { q } _ { \\\\mathrm { t } }$ . Intuitively: by allowing for additional freedom in the fit, the signal-to-noise is boosted, as one is effectively fitting noise. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,800,922,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In summary, $P ( q _ { \\\\mathrm { o p t } } | \\\\bar { q } _ { \\\\mathrm { t } } )$ is a non-Gaussian distribution with moments given by Eq. (8) and whose mean can be also written as in Eq. (13). In order for a set of $q _ { \\\\mathrm { o p t } }$ measurements to be used in practice, one has to determine how much $P ( q _ { \\\\mathrm { o p t } } | \\\\bar { q } _ { \\\\mathrm { t } } )$ deviates from Gaussianity, as well as the values of $f _ { \\\\mathrm { e f f } }$ and $\\\\sigma _ { \\\\mathrm { o p t } }$ , both of which can be a function of $\\\\bar { q } _ { \\\\mathrm { t } }$ . In Section 3 we do so using MC simulations for the case in which the signal to be extracted is the tSZ signal from a galaxy cluster, finding that, for sufficiently large values of $\\\\bar { q } _ { \\\\mathrm { t } }$ $( \\\\simeq 6 )$ , $P ( q _ { \\\\mathrm { o p t } } | \\\\bar { q } _ { \\\\mathrm { t } } )$ approaches a unit-variance Gaussian and $f _ { \\\\mathrm { e f f } }$ approaches the actual number of additional fitting parameters, $f$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[561,35,921,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Matched filters for precision cosmology 3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[776,955,921,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MNRAS 000, 1–13 (2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,67,225,81]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.4 Partial optimisation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,89,478,299]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Thus far we have assumed that the optimisation procedure finds the true signal-to-noise maximum, i.e., that the true maximum likelihood solution is obtained. In some applications of matched filtering, however, the signal-to-noise is evaluated on a given parameter grid, with the ‘matched filter solution’ and its associated signal-to-noise, $q _ { \\\\mathrm { o p t } }$ , now being the grid coordinates at which the signal-to-noise is maximised and the corresponding signal-to-noise value, respectively. As we will see in Section 3, this partial optimisation can have an impact on the statistics of $q _ { \\\\mathrm { o p t } }$ . In general, a dependency on the grid chosen is introduced, with the statistics of the partially-optimised $q _ { \\\\mathrm { o p t } }$ being obviously expected to approach those of the true $q _ { \\\\mathrm { o p t } }$ as the grid spacing is decreased. As we illustrate in Section 3, the impact of this partial optimisation must be carefully considered if unbiased information is to be extracted from partially-optimised $q _ { \\\\mathrm { o p t } }$ measurements. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,335,465,361]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 A PRACTICAL APPLICATION: SZ GALAXY CLUSTER DETECTION AND NUMBER COUNTS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[67,370,391,384]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1 Matched filtering in the galaxy cluster context \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,393,480,742]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As noted in the Introduction, matched filters are now routinely used in order to detect and characterise galaxy clusters from mm data. They have indeed been used in experiments such as SPT, ACT, and Planck (Vanderlinde et al. 2010; Hasselfield et al. 2013; Planck 2013 results XXIX 2014; Bleem et al. 2015; Planck 2015 results XXVII 2016; Hilton et al. 2021; Melin et al. 2021), and will also continue to be used in upcoming experiments such as SO and CMB-S4 (Abazajian et al. 2016; Simons Observatory Collaboration 2019). In these works, galaxy clusters are detected following, roughly, the same general procedure. First, the cluster search sky area is divided into a set of patches, which allows for local noise estimation. Then, a model for the cluster tSZ signal is assumed. This model is parametrised as our signal in Eq. (1), with an overall amplitude parameter and a template function, which is typically taken to depend on two sky location parameters and on an angular size parameter. For each of the patches, this template is used to construct a matched filter, for which the signal-to-noise (in our notation, $q$ ) is evaluated across a number of sky locations (usually, for each pixel) and angular sizes. We note that if observations at more than one frequency channel are used, the matched filter operates across the maps at the different frequencies considered, and is usually referred to as a multifrequency matched filter (MMF). If we put the frequency and spatial indices on the same footing, however, an MMF can be seen as a ‘singlefrequency’ matched filter, which means that the formalism and the insights presented in Section 2 remain entirely valid. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,744,478,938]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For each patch, the sky locations of the cluster candidates in it are then obtained from the local peaks in the signal-to-noise map, with the specific procedure varying from analysis to analysis, but being in essence a maximisation of the signal-to-noise over sky location (a ‘partial’ maximisation, however; see Section 2.4). The characterisation of the cluster signal, nonetheless, depends more significantly on the analysis considered. In Planck and SPT, the signal-to-noise (partially) maximised over sky location and angular size is used $\\\\scriptstyle \\\\mathbf { \\\\bar { \\\\varphi } } _ { q _ { 0 } { \\\\mathrm { p t } } }$ in our notation; e.g., Vanderlinde et al. 2010; Planck 2013 results XXIX 2014). In ACT, on the other hand, the signal-to-noise is maximised only to assign a sky location, the matched filter being only used at a single fixed angular size, at which the signal amplitude ( $\\\\hat { s } _ { 0 }$ in our notation) is computed and used as the cluster observable. In the likelihood, however, this $\\\\hat { s } _ { 0 }$ measurement has as associated standard deviation the corresponding matched filter standard deviation (given by Eq. 4), so using $\\\\hat { s } _ { 0 }$ at a fixed angular scale as an observable is equivalent to using the corresponding $q$ measurement. There is an obvious loss of statistical power due to fixing the angular scale, but, as argued in Hasselfield et al. (2013) and Hilton et al. (2021), doing this should partially mitigate against what we understand is the optimisation bias. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,67,921,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,166,921,491]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In short, as the cluster tSZ observable, SPT and Planck use $q _ { \\\\mathrm { o p t } }$ with (partial) optimisation over sky location and angular size, whereas ACT effectively uses $q _ { \\\\mathrm { o p t } }$ with only (partial) optimisation over sky location, fixing the angular size to a fiducial value. In the associated cosmological analyses, these tSZ observables are modelled differently. All three sets of analyses assume that $q _ { \\\\mathrm { o p t } }$ follows a unit-variance Gaussian distribution. The mean it is assigned, however, differs from analysis to analysis. The SPT cluster number counts analyses (Vanderlinde et al. 2010; Bleem et al. 2015; Bocquet et al. 2019) account for the optimisation bias at the likelihood level, using as the expected value of $q _ { \\\\mathrm { o p t } }$ (their ‘biased significance’, $\\\\xi ,$ ) $\\\\bar { q } _ { \\\\mathrm { o p t } } = ( \\\\bar { q } _ { \\\\mathrm { t } } ^ { 2 } + 3 ) ^ { 1 / 2 }$ . This corresponds to our formula for $\\\\bar { q } _ { \\\\mathrm { o p t } }$ , given in Eq. (13), if we set $\\\\Delta \\\\sigma ^ { 2 } = 0$ and $f _ { \\\\mathrm { e f f } } = f$ ; a rather heuristic justification for this prescription is given in Vanderlinde et al. (2010). The Planck cluster number counts analyses (Planck 2013 results XX 2014; Planck 2015 results XXIV 2016), despite using $q _ { \\\\mathrm { o p t } }$ as an observable, do not account for the optimisation bias at all, as neither does the reanalysis with CMB lensing mass calibration of Zubeldia & Challinor (2019). Finally, the ACT analysis (Hasselfield et al. 2013), which uses $q _ { \\\\mathrm { o p t } }$ at a fixed angular scale in order to mitigate against the optimisation bias, does not account for optimisation over sky location, which means that in principle it suffers from the bias, although from a somewhat smaller one. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,492,921,617]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Thanks to the insights gained in Section 2, it should be clear that if the signal-to-noise is maximised over some set of parameters, the consequences of doing so (non-Gaussianity, standard deviation different from unity, and optimisation bias) should be carefully quantified and, if deemed non-negligible, properly accounted for. As an illustration of how this can be done, as well as of the general theoretical arguments presented in Section 2, in the next section we quantify these effects for an idealised SZ experiment using a set of MC mock observations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,664,890,679]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2 Quantifying the statistics of $q _ { \\\\mathrm { o p t } }$ with MC observations \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,686,690,699]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2.1 Production of MC data \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,708,921,890]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this section, we quantify the statistics of $q _ { \\\\mathrm { o p t } }$ for a set of idealised tSZ observations produced with MC simulations. As our signal we take the Compton- $y$ map due to a set of galaxy clusters of some given masses $M _ { 5 0 0 }$ (defined, as customary, as the mass within $R _ { 5 0 0 }$ the radius within which the mean enclosed density is 500 times the critical density at the cluster’s redshift) and at some redshift $z$ . We take our clusters to be at $z = 0 . 3$ and consider a set of 16 masses such that the mean signal-to-noise $\\\\bar { q } _ { \\\\mathrm { t } }$ , as given by Eq. (5) after ensemble averaging over noise realisations, is logarithmically spaced between $\\\\bar { q } _ { \\\\mathrm { t } } = 3$ and $\\\\bar { q } _ { \\\\mathrm { t } } = 3 0$ (see our assumed experimental specifications below). We assume that our clusters have the pressure profile of Arnaud et al. (2010) (used, e.g., in the Planck analyses), from which the Compton- $y$ signal at a given sky location can be computed, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[657,911,773,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0767/a4f0669dd3b9ac500e469f2a746c51907f182a1370d7e3046f215738f3618cbd.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\ny = \\\\frac { \\\\sigma _ { \\\\mathrm { T } } } { m _ { \\\\mathrm { e } } c ^ { 2 } } \\\\int P d l ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[68,955,215,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MNRAS 000, 1–13 (2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,34,242,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 Í. Zubeldia et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,67,478,136]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $P$ is the cluster electron pressure, $\\\\sigma _ { \\\\mathrm { T } }$ is the electron Thomson scattering cross-section, $m _ { \\\\mathrm { e } }$ is the electron mass, and $d l$ is the proper distance element along the line of sight. Following the Planck analyses, we fix the concentration to $c = 1 . 1 7 7$ (e.g., Planck 2013 results $\\\\mathrm { X X } 2 0 1 4 )$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,139,478,299]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Adopting this cluster model, our signal vector $s _ { 0 } \\\\pmb { s }$ is the cluster Compton- $y$ parameter map, as given by Eq. (14), convolved with a Gaussian beam with a FWHM of 5 arcmin and evaluated on a square map of $1 2 8 \\\\times 1 2 8$ pixels. We use a pixel size of 1.7 arcmin and place the cluster at the centre of the map. We then add Gaussian white noise with a standard deviation per pixel of $\\\\sigma _ { \\\\mathrm { p i x e l } } = 8 . 8 3 \\\\times 1 0 ^ { - 7 }$ , which corresponds to a noise level of $\\\\sigma _ { n } = 1 . 5 \\\\times 1 0 ^ { - 6 }$ arcmin. That is, our noise covariance matrix C is diagonal, with all diagonal elements equal to ??2pixel. This procedure generates a simulated data vector ?? within the formalism of Section 2. We generate $1 0 ^ { 5 }$ such mock data vectors for each of our 16 values of $\\\\bar { q } _ { \\\\mathfrak { t } }$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,300,480,732]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We then use our signal, $s _ { 0 } \\\\pmb { s }$ , in order to construct a matched filter template, $\\\\pmb { s }$ , using as the amplitude (or normalisation) parameter $s _ { 0 }$ the value of the signal at $R _ { 5 0 0 }$ . We regard this template as a function of three parameters $\\\\pmb \\\\theta$ : the cluster angular size, $\\\\theta _ { 5 0 0 }$ , defined as $R _ { 5 0 0 } / d _ { A }$ , where $d _ { A }$ is the angular diameter distance to the cluster, and the two angular coordinates of its centre with respect to the centre of the map (i.e., with respect to the true cluster centre), $\\\\theta _ { x }$ and $\\\\theta _ { y }$ . That is, within the theoretical framework of Section 2, the number of additional fitting parameters (or ‘template parameters’) is $f = 3$ . Throughout this section we assume the noise covariance to be known; in Section 3.3, however, we consider the impact of noise covariance estimation. Using the matched filter constructed this way, for each of our mock data vectors we make a signal-to-noise measurement at the true parameter values $( \\\\theta _ { 5 0 0 } = \\\\theta _ { 5 0 0 } ^ { \\\\mathrm { t r u e } }$ and $\\\\theta _ { x } = \\\\theta _ { y } = 0 \\\\mathrm { \\\\Omega }$ ), $q _ { \\\\mathrm { t } }$ , an optimal signal-to-noise $q _ { \\\\mathrm { o p t } }$ , obtained by maximising the signal-to-noise over the three template parameters, and a partially-optimal signal-to-noise $q _ { \\\\mathrm { p - o p t } }$ , obtained by evaluating the signal-to-noise on a parameter grid and picking the maximum value. For this last set of measurements we use the parameter grid spanned by 80 values of $\\\\theta _ { 5 0 0 }$ logarithmically spaced between $\\\\theta _ { 5 0 0 } = 0 . 9 4$ arcmin and $\\\\theta _ { 5 0 0 } = 1 0 1 . 5 7$ arcmin and the angular coordinates of the centres of each pixel. This procedure generates a set of $q _ { \\\\mathrm { t } }$ , $q _ { \\\\mathrm { o p t } }$ and $q _ { \\\\mathrm { p - o p t } }$ mock measurements generated according to the formalism of Section 2. For each data vector we also compute $- 2 \\\\ln \\\\mathcal { L }$ for four different cases: (i) at the true value of the template parameters $\\\\pmb \\\\theta$ and of the amplitude parameter $s _ { 0 }$ , i.e., for the true model (the ‘true case’), (ii) at the true value of $\\\\pmb \\\\theta$ and the matched filter estimate of $s _ { 0 }$ at that value of $\\\\pmb \\\\theta$ , $\\\\hat { s } _ { 0 } ( \\\\pmb { \\\\theta } ^ { \\\\mathrm { t r u e } } )$ (the ‘fixed case’), (iii) at the matched filter solution for $\\\\theta , \\\\hat { \\\\pmb \\\\theta }$ , and its corresponding matched filter estimate of $s _ { 0 }$ , $\\\\hat { s } _ { 0 } ( \\\\hat { \\\\pmb { \\\\theta } } )$ (the ‘optimal case’), and (iv), at the partially-optimised parameter values and the corresponding matched filter estimate (the ‘partially optimal’ case). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,734,478,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We note that our setup may not seem equivalent to what is usually done in practice in order to detect and characterise galaxy clusters in mm surveys, which is to use multi-frequency matched filters (MMF) that operate directly on the experiment frequency maps, rather than on an estimated Compton-?? map (e.g., Planck 2013 results XX 2014). In Appendix A, however, we show that if the Compton- $\\\\boldsymbol { \\\\cdot } \\\\boldsymbol { y }$ map is obtained through an Internal Linear Combination (ILC; see, e.g., Delabrouille & Cardoso 2007), these two approaches are mathematically equivalent. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,890,351,904]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2.2 Standard deviation and non-Gaussianity \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,911,478,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We first investigate the standard deviation of $q _ { \\\\mathrm { o p t } }$ and $q _ { \\\\mathrm { p - o p t } }$ and the extent of their departure from Gaussianity. Fig. 1 shows the standard deviation $\\\\sigma _ { q }$ , reduced skewness $\\\\lambda _ { 3 , q }$ , and reduced kurtosis $\\\\lambda _ { 4 , q }$ of the distribution of $q _ { \\\\mathrm { o p t } }$ (orange error bars) and of $q _ { \\\\mathrm { p - o p t } }$ (red error bars) as a function of true mean signal-to-noise $\\\\bar { q } _ { \\\\mathrm { t } }$ , as estimated with our set of mock measurements. We note that the error bars of the estimates of the standard deviation have been increased by a factor of 10 to allow for better visualisation. It can be seen that these three statistics are essentially the same for both $q _ { \\\\mathrm { o p t } }$ and $q _ { \\\\mathrm { p - o p t } }$ . Both $q _ { \\\\mathrm { o p t } }$ and $q _ { \\\\mathrm { p - o p t } }$ become progressively more Gaussian as ${ \\\\bar { q } } _ { \\\\mathfrak { t } }$ is increased, their skewness and kurtosis being driven to zero. In addition, their standard deviation approaches unity with increasing $\\\\bar { q } _ { \\\\mathrm { t } }$ . Roughly, for values of $\\\\bar { q } _ { \\\\mathrm { t } }$ greater than $\\\\simeq 6$ , $q _ { \\\\mathrm { o p t } }$ can be approximately taken to follow a unit-variance Gaussian distribution. For comparison, the standard deviation, skewness, and kurtosis of $q _ { \\\\mathrm { t } }$ , as estimated from our mock measurements, are also shown. As expected, the standard deviation is consistent with unity throughout, as are the skewness and kurtosis with zero. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[529,120,895,516]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 1. Standard deviation (top panel), reduced skewness (middle panel), and reduced kurtosis (bottom panel) of $q _ { \\\\\\\\mathrm { o p t } }$ (orange error bars), $q _ { \\\\\\\\mathrm { p - o p t } }$ (red error bars), and $q _ { \\\\\\\\mathrm { t } }$ (blue error bars) as a function of true mean signal-to-noise, $\\\\\\\\bar { q } _ { \\\\\\\\mathrm { t } }$ , as estimated with our set of mock observations. The reference values of $\\\\\\\\sigma _ { q } = 1$ , $\\\\\\\\lambda _ { 3 , q } = 0$ , $\\\\\\\\lambda _ { 4 , q } = 0$ , and $\\\\\\\\bar { q } _ { \\\\\\\\mathrm { t } } = 6$ are shown as straight lines. We note that the error bars have been increased by a factor of 10 for better visualisation. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0193/cc9acfcab1224780019a1514f3d4b0f048590906b0ccc6c605f93f2709ff76b3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[512,716,922,938]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[561,35,921,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Matched filters for precision cosmology 5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[776,955,921,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MNRAS 000, 1–13 (2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,69,470,81]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2.3 Effective number of fitting parameters and optimisation bias \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,85,480,640]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We now quantify, as a function of the mean signal-to-noise, the effective number of additional fitting parameters $f _ { \\\\mathrm { e f f } }$ associated with optimising the signal-to-noise over our three template parameters. We do so with our measured values of $- 2 \\\\ln \\\\mathcal { L }$ . The top panel of Fig. 2 shows the empirical mean of this quantity as a function of $\\\\bar { q } _ { \\\\mathrm { t } }$ for the four cases for which we have computed it: the ‘true case’ (green error bars), the ‘fixed case’ (blue error bars), the optimal case (orange error bars), and the partially optimal case (red error bars). For the true case, for which $- 2 \\\\ln \\\\mathcal { L }$ is $\\\\chi ^ { 2 }$ -distributed with $n$ degrees of freedom, where $n$ is the number of data points, the estimated mean is consistent with $1 6 3 8 4 = 1 2 8 ^ { 2 }$ throughout, as expected. Similarly, for the fixed case, for which $- 2 \\\\ln \\\\mathcal { L }$ is also $\\\\chi ^ { 2 }$ -distributed, though with $n - 1$ degrees of freedom, the estimated mean is consistent with $1 2 8 ^ { 2 } - 1$ , also as expected. However, for the optimal and partially optimal cases, the situation is different, as a result of $- 2 \\\\ln \\\\mathcal { L }$ no longer being $\\\\chi ^ { 2 }$ - distributed. For the optimal case, the estimated mean of $- 2 \\\\ln \\\\mathcal { L }$ is consistent with $1 2 8 ^ { 2 } - 4 = 1 6 3 8 0$ for large values of $\\\\bar { q } _ { \\\\mathfrak { t } }$ (roughly, for $\\\\bar { q } _ { \\\\mathrm { t } } > 6$ ), as it would be naively (and wrongly) expected for three additional fitting parameters, but it drops to lower values for small values of $\\\\bar { q } _ { \\\\mathrm { t } }$ : at the low signal-to-noise end, our model ‘fits the data better’ than a linear model would. For the partially optimal case, the estimated mean of $- 2 \\\\ln \\\\mathcal { L }$ is consistent with $1 2 8 ^ { 2 } - 2 = 1 6 3 8 0$ for large values of $\\\\bar { q } _ { \\\\mathrm { t } }$ , dropping to lower values for smaller values of $\\\\bar { q } _ { \\\\mathrm { t } }$ , as in the optimal case. The high signal-to-noise behaviour, indicative of just one additional fitting parameter, can be explained by the fact that, at high signal-to-noise, the true central pixel is almost always chosen in the grid optimisation process, and therefore no overfitting arising from location can take place. Effectively, there is just one additional fitting parameter, the cluster angular size. We note that this is a feature of our true signal being placed in the centre of a pixel, which allows for the possibility of the grid optimisation algorithm matching the sky location perfectly. This will obviously not be the case in a real experimental setting, in which there will always be an offset between the centre of the chosen pixel and the true cluster sky location. This implies that, in a real setting, the fit will be worse, and $- 2 \\\\ln \\\\mathcal { L }$ will not converge to $n ^ { 2 } - 2$ , but will take larger values. We note that true optimisation does not suffer from this artefact, which means that our results in that instance are applicable to a real experimental setting in which the cluster may not be centred in the centre of a pixel. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,641,480,754]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the bottom panel of Fig. 2 we rephrase the problem in terms of the effective number of additional fitting parameters, $f _ { \\\\mathrm { e f f } }$ , where we recall that $\\\\langle - 2 \\\\ln \\\\mathcal { L } \\\\rangle = n - 1 - f _ { \\\\mathrm { e f f } }$ . As expected from the top panel, for the fixed case, $f _ { \\\\mathrm { e f f } }$ is consistent with zero throughout; for the optimal case, $f _ { \\\\mathrm { e f f } } \\\\simeq 3$ for large values of $\\\\bar { q } _ { \\\\mathrm { t } }$ (roughly, for $\\\\bar { q } _ { \\\\mathrm { t } } > 6$ ), progressively taking larger values for smaller values of ${ \\\\bar { q } } _ { \\\\mathfrak { t } }$ ; and for the partially optimal case, $f _ { \\\\mathrm { e f f } } \\\\simeq 1$ for large values of $\\\\bar { q } _ { \\\\mathrm { t } }$ , similarly taking larger values with decreasing $\\\\bar { q } _ { \\\\mathrm { t } }$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,757,478,938]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Now that we have determined the standard deviation of $q _ { \\\\mathrm { o p t } }$ and $f _ { \\\\mathrm { e f f } }$ as a function of $\\\\bar { q } _ { \\\\mathrm { t } }$ , we are in a position to compute $\\\\bar { q } _ { \\\\mathrm { o p t } }$ using Eq. (13). We do so by interpolating over our values of $\\\\sigma _ { q }$ and $f _ { \\\\mathrm { e f f } }$ . Fig. 3 shows such prediction (shown as $\\\\bar { q } _ { \\\\mathrm { o p t } } / \\\\bar { q } _ { \\\\mathrm { t } } )$ as a function of ${ \\\\bar { q } } _ { \\\\mathfrak { t } }$ (solid orange curve), along with the associated direct estimates of $\\\\bar { q } _ { \\\\mathrm { o p t } }$ obtained by ensemble averaging over our $q _ { \\\\mathrm { o p t } }$ measurements (orange error bars). To illustrate the relative importance of accounting for the deviation form unity in the variance and for the change in $f _ { \\\\mathrm { e f f } }$ from the ‘naive’ value of $f = 3$ , we also show the curve that is obtained if we ignore the change in the variance and set $f _ { \\\\mathrm { e f f } } = f = 3$ , which we refer to as the $f$ correction (dotted orange curve), and the one that is obtained if we ignore the change in the variance but use the MC-estimated value of $f _ { \\\\mathrm { e f f } }$ (dashed orange curve). It can be seen that for, roughly, $\\\\bar { q } _ { \\\\mathrm { o p t } } > 6$ , $\\\\bar { q } _ { \\\\mathrm { o p t } }$ is essentially given by $\\\\bar { q } _ { \\\\mathrm { o p t } } \\\\simeq ( \\\\bar { q } _ { \\\\mathrm { t } } ^ { 2 } + f ) ^ { 1 / 2 }$ , i.e., by the $f$ correction alone. This was to be expected from our MC measurements of $\\\\sigma _ { q }$ and of $f _ { \\\\mathrm { e f f } }$ , which we recall converge to 1 and to $f$ , respectively, by $\\\\bar { q } _ { \\\\mathrm { o p t } } \\\\simeq 6$ . This constitutes a remarkable result, as it means that for signal-to-noise values similar to those typically used as selection thresholds in cosmological tSZ catalogues (e.g., in Planck, a threshold of $q _ { \\\\mathrm { o p t } } = 6$ was chosen), as well as for higher values, $\\\\bar { q } _ { \\\\mathrm { o p t } }$ can be computed accurately (e.g., in a likelihood) in a straightforward way without the need to resort to MC data. If a more accurate expression at low values of $\\\\bar { q } _ { \\\\mathrm { o p t } }$ is needed (e.g., if a lower selection threshold is used in an analysis), one could interpolate over the numerical results, either over $f _ { \\\\mathrm { e f f } }$ and $\\\\sigma _ { q }$ , or directly over $\\\\bar { q } _ { \\\\mathrm { o p t } }$ ; alternatively, one could fit a function (e.g., a polynomial) to them. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[521,93,895,304]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 2. Top panel: Expected value of $- 2 \\\\\\\\ln$ $\\\\\\\\mathcal { L }$ for the true, fixed, optimal, and partially optimal cases (green, blue, orange, and red error bars, respectively) as a function of the mean true signal-to-noise, $\\\\\\\\bar { q } _ { \\\\\\\\mathrm { t } }$ , as estimated with our mock observations, shown along their associated reference values of 16384, 16383, 16382, and 16380, respectively. Bottom panel: Effective number of additional fitting parameters, $f _ { \\\\\\\\mathrm { e f f } }$ , for the fixed, optimal, and partially optimal cases (blue, orange, and red error bars, respectively) as a function of $\\\\\\\\bar { q } _ { \\\\\\\\mathrm { t } }$ , as estimated with our mock observations, shown along their reference values of 0, 1 and 3. The reference value of $\\\\\\\\bar { q } _ { \\\\\\\\mathrm { t } } = 6$ is also shown. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0634/092f14ccfaf6b20fb9ed099555dc0651da607cdef2041dc96aa3d36e100a0a1e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[510,471,922,653]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,656,922,822]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We remark that we have obtained our numerical results for the case in which three parameters (one angular size parameter and two sky coordinates) are optimised over. This was the case of the Planck and SPT analyses (e.g., Planck 2015 results XXVII 2016; Bocquet et al. 2019), and we thus expect our results to be relevant for them. In ACT, on the other hand, the signal-to-noise over was optimised only over two sky coordinates (e.g, Hilton et al. 2021). Since this involves less parameters than the case considered here, and since these are the same as two of our three parameters, we expect our results to also be relevant for ACT. In particular, the $f$ correction should be accurate in a similar, if not broader, signal-to-noise range, noting that, in this case, $f = 2$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,847,635,861]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2.4 Gridding bias \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,870,921,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Fig. 3 also shows the empirical means of our $q _ { \\\\mathrm { p - o p t } }$ and $q _ { \\\\mathrm { t } }$ measurements as a function of ${ \\\\bar { q } } _ { \\\\mathfrak { t } }$ , shown, too, normalised by $\\\\bar { q } _ { \\\\mathrm { t } }$ (red and blue error bars, respectively). As expected, the mean of the $q _ { \\\\mathrm { t } }$ measurements is consistent with $\\\\bar { q } _ { \\\\mathrm { t } }$ and the mean of $q _ { \\\\mathrm { p - o p t } }$ is always below that of $q _ { \\\\mathrm { o p t } }$ , as, due to gridding, there is less ‘overfitting’. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,955,215,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MNRAS 000, 1–13 (2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,34,242,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 Í. Zubeldia et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[70,67,478,277]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This can be understood as a ‘gridding bias’ acting in the direction opposite to the optimisation bias (in the context of just sky location, this would be the usual miscentering bias). We remark that this bias depends on the grid chosen: a coarser grid would lead to a larger gridding bias, which could even lead to an overall negative bias, whereas a grid with infinitesimal cells would yield a vanishingly small gridding bias, $q _ { \\\\mathrm { p - o p t } }$ being equal to $q _ { \\\\mathrm { o p t } }$ . Due to the presence of this additional bias, which does not exist for true optimisation, and to the fact that for true optimisation the optimisation bias can be accurately modelled with the simple $f$ correction for reasonably large values of signal-to-noise, we advocate for the use of the ‘true’ optimal signal-to-noise, $q _ { \\\\mathrm { o p t } }$ , as a cluster observable, in detriment to the commonly-used partially-optimal signal-to-noise. In practice, this can be realised, if not with an optimisation algorithm, with the use of an appropriately finely-spaced grid. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,280,478,418]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Regarding the spatial gridding, we should note that in our mock observations, each pixel receives an independent noise realisation; as a consequence, the ‘optimal limit’ is not reached by evaluating the signal-to-noise at the centre of each pixel, as there is structure in the data down to the pixel level. This is not typically the case in real maps, which tend to be well oversampled: the ‘optimal limit’ in the angular coordinates may therefore be reached by just evaluating the signal-to-noise at the centre of each pixel. Care should still be taken, however, with the grid optimisation of the angular scale parameter (and of any other additional parameters). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[72,507,368,520]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2.5 Parameter estimates: $\\\\theta _ { 5 0 0 }$ and sky position \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,530,478,753]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Although the signal-to-noise is usually the main quantity of interest in tSZ galaxy cluster studies, maximising the matched filter signalto-noise over a set of parameters $\\\\pmb \\\\theta$ also yields an estimator for $\\\\mathbf { \\\\hat { \\\\theta } } , \\\\hat { \\\\pmb { \\\\theta } }$ , which we refer to as the matched filter solution. As shown in Section 2, this matched filter solution is equal to the maximum-likelihood estimator for $\\\\pmb \\\\theta$ , and therefore it is, in general, biased (see Section 2.2). As an illustration of this point, Fig. 4 shows the empirical means of the matched filter solutions of two of our parameters, $\\\\theta _ { 5 0 0 }$ (upper panel) and $\\\\theta _ { x }$ (middle panel), as a function of ${ \\\\bar { q } } _ { \\\\mathrm { t } }$ , as obtained with our mock measurements for true optimisation (orange error bars) and partial optimisation (red error bars). (The results for $\\\\theta _ { y }$ are analogous to those of $\\\\theta _ { x }$ and hence not shown.) It can be observed that the matched filter estimates of $\\\\theta _ { 5 0 0 }$ are biased high for both true and partial optimisation, the bias decreasing with increasing signalto-noise. The estimates of $\\\\theta _ { x }$ , on the other hand, are not biased, as expected from the symmetry of the problem. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,755,478,938]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In order to illustrate the point made in Section 2.2 that the extent, and even the existence, of a bias in the parameter estimates is entirely parametrisation-dependent, the bottom panel of Fig. 4 shows the empirical means of the parameter $\\\\theta _ { r } \\\\equiv \\\\mathbf { \\\\dot { \\\\Gamma } } ( \\\\theta _ { x } ^ { 2 } + \\\\theta _ { y } ^ { 2 } ) ^ { 1 / 2 }$ , which along with $\\\\phi \\\\equiv \\\\tan ^ { - 1 } ( \\\\theta _ { y } / \\\\theta _ { x } )$ constitute a fully equivalent parametrisation to $\\\\theta _ { x }$ and $\\\\theta _ { y }$ . As expected, the estimates of $\\\\theta _ { r }$ are biased high, as they receives contributions from the second-order moments of $\\\\theta _ { x }$ and $\\\\theta _ { y }$ . We note that for the partially-optimised case, the bias disappears at high signal-to-noise. This is an artefact of our simulated clusters being centred at the centre of a pixel, which allows, at the high signal-to-noise end, for the true location to be chosen perfectly by the grid optimisation algorithm. This will of course not happen in a real experimental setting (see Section 3.2.3 for a similar discussion). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,67,811,81]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2.6 Dependence on redshift and on noise levels \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,89,921,327]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The results presented in the previous sections were obtained as a function of mean true signal-to-noise, $\\\\bar { q } _ { \\\\mathfrak { t } }$ , by fixing the cluster redshift at $z = 0 . 3$ and varying the cluster mass $M _ { 5 0 0 }$ . There is, of course, a perfect degeneracy in $\\\\bar { q } _ { \\\\mathrm { t } }$ , whereby a given value of ${ \\\\bar { q } } _ { \\\\mathfrak { t } }$ can be obtained by moving along some curve in the $M _ { 5 0 0 } – z$ plane. However, although $\\\\bar { q } _ { \\\\mathrm { t } }$ may be perfectly degenerate along this curve, the actual observation (the Compton-?? map) will not be so. As a consequence, the statistics of $q _ { \\\\mathrm { o p t } }$ and, in particular, the magnitude of the optimisation bias are not guaranteed to depend exclusively on $\\\\bar { q } _ { \\\\mathrm { t } }$ , but should in general be regarded as a function of both $M _ { 5 0 0 }$ and $z$ . One can also regard them as dependent on the assumed observational specifications, e.g., the white noise levels, under which $\\\\bar { q } _ { \\\\mathrm { t } }$ is also perfectly degenerate, with the data not being so either. This poses the question of to what extent can our results, especially the magnitude of the optimisation bias, be regarded as a function of only $\\\\bar { q } _ { \\\\mathrm { t } }$ , i.e., whether the higherdimensional dependency on $M _ { 5 0 0 }$ , ??, noise levels, etc. can be safely condensed into a dependency on just $\\\\bar { q } _ { \\\\mathrm { t } }$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,328,922,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In order to address this question, we produce a new set of mock observations following exactly the same procedure as the one detailed in Section 3.2.1, but for a set of 16 points lying in the curve of the $M _ { 5 0 0 } – z$ plane defined by $\\\\bar { q } _ { \\\\mathrm { t } } ( M _ { 5 0 0 } , z ) = 6$ . Specifically, we consider 16 values of $z$ linearly spaced between $z = 0 . 1$ and $z = 0 . 8$ and compute the corresponding value of $M _ { 5 0 0 }$ that yields $\\\\bar { q } _ { \\\\mathrm { t } } = 6$ . We produce $1 0 ^ { 4 }$ mock data vectors for each point along this curve, and we do so for three different white noise levels: $\\\\sigma _ { n } = 1 . 5 { \\\\times } 1 0 ^ { - 6 }$ arcmin (the same as used for the mock data of the previous sections), $\\\\sigma _ { n } =$ $3 \\\\times 1 0 ^ { - 6 }$ arcmin, and $\\\\sigma _ { n } = 0 . 7 5 \\\\times 1 0 ^ { - 6 }$ arcmin. Here we consider only true optimisation, computing the value of $q _ { \\\\mathrm { o p t } }$ for each mock data vector. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,497,921,750]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Fig. 5 shows the empirical mean (upper panel) and standard deviation (lower panel) of these $q _ { \\\\mathrm { o p t } }$ measurements as a function of $M _ { 5 0 0 }$ for the the three instances of noise levels (blue, orange, and red error bars). The upper panel also shows as straight lines the reference values of $q = 6$ , which is the value of ${ \\\\bar { q } } _ { \\\\mathrm { t } }$ for all the measurements (blue line), and that of $\\\\bar { q } _ { \\\\mathrm { o p t } }$ computed with only the $f$ correction, i.e., $\\\\bar { q } _ { \\\\mathrm { o p t } } = ( \\\\bar { q } _ { \\\\mathrm { t } } ^ { 2 } + f ) ^ { 1 / 2 }$ with $f = 3$ , which we know is an accurate approximation for $\\\\bar { q } _ { \\\\mathrm { o p t } }$ at $\\\\bar { q } _ { \\\\mathrm { t } } = 6$ (orange line). On the other hand, the lower panel also shows the reference value of unity standard deviation (blue line). It can be seen that any variation of $\\\\bar { q } _ { \\\\mathrm { o p t } }$ and $\\\\sigma _ { q }$ across the curve $\\\\bar { q } _ { \\\\mathrm { t } } ( M _ { 5 0 0 } , z ) = 6$ is clearly subdominant with respect to the overall differences with respect to $\\\\bar { q } _ { \\\\mathrm { t } } = 6$ and $\\\\sigma _ { q } = 1$ , respectively, and that this is true for the three noise levels that we have considered. We expect this to also be the case for $\\\\bar { q } _ { \\\\mathrm { t } } > 6$ , as with increasing $\\\\bar { q } _ { \\\\mathrm { t } }$ the $f$ correction becomes progressively more accurate and $\\\\sigma _ { q }$ gets closer to unity. In brief, within the mass–redshift and noise levels range that we have considered, the optimisation bias and $\\\\sigma _ { q }$ can be safely regarded as just a function of ${ \\\\bar { q } } _ { \\\\mathfrak { t } }$ for, at least, $\\\\bar { q } _ { \\\\mathrm { t } } > 6$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,777,825,791]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.3 Noise covariance estimation and other biases \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,799,921,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Throughout this paper we have assumed the noise covariance to be perfectly known. In a real setting, however, the noise covariance is typically estimated from the data itself. If the signal to be extracted is small enough, it can be taken to be equal to the total data covariance. This was the case, e.g., of the Planck analysis, in which the noise covariance was taken to be the empirically-estimated data covariance (Planck 2015 results XXVII 2016). While this is a good approximation at the low signal-to-noise end, it is no longer so for larger signalto-noise values, where the signal becomes comparable to the noise, potentially leading to a bias in the retrieved signal. This is illustrated in Figure 6, which shows the empirical mean and standard deviation of two sets of $q _ { \\\\mathrm { o p t } }$ mock measurements as a function of $\\\\bar { q } _ { \\\\mathrm { t } }$ (1000 data points for each value of ${ \\\\bar { q } } _ { \\\\mathrm { t } }$ each). In order to generate these two data sets, we produced mock data vectors (Compton-?? maps) with the same specifications as used in Section 3.2 and we then applied a matched filter on each of them, maximising the signal-to-noise over angular size and sky location. For one of the data sets (orange error bars), the noise covariance used to construct the matched filter was the true noise covariance (i.e., this mock data set is equivalent to that analysed throughout Section 3.2). For the other data set (green error bars), the noise covariance was taken to be equal to the data covariance, which was estimated empirically from the data vector by taking its standard deviation (that is, assuming the noise to be white). Is is apparent that while the empirical means of these two sets are essentially the same at low signal-to-noise, where noise is dominant, they deviate at the high signal-to-noise end, with noise estimation biasing $q _ { \\\\mathrm { o p t } }$ low. This negative bias has a simple explanation (see, e.g., Eq. 5): as the noise covariance is overestimated, the signal-tonoise is underestimated. The standard deviation is also affected at the high signal-to-noise end, although less so. Approaches in which an estimate of the signal is subtracted from the data, allowing for better noise covariance estimation (something that can be done, e.g., iteratively), can be followed to mitigate against this bias. An assessment of these approaches is, however, beyond the scope of this paper. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[776,955,921,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MNRAS 000, 1–13 (2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[561,35,921,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Matched filters for precision cosmology 7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[176,111,766,445]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 3. Empirical means of our $q _ { \\\\\\\\mathrm { o p t } }$ , $q _ { \\\\\\\\mathrm { p - o p t } }$ , and $q _ { \\\\\\\\mathrm { t } }$ measurements (orange, red, and blue error bars, respectively), shown along with three predictions for the mean of $q _ { \\\\\\\\mathrm { o p t } }$ , $\\\\\\\\bar { q } _ { \\\\\\\\mathrm { o p t } }$ : the full prediction given by Eq. 13 (solid orange curve), that given by Eq. 13 neglecting the variance change term (i.e., $\\\\\\\\bar { \\\\\\\\Delta } \\\\\\\\sigma ^ { 2 } = 0$ ) (dashed orange curve), and that given by the simple $f$ correction, with $f _ { \\\\\\\\mathrm { e f f } } = f = 3$ (dotted orange curve). All the error bars have been multiplied by a factor of 10 to allow for better visualisation, and the reference value of $\\\\\\\\bar { q } _ { \\\\\\\\mathrm { t } } = 6$ is shown as a vertical dashed line. As noted in Section 3.2.3, the $f$ correction is the most significant contribution to $\\\\\\\\bar { q } _ { \\\\\\\\mathrm { o p t } }$ for $\\\\\\\\bar { q } _ { \\\\\\\\mathrm { t } } \\\\\\\\gtrsim 6$ . \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0574/73e47882dc991663c68dc7160327efb7e4667da194da66f8ce22e00491ad8e6d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[80,583,455,795]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 4. Matched filter estimates of $\\\\\\\\pmb { \\\\\\\\theta } _ { 5 0 0 }$ , $\\\\\\\\theta _ { x }$ , and $\\\\\\\\theta _ { r }$ , as obtained from our mock data for both true and partial optimisation (orange and red error bars, respectively). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0642/c84b0d94a793c31b8a43492787172a4481dc118078f6542747fc7c3929245fad.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[67,897,478,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[529,583,897,795]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 5. Empirical mean (upper panel) and standard deviation (lower panel) of our $q _ { \\\\\\\\mathrm { o p t } }$ measurements produced along the $\\\\\\\\bar { q } _ { \\\\\\\\mathrm { t } } ( M _ { 5 0 0 } , z ) = 6$ curve for three different noise levels (blue, orange, and red error bars). In the upper panel, the reference values of $q = 6$ and $q = ( 6 ^ { 2 } + 3 ) ^ { 1 / 2 }$ are shown as straight lines (blue and orange lines, respectively), as is $\\\\\\\\sigma _ { q } = 1$ in the lower panel (blue line). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0539/e14a72e30efe57496b47668aa5b421af5c80d75ff097066e90ab0e8d527318b3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[68,955,215,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MNRAS 000, 1–13 (2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,35,242,49]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8 Í. Zubeldia et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[87,93,453,304]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 6. Empirical mean and standard deviation of our $q _ { \\\\\\\\mathrm { o p t } }$ measurements produced using the true noise covariance (orange error bars) and estimating it from the data (green error bars). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0346/891a3f955adcbb3e2420c89e79a2b5b08f07d511d7346ccc68737080e4dab222.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[68,398,480,693]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,694,478,833]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Other potential sources of bias include, but are not limited to, the wrong modelling of the signal to be extracted, i.e., the matched filter not matching the true cluster tSZ signal, both spatially and spectrally, the latter possible if the relativistic SZ effect (e.g., Sazonov & Sunyaev 1998; Challinor & Lasenby 1998; Chluba et al. 2012) is non-negligible, and the presence of other, ‘foreground’ signals such as the CMB, the kSZ effect, radio emission from the cluster’s galaxies, and point sources (see, e.g., Mroczkowski et al. 2019; Erler et al. 2019). Any assessment of these potential sources of systematics is beyond the scope of this paper. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,863,462,888]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.4 Impact of optimisation on cluster number counts: Planck and the Simons Observatory \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,898,478,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We now shift our attention to the impact of the effects of optimisation that were described theoretically in Section 2 and illustrated numerically in Section 3.2 may have on cluster number counts analyses that use $q _ { \\\\mathrm { o p t } }$ as an observable. We will focus solely on the optimisation bias, as indeed the non-Gaussianity of $q _ { \\\\mathrm { o p t } }$ and the deviation of its standard deviation from unity are small for signal-to-noise values of about 6 and above, which is the typical selection threshold in such analyses. In particular, we will determine whether the optimisation bias can be safely neglected in the analysis of cluster samples from Planck and the Simons Observatory (SO; Simons Observatory Collaboration 2019), or whether doing so may lead to biased cosmological constraints. To do so, we will compute the cluster abundances to be detected by these experiments both if the optimisation bias is neglected and if it is accounted for, comparing them appropriately. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,67,921,222]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,246,660,259]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.4.1 Experiment model \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,267,921,519]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We model our cluster number counts analysis as follows. We assume that an Internal Linear Combination (ILC; see, e.g., Delabrouille & Cardoso 2007) is applied on its temperature frequency maps in order to produce a Compton- $\\\\boldsymbol { \\\\cdot } \\\\boldsymbol { y }$ map covering a fraction $f _ { \\\\mathrm { s k y } }$ of the sky. For Planck we take $f _ { \\\\mathrm { s k y } } = 0 . 6 2$ (e.g., Planck 2015 results XXIV 2016), whereas for SO we take $f _ { \\\\mathrm { s k y } } = 0 . 4$ (Simons Observatory Collaboration 2019). We then assume that galaxy clusters are detected by applying a matched filter on this Compton- $\\\\boldsymbol { \\\\cdot } \\\\boldsymbol { y }$ map, which is previously subdivided appropriately into a number of tiles, maximising the signal-to-noise over angular size and sky location (i.e., three parameters) and imposing a selection threshold $q _ { \\\\mathrm { t h } }$ . For Planck we take a selection threshold of $q _ { \\\\mathrm { t h } } = 6$ , which is equal to that used to construct the MMF3 cosmology sample used in the Planck baseline analysis (Planck 2015 results XXIV 2016), whereas for SO we consider two selection thresholds, $q _ { \\\\mathrm { t h } } = 5$ and $q _ { \\\\mathrm { t h } } = 6$ . We note that, as we show in Appendix A, this $\\\\mathrm { I I } C +$ matched filter approach is equivalent to a multi-frequency matched filter approach, which was followed, e.g., in the real Planck analysis (see, e.g., Planck 2013 results XX 2014). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,520,922,745]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Construction of the matched filter requires as input a model for the signal to be detected, that is, a model for the cluster Compton- $y$ signal in our case, as well as the noise covariance. As the cluster model we assume the Arnaud et al. (2010) universal pressure profile, which integrated along the line-of-sight (see Eq. 14) gives the cluster Compton- $y$ signal at given mass $( 1 - b ) M _ { 5 0 0 }$ and redshift $z$ , where $1 - b$ is the so-called ‘hydrostatic’ mass bias. We use the best-fit parameters of Arnaud et al. (2010) and a mass bias of $1 - b \\\\ =$ 0.62 (taken from Planck 2018 results I 2020). We write our model as $y _ { \\\\mathrm { c } } ( M _ { 5 0 0 } , z ) = y _ { 0 } y _ { \\\\mathrm { t } } ( \\\\theta _ { 5 0 0 } ( M _ { 5 0 0 } , z ) )$ , where $y _ { 0 }$ is an amplitude parameter defined as the value of $\\\\boldsymbol { y } _ { \\\\mathbf { c } }$ at $R _ { 5 0 0 }$ , and $y _ { \\\\mathrm { t } }$ is an angular function that depends on mass and redshift only through the cluster’s angular size, $\\\\theta _ { 5 0 0 } = \\\\mathrm { \\\\Delta } R _ { 5 0 0 } / d _ { \\\\mathrm { A } }$ , where $d _ { \\\\mathrm { A } }$ is the angular diameter distance to the cluster. Assuming this model for the cluster signal and the noise covariance, the matched filter noise at a given angular size $\\\\theta _ { 5 0 0 }$ is then given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[593,760,836,797]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"1003/1af8084f19f54245dc8f1d1d55112da19cf2182d4f7446370fd709adb4399771.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\sigma ( \\\\theta _ { 5 0 0 } ) = \\\\left[ \\\\int d ^ { 2 } l \\\\frac { | y _ { \\\\mathrm { t } } ( \\\\theta _ { 5 0 0 } ; l ) | ^ { 2 } } { N ( l ) } \\\\right] ^ { - 1 / 2 } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[510,803,921,901]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $N ( l )$ is the noise power spectrum. For Planck, we take $N ( l )$ to be the power spectrum of the Full Mission NILC Compton- $y$ map, which we estimate directly from the map, which is publicly available in the Planck Legacy Archive1. This estimated power spectrum includes the tSZ signal of galaxy clusters: this is analogous to what was done in the actual Planck analysis, in which the clusters’ tSZ signal was not subtracted from the frequency maps when estimating their power spectra. For SO, we take it to be the sum of the forecast baseline tSZ reconstruction noise power spectrum of Simons Observatory Collaboration (2019) (namely, the solid orange curve of Fig. 36 of this paper) and the Compton- $y$ power spectrum due to halos up to masses of $M _ { 5 0 0 } = 1 0 ^ { 1 4 } \\\\tilde { M _ { \\\\odot } }$ , which we compute with the pubicly-available code pysz2. This assumes that that the tSZ signal due to more massive halos will be identified and removed for noise estimation purposes. The mean signal-to-noise at given mass $M _ { 5 0 0 }$ and redshift $z$ is then given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[776,955,921,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MNRAS 000, 1–13 (2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[561,35,922,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Matched filters for precision cosmology 9 9 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[510,927,636,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 pla.esac.esa.int \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,67,478,194]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[173,213,374,244]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"1017/5874aea9729bf5181bd21315c1031566e1cd293b51088abced24c7abcb5f02e7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\bar { q } ( M _ { 5 0 0 } , z ) = \\\\frac { y _ { 0 } ( M _ { 5 0 0 } , z ) } { \\\\sigma ( \\\\theta _ { 5 0 0 } ( M _ { 5 0 0 } , z ) ) } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[68,250,478,318]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where the dependency on the mass bias is left implicit. Note that Eq. (15) is simply a Fourier space, cluster-specific version of Eq. (4). In order to evaluate the matched filter integral, we assume flat sky tiles of $1 0 2 4 \\\\times 1 0 2 4$ pixels, with a pixel size of 0.8 arcmin for Planck and of 0.2 arcmin for SO. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,319,480,446]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In order to link the mean signal-to-noise, given by Eq. (16), to $q _ { \\\\mathrm { o p t } }$ , we first assume a layer of log-normal intrinsic scatter. This introduces the variable $\\\\ln q _ { \\\\mathrm { t } }$ , which is given by a Gaussian centred on $\\\\ln \\\\bar { q } ( M _ { 5 0 0 } , z )$ and with a standard deviation of $\\\\sigma _ { \\\\ln \\\\mathrm { q } } ~ = ~ 0 . 1 7 3$ (taken from Planck 2015 results XXIV 2016). We then consider a layer of ‘observational scatter’ due to what is understood as noise in the matched filtering process, finally linking $q _ { \\\\mathrm { t } }$ to $q _ { \\\\mathrm { o p t } }$ . Motivated by our numerical results of Section 3.2, we take this scatter to be Gaussian-distributed with unit variance and with a mean equal to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[216,465,331,491]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0490/55888c7d9d014724918fdc6374f7c7a6b9c9163385aad849d86825b610e33ef3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\bar { q } _ { \\\\mathrm { o p t } } = \\\\sqrt { q _ { \\\\mathrm { t } } ^ { 2 } + f _ { \\\\mathrm { e f f } } } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[68,496,480,594]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $f _ { \\\\mathrm { e f f } }$ is the effective number of fitting parameters, and where we note that we have neglected the contribution due to the change in the variance (compare with Eq. 17), as it is small for $q \\\\gtrsim 5$ (see Figure 3). As discussed in Section 3.2, for $q \\\\gtrsim 6$ , $f _ { \\\\mathrm { e f f } } \\\\simeq f = 3$ . Thus, we take $f _ { \\\\mathrm { e f f } } = 3$ when accounting for the bias; we take $f _ { \\\\mathrm { e f f } } = 0$ when ignoring it. The differential mean number of clusters to be detected as a function of $q _ { \\\\mathrm { o p t } }$ is then given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,612,472,647]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0429/1a2876e0349b39327c52eaf910484d5f80b8df10e1285fdb650a93d8bee5000e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\frac { d \\\\bar { N } } { d q _ { \\\\mathrm { o p t } } } = 4 \\\\pi f _ { \\\\mathrm { s k y } } \\\\int P ( q _ { \\\\mathrm { o p t } } | M _ { 5 0 0 } , z ) \\\\frac { d ^ { 4 } N } { d ^ { 3 } V d M _ { 5 0 0 } } \\\\frac { d ^ { 3 } V } { d z d ^ { 2 } \\\\Omega } d M _ { 5 0 0 } d z .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[68,657,478,728]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Here, $d ^ { 4 } N / ( d ^ { 3 } V d M _ { 5 0 0 } )$ is the halo mass function, which we take to be that of Tinker et al. (2008), $d ^ { 3 } V / ( d z d ^ { 2 } \\\\Omega )$ is the differential volume element, and $P ( q _ { \\\\mathrm { o p t } } | M _ { 5 0 0 } , z )$ is the probability for a cluster of mass $M _ { 5 0 0 }$ and redshift $z$ to have an optimal signal-to-noise $q _ { \\\\mathrm { o p t } }$ , which is given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[99,746,423,777]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0895/8b15a0406e872fcabf464a817bc3086323e83e7418fc897049eabfd3d436c35b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP ( q _ { \\\\mathrm { o p t } } | M _ { 5 0 0 } , z ) = \\\\int _ { 0 } ^ { \\\\infty } P ( q _ { \\\\mathrm { o p t } } | q _ { \\\\mathrm { t } } ) P ( q _ { \\\\mathrm { t } } | M _ { 5 0 0 } , z ) d q _ { \\\\mathrm { t } } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[67,783,478,841]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where the first factor of the integrand is the Gaussian describing observational scatter, and the second one is the log-normal distribution accounting for intrinsic scatter. The mean number of clusters with $q _ { \\\\mathrm { o p t } }$ between $q _ { \\\\mathrm { m i n } }$ and $q _ { \\\\mathrm { m a x } }$ is then given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[196,859,351,892]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0069/39d404a53dc6b7f85f75a994ac96107047eb6a58deace430992ace9da51c3278.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\bar { N } = \\\\int _ { q _ { \\\\mathrm { m i n } } } ^ { q _ { \\\\mathrm { m a x } } } \\\\frac { d \\\\bar { N } } { d q _ { \\\\mathrm { o p t } } } d q _ { \\\\mathrm { o p t } } .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[510,67,921,108]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We perform our calculations fixing all the cosmological parameters to their Planck 2018 TT,TE,EE+lowE+lensing best-fit values (Planck 2018 results VI 2020). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,136,685,149]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.4.2 Results and discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,158,922,326]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 7 shows the mean number of clusters as a function of $q _ { \\\\mathrm { o p t } }$ for our reference Planck and SO-like experiments both if the optimisation bias is taken into account (‘corrected’ orange bars) and if it is ignored by setting $f _ { \\\\mathrm { e f f } } = 0$ (‘uncorrected’ blue bars). Specifically, for each experiment, the mean number of clusters is computed using Eq. (20) for 14 logarithmically-spaced bins between $q _ { \\\\mathrm { o p t } } = 6$ and $q _ { \\\\mathrm { o p t } } = 2 5$ . As expected, in any bin more clusters are found if the optimisation bias is accounted for, since the cluster abundance decreases with $q _ { \\\\mathrm { o p t } }$ and the optimisation bias boosts the signal-tonoise at given mass and redshift. Also as expected, the effect of the optimisation bias on the number counts is most significant at low signal-to-noise, quickly decreasing with increasing signal-to-noise. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,327,922,493]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 7 also shows, as black error bars, the Poisson errors associated with the corrected number counts, which for each bin are given by $\\\\Delta \\\\bar { N } _ { \\\\mathrm { P o i s s o n } } = \\\\bar { N } ^ { 1 / 2 }$ . They provide a measure of the change in the number counts that the analysis is sensitive to: if the change due to neglecting the optimisation bias is much smaller than the Poisson error, then it can be safely neglected, whereas if it is larger, it may have to be taken into account in order to avoid biasing the inference. It can be seen how for Planck this change is smaller than the Poisson error across all the bins, whereas for SO it is larger for the lowest signal-to-noise bins. This implies that the impact of neglecting the optimisation bias in Planck is probably negligible, but that this may not the case for SO. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,494,922,690]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Table 1 shows the total mean number of clusters detected by each experiment, which is given by Eq. (20) by setting its lower and upper integration limits to $q _ { \\\\mathrm { t h } }$ and infinity, respectively. For Planck we have imposed a selection threshold of $q _ { \\\\mathrm { t h } } = 6$ (as in the real baseline analysis, see Planck 2015 results XXIV 2016), whereas for SO we have considered two selection thresholds, $q _ { \\\\mathrm { t h } } = 6$ and $q _ { \\\\mathrm { t h } } = 5$ . As with Figure 7, the number counts are given both if the optimisation bias is accounted for and if it is neglected; their difference and the associated Poisson errors are also shown. As expected from Figure 7, while the change in the number counts for Planck is well within the Poisson error, this is not the case for SO, especially if the selection threshold is lowered to $q _ { \\\\mathrm { t h } } = 5$ . This again implies that the optimisation bias probably has to be taken into account in SO, especially if a selection threshold as low as $q _ { \\\\mathrm { t h } } = 5$ is chosen. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,691,922,872]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The number counts in Figure 7 and in Table 1 were computed at fixed cosmological and scaling relation parameters. The uncertainty in the scaling relation parameters inherent to any real analysis means that the changes in the number counts shown in both Figure 7 and Table 1 can thus be interpreted as an upper limit on the change that is discernible by the analysis and that can be (wrongly) attributed to cosmology. Indeed, if the tSZ-mass scaling relation is given enough freedom, the optimisation bias may be calibrated away to some extent3. Quantifying the extent to which this can happen is beyond the scope of this paper. It could be done by generating a set of mock cluster samples (e.g., by sampling from the halo mass function and adding the appropriate scatter) and analysing them with a number counts likelihood (e.g., with the one used in Zubeldia & Challinor \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,900,922,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 While the optimisation bias is not completely degenerate with a power law tSZ–mass scaling relation (the form that is usually assumed), as it does not have a power law behaviour, some degeneracy is expected. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,955,215,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MNRAS 000, 1–13 (2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[70,34,252,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10 Í. Zubeldia et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,927,260,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 github.com/ryumakiya/pysz \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[84,107,455,414]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 7. Cluster abundances as a function of optimal signal-to-noise, $q _ { \\\\\\\\mathrm { o p t } }$ for Planck (upper panel) and SO (lower panel), both if the optimisation bias is neglected (blue bars) and if it is accounted for (orange bars, shown along the associated Poisson errors). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0241/6d9c6c073adaa8ea58c077690d7257b6bec403ac49b770b46650b82a7c5d5628.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[97,590,448,658]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0391/2920ce6ade57c5ac792844d8cd6a689abb7c6736846edeb57984b360ed5fe887.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Experiment</td><td>N (corr.)</td><td>N (uncorr.)</td><td>AN</td><td>△NPoisson</td></tr><tr><td>Planck</td><td>334.0</td><td>320.7</td><td>13.3</td><td>18.3</td></tr><tr><td>SO (qth = 6)</td><td>9400.9</td><td>9116.9</td><td>284.0</td><td>97.0</td></tr><tr><td>SO (qth = 5)</td><td>14837.6</td><td>14090.8</td><td>746.8</td><td>121.8</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. Mean number of clusters to be detected by our Planck and SO-like experiments, with and without optimisation bias taken into account (first and second columns, respectively). Their difference is also shown (third column), along with the corresponding Poisson error (fourth column). \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[68,675,478,855]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2019) with and without the optimisation bias taken into account. One could then look at the differences in the derived constraints on the relevant cosmological parameters (e.g., $\\\\Omega _ { \\\\mathrm { m } }$ and $\\\\sigma _ { 8 }$ ). We have decided not to pursue this avenue, as our conclusions would be dependent on how well the tSZ-mass scaling relation is calibrated, which is yet to be determined for SO, the experiment for which this full analysis would be interesting to perform. Furthermore, since the optimisation bias can be accounted for, and, indeed, implemented numerically in a very simple way (to lowest order, at least), we do not find it necessary to analyse its impact on our idealised experiments in any more detail. We simply recommend it to be considered in any future number counts analysis that makes use of $q _ { \\\\mathrm { o p t } }$ , or any equivalent quantity, as an observable. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,890,186,904]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 CONCLUSION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[67,911,480,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this paper, we have studied in detail the statistical properties of the matched filter optimal signal-to-noise, $q _ { \\\\mathrm { o p t } }$ , in the context of galaxy cluster tSZ detection and characterisation. In particular, we have shown that $q _ { \\\\mathrm { o p t } }$ is, in general, a non-Gaussian variable with a standard deviation different from unity and an expected value that is biased high with respect to the true mean signal-to-noise, a bias that we have referred to as optimisation bias. We have shown that this bias arises from the fact that $q _ { \\\\mathrm { o p t } }$ is obtained from an optimisation procedure on noisy data. As such, it is present even if the signal is modelled perfectly, no foregrounds are present, and the noise in the data is Gaussian. After presenting these arguments in a general way in Section 2, we have then used a set of MC mock observations in order to study numerically these effects of optimisation in the tSZ galaxy cluster context. We have found that, if optimisation is carried out over three parameters (an angular size and two location parameters), $q _ { \\\\mathrm { o p t } }$ can be taken to be approximately Gaussian-distributed and with a standard deviation approximately equal to unity for $q _ { \\\\mathrm { o p t } } ~ \\\\gtrsim ~ 6$ Similarly, for $q _ { \\\\mathrm { o p t } } \\\\gtrsim 6$ , the optimisation bias can be accounted for with a simple expression, $\\\\bar { q } _ { \\\\mathrm { o p t } } = ( q _ { \\\\mathrm { t } } ^ { 2 } + f ) ^ { 1 / 2 }$ , where $\\\\bar { q } _ { \\\\mathrm { o p t } }$ is the expected value of $q _ { \\\\mathrm { o p t } }$ , $\\\\bar { q } _ { \\\\mathrm { t } }$ is the expected value of the true signal-tonoise, and $f$ is the number of fitting parameters (three in our case). We stress that this correction, which we have refer to as the $\\\\cdot _ { f }$ correction’, is accurate if ‘true’ optimisation is achieved: if the signal-to-noise is only partially optimised by evaluating it on a coarse parameter grid, an additional, grid-dependent negative bias on the retrieved signal-to-noise will be induced (see Section 3.2.4). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,69,921,405]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,414,922,622]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In addition, we note that if in a given context the $f$ correction may be suspected not be accurate enough, or the standard deviation of $q _ { \\\\mathrm { o p t } }$ may be significantly different from unity, this paper offers a route through which these aspects can be quantified, namely through the generation and analysis of a set of mock $q _ { \\\\mathrm { o p t } }$ observations. This may be the case if low signal-to-noise clusters are considered, or if the parameters over which the optimisation is carried out are different from the ones we have considered, either in nature and/or in number. Indeed, while in this paper we have considered optimisation of the signal-to-noise over three parameters, in future experiments additional parameters could be considered, e.g., including extensions in the modelling of the cluster atmosphere (e.g., Moser et al. 2021), or the cluster temperature (Remazeilles et al. 2019; Remazeilles & Chluba 2020) in experiments sensitive to the relativistic SZ effect such as PICO (Hanany et al. 2019). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,630,921,938]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Our results have implications for any cluster number counts analysis that may use $q _ { \\\\mathrm { o p t } }$ as a mass observable. In these analyses, a signal-to-noise threshold of around 6 is typically used as the selection criterion for the construction of the cluster sample. Thus, our results suggest that, while the non-Gaussianity of $q _ { \\\\mathrm { o p t } }$ and the deviation of its standard deviation from unity are small and probably negligible, the optimisation bias, which is a $\\\\sim 5 \\\\%$ effect at signalto-noise of 6, may have a significant impact. In the past, analyses using both Planck and ACT clusters have ignored this bias, even if optimisation over a number of parameters was carried out (three parameters in Planck and two in ACT; Hasselfield et al. 2013; Planck 2013 results XX 2014; Planck 2015 results XXIV 2016; Zubeldia & Challinor 2019). Only the SPT analyses, in which the signal-to-noise was optimised over three parameters, have properly accounted for it using a correction equal to ours (Vanderlinde et al. 2010; Bleem et al. 2015; Bocquet et al. 2019), offering a rather heuristic justification for its use (Vanderlinde et al. 2010). Here we have quantified the relevance of the bias in Planck and SO by computing its effect on the expected number counts across signal-to-noise. We have found it to be negligible for Planck and potentially significant for SO, the latter being especially true if a precise mass–observable tSZ scaling relation is used in the analysis. We also expect the bias to be relevant for CMB-S4, which is forecast to find about an order of magnitude more clusters than SO (Abazajian et al. 2016). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[776,955,921,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MNRAS 000, 1–13 (2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[551,35,919,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Matched filters for precision cosmology 11 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,67,478,94]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,97,478,249]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This paper highlights the well-known fact that, though galaxy clusters are and will continue to be a very powerful cosmological probe from a statistical point of view, accurately determining the mass-observable relation is crucial for this statistical power to be realised in practice. For the specific case considered here, that of SZ surveys using matched filters, we have evidenced that, for upcoming surveys, accurately calibrating the mass– $\\\\cdot q _ { \\\\mathrm { o p t } }$ relation will probably require proper modelling of the optimisation bias. Here we have shown that this can be done in a numerically straightforward way. We thus encourage that the bias is duly accounted for in any future analysis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,251,480,585]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, although in this work we have focused on tSZ detection and characterisation of galaxy clusters, matched filters can also be used for cluster detection in photometric surveys (e.g., Bellagamba et al. 2018) and using jointly mm and X-ray observations (Tarrío et al. 2018), as well as for the confirmation of X-ray detected clusters using optical photometric data (Klein et al. 2018). They also have a variety of other applications, such as the detection of the CMB lensing signal of galaxy clusters (Melin & Bartlett 2015; Horowitz et al. 2019; Zubeldia & Challinor 2019) and voids (Raghunathan et al. 2020), of the moving lens effect (Hotinli et al. 2021), of line intensity mapping sources (Schaan & White 2021), of large-scale structures such as voids in $2 1 \\\\mathrm { c m }$ data (White & Padmanabhan 2017), and of the ISW signal of large-scale structures (Nadathur & Crittenden 2016). They are also widely used for gravitational wave detection (see, e.g., Pitkin et al. 2011 for a review). All the theoretical insights of Section 2, including the non-Gaussianity of the signal-to-noise and the existence of a positive optimisation bias, are completely general and hold in any other applications of matched filters. We expect the general numerical trends presented in Section 3 (e.g., the non-Gaussianity and the optimisation bias both decreasing with increasing signal-tonoise) to apply in other contexts as well. Considering other uses of matched filters in any detail is beyond the scope of this paper, but we hope that the insights and results presented here may find useful applications in some of these other areas too. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,625,245,638]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ACKNOWLEDGEMENTS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,647,478,702]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This work was supported by the ERC Consolidator Grant CMBSPEC (No. 725456). JC was furthermore supported by the Royal Society as a Royal Society University Research Fellow at the University of Manchester, UK. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,740,223,754]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"DATA AVAILABILITY \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,763,478,790]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The data underlying this article will be shared on reasonable request to the corresponding author. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,828,171,841]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"REFERENCES \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,850,478,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abazajian K. 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Rev., 215, 17 \\nNadathur S., Crittenden R., 2016, ApJ, 830, L19 \\nNicola A., Dunkley J., Spergel D. N., 2020, Phys. Rev. D, 102, 083505 \\nPitkin M., Reid S., Rowan S., Hough J., 2011, Living Reviews in Relativity, 14, 5 \\nPlanck 2013 results XX 2014, A&A, 571, A20 \\nPlanck 2013 results XXIX 2014, A&A, 571, A29 \\nPlanck 2015 results XXIV 2016, A&A, 594, A24 \\nPlanck 2015 results XXVII 2016, A&A, 594, A27 \\nPlanck 2018 results I 2020, A&A, 641, A1 \\nPlanck 2018 results VI 2020, A&A, 641, A6 \\nPratt G. W., Arnaud M., Biviano A., Eckert D., Ettori S., Nagai D., Okabe N., Reiprich T. H., 2019, Space Sci. Rev., 215, 25 \\nRaghunathan S., Nadathur S., Sherwin B. D., Whitehorn N., 2020, ApJ, 890, 168 \\nRemazeilles M., Chluba J., 2020, MNRAS, 494, 5734 \\nRemazeilles M., Bolliet B., Rotti A., Chluba J., 2019, MNRAS, 483, 3459 \\nSazonov S. Y., Sunyaev R. A., 1998, ApJ, 508, 1 \\nSchaan E., White M., 2021, arXiv e-prints, p. arXiv:2103.01971 \\nSimons Observatory Collaboration 2019, J. Cosmology Astropart. Phys., 2019, 056 \\nTarrío P., Melin J. B., Arnaud M., 2018, A&A, 614, A82 \\nTinker J., Kravtsov A. V., Klypin A., Abazajian K., Warren M., Yepes G., Gottlöber S., Holz D. E., 2008, ApJ, 688, 709 \\nVanderlinde K., Crawford T. M., de Haan T., Dudley J. P., Shaw L., et al., 2010, ApJ, 722, 1180 \\nWhite M., Padmanabhan N., 2017, MNRAS, 471, 1167 \\nZubeldia Í., Challinor A., 2019, MNRAS, 489, 401 \\nZubeldia Í., Challinor A., 2020, MNRAS, 497, 5326 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,63,924,753]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,777,885,805]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"APPENDIX A: EQUIVALENCE BETWEEN MMF AND $\\\\mathbf { I L C { + } M F }$ \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,813,921,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"When multi-frequency mm data is available, galaxy clusters are typically detected using a multi-frequency matched filter (MMF), which operates directly on the frequency maps (Melin et al. 2006; for an application on real data, see, e.g., Planck 2015 results XXVII 2016). Throughout this paper, however, we have considered a ‘singlefrequency’ matched filter acting on a Compton-?? map. In this appendix, we show that these two approaches are mathematically equivalent if the Compton-?? map is produced with an Internal Linear Combination (ILC; see, e.g., Delabrouille & Cardoso 2007). Thus, the results presented in this work are also applicable to multi-frequency matched filters. We restrict our proof to the case in which the noise covariance is isotropic. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,34,252,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"12 Í. Zubeldia et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,955,215,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MNRAS 000, 1–13 (2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[67,67,478,109]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[67,109,478,166]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Consider a set of beam-deconvolved intensity maps at different frequencies, $\\\\pmb { d } ( \\\\pmb { x } )$ , where the vector dimension of $\\\\mathbf { \\\\Delta } \\\\mathbf { d }$ is equal to the number of frequency channels and where $\\\\boldsymbol { x }$ denotes angular position. We assume that $\\\\pmb { d } ( \\\\pmb { x } )$ can be written as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[205,186,341,203]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0355/7446ee7e8a0c266ad3187e203705ed2fb2ff032d031d0c355fc7a77d0e2e196a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\pmb { d } ( \\\\pmb { x } ) = \\\\pmb { j } _ { \\\\nu } \\\\pmb { y } ( \\\\pmb { x } ) + \\\\pmb { n } ( \\\\pmb { x } ) ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[68,209,480,306]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $j _ { \\\\nu }$ is the frequency dependency of the signal of interest (the tSZ effect in our case), $y ( \\\\pmb { x } )$ is its spatial variation (the Compton-$y$ map in our case), and $\\\\pmb { n } ( \\\\pmb { x } )$ is some additive ‘noise’, which also includes all other signals different from the component of interest (in our case, the CMB, the kSZ signal, etc.). Assuming the covariance of the noise to be isotropic, a Fourier-space ILC estimate of $y ( x )$ can be written as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[206,323,341,360]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0214/2d6b370cf2b0849de7a9e30aba48306c47e17e5bcdcda511d88a3b875e702bd0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\hat { y } ( l ) = \\\\frac { j _ { \\\\nu } ^ { T } \\\\mathsf { N } ^ { - 1 } ( l ) d ( l ) } { j _ { \\\\nu } ^ { T } \\\\mathsf { N } ^ { - 1 } ( l ) j _ { \\\\nu } } ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[68,364,478,392]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where ${ \\\\pmb { \\\\mathsf { N } } } ( l )$ is the noise covariance matrix, and which has an associated variance equal to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[196,409,351,437]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0854/72fdd8784b6db935626a47e93b686e236ac56b4491c6a9bbcbbcfd881ef075b1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nN ( l ) = \\\\left[ j _ { \\\\nu } ^ { T } \\\\mathsf { N } ^ { - 1 } ( l ) j _ { \\\\nu } \\\\right] ^ { - 1 } .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[68,442,478,484]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If we then assume that the signal $y ( l )$ can be written as $y ( l ) = y _ { 0 } y _ { \\\\mathrm { t } } ( l )$ , where $y _ { 0 }$ is an amplitude parameter and $y _ { \\\\mathrm { t } } ( l )$ is a spatial template, a matched filter estimate for $y _ { 0 }$ can then be written as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[142,489,403,525]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0407/c9f10113a42d741223e34fe8e28f8919a062be84d497440c1ca65049b68c065e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\hat { y } _ { 0 } = \\\\left[ \\\\int d ^ { 2 } { l } \\\\frac { | y _ { \\\\mathrm { t } } ( l ) | ^ { 2 } } { N ( l ) } \\\\right] ^ { - 1 } \\\\int d ^ { 2 } { l } \\\\frac { y _ { \\\\mathrm { t } } ^ { \\\\ast } ( l ) \\\\hat { y } ( l ) } { N ( l ) } .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[67,530,478,571]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This is the ‘single-frequency’ matched filter that we have considered in this work. If we now substitute the ILC expression for $\\\\hat { y } ( I )$ of Eq. (A2), we find \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,588,470,624]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0734/90f683090988e4c1b155c4c76f9a26d62e7c0635af905177657395dad5759e36.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\hat { y } _ { 0 } = \\\\left[ \\\\int d ^ { 2 } l y _ { \\\\mathrm { t } } ^ { * } ( l ) j _ { \\\\nu } ^ { T } { \\\\bf N } ^ { - 1 } ( l ) j _ { \\\\nu } y _ { \\\\mathrm { t } } ( l ) \\\\right] ^ { - 1 } \\\\int d ^ { 2 } l y _ { \\\\mathrm { t } } ^ { * } ( l ) j _ { \\\\nu } ^ { T } { \\\\bf N } ^ { - 1 } ( l ) d ( l ) .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[67,634,480,690]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This is a multi-frequency matched filter, acting directly on the frequency maps $\\\\pmb { d } ( l )$ (for comparison, see, e.g., Melin et al. 2006). Thus, it is equivalent to a ‘single-frequency’ matched filter operating on an ILC estimate of the Compton- $y$ map. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[67,708,465,721]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This paper has been typeset from a $\\\\mathrm { T e X / I A T _ { E } X }$ file prepared by the author. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[549,35,922,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Matched filters for precision cosmology 13 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[774,955,922,966]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MNRAS 000, 1–13 (2015) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1093/mnras/stab2461"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Astronomy and Space Sciences"},"sha256":{"kind":"string","value":"c32e983da368f0bfd70bcd533bf860722dde647f5f9e0d2bdddc57134b4cc8d2"},"title":{"kind":"string","value":"Understanding matched filters for precision cosmology"}}},{"rowIdx":252,"cells":{"abstract":{"kind":"string","value":"A momentum-dependent formulation based on a stationary spin-0 and isospin-1 dibaryon field is proposed to improve convergence of chiral effective field theory in the S-1(0) channel of NN scattering. | As an application beyond the two-body level, the triton binding energy is studied and compared to standard chiral effective field theory with partly perturbative pions. The consistency of the chiral | Lagrangian for the new formulation is examined by working out the pionic radiative corrections, and consequences of nontrivial chiral-connection terms are discussed. | Although the two-parameter leading-order interaction appears to be unnatural, it nevertheless has the necessary features of an effective field theory. A rapid order-by-order convergence is found in S-1(0). "},"author":{"kind":"string","value":"Rui Peng|Songlin Lyu|Bingwei Long|Sebastian König"},"content_list":{"kind":"list like","value":[{"bbox":"[125,114,870,133]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Constructing chiral effective field theory around unnatural leading-order interactions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[246,147,750,164]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Rui Peng,1 Songlin Lyu,1\\* Sebastian Konig,2 and Bingwei Long 1 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[269,164,728,178]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"<sup>1</sup>College of Physics, Sichuan University, Chengdu, Sichuan 610065, China ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[205,178,791,191]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{2}$ Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[162,204,190,222]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0544/7d21f99ea4c33196e4c9f352729f6b7299229978888b4f1bb72e0b805e83416f.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[193,205,835,220]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(Received 9 December 2021; revised 16 March 2022; accepted 30 March 2022; published 12 May 2022) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[154,237,840,339]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A momentum-dependent formulation based on a stationary spin-0 and isospin-1 dibaryon field is proposed to improve convergence of chiral effective field theory in the $^1 S_0$ channel of $NN$ scattering. Although the two-parameter leading-order interaction appears to be unnatural, it nevertheless has the necessary features of an effective field theory. A rapid order-by-order convergence is found in $^1 S_0$ . As an application beyond the two-body level, the triton binding energy is studied and compared to standard chiral effective field theory with partly perturbative pions. The consistency of the chiral Lagrangian for the new formulation is examined by working out the pionic radiative corrections, and consequences of nontrivial chiral-connection terms are discussed. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[154,349,390,363]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"DOI: 10.1103/PhysRevC.105.054002 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,400,346,412]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"I. INTRODUCTION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[66,421,485,768]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It is a lore about the nuclear force that it has attractive long-range and repulsive short-range components. This can be inferred phenomenologically from the $^1 S_0$ and $^3 S_1$ phase shifts, both showing strong attraction near threshold and vanishing around center-of-mass (c.m.) momentum $k \\sim 350 \\mathrm{MeV}$ . But nuclear forces derived from chiral effective field theory (EFT) are characteristically different in the two channels at leading order (LO): in $^3 S_1 - ^3 D_1$ , the tensor part of one-pion exchange (OPE) is singularly attractive, providing sufficiently strong attraction at long distances to generate the shallow deuteron bound state. A contact term in $^3 S_1$ provides repulsion at short distances to avoid a collapse of the two-nucleon system into an infinitely deep bound state. This mechanism is well understood to ensure renormalization [1,2]. In $^1 S_0$ , however, OPE turns out to be numerically weak, thus it can in principle be treated as a perturbation [3-5]. This implies that in $^1 S_0$ the short-range interaction alone needs to provide strong attraction at long distances and strong repulsion at short distances in order to produce the phenomenological behavior of the phase shift. A single $^1 S_0$ contact term at LO as proposed by Weinberg [6,7] is too simple to generate both features simultaneously, which is likely the reason why chiral forces have been found to converge rather slowly in $^1 S_0$ [8-11], unless a soft cutoff is carefully chosen [9]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,768,485,857]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As first calculated in Ref. [12] and then argued further in Ref. [13], the slow convergence can be attributed to the quite large value of the generalized effective range in $^{1}S_{0}$ , which is defined in an expansion similar to the effective-range expansion while incorporating iteration of OPE. To improve the convergence, a power counting based on a spin-0 and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,398,932,428]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"isospin-1 auxiliary dibaryon field [14-16] was suggested in Ref. [13], and subsequently developed in Ref. [17]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,429,932,744]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A mere reproduction of empirical phase shifts does not bring much to the discussion of nuclear forces, as there exist several phenomenological models that fit nucleon-nucleon scattering data very well [18-20]. We therefore use the following requirements as guidelines to reformulate power counting of chiral forces in order to address the slow $^{1}S_{0}$ convergence. First, as any other consistent EFT, the formulation sets up a controlled expansion, allowing for a highly unnatural LO that includes more than one low-energy constant (LEC) (two in Ref. [13] and three in Ref. [17]) in the $^{1}S_{0}$ channel. Second, renormalization-group (RG) invariance is enforced at each order. Third, the symmetries of the chiral Lagrangian are observed, in particular the nonlinearly realized chiral symmetry. The dibaryon formalism has been shown to meet all these requirements, and in particular it does not alter the well-established hierarchy of long-range chiral forces that follows from naive dimensional analysis (NDA) [6,7]: OPE is LO, two-pion-exchange (TPE) contributions are two powers down or more, and so on. This is in contrast to a recent proposal that TPE should be promoted to LO in order to address the convergence issue in $^{1}S_{0}$ [21]; see also Ref. [22] for a related discussion regarding the promotion of TPE. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,746,932,805]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Unfortunately, the resulting ${}^{1}S_{0}$ potential is energy-dependent, making it difficult to apply the overall interaction in many-body calculations. For example, the dibaryon-exchange potential, part of LO, is given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[651,825,932,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV _ {\\phi} (E) = \\sigma \\frac {y ^ {2}}{E + \\Delta}, \\tag {1}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,876,932,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $E$ is the center-of-mass (c.m.) energy, $\\Delta$ the dibaryon mass, $y$ the dibaryon coupling constant, and $\\sigma = \\pm 1$ . In order to facilitate many-body calculations, we discuss in Sec. II a separable, momentum-dependent force to replace the original ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[300,49,696,66]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PHYSICAL REVIEW C 105, 054002 (2022) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[73,905,208,920]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"* songlin@scu.edu.cn ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[74,921,213,934]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{\\dagger}$ bingwei@scu.edu.cn ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[66,950,290,964]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2469-9985/2022/105(5)/054002(12) ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[473,950,533,963]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"054002-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[716,950,932,965]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"©2022 American Physical Society ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[64,80,310,170]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0313/ef26c3c2ba026794bfd07cc25e08272799d3112a43fb8d115c22ff738050e6d7.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[327,80,488,170]","code_body":null,"code_caption":null,"image_caption":"[\"FIG. 1. Radiation-pion Feynman diagrams contributing to $\\\\mathrm{N}^2\\\\mathrm{LO}$ potentials. The solid (dashed) lines represent nucleons (pions), and the solid blobs are the $\\\\phi NN$ vertex function (10). (a) The pion line connects both nucleons either in the initial or in the final states. (b) The pion line connects one of the incoming nucleon lines to one of the final nucleon legs. Other variants due to permuting the pion line on different nucleon external lines are not shown. \"]","image_footnote":"[]","img_path":"images/0058/bdfb278a493713b981012bb3a3ef85892bed264d7b8884b52f01eab696c1357c.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[64,301,307,318]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"dibaryon exchange potential in $^1 S_0$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[113,325,487,362]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV _ {\\mathrm {s p r}} \\left(p ^ {\\prime}, p\\right) = - \\frac {4 \\pi}{m _ {N}} \\frac {\\lambda}{\\sqrt {p ^ {\\prime 2} + m _ {N} \\Delta} \\sqrt {p ^ {2} + m _ {N} \\Delta}}, \\tag {2}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,369,485,470]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $p(p')$ is the incoming (outgoing) c.m. momentum. The potential (2) is clearly motivated by the energy-dependent dibaryon potential (1), and the two potentials (1) and (2) have the same functional dependence on the energy when the Born approximation is taken and the nucleons are on the energy shell, $E = p^{\\prime 2} / m_{N} = p^{2} / m_{N}$ (while still featuring different coupling constants). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,472,485,587]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Potentials of the same (or similar) form as in Eq. (2) were investigated elsewhere in the literature. Reference [23] used it to construct a model potential in the context of discussing pionless EFT. More recently, Ref. [24] derived a potential with similar square-root form factors based on the so-called UV/IR symmetry of the $S$ matrix, assuming a separable form as in Eq. (2). An attempt to derive a similar potential from the Low equation can be found in Ref. [25]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,588,485,789]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Radiative corrections to nucleon-nucleon contact terms generated by pions (see Fig. 1) appear suppressed by $Q^2 /M_{\\mathrm{hi}}^2$ relative to OPE in a given partial wave. If the contact vertex has a single parameter, e.g., a constant in $S$ waves, the radiative corrections can be shown to generate only terms which are polynomials in momenta or energies because the diagrams are dominated by static intermediate nucleons. Owing to this lack of nonanalytic structures, radiative pions are typically not included in chiral nuclear forces unless chiral extrapolations [26-28] or pion productions are concerned. This is still the case with the energy-dependent dibaryon exchange. However, as will be discussed in Sec. III, the pionic radiative corrections to the momentum-dependent potential (2) can no longer be trivially cast into pure contact form. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,790,485,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In Sec. IV we discuss two- and three-body observables calculated with the momentum-dependent potential (plus additional nucleon-nucleon channels) and compare our results to other calculations. As a matter of fact, several nuclear-structure calculations have already used potentials with a similar form to various orders [29-31]. The results in Ref. [29] suggest that some nuclei are not bound with the proposed potentials up to NLO, based on which the authors argue that some three-body forces need to be considered at LO. While the role of three-body forces may continue to be debated, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,80,933,125]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"we believe that efforts to improve the overall convergence based on two-body and three-body forces can complement each other. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,125,933,268]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The momentum-dependent dibaryon potential can alternatively be thought of as a way to partially resum derivative-coupled NNNN operators in the effective Lagrangian. With the nonlinearly realized chiral symmetry, derivatives acting on baryon fields must be \"chiral-covariant\" so that chiral symmetry and its spontaneous breaking are properly implemented. This results in, among other things, a nontrivial $\\pi \\pi$ NNNN vertex function. We discuss the construction of this vertex and its phenomenological impacts in Sec. V. Finally, we summarize and conclude in Sec. VI. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[519,287,923,301]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"II. MOMENTUM-DEPENDENT DIBARYON POTENTIAL ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,308,932,354]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We begin with the $^1 S_0$ power counting developed in Ref. [8]. Thus, OPE is the LO long-range force, and its $^1 S_0$ projection reads ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[597,358,932,393]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV _ {1 \\pi} \\left(p ^ {\\prime}, p\\right) = \\frac {g _ {A} ^ {2}}{4 f _ {\\pi} ^ {2}} \\left(1 - \\frac {m _ {\\pi} ^ {2}}{q ^ {2} + m _ {\\pi} ^ {2}}\\right), \\tag {3}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,398,933,470]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where the momentum transfer $\\vec{q} = \\vec{p}' - \\vec{p}$ , the pion mass $m_{\\pi} = 138.0$ MeV, the pion decay constant $f_{\\pi} = 92.4$ MeV, and the axial coupling $g_{A} = 1.29$ . Counting external momenta $Q, m_{\\pi}$ , and $f_{\\pi}$ collectively as the infrared mass scale $M_{\\mathrm{lo}}$ , OPE scales as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[617,474,932,508]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV _ {1 \\pi} \\left(p ^ {\\prime}, p\\right) \\sim \\frac {1}{f _ {\\pi} ^ {2}} \\sim \\frac {4 \\pi}{m _ {N}} \\frac {1}{M _ {\\mathrm {l o}}}, \\tag {4}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,516,932,575]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $m_N \\sim 4\\pi f_\\pi$ is used. The contact term $V_S^{(0)} = C_0$ enters also at LO. As argued in Ref. [8], RG invariance requires a nonvanishing NLO generated by a momentum-dependent contact term, one order earlier than estimated from NDA, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[604,580,932,612]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV _ {S} ^ {(1)} = \\frac {C _ {2}}{2} \\left(p ^ {\\prime 2} + p ^ {2}\\right) \\sim \\frac {4 \\pi}{m _ {N}} \\frac {1}{M _ {\\mathrm {h i}}}. \\tag {5}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,616,933,863]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Even with this promotion, chiral EFT still converges slowly in $^1 S_0$ (see, e.g., Ref. [8]). It was later proposed in Ref. [13] that the mass scale embedded in $C_2$ is actually quite small and can be identified with the inverse of the so-called generalized effective range $\\simeq 130 \\mathrm{MeV}$ that was first extracted in Ref. [12]. This light mass scale needs to enter the LO amplitude, and promoting the $C_2$ term to LO is a choice to achieve this. The simplistic treatment of taking the sum of the $C_0$ and $C_2$ terms as the LO short-range potential has several obstacles, including satisfying RG invariance [23,32] and overcoming the Wigner bound [23,33]. However, these constraints do not necessarily mean that building a highly unnatural LO interaction with two adjustable parameter is a no-go scenario. Indeed, the dibaryon formalism used in Ref. [13] has been shown to be a viable implementation, making use of the kinetic energy of the dibaryon field to provide the much needed energy dependence of the potential. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,863,933,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"On the other hand, no principle states that implementation of a two-parameter LO potential is unique. As long as a formulation incorporating both infrared scales satisfies the criteria introduced in Sec. I, it is acceptable. In fact, there is a clear practical motivation to search for other ways ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[64,47,293,63]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PENG, LYU, KÖNIG, AND LONG ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[651,49,933,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PHYSICAL REVIEW C 105, 054002 (2022) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[466,950,529,963]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"054002-2 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[62,82,488,170]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"to improve the $^1 S_0$ convergence: one encounters difficulties when applying the energy-dependent dibaryon potential (1) to many-nucleon calculations. It is the goal of the present paper to show that the separable, momentum-dependent alternative (2) provides a satisfactory foundation to be expanded around upon. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,80,933,156]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We find it useful to cast the separable potential (2) into the form of a Lagrangian. An auxiliary dibaryon field $\\phi$ with spin-0 and isospin-1 is introduced, but $\\phi$ is stationary, namely, it does not have a kinetic term. The Lagrangian terms involving $\\phi$ are given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[229,194,935,239]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {L} _ {\\phi} = \\sigma \\Delta \\boldsymbol {\\phi} ^ {\\dagger} \\cdot \\boldsymbol {\\phi} - \\sqrt {\\frac {4 \\pi}{m _ {N}}} \\sum_ {m = 1} ^ {3} \\sum_ {n = 0} ^ {\\infty} \\frac {g _ {2 n}}{2} \\left[ \\phi_ {m} ^ {\\dagger} N ^ {T} \\mathcal {P} _ {m} \\left(\\frac {- \\overleftrightarrow {\\nabla} ^ {2}}{4 m _ {N} \\Delta}\\right) ^ {n} N + H. c. \\right] + \\dots , \\tag {6}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,268,112,280]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[213,285,485,319]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {P} _ {m} = \\frac {1}{\\sqrt {8}} \\tau_ {2} \\tau_ {m} \\sigma_ {2} \\tag {7}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,323,485,356]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"is the spin and isospin projector to ensure that $\\phi$ couples only to the $^1 S_0$ channel and $\\overleftrightarrow{\\nabla}$ is defined so that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[176,361,485,381]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nN ^ {T} \\overleftrightarrow {\\nabla} N \\equiv N ^ {T} (\\overleftarrow {\\nabla} - \\overrightarrow {\\nabla}) N. \\tag {8}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,387,488,431]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Here, $\\sigma$ is normalized to $\\pm 1$ by rescaling $\\phi$ , and it will be determined by fitting to scattering data. If $g_{2n}$ are correlated by the binomial coefficients as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[222,436,485,472]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\frac {g _ {2 n}}{g} = \\binom {- \\frac {1}{2}} {n}, \\tag {9}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,478,485,506]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"then we can obtain the $\\phi NN$ vertex function after summing over all powers of relative momenta, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[171,513,485,551]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {A} _ {\\phi N N} = - \\frac {\\sqrt {4 \\pi} g}{\\sqrt {p ^ {2} / \\Delta + m _ {N}}} \\mathcal {P} _ {m}. \\tag {10}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,558,485,588]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The desired separable ${}^{1}S_{0}$ potential then follows from the $s$ -channel exchange of $\\phi$ , ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[98,593,485,628]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV _ {\\operatorname {s p r}} ^ {(0)} \\left(p ^ {\\prime}, p\\right) = - \\frac {4 \\pi}{m _ {N}} \\frac {\\lambda}{\\sqrt {p ^ {\\prime 2} + m _ {N} \\Delta} \\sqrt {p ^ {2} + m _ {N} \\Delta}}, \\tag {11}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,633,215,650]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\lambda \\equiv \\sigma m_N g^2 / 4$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[64,650,485,679]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In order to justify summing the $g_{2n}$ terms, $\\lambda$ and $\\Delta$ must be identified as two independent infrared mass scales, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[205,685,485,705]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\sqrt {m _ {N} \\Delta} \\sim \\lambda \\sim M _ {\\mathrm {l o}}, \\tag {12}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,710,261,724]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"which in turn translates into ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[232,729,485,770]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\ng \\sim \\sqrt {\\frac {M _ {\\mathrm {l o}}}{M _ {\\mathrm {h i}}}}. \\tag {13}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,775,485,819]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We will see that the expected scaling of $\\lambda$ and $\\Delta$ is verified once their values are obtained from fitting to the $^1 S_0$ empirical phase shifts. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,819,485,934]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Summing an infinite sequence of derivative coupling terms prompts concerns regarding chiral symmetry. Derivatives acting on the nucleon field must be accompanied by so-called chiral-connection operators involving the pion fields so that chiral symmetry is nonlinearly realized by these hadronic degrees of freedom [34,35]. We will come back to this in Sec. V to discuss chiral-connection operators of the $\\phi NN$ transition vertex. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,268,932,299]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The LO ${}^{1}S_{0}$ amplitude is the resummation of $V_{\\mathrm{spr}}^{(0)}$ and $V_{Y}$ to all orders by way of the partial-wave LS equation, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[546,304,932,372]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} T \\left(p ^ {\\prime}, p; E\\right) = V _ {\\mathrm {L O}} \\left(p ^ {\\prime}, p\\right) + \\frac {1}{2 \\pi^ {2}} \\int d l l ^ {2} V _ {\\mathrm {L O}} \\left(p ^ {\\prime}, l\\right) \\\\ \\times \\frac {T (l , p ; E)}{E - l ^ {2} / m _ {N} + i \\epsilon} \\tag {14} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[511,377,546,390]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"with ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[590,397,932,417]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV _ {\\mathrm {L O}} \\left(p ^ {\\prime}, p\\right) = V _ {\\mathrm {s p r}} ^ {(0)} \\left(p ^ {\\prime}, p\\right) + V _ {Y} \\left(p ^ {\\prime}, p\\right), \\tag {15}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[599,421,932,455]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV _ {Y} \\left(p ^ {\\prime}, p\\right) = - \\frac {g _ {A} ^ {2}}{4 f _ {\\pi} ^ {2}} \\frac {m _ {\\pi} ^ {2}}{q ^ {2} + m _ {\\pi} ^ {2}}. \\tag {16}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,460,852,476]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The LS equation is often schematically written as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[631,481,932,500]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nT ^ {(0)} = V _ {\\mathrm {L O}} + V _ {\\mathrm {L O}} G _ {0} T ^ {(0)}, \\tag {17}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,505,932,564]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $G_{0}$ is the nonrelativistic free-particle propagator. When solving the LS equation, we regularize the ultraviolet part of the potentials with a separable regulator to ensure that the regularization in one partial wave does not interfere another: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[577,569,932,604]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV ^ {\\Lambda} \\left(\\vec {p} ^ {\\prime}, \\vec {p}\\right) = f _ {R} \\left(\\frac {p ^ {\\prime 2}}{\\Lambda^ {2}}\\right) V \\left(\\vec {p} ^ {\\prime}, \\vec {p}\\right) f _ {R} \\left(\\frac {p ^ {2}}{\\Lambda^ {2}}\\right). \\tag {18}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,609,932,637]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In particular, a Gaussian regulator is used in our numerical calculations: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[672,642,932,662]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nf _ {R} (x) = e ^ {- x ^ {2}}. \\tag {19}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,667,932,712]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Using the two-potential method [32], the $\\mathrm{LO}^{1}\\mathrm{S}_{0}$ amplitude can be rewritten to facilitate analysis. We start by defining the off-shell Yukawa amplitude ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[650,719,932,734]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nT _ {Y} = V _ {Y} + V _ {Y} G _ {0} T _ {Y}, \\tag {20}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,739,932,784]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and the origin value of its scattering wave function, dressed by the square-root dipole form factor of the $\\phi NN$ transition vertex (10): ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[541,789,932,864]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\chi (p; E) = \\frac {1}{\\sqrt {p ^ {2} + m _ {N} \\Delta}} + \\int \\frac {d ^ {3} l}{(2 \\pi) ^ {3}} \\left(l ^ {2} + m _ {N} \\Delta\\right) ^ {- \\frac {1}{2}} \\\\ \\times \\frac {T _ {Y} (l , p)}{E - l ^ {2} / m _ {N} + i \\epsilon}. \\tag {21} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,869,752,883]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The LO amplitude is then given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[528,888,932,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nT ^ {(0)} (k, k; E) = T _ {Y} (k, k) - \\frac {4 \\pi}{m _ {N}} \\frac {\\chi (k ; E) ^ {2}}{\\lambda^ {- 1} \\left(k ^ {2} + m _ {N} \\Delta\\right) + I (E)}, \\tag {22}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,47,463,63]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CONSTRUCTING CHIRAL EFFECTIVE FIELD THEORY ... ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[651,49,932,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PHYSICAL REVIEW C 105, 054002 (2022) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[466,950,529,963]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"054002-3 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[64,97,488,181]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0499/9c68a85999c6b5deab68570760596919b4c6fc26902da21cae8e8a945d46da0b.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":"<table><tr><td>Λ</td><td>Δ(0)</td><td>λ(0)</td></tr><tr><td>600</td><td>27.1</td><td>270</td></tr><tr><td>1200</td><td>24.6</td><td>223</td></tr><tr><td>2400</td><td>24.1</td><td>209</td></tr></table>","table_caption":"[\"TABLE I. Running of $\\\\lambda$ (MeV) and $\\\\Delta$ (MeV) with $\\\\Lambda$ (MeV) at LO. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[64,214,112,227]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[74,242,485,280]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nI (E) \\equiv \\frac {4 \\pi}{m _ {N}} \\int \\frac {d ^ {3} l}{(2 \\pi) ^ {3}} \\left(l ^ {2} + m _ {N} \\Delta\\right) ^ {- \\frac {1}{2}} \\frac {\\chi (l ; E)}{E - l ^ {2} / m _ {N} + i \\epsilon}. \\tag {23}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,292,485,454]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Compared with the energy-dependent dibaryon potential, the factor $(p^2 + m_N\\Delta)^{-\\frac{1}{2}}$ brings so much UV suppression that the integral would be finite even without the regulator, and $\\Delta(\\Lambda)$ and $\\lambda(\\Lambda)$ approach finite values for $\\Lambda \\rightarrow \\infty$ . Table I shows their values as a function of $\\Lambda$ . The fitting to empirical $^1 S_0$ phase shifts will be explained in Sec. IV. Using these values, we have $\\sqrt{m_N\\Delta} \\simeq 150 \\mathrm{MeV}$ and $\\lambda \\simeq 200 \\mathrm{MeV}$ , which confirms the expected scaling given in Eq. (12). The inverse of $\\sqrt{m_N\\Delta}$ comes out close to the pion Compton wave length $\\simeq 1.4 \\mathrm{fm}$ , suggesting that the dibaryon potential has a range similar to that of OPE. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,80,932,125]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let us turn to higher orders. Although $\\lambda (\\Lambda)$ and $\\Delta (\\Lambda)$ appear at LO, their running with $\\Lambda$ can be modified at subleading orders: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[551,132,932,150]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\lambda (\\Lambda) = \\lambda^ {(0)} (\\Lambda) + \\lambda^ {(1)} (\\Lambda) + \\lambda^ {(2)} (\\Lambda) + \\dots , \\tag {24}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[544,160,932,179]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\Delta (\\Lambda) = \\Delta^ {(0)} (\\Lambda) + \\Delta^ {(1)} (\\Lambda) + \\Delta^ {(2)} (\\Lambda) + \\dots . \\tag {25}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,186,932,231]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The $\\lambda^{(\\nu)}$ and $\\Delta^{(\\nu)}$ are formally smaller than their LO value by $Q^{\\nu} / M_{\\mathrm{hi}}^{\\nu}$ . These modifications play a role at higher orders, which can be constructed by the generating function ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[524,234,932,290]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {F} _ {\\operatorname {s p r}} \\left(p ^ {\\prime}, p; x\\right) \\equiv - \\frac {4 \\pi}{m _ {N}} \\frac {\\lambda (x)}{\\sqrt {p ^ {\\prime 2} + m _ {N} \\Delta (x)} \\sqrt {p ^ {2} + m _ {N} \\Delta (x)}}, \\tag {26}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,297,932,311]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $x$ is an auxiliary variable to generate the expansion and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[595,318,932,337]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\lambda (x) = \\lambda^ {(0)} + x \\lambda^ {(1)} + x ^ {2} \\lambda^ {(2)} + \\dots , \\tag {27}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[589,347,932,364]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\Delta (x) = \\Delta^ {(0)} + x \\Delta^ {(1)} + x ^ {2} \\Delta^ {(2)} + \\dots . \\tag {28}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,372,911,387]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"From there, the dibaryon part at each order is generated by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[577,391,932,435]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\mathcal {F} _ {\\mathrm {s p r}} (p ^ {\\prime}, p; x) = V _ {\\mathrm {s p r}} ^ {(0)} (p ^ {\\prime}, p) + x V _ {\\mathrm {s p r}} ^ {(1)} (p ^ {\\prime}, p) \\\\ + x ^ {2} V _ {\\mathrm {s p r}} ^ {(2)} \\left(p ^ {\\prime}, p\\right) + \\dots \\tag {29} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,439,840,455]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"with the first two corrections explicitly given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[129,478,932,516]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV _ {\\mathrm {s p r}} ^ {(1)} \\left(p ^ {\\prime}, p\\right) = - \\frac {4 \\pi}{m _ {N}} \\frac {1}{\\sqrt {p ^ {2} + m _ {N} \\Delta^ {(0)}} \\sqrt {p ^ {\\prime 2} + m _ {N} \\Delta^ {(0)}}} \\left\\{\\lambda^ {(1)} - \\frac {m _ {N} \\lambda^ {(0)}}{2} \\left(\\frac {1}{p ^ {2} + m _ {N} \\Delta^ {(0)}} + \\frac {1}{p ^ {\\prime 2} + m _ {N} \\Delta^ {(0)}}\\right) \\Delta^ {(1)} \\right\\} \\tag {30}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,520,96,534]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[144,537,932,651]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} V _ {\\mathrm {s p r}} ^ {(2)} (p ^ {\\prime}, p) = - \\frac {4 \\pi}{m _ {N}} \\frac {1}{\\sqrt {(p ^ {2} + m _ {N} \\Delta^ {(0)})} \\sqrt {(p ^ {\\prime 2} + m _ {N} \\Delta^ {(0)})}} \\\\ \\times \\left\\{\\lambda^ {(2)} - \\frac {m _ {N}}{2} \\left[ \\frac {1}{\\left(p ^ {2} + m _ {N} \\Delta^ {(0)}\\right)} + \\frac {1}{\\left(p ^ {\\prime 2} + m _ {N} \\Delta^ {(0)}\\right)} \\right] \\left(\\lambda^ {(0)} \\Delta^ {(2)} + \\lambda^ {(1)} \\Delta^ {(1)}\\right) \\right. \\\\ + \\frac {m _ {N} ^ {2} \\lambda^ {(0)}}{8} \\left[ \\frac {3}{\\left(p ^ {2} + m _ {N} \\Delta^ {(0)}\\right) ^ {2}} + \\frac {2}{\\left(p ^ {2} + m _ {N} \\Delta^ {(0)}\\right) \\left(p ^ {\\prime 2} + m _ {N} \\Delta^ {(0)}\\right)} + \\frac {3}{\\left(p ^ {\\prime 2} + m _ {N} \\Delta^ {(0)}\\right) ^ {2}} \\right] \\Delta^ {(1) ^ {2}} \\}. \\tag {31} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,679,485,781]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If one expands the potential (11) in powers of momenta, a series of $^1 S_0$ contact terms emerges. Therefore, the values of $\\Delta$ and $\\lambda$ span a surface in the parameter space of $^1 S_0$ contact couplings. The deviation away from the surface can be described by residual values of $^1 S_0$ contact terms. Reference [13] has shown that higher-order short-range forces are parametrized by conventional four-nucleon operators ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[183,791,485,830]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV _ {S} = \\sum_ {n = 0} ^ {\\infty} \\frac {C _ {2 n}}{2} \\left(p ^ {\\prime 2 n} + p ^ {2 n}\\right) \\tag {32}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,839,303,854]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"with the following scaling for $C_{2n}$ : ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,863,485,898]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nC _ {2 n} \\sim \\frac {4 \\pi}{m _ {N}} \\frac {1}{M _ {\\mathrm {l o}} ^ {n} M _ {\\mathrm {h i}} ^ {n + 1}}. \\tag {33}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,905,485,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"NLO and higher-orders amplitudes are built as perturbations on top of LO, i.e., they are diagrammatically perturbative ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,679,923,695]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"insertions of $V_{\\mathrm{NLO}}$ , $V_{\\mathrm{N}^2\\mathrm{LO}}$ (and so on) into the LO amplitude: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[524,700,796,720]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nT ^ {(1)} = (1 + T ^ {(0)} G _ {0}) V _ {\\mathrm {N L O}} \\left(G _ {0} T ^ {(0)} + 1\\right),\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[526,724,916,765]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} T ^ {(2)} = (1 + T ^ {(0)} G _ {0}) [ V _ {\\mathrm {N} ^ {2} \\mathrm {L O}} + V _ {\\mathrm {N L O}} G _ {0} (1 + T ^ {(0)} G _ {0}) V _ {\\mathrm {N L O}} ] \\\\ \\times \\left(G _ {0} T ^ {(0)} + 1\\right). \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[558,773,930,801]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\dots . \\tag {34}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,811,930,842]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In particular, since there is no pion-exchanges at NLO, the $^1 S_0$ potential is given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[606,847,932,868]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV _ {\\mathrm {N L O}} \\left(p ^ {\\prime}, p\\right) = C _ {0} ^ {(0)} + V _ {\\mathrm {s p r}} ^ {(1)} \\left(p ^ {\\prime}, p\\right). \\tag {35}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[602,883,840,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"III. RADIATIVE CORRECTIONS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,905,932,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The scaling (12) has so far led us to have the momentum-dependent dibaryon potential (and its subleading corrections) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[64,47,293,63]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PENG, LYU, KÖNIG, AND LONG ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[651,49,932,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PHYSICAL REVIEW C 105, 054002 (2022) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[466,950,529,964]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"054002-4 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[62,80,485,224]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"simply substitute the energy-dependent one. But there is an important difference at $\\mathrm{N}^2\\mathrm{LO}$ . Besides the leading two-pion exchange $V_{\\mathrm{TPE0}}$ [36], pionic radiative corrections to the dibaryon potential, depicted in Fig. 1, appear at this order. For a dynamically propagating dibaryon, the radiative corrections are zero-range interactions (much like the radiative corrections to pure $NN$ contact operators [37,38]); therefore, they do not change the form of the potentials in any nontrivial way. For the momentum-dependent dibaryon vertex, this is no longer the case because the vertex is finite-ranged. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[64,226,485,470]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In Fig. 1, $\\vec{p} (\\vec{p}^{\\prime})$ is the incoming (outgoing) nucleon c.m. momentum, and $k,n,r,$ and $s(a,b,c,$ and $d$ ) are spin (isospin) indexes. While Fig. 1(a) contributes only to $^1 S_0$ , the impact of Fig. 1(b) is confined to the triplet channels, as will be shown later in the section. Without the dibaryon field, the convergence in the triplet channels is already quite good [39,40]. Thus, it is important for the purpose of validating the dibaryon potential to examine how it affects the triplet channels through radiative corrections. If Fig. 1(b) interferes with the triplet channels so much that a satisfactory description of data is spoiled, we will have to give up the momentum-dependent dibaryon formalism even if it does improve $^1 S_0$ . Fortunately, it turns out that these radiative corrections for the most part only renormalize the $NN$ contact terms in $^3 S_1 - ^3 D_1$ and do not significantly change the on-shell amplitudes. Before turning to the phase shifts, we discuss calculation of the Feynman diagrams in Fig. 1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,472,485,617]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As mentioned previously, the diagram of Fig. 1(a) is expected to contribute only to ${}^{1}S_{0}$ , for it can be broken by cutting the dibaryon propagator. The $NN$ reducible part of the diagram is the contribution from picking up the nucleon pole when integrating out the zeroth component of the loop momentum, which is part of the LO amplitude and has been accounted for when iterating $V_{\\mathrm{LO}}$ in Eq. (14). What is counted as $\\mathrm{N}^2\\mathrm{LO}$ is the irreducible part of the diagram that results from picking up the pion pole and is given by the three-dimensional integral ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[83,625,485,708]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\mathcal {A} _ {\\mathrm {r a d}} ^ {(a)} = - \\frac {4 \\pi}{m _ {N}} \\frac {g _ {A} ^ {2}}{4 f _ {\\pi} ^ {2}} \\lambda^ {(0)} (\\Lambda) \\sum_ {m} [ (\\mathcal {P} _ {m} ^ {\\dagger}) _ {r s, a b} (\\mathcal {P} _ {m}) _ {k n, c d} ] \\\\ \\times \\int \\frac {d ^ {3} l}{(2 \\pi) ^ {3}} \\frac {l ^ {2}}{\\left(l ^ {2} + m _ {\\pi} ^ {2}\\right) ^ {\\frac {3}{2}}} \\mathcal {R} (| \\vec {p} ^ {\\prime} |, | \\vec {p} - \\vec {l} |; \\Lambda) \\tag {36} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,715,230,729]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"with the scalar function ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,734,485,776]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {R} (x, y; \\Lambda) \\equiv \\frac {f _ {R} \\left(\\frac {x ^ {2}}{\\Lambda^ {2}}\\right) f _ {R} \\left(\\frac {y ^ {2}}{\\Lambda^ {2}}\\right)}{\\sqrt {x ^ {2} + m _ {N} \\Delta^ {(0)} (\\Lambda)} \\sqrt {y ^ {2} + m _ {N} \\Delta^ {(0)} (\\Lambda)}}. \\tag {37}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,782,485,842]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\lambda^{(0)}(\\Lambda)$ and $\\Delta^{(0)}(\\Lambda)$ are the LO values, determined by fitting to empirical $^1 S_0$ phase shifts (see Table I). On the ground of satisfying unitarity up to this order, one must use the same regularization function adopted for the LO resummation (18). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,842,485,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The amplitude of the diagram in which the pion propagator connects the outgoing nucleon lines (not shown in Fig. 1) can be obtained by making the following replacements: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,895,485,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} (a, b) (c, d) \\rightarrow (c, d) (a, b); \\quad (r, s) (k, n) \\rightarrow (k, n) (r, s); \\\\ (\\bar {p}, \\bar {p} ^ {\\prime}) \\rightarrow (- \\bar {p} ^ {\\prime}, - \\bar {p}). \\tag {38} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,80,932,167]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The integrals are calculated numerically, and the trace formalism of Ref. [41] is used to obtain partial-wave projected amplitudes before the loop momentum is integrated over. With a bit of spin-isospin algebra, the contribution of Fig. 1(a) and its permutation to $^1 S_0$ is obtained by evaluating the following integral: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[519,174,932,239]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} V _ {\\text {r a d}} ^ {1 S _ {0}} = - \\frac {\\pi}{m _ {N}} \\frac {g _ {A} ^ {2}}{4 f _ {\\pi} ^ {2}} \\lambda^ {(0)} (\\Lambda) \\int \\frac {d ^ {3} l}{(2 \\pi) ^ {3}} \\frac {l ^ {2}}{\\left(l ^ {2} + m _ {\\pi} ^ {2}\\right) ^ {\\frac {3}{2}}} \\\\ \\times \\left[ \\mathcal {R} \\left(\\left| \\vec {p} ^ {\\prime} \\right|, \\left| \\vec {p} - \\vec {l} \\right|; \\Lambda\\right) + \\mathcal {R} \\left(\\left| \\vec {p} \\right|, \\left| \\vec {p} ^ {\\prime} + \\vec {l} \\right|; \\Lambda\\right) \\right]. \\tag {39} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,246,932,276]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The corrections to the triplet channels come from the diagrams in Fig. 1(b), ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[531,282,932,391]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\mathcal {A} _ {\\mathrm {r a d}} ^ {(b)} = \\frac {4 \\pi}{m _ {N}} \\frac {g _ {A} ^ {2}}{1 6 f _ {\\pi} ^ {2}} \\lambda^ {(0)} (\\Lambda) \\sum_ {e, m, \\alpha , \\beta} \\frac {1}{8} [ (\\tau_ {e} \\tau_ {2} \\tau_ {m}) _ {b a} (\\tau_ {2} \\tau_ {e} \\tau_ {m}) _ {c d} \\\\ \\times \\left(\\sigma_ {\\alpha} \\sigma_ {2}\\right) _ {r s} \\left(\\sigma_ {2} \\sigma_ {\\beta}\\right) _ {k n} ] \\int \\frac {d ^ {3} l}{(2 \\pi) ^ {3}} \\frac {l _ {\\alpha} l _ {\\beta}}{\\left(l ^ {2} + m _ {\\pi} ^ {2}\\right) ^ {\\frac {3}{2}}} \\\\ \\times \\mathcal {R} (| \\vec {p} _ {-} |, | \\vec {p} _ {+} ^ {\\prime} |; \\Lambda), \\tag {40} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,397,558,410]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[604,416,932,450]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\vec {p} _ {\\pm} \\equiv \\vec {p} \\pm \\frac {\\vec {l}}{2}, \\quad \\vec {p} _ {\\pm} ^ {\\prime} \\equiv \\vec {p} ^ {\\prime} \\pm \\frac {\\vec {l}}{2}. \\tag {41}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,457,933,516]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Projection of $\\mathcal{A}_{\\mathrm{rad}}^{(b)}$ is again performed with the trace formalism. After taking all the variants due to permutations of the pion line into account, the radiative corrections to the $^3 S_1 - ^3 D_1$ potential is given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[522,522,932,628]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} V _ {\\text {r a d}} ^ {3 S _ {1} - 3 D _ {1}} = - \\frac {\\pi}{m _ {N}} \\frac {g _ {A} ^ {2}}{1 6 f _ {\\pi} ^ {2}} \\lambda^ {(0)} (\\Lambda) \\int \\frac {d ^ {3} l}{(2 \\pi) ^ {3}} \\frac {l ^ {2}}{\\left(l ^ {2} + m _ {\\pi} ^ {2}\\right) ^ {\\frac {3}{2}}} \\\\ \\times \\mathcal {T} (\\hat {p}, \\hat {p} ^ {\\prime}, \\hat {l}) [ \\mathcal {R} (| \\vec {p} _ {-} |, | \\vec {p} _ {+} ^ {\\prime} |; \\Lambda) \\\\ + \\mathcal {R} (| \\vec {p} _ {-} |, | \\vec {p} _ {-} ^ {\\prime} |; \\Lambda) \\\\ + \\mathcal {R} (| \\bar {p} _ {+} |, | \\bar {p} _ {-} ^ {\\prime} |; \\Lambda) + \\mathcal {R} (| \\bar {p} _ {+} |, | \\bar {p} _ {-} ^ {\\prime} |; \\Lambda) ], \\tag {42} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,636,840,652]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where the $2 \\times 2$ matrix $\\mathcal{T}(\\hat{p},\\hat{p}^{\\prime},\\hat{l})$ is defined by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[526,659,640,676]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\langle^ {3} S _ {1} | \\mathcal {T} | ^ {3} S _ {1} \\rangle = 1,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[522,681,740,718]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\langle^ {3} S _ {1} | \\mathcal {T} | ^ {3} D _ {1} \\rangle = \\frac {3 (\\hat {p} \\cdot \\hat {l}) ^ {2}}{\\sqrt {2}} - \\frac {1}{\\sqrt {2}},\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[522,722,741,757]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\langle^ {3} D _ {1} | \\mathcal {T} | ^ {3} S _ {1} \\rangle = \\frac {3 (\\hat {p} ^ {\\prime} \\cdot \\hat {l}) ^ {2}}{\\sqrt {2}} - \\frac {1}{\\sqrt {2}},\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[519,761,932,825]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\langle^ {3} D _ {1} | \\mathcal {T} | ^ {3} D _ {1} \\rangle = \\frac {9}{2} (\\hat {p} \\cdot \\hat {l}) (\\hat {p} ^ {\\prime} \\cdot \\hat {l}) \\hat {p} \\cdot \\hat {p} ^ {\\prime} - \\frac {3}{2} [ (\\hat {p} ^ {\\prime} \\cdot \\hat {l}) ^ {2} + (\\hat {p} \\cdot \\hat {l}) ^ {2} ] \\\\ + \\frac {1}{2}. \\tag {43} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[521,840,921,869]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IV. NUCLEON-NUCLEON PHASE SHIFTS AND TRITON BINDING ENERGY ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,877,932,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this section we show how well the momentum-dependent dibaryon potential agrees with empirical phase shifts of $NN$ scattering and its prediction for the triton binding energy at LO and NLO. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[64,47,461,63]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CONSTRUCTING CHIRAL EFFECTIVE FIELD THEORY ... ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[651,49,932,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PHYSICAL REVIEW C 105, 054002 (2022) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[466,950,529,964]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"054002-5 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[166,82,495,261]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0072/063531139f14c2447eba0e98d974df36f556a7c5775d3e62dafe663ecf8fd730.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[500,80,831,262]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0910/3957b1bb39eeb48e484d264a820e1ccca3a38237ee32f919608de98330033d80.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[337,266,663,448]","code_body":null,"code_caption":null,"image_caption":"[\"FIG. 2. The $^1 S_0$ phase shifts as a function of c.m. momentum $k$ up to $\\\\mathrm{N}^2\\\\mathrm{LO}$ . The blue, orange and black bands represent LO, NLO, and $\\\\mathrm{N}^2\\\\mathrm{LO}$ respectively, and the bands show the variation with $\\\\Lambda$ from 600 to $2400\\\\mathrm{MeV}$ . The potentials used in (a), (b), and (c) are momentum-dependent dibaryon potentials, MMW scheme and dynamic dibaryon potentials, respectively. \"]","image_footnote":"[]","img_path":"images/0628/79becbdf2d4a10b40c8fbb5d21211d8e9a4b27b5b3dcb1ba5de0340f34899326.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[224,515,329,529]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A. ${}^{1}{S}_{0}$ channel ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[64,534,485,565]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Having computed the radiative corrections, we write the NNLO $^1 S_0$ potential explicitly as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[120,574,485,633]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} V _ {\\mathrm {N} ^ {2} \\mathrm {L O}} = C _ {0} ^ {(2)} + \\frac {C _ {2} ^ {(0)}}{2} \\left(p ^ {2} + p ^ {\\prime 2}\\right) + V _ {\\mathrm {s p r}} ^ {(2)} \\left(p ^ {\\prime}, p\\right) \\\\ + V _ {\\mathrm {T P E 0}} + V _ {\\mathrm {r a d}} ^ {1 S _ {0}} \\left(p ^ {\\prime}, p\\right). \\tag {44} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,643,485,847]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The $^1 S_0$ phase shifts up to $\\mathrm{N}^2\\mathrm{LO}$ are shown in Fig. 2(a). The bands represent the cutoff variation spanning from $\\Lambda = 600$ MeV to $2400\\mathrm{MeV}$ . The LECs are determined by fitting the EFT amplitudes to the empirical phase shifts provided by the partial-wave analysis (PWA) of the Nijmegen group [42,43] by a least-square procedure. For LO and NLO, PWA points with c.m. momentum $k \\lesssim 150\\mathrm{MeV}$ are used, and at $\\mathrm{N}^2\\mathrm{LO}$ inputs from $k = 150 - 300\\mathrm{MeV}$ are added. For comparison, the phase shifts up to $\\mathrm{N}^2\\mathrm{LO}$ obtained with the dynamic dibaryon potentials of Ref. [13] and the power counting of Ref. [8]—referred to as minimally modified Weinberg (MMW) in the current paper—are shown in Fig. 2(b) and 2(c). The LECs for this interaction were determined with the same set of PWA inputs. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,848,485,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The rather mild sensitivity to the cutoff $\\Lambda$ , manifest in the narrowness of the cutoff-variation bands, is somewhat expected based on the ultraviolet suppression afforded by the momentum-dependent $\\phi NN$ vertex. The rapid order-by-order convergence is also retained from the energy-dependent dibaryon potential, as illustrated in Ref. [13]. Moreover, the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,516,933,550]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"radiative correction $V_{\\mathrm{rad}}^{\\mathrm{ls}_0}$ does not spoil the cutoff independence or the convergence of the EFT expansion. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[640,566,804,580]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"B. Spin-triplet channels ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,583,933,688]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^3 S_1 - ^3 D_1$ is the spin-triplet channel that is most likely affected by the pion cloud because the centrifugal barrier in higher waves tends to suppress the radiated pions. In calculating the phase shifts of $^3 S_1 - ^3 D_1$ , we follow the power counting of Ref. [39], with OPE and one $S$ -wave counterterm at LO, NLO vanishing, and two more counterterms, TPE0, and $V_{\\mathrm{rad}}^{3S_1 - 3D_1}$ (42) at $\\mathrm{N}^2\\mathrm{LO}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,689,933,847]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The cutoff dependence has typically been more of a concern for the triplet channels because the singular attraction of OPE was a major source to upset NDA from the perspective of RG invariance. We determine the values of LECs by demanding that several PWA phase shifts are reproduced exactly. Specifically, the following PWA phase shifts are used: the $^3 S_1$ phase shift $\\delta_{^3 S_1}$ at $k = 118 \\mathrm{MeV}$ and $153 \\mathrm{MeV}$ and the mixing angle $\\epsilon_1$ at $153 \\mathrm{MeV}$ . Shown in Fig. 3, $^3 S_1 - ^3 D_1$ phase shifts and mixing angles for representative momenta ( $k = 100$ and $200 \\mathrm{MeV}$ ) become insensitive to the cutoff value $\\Lambda$ when $\\Lambda$ is sufficiently large. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,847,933,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 4 compares the $^3 S_1 - ^3 D_1$ phase shifts produced by the radiatively corrected dibaryon potential and the MMW scheme. The difference is minuscule: for the $^3 S_1$ phase shifts, the discrepancy is no more than about one degree, whereas the differences of the $^3 D_1$ phase shifts and the mixing angle is smaller than one degree. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[64,47,293,63]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PENG, LYU, KÖNIG, AND LONG ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[651,47,933,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PHYSICAL REVIEW C 105, 054002 (2022) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[466,950,534,964]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"054002-6 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[169,80,395,306]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0722/e777b266aedb7d1c48e1104f565ff5897ea53686f2f1f891351cd517e2c254af.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[405,80,626,306]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0990/29ff20de74ddeb0ea575610a6d51e43fc0352d51fef34755cfa33656a114616b.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[634,80,830,306]","code_body":null,"code_caption":null,"image_caption":"[\"FIG. 3. The $^3 S_1 - ^3 D_1$ phase shifts and mixing angle at $k = 100 \\\\, \\\\mathrm{MeV}$ (red) and $200 \\\\, \\\\mathrm{MeV}$ (blue), as functions of momentum cutoff $\\\\Lambda$ . The dashed (solid) lines represent the LO ( $\\\\mathrm{N}^2\\\\mathrm{LO}$ ) result. \"]","image_footnote":"[]","img_path":"images/0937/4d28dcba5a5f2546fc83c33e68e20d0f89317313a2c4e52a536e94b55857b8d8.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[62,356,488,518]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, the values of $^3 S_1 - ^3 D_1$ counterterms are renormalized by these radiative corrections, varying up to $50\\%$ compared to their MMW values. Thus, the impact of the radiative corrections on the triplet channels appears to be almost entirely short-ranged. This is further confirmed by the numerically tiny contributions to higher partial waves such as $^3 P_0$ , $^3 P_1$ , and $^3 D_2$ . We have computed the phase shifts of these partial waves, using partially-perturbative-pion power counting, Ref. [44] for $^3 P_0$ and Ref. [45] for $^3 P_1$ and $^3 D_2$ . Within numerical precision of our calculations, the differences are found to be negligible. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[190,547,361,561]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"C. Triton binding energy ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,565,488,652]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The success of the momentum-dependent dibaryon potential in $^1 S_0$ was more or less expected because it is unitarily equivalent to the energy-dependent version in $^1 S_0$ , at least at tree level. A third particle can assess its impact beyond the two-nucleon system. The exchanged pion in the radiative corrections considered in Sec. III plays the role of a third ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,354,933,383]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"particle, but it is virtual. We therefore now assess what the theory predicts for the triton binding energy up to NLO. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,383,933,558]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The calculation is set up following the power counting of partially perturbative pions. At LO, we iterate to all orders the potential (11) plus OPE in $^1 S_0$ , and one contact term plus OPE in $^3 S_1 - ^3 D_1$ and $^3 P_0$ [1]. This is done by solving the Faddeev equations to obtain binding energies as LO. At NLO, in addition to the NLO $^1 S_0$ force, OPE is included in channels up to $D$ waves $(^1 P_1, ^3 P_1, ^3 P_2 - ^3 F_2, ^1 D_2, ^3 D_2,$ and $^3 D_3 - ^3 G_3)$ . Perturbative corrections to the binding energy are obtained by evaluating the NLO potentials between LO wave functions, obtained from the Faddeev equations along with the LO energies. For all calculations we include channels with angular momentum up to $j_{\\mathrm{max}} = 4$ in the Faddeev equations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,558,933,647]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The results for various cutoff are shown in Table II as columns of labeled \"SEP.\" For comparison, we also show the results for the MMW scheme. Since the triton is relatively shallow, with an average binding momentum $\\sqrt{2m_NB_{3\\mathrm{H}} / 3}\\simeq$ $73~\\mathrm{MeV}$ we do not expect the dibaryon potential to necessarily perform much better in reproducing the triton binding ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[169,674,398,883]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0090/67f08a0422487e5810e985544148cc782ab9666384a6de7f761fb10a3da26014.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[402,672,619,883]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/1008/acda9d4f235e92efd2ada28422c1524d4df14a286a55d5747c2c2a03a2f4b3ff.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[624,672,830,883]","code_body":null,"code_caption":null,"image_caption":"[\"FIG. 4. The $^3 S_1 - ^3 D_1$ phase shifts and mixing angle as functions of the c.m. momentum $k$ , for cutoff $\\\\Lambda = 600 \\\\, \\\\mathrm{MeV}$ (red) and $2400 \\\\, \\\\mathrm{MeV}$ (green). The solid lines represent the results with radiative corrections to the dibaryon potential, and the dashed lines correspond to the MMW scheme. The circles are the PWA values. See the text for more detailed explanation. \"]","image_footnote":"[]","img_path":"images/0594/8b1c5a9057955edde8b9b2dce408c45e14b454addeeb3d49d42244797031e769.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[64,47,465,63]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CONSTRUCTING CHIRAL EFFECTIVE FIELD THEORY ... ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[651,47,933,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PHYSICAL REVIEW C 105, 054002 (2022) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[466,950,529,963]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"054002-7 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[64,112,488,229]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0317/83927de3a84836a722f96664d078ab474b3a1e9731f0f3f7cf60d461088afc92.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":"<table><tr><td rowspan=\"2\">Λ (MeV)</td><td colspan=\"2\">SEP</td><td colspan=\"2\">MMW</td></tr><tr><td>LO</td><td>NLO</td><td>LO</td><td>NLO</td></tr><tr><td>400</td><td>-8.67</td><td>-8.50</td><td>-11.02</td><td>-7.68</td></tr><tr><td>600</td><td>-6.10</td><td>-6.10</td><td>-6.46</td><td>-6.90</td></tr><tr><td>800</td><td>-5.57</td><td>-5.58</td><td>-5.30</td><td>-6.64</td></tr><tr><td>1600</td><td>-5.37</td><td>-5.51</td><td>-4.89</td><td>-6.49</td></tr></table>","table_caption":"[\"TABLE II. The binding energy of the triton (MeV). See the text for more explanations. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[66,253,485,484]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"energy. In fact, the NLO of MMW has a smaller cutoff variation, and the large $\\Lambda$ limit is closer to the experimental value of $\\simeq 8.5\\mathrm{MeV}$ . However, cutoff variation at best should be taken as a lower bound for the full theoretical uncertainty. The NLO correction of SEP is much smaller than MMW, which might imply that the actual EFT truncation error is smaller with SEP than with MMW. While a more systematic comparison of the two schemes in few- or many-nucleon is definitely interesting, it is beyond the scope of the paper, as is a triton calculation involving the energy-dependent dibaryon potential. We are for now content with finding that the dibaryon potential gives a description of the three-nucleon system that is comparable to the MMW scheme. Both the SEP and MMW interactions yield the triton slightly more bound compared to earlier calculations using a similar perturbative power-counting scheme [46,47]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,484,488,602]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nuclear-structure calculations using the dibaryon interaction [29] or an interaction inspired by it [31] have been carried out previously. In Ref. [31], some of the light nuclei with $A = 3 - 6$ were investigated. A direct comparison between the triton binding energy calculated in Ref. [31] and this work is however difficult because different power-counting and regularization schemes have been used. We only note that results agree within $10\\%$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[185,621,366,633]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"V. CHIRAL SYMMETRY ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,642,488,702]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nonlinear realization of spontaneously broken chiral symmetry requires derivatives acting on hadronic fields to be chirally covariant. The chiral-covariant derivative $\\mathcal{D}_i$ for the nucleon, which is an isospin- $1 / 2$ field, is given as [48] ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[188,708,485,736]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathscr {D} _ {i} N \\equiv \\left(\\nabla_ {i} + \\frac {\\boldsymbol {\\tau}}{2} \\cdot \\boldsymbol {E} _ {i}\\right) N, \\tag {45}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,742,422,757]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where the so-called chiral connection $E_{i}$ is given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[215,763,485,794]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\boldsymbol {E} _ {i} \\equiv i \\frac {\\boldsymbol {\\pi}}{f _ {\\pi}} \\times \\boldsymbol {D} _ {i} \\tag {46}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,801,101,814]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"with ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[142,820,485,856]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\boldsymbol {D} _ {i} \\equiv D ^ {- 1} \\frac {\\nabla_ {i} \\boldsymbol {\\pi}}{2 f _ {\\pi}} \\quad \\text {a n d} \\quad D \\equiv 1 + \\frac {\\boldsymbol {\\pi} ^ {2}}{4 f _ {\\pi} ^ {2}}. \\tag {47}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,863,488,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The moral here is that derivatives acting on $N$ must be accompanied by composite chiral-connection terms consisting of $\\pi$ and $N$ , with two types of operators sharing the same set of LECs. Because the $\\phi NN$ vertex function (10) is constructed out of an infinite series of derivative couplings acting on $N$ , ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[638,84,806,191]","code_body":null,"code_caption":null,"image_caption":"[\"FIG. 5. The transition vertex of $NN\\\\pi \\\\pi \\\\rightarrow \\\\phi$ . \"]","image_footnote":"[]","img_path":"images/0829/8221006afbfca54a7be6315fb872ead9a8b009eb5f6f77cf02673e4b3423fad3.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[507,234,932,306]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"it is less straightforward than usual to write down the corresponding chiral-connection operators. Furthermore, in light of the proposed two-parameter fine-tuning at LO in $^1 S_0$ , these chiral-connection operators could be enhanced in comparison with NDA. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,308,933,469]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Chiral-connection operators that include products of two pion fields, the minimal number of pion fields such operators expected to have, are normally the most phenomenologically important for low-energy nuclear physics. We therefore focus on the transition vertex of $NN\\pi \\pi \\rightarrow \\phi$ , depicted in Fig. 5, where $\\alpha_{1,2}$ denotes collectively the spin and isospin indices of the incoming nucleons, $\\vec{p} \\equiv (\\vec{p}_1 - \\vec{p}_2) / 2$ their relative momentum, $a, b, c$ the isospin indices of the pions and the isovector dibaryon, and $\\vec{k}_{1,2}$ the momentum of the incoming pions. Following the derivations in the Appendix, one finds the vertex function of $\\phi NN\\pi \\pi$ to be ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[558,476,932,555]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\mathcal {A} _ {\\phi N N \\pi \\pi} = \\frac {i g}{4 f _ {\\pi} ^ {2}} \\sqrt {\\frac {4 \\pi}{m _ {N}}} \\left\\{i (\\delta_ {b c} \\mathcal {P} _ {a} - \\delta_ {a c} \\mathcal {P} _ {b}) _ {\\alpha_ {2} \\alpha_ {1}} \\mathcal {B} _ {+} \\right. \\\\ \\left. + \\frac {1}{\\sqrt {8}} \\epsilon_ {a b c} \\left(\\sigma_ {2} \\tau_ {2}\\right) _ {\\alpha_ {2} \\alpha_ {1}} \\mathcal {B} _ {-} \\right\\}, \\tag {48} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,560,672,574]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where we have defined ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[570,578,930,628]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\mathcal {B} _ {\\pm} \\equiv u (| \\vec {p} + \\vec {k} _ {1} / 2 |, | \\vec {p} + \\vec {k} _ {2} / 2 |) \\\\ \\pm u \\left(\\left| \\vec {p} - \\vec {k} _ {1} / 2 \\right|, \\left| \\vec {p} - \\vec {k} _ {2} / 2 \\right|\\right), \\tag {49} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[548,628,867,666]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nu (x, y) \\equiv \\left(1 + \\frac {x ^ {2}}{m _ {N} \\Delta}\\right) ^ {- \\frac {1}{2}} - \\left(1 + \\frac {y ^ {2}}{m _ {N} \\Delta}\\right) ^ {- \\frac {1}{2}}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,670,930,699]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Using the scalings (12) and (13), one has the vertex function scale as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[631,703,932,738]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {A} _ {\\phi N N \\pi \\pi} \\sim \\frac {4 \\pi}{m _ {N}} \\frac {1}{\\sqrt {M _ {\\mathrm {h i}}}} \\frac {1}{f _ {\\pi}}. \\tag {50}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,750,933,808]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Combining then the scaling (50) with the standard counting rule for irreducible pion loops, we find that the $\\phi NN\\pi \\pi$ vertex contributes to the two-nucleon force at $\\mathrm{N}^2\\mathrm{LO}$ , illustrated in Fig. 6. However, the amplitude of this diagram vanishes, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[624,830,820,912]","code_body":null,"code_caption":null,"image_caption":"[\"FIG. 6. Irreducible $NN$ diagram built out of a $\\\\phi NN\\\\pi \\\\pi$ vertex. \"]","image_footnote":"[]","img_path":"images/0948/b0908bd3c89d84750dd1a8c5f5bfc96f9c44aabcb75d958541437c794058e724.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[64,47,293,63]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PENG, LYU, KÖNIG, AND LONG ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[651,49,932,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PHYSICAL REVIEW C 105, 054002 (2022) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[466,950,529,964]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"054002-8 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[64,83,249,165]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0273/2c13e89795402b742fff7c1dd7dd453362b51cd490897bed49affa2fd8fc1d49.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[305,82,487,165]","code_body":null,"code_caption":null,"image_caption":"[\"FIG. 7. The Feynman diagrams contributing to three-body and four-body forces with the $\\\\phi NN\\\\pi \\\\pi$ vertex. \"]","image_footnote":"[]","img_path":"images/0591/ad6874bbcccf8de9f9299ce4478b5afcbaaba53f77d9c64b409a910d5b858e8a.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[62,222,485,251]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"which can be seen by evaluating the isospin factors of $\\mathcal{A}_{\\phi NN\\pi \\pi}$ under exchange of the pion isospin index $a$ and $b$ : ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[147,258,485,273]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\epsilon_ {a a c} = 0 \\quad \\text {a n d} \\quad \\delta_ {a c} \\mathcal {P} _ {a} - \\delta_ {a c} \\mathcal {P} _ {a} = 0. \\tag {51}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,281,485,468]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As shown in Fig. 7, the $\\phi NN\\pi \\pi$ vertex (48) contributes to three-nucleon forces and four-nucleon forces. If we follow Weinberg's counting for long-range few-nucleon forces, these both enter at $\\mathrm{N}^4\\mathrm{LO}$ , four orders higher than the LO two-nucleon forces. If one ever ventures to describe two-pion production by nucleon-nucleon collision, the $\\phi NN\\pi \\pi$ will become relevant. These contributions are either quite high-order effects (3N or 4N forces) or become sizable only at such high momenta ( $NN\\rightarrow NN\\pi \\pi$ ), where the applicability of chiral EFT is questionable at best. In conclusion, the enhancement due to the momentum-dependent dibaryon vertex does not give rise to particularly significant extraneous contributions to nuclear structures or reactions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[142,488,407,500]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"VI. SUMMARY AND CONCLUSIONS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,508,485,594]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We have considered a new formulation of chiral EFT to improve the slow convergence of the $^1 S_0$ phase shifts. The key idea is to replace the energy-dependent dibaryon potential proposed in Ref. [13] with a momentum-dependent formulation that it is more amenable to many-body methods used for nuclear-structure calculations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[64,595,485,626]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The main ingredient is a transition form factor, from ${}^{1}{\\mathrm{S}}_{0}$ ${NN}$ states to the spin-0 and isospin-1 dibaryon: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[174,632,485,669]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {A} _ {\\phi N N} = - \\frac {\\sqrt {4 \\pi} g}{\\sqrt {p ^ {2} / \\Delta + m _ {N}}} \\mathcal {P} _ {m} \\tag {52}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,674,485,818]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"with two parameters $g$ and $\\Delta$ characterizing, respectively, the strength and momentum range of the transition. The vertex function (52) is interpreted as the sum of an infinite sequence of $\\phi NN$ derivative-coupling operators, correlated by $g$ and $\\Delta$ , which in turn correspond to two independent low-energy mass scales, as shown in Sec. II. With $g$ and $\\Delta$ varying, the resulting momentum-dependent potential traces out a two-dimensional surface in the EFT parameter space, in contrast to the one-dimensional line for the more conventional $^1 S_0$ LO chiral forces. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,819,485,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This phenomenologically inspired potential must demonstrate its consistency with the chiral Lagrangian. For instance, the $\\phi NN$ vertex can be radiatively corrected by the pion and could contribute non-trivial force to $^1 S_0$ at $\\mathrm{N}^2\\mathrm{LO}$ [see Fig. 1(a)]. When one of the incoming nucleons is connected to one of the outgoing nucleons by a radiation pion, triplet-channel amplitudes receive corrections as well [see Fig. 1(b)]. We examined these radiative corrections and found that they ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,80,932,125]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"turn out to modify the long-range chiral forces only modestly. In particular, they leave the already satisfactory convergence in the triplet channels intact. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,125,932,181]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We investigated further along this line, studying the case where a third nucleon is present. More specifically, the triton binding energy was calculated up to NLO using a power-counting scheme with partially perturbative pions [39,45]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,183,933,268]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Since the $\\phi NN$ transition form factor is interpreted as an infinite series of nucleonic derivative couplings, it is accompanied by a $\\phi NN\\pi \\pi$ vertex in order to satisfy chiral symmetry. We worked out the expression of this $\\phi NN\\pi \\pi$ vertex function and discussed its phenomenological impacts, concluding that it only modifies chiral nuclear forces at quite high orders. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,270,933,428]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Because of our practical motivation of nuclear-structure studies, we did not touch the issue of chiral extrapolation, analytical continuation of observables in the light quark mass $m_{u,d}$ . The chiral symmetry-breaking parts of $^1 S_0$ contact terms have been argued to defy NDA based on RG considerations [4]. We conjecture here that the UV-suppressing dibaryon vertex offers an intriguing opportunity to reduce the divergences proportional to $m_{\\pi}^{2}$ , and then this might change the degree to which RG invariance modifies the NDA-based power counting. However, it is unclear how this can be implemented in a model-independent fashion. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,429,933,515]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In closing we note that likely further versions of a multiparameter LO in the $^1 S_0$ channel can be constructed with yet another formulation. What was done in this paper for the momentum-dependent $^1 S_0$ dibaryon potential provides guidance for inspecting whether the specific choice of interaction can be incorporated into chiral EFT. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[634,537,806,549]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ACKNOWLEDGMENTS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,558,933,775]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We thank Bira van Kolck for valuable comments on the manuscript. B.L. and S.K. thank the Institute for Nuclear Theory at the University of Washington and the organizers of the program \"Nuclear Structure at the Crossroads\" for hospitality while part of this work was carried out. This work was supported by the National Natural Science Foundation of China (NSFC) under Grants No. 11775148 and No. 11735003, the Fundamental Research Funds for the Central Universities, and by the National Science Foundation under Grant No. PHY-2044632. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under the FRIB Theory Alliance, Award No. DE-SC0013617. Computational resources for parts of this work have been provided by the Jülich Supercomputing Center. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[546,797,896,811]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"APPENDIX: VERTEX FUNCTION OF $NN\\pi \\pi \\to \\phi$ ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,819,932,876]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In order to satisfy chiral symmetry, there must be pion-absorption vertices entering along with $\\mathcal{A}_{NN\\phi}$ defined in Eq. (10). In this Appendix, we work out the vertex function for the transition $NN\\pi \\pi \\rightarrow \\phi$ , discussed in Sec. V. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,877,933,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A nonlinearly realized chiral transformation acts on the nucleon field like an isospin rotation with an angle depending on the local pion field. Let us focus on the axial sector $SU(2)_A$ of chiral symmetry, parametrized by $\\theta^A$ with stereographic ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[64,49,463,61]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CONSTRUCTING CHIRAL EFFECTIVE FIELD THEORY ... ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[651,49,932,63]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PHYSICAL REVIEW C 105, 054002 (2022) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[466,950,529,963]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"054002-9 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[64,80,154,94]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"coordinates: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[144,99,353,133]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\delta_ {A} N = - i \\left(\\boldsymbol {\\theta} ^ {A} \\times \\frac {\\boldsymbol {\\pi}}{2 f _ {\\pi}}\\right) \\cdot \\frac {\\boldsymbol {\\tau}}{2} N,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[147,137,485,172]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\delta_ {A} \\boldsymbol {\\pi} = f _ {\\pi} \\boldsymbol {\\theta} ^ {A} \\left(1 - \\frac {\\boldsymbol {\\pi} ^ {2}}{4 f _ {\\pi} ^ {2}}\\right) + \\left(\\frac {\\boldsymbol {\\theta} ^ {A} \\cdot \\boldsymbol {\\pi}}{2 f _ {\\pi}}\\right) \\boldsymbol {\\pi}, \\tag {A1}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[130,176,351,212]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left(\\delta_ {A} \\boldsymbol {\\phi}\\right) _ {c} = \\left[ \\left(\\boldsymbol {\\theta} ^ {A} \\times \\frac {\\boldsymbol {\\pi}}{2 f _ {\\pi}}\\right) \\times \\boldsymbol {\\phi} \\right] _ {c}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,215,488,273]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We first seek the chiral-connection operator that has two pion fields, the fewest number of pion fields required by chiral symmetry, and then study its vertex function in momentum space. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,80,933,112]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As an illustration of our approach, we first derive the chiral-connection terms for the following operator: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[643,123,932,156]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\sum_ {m} \\phi_ {m} ^ {\\dagger} \\left[ N ^ {T} \\mathcal {P} _ {m} \\overleftrightarrow {\\nabla} ^ {2} N \\right]. \\tag {A2}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,167,933,275]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Unless noted otherwise, derivatives here and in the following act only on the fields within brackets. $\\phi_m^{\\dagger}$ in the above equation, for instance, is not acted upon. The most straightforward way to account for chiral symmetry is to replace the derivative $\\overleftrightarrow{\\nabla}$ with the chiral-covariant derivative $\\overleftrightarrow{\\mathcal{D}}$ defined in Eq. (45). Expanding in powers of $\\pi$ , we can read off the corresponding chiral-connection terms up to $\\mathcal{O}(\\pi^2 /f_\\pi^2)$ : ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[161,301,933,362]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\sum_ {b c d m} \\frac {i \\epsilon_ {b c d}}{4 f _ {\\pi} ^ {2}} \\phi_ {m} ^ {\\dagger} \\sum_ {i} \\left\\{\\left[ 2 (\\nabla_ {i} N) ^ {T} \\tau_ {d} ^ {T} \\mathcal {P} _ {m} \\pi_ {b} (\\nabla_ {i} \\pi_ {c}) N + N ^ {T} \\tau_ {d} ^ {T} \\mathcal {P} _ {m} \\pi_ {b} (\\nabla^ {2} \\pi_ {c}) N - 2 N ^ {T} \\tau_ {d} ^ {T} \\mathcal {P} _ {m} \\pi_ {b} (\\nabla_ {i} \\pi_ {c}) (\\nabla_ {i} N) \\right] \\right. \\\\ \\left. + \\left[ 2 N ^ {T} \\mathcal {P} _ {m} \\tau_ {d} \\pi_ {b} (\\nabla_ {i} \\pi_ {c}) (\\nabla_ {i} N) + N ^ {T} \\mathcal {P} _ {m} \\tau_ {d} \\pi_ {b} (\\nabla^ {2} \\pi_ {c}) N - 2 (\\nabla_ {i} N) ^ {T} \\mathcal {P} _ {m} \\tau_ {d} \\pi_ {b} (\\nabla_ {i} \\pi_ {c}) N \\right] \\right\\}. \\tag {A3} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,369,933,398]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, the expansion becomes cumbersome if we substitute the chiral-covariant derivatives in the following operator, which is part of the Lagrangian (6), when $n$ is large: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[400,406,932,440]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\sum_ {m} \\phi_ {m} ^ {\\dagger} \\left[ N ^ {T} \\mathcal {P} _ {m} (- i \\overleftrightarrow {\\bigvee}) ^ {2 n} N \\right]. \\tag {A4}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,448,806,464]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We therefore try a slightly different approach and consider the axial transform $\\delta_A$ of the operator in Eq. (A2): ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[183,470,933,510]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\sum_ {b c d m} \\phi_ {m} ^ {\\dagger} \\left[ N ^ {T} \\mathcal {P} _ {m} (\\overleftrightarrow {\\nabla} - \\overrightarrow {\\nabla}) ^ {2} \\left(- i \\epsilon_ {b c d} \\theta_ {b} \\frac {\\pi_ {c}}{4 f _ {\\pi}} \\tau_ {d} N\\right) + N ^ {T} \\left(- i \\epsilon_ {b c d} \\theta_ {b} \\frac {\\pi_ {c}}{4 f _ {\\pi}}\\right) \\tau_ {d} ^ {T} \\mathcal {P} _ {m} (\\overleftrightarrow {\\nabla} - \\overrightarrow {\\nabla}) ^ {2} N \\right]. \\tag {A5}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,518,414,537]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Noticing that to the lowest order in $\\pi^2 /f_\\pi^2$ we have ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[405,544,933,564]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\delta_ {A} \\boldsymbol {\\pi} = f _ {\\pi} \\boldsymbol {\\theta} ^ {A} + \\mathcal {O} \\left(\\boldsymbol {\\pi} ^ {2} / f _ {\\pi} ^ {2}\\right), \\tag {A6}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,571,760,587]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"we tentatively propose the following operator to cancel the preceding chiral-symmetry violation (A5): ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[269,594,933,659]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\sum_ {b c d m} \\frac {i}{4 f _ {\\pi} ^ {2}} \\epsilon_ {b c d} \\pi_ {b} \\phi_ {m} ^ {\\dagger} \\big \\{[ N ^ {T} \\mathcal {P} _ {m} \\tau_ {d} (\\overleftarrow {\\nabla} - \\overrightarrow {\\nabla}) ^ {2} \\pi_ {c} N - N ^ {T} \\mathcal {P} _ {m} \\tau_ {d} \\overleftarrow {\\nabla} ^ {2} \\pi_ {c} N ]. \\\\ + \\left[ N ^ {T} \\pi_ {c} \\tau_ {d} ^ {T} \\mathcal {P} _ {m} (\\overleftarrow {\\nabla} - \\overrightarrow {\\nabla}) ^ {2} N - N ^ {T} \\pi_ {c} \\tau_ {d} ^ {T} \\mathcal {P} _ {m} \\overrightarrow {\\nabla} ^ {2} N \\right] \\}. \\tag {A7} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,666,910,696]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It is straightforward to verify that the combination of the operators in Eqs. (A2) and (A7) is chiral invariant up to $\\mathcal{O}(\\pi^2 /f_\\pi^2)$ . Coming back to the more general case, we expand Eq. (A4) as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[159,705,933,755]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\sum_ {m} \\phi_ {m} ^ {\\dagger} \\left[ N ^ {T} \\mathcal {P} _ {m} (- i \\overleftrightarrow {\\nabla}) ^ {2 n} N \\right] = \\sum_ {m} \\sum_ {k + l + q = n} C (k, l, q) \\phi_ {m} ^ {\\dagger} \\left[ N ^ {T} \\mathcal {P} _ {m} \\left(\\frac {\\overleftarrow {\\nabla}}{i}\\right) ^ {2 k} \\left(- \\frac {\\overleftarrow {\\nabla}}{i} \\cdot \\frac {\\overrightarrow {\\nabla}}{i}\\right) ^ {l} \\left(\\frac {\\overrightarrow {\\nabla}}{i}\\right) ^ {2 q} N \\right], \\tag {A8}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,762,356,777]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $C(k,l,q)$ are binomial coefficients, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[354,786,933,821]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n(x + y) ^ {2 n} = \\sum_ {k + l + q = n} C (k, l, q) x ^ {2 k} (x y) ^ {l} y ^ {2 q}, \\tag {A9}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,829,137,844]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"satisfying ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[415,853,932,869]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nC (k, l, q) = C (q, l, k). \\tag {A10}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,878,567,895]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The chiral-connection operator for Eq. (A8), in analogy with Eq. (A7), is ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[342,904,932,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\sum_ {k + l + q = n} C (k, l, q) \\left[ \\mathcal {O} _ {B} (k, l, q) + \\mathcal {O} _ {C} (k, l, q) \\right], \\tag {A11}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,47,293,63]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PENG, LYU, KÖNIG, AND LONG ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[651,49,932,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PHYSICAL REVIEW C 105, 054002 (2022) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[463,950,534,964]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"054002-10 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[64,82,112,94]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[205,98,770,147]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {O} _ {B} (k, l, q) \\equiv \\sum_ {b c d m} \\frac {i}{4 f _ {\\pi} ^ {2}} \\epsilon_ {b c d} \\pi_ {b} \\phi_ {m} ^ {\\dagger} \\left[ N ^ {T} \\mathcal {P} _ {m} \\tau_ {d} \\left(\\frac {\\overleftarrow {\\nabla}}{i}\\right) ^ {2 k} \\left(- \\frac {\\overleftarrow {\\nabla}}{i} \\cdot \\frac {\\overrightarrow {\\nabla}}{i}\\right) ^ {l} \\left(\\frac {\\overrightarrow {\\nabla}}{i}\\right) ^ {2 q} \\pi_ {c} N \\right],\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[205,151,933,200]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {O} _ {C} (k, l, q) \\equiv \\sum_ {b c d m} \\frac {i}{4 f _ {\\pi} ^ {2}} \\epsilon_ {b c d} \\pi_ {b} \\phi_ {m} ^ {\\dagger} \\left[ N ^ {T} \\pi_ {c} \\tau_ {d} ^ {T} \\mathcal {P} _ {m} \\left(\\frac {\\overleftarrow {\\nabla}}{i}\\right) ^ {2 k} \\left(- \\frac {\\overleftarrow {\\nabla}}{i} \\cdot \\frac {\\overrightarrow {\\nabla}}{i}\\right) ^ {l} \\left(\\frac {\\overrightarrow {\\nabla}}{i}\\right) ^ {2 q} N \\right]. \\tag {A12}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,207,933,239]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For $\\mathcal{O}_B(k,l,q)$ , either $l$ or $q$ must be positive so that there is at least one $\\vec{\\nabla}$ acting on $\\pi_cN$ . Similarly, either $l$ or $k$ must be positive for $\\mathcal{O}_C(k,l,q)$ . Transposing the operator inside the square brackets, say, of $\\mathcal{O}_B$ and using $\\mathcal{P}_a^T = -\\mathcal{P}_a$ , we realize ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[407,244,932,261]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {O} _ {C} (k, l, q) = \\mathcal {O} _ {B} (q, l, k). \\tag {A13}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,267,563,281]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Combining this with Eq. (A10), one concludes that Eq. (A11) reduces to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[390,287,932,321]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n2 \\sum_ {k + l + q = n} C (k, l, q) \\mathcal {O} _ {B} (k, l, q). \\tag {A14}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,327,933,356]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We then consider the following matrix element of $\\mathcal{O}_B(k,l,q)$ between the free-particle states whose quantum numbers are specified in Fig. 5: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[83,364,932,463]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\int d ^ {4} x \\langle \\phi_ {c}, p _ {3} | \\mathcal {O} _ {B} (k, l, q; x) | k _ {1}, a; k _ {2}, b; p _ {1}, \\alpha_ {1}; p _ {2}, \\alpha_ {2} \\rangle \\\\ = \\frac {i}{4 f _ {\\pi} ^ {2}} \\sum_ {b ^ {\\prime} c ^ {\\prime} d ^ {\\prime} m} \\epsilon_ {b ^ {\\prime} c ^ {\\prime} d ^ {\\prime}} \\int d ^ {4} x \\left\\langle \\phi_ {c}, p _ {3} \\right| \\pi_ {b ^ {\\prime}} \\phi_ {m} ^ {\\dagger} \\left[ N ^ {T} \\mathcal {P} _ {m} \\tau_ {d ^ {\\prime}} \\left(\\frac {\\overleftarrow {\\nabla}}{i}\\right) ^ {2 k} \\left(- \\frac {\\overleftarrow {\\nabla}}{i} \\cdot \\frac {\\overrightarrow {\\nabla}}{i}\\right) ^ {l} \\left(\\frac {\\overrightarrow {\\nabla}}{i}\\right) ^ {2 q} \\left(\\pi_ {c ^ {\\prime}} N\\right) \\right] _ {x} | k _ {1}, a; k _ {2}, b; p _ {1}, \\alpha_ {1}; p _ {2}, \\alpha_ {2} \\rangle . \\tag {A15} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,472,933,502]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Here, $a$ , $b$ , $c$ are the isospin indexes of the external pions and intermediate dibaryon. After counting all contractions and stripping the $\\delta$ function that enforces momentum conservation we obtain ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[91,506,933,592]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} - \\frac {i}{4 f _ {\\pi} ^ {2}} \\left\\{\\left[ \\frac {1}{\\sqrt {8}} \\epsilon_ {a b c} \\sigma_ {2} \\tau_ {2} + i \\left(\\delta_ {b c} \\mathcal {P} _ {a} - \\delta_ {a c} \\mathcal {P} _ {b}\\right) \\right] _ {\\alpha_ {2}, \\alpha_ {1}} \\vec {p} _ {2} ^ {2 k} \\left\\{\\left[ - \\vec {p} _ {2} \\cdot (\\vec {p} _ {1} + \\vec {k} _ {1}) \\right] ^ {l} (\\vec {p} _ {1} + \\vec {k} _ {1}) ^ {2 q} - \\left[ - \\vec {p} _ {2} \\cdot (\\vec {p} _ {1} + \\vec {k} _ {2}) \\right] ^ {l} (\\vec {p} _ {1} + \\vec {k} _ {2}) ^ {2 q} \\right\\} \\right. \\\\ \\left. + \\left[ - \\frac {1}{\\sqrt {8}} \\epsilon_ {a b c} \\sigma_ {2} \\tau_ {2} + i \\left(\\delta_ {b c} \\mathcal {P} _ {a} - \\delta_ {a c} \\mathcal {P} _ {b}\\right) \\right] _ {\\alpha_ {2}, \\alpha_ {1}} \\vec {p} _ {1} ^ {2 k} \\left\\{\\left[ - \\vec {p} _ {1} \\cdot (\\vec {p} _ {2} + \\vec {k} _ {1}) \\right] ^ {l} (\\vec {p} _ {2} + \\vec {k} _ {1}) ^ {2 q} - \\left[ - \\vec {p} _ {1} \\cdot (\\vec {p} _ {2} + \\vec {k} _ {2}) \\right] ^ {l} (\\vec {p} _ {2} + \\vec {k} _ {2}) ^ {2 q} \\right\\} \\right\\}. \\tag {A16} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,597,930,625]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The dibaryon momentum $\\vec{p}_3$ does not appear in the above equation because the derivatives in Eq. (A12) act only on the fields inside the brackets. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,625,933,669]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To obtain the $\\phi NN\\pi \\pi$ vertex function $\\mathcal{A}_{\\phi NN\\pi \\pi}$ (48), we need to carry out two summations of the above matrix elements. The first is over all the combinations of $(k,l,q)$ prescribed by Eq. (A14), using Eq. (A10). The second is given by summing $n$ from 0 to $\\infty$ , as defined in the Lagrangian (6), using the identity ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[363,676,933,715]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\sum_ {n = 0} ^ {\\infty} g _ {2 n} t ^ {2 n} = g \\sum_ {n = 0} ^ {\\infty} \\binom {- \\frac {1}{2}} {n} t ^ {2 n} = g W (t) \\tag {A17}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,720,100,733]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"with ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[422,739,932,758]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nW (t) \\equiv (1 + t ^ {2}) ^ {- \\frac {1}{2}}. \\tag {A18}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[62,767,933,797]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We can apply these two summations to any individual term in the expression (A16). Take the following term as an example. The first summation is given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[252,805,933,840]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\sum_ {k + l + q = n} C (k, l, q) \\vec {p} _ {2} ^ {2 k} [ - \\vec {p} _ {2} \\cdot (\\vec {p} _ {1} + \\vec {k} _ {1}) ] ^ {l} (\\vec {p} _ {1} + \\vec {k} _ {1}) ^ {2 q} = (\\vec {p} _ {1} - \\vec {p} _ {2} + \\vec {k} _ {1}) ^ {2 n}, \\tag {A19}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,848,307,863]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"followed by the second summation ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[344,871,932,912]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\sum_ {n = 0} ^ {\\infty} g _ {2 n} \\left[ \\frac {(2 \\vec {p} + \\vec {k} _ {1}) ^ {2}}{4 m _ {N} \\Delta} \\right] ^ {n} = g W \\left(\\frac {| p + \\vec {k} _ {1} / 2 |}{\\sqrt {m _ {N} \\Delta}}\\right). \\tag {A20}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[64,920,687,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Adding up the contributions from every term in Eq. (A16), we eventually arrive at Eq. (48). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[64,49,463,63]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CONSTRUCTING CHIRAL EFFECTIVE FIELD THEORY ... ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[651,49,932,64]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PHYSICAL REVIEW C 105, 054002 (2022) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[463,950,534,964]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"054002-11 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[67,82,485,619]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[1] A. Nogga, R. G. E. Timmermans, and U. van Kolck, Phys. Rev. C 72, 054006 (2005). \",\"[2] M. P. Valderrama and E. R. Arriola, Phys. Rev. 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Rev. 177, 2239 (1969). \",\"[35] C. G. Callan, Jr., S. R. Coleman, J. Wess, and B. Zumino, Phys. Rev. 177, 2247 (1969). \",\"[36] N. Kaiser, R. Brockmann, and W. Weise, Nucl. Phys. A 625, 758 (1997). \",\"[37] C. Ordonez, L. Ray, and U. van Kolck, Phys. Rev. C 53, 2086 (1996). \",\"[38] E. Epelbaum, W. Gloeckle, and U.-G. Meissner, Nucl. Phys. A 671, 295 (2000). \",\"[39] B. Long and C. J. Yang, Phys. Rev. C 85, 034002 (2012). \",\"[40] M. Pavon Valderrama, Phys. Rev. C 84, 064002 (2011). \",\"[41] S. Fleming, T. Mehen, and I. W. Stewart, Nucl. Phys. A 677, 313 (2000). \",\"[42] The nn-online, http://nn-online.org. \",\"[43] V. G. J. Stoks, R. A. M. Klomp, M. C. M. Rentmeester, and J. J. de Swart, Phys. Rev. C 48, 792 (1993). \",\"[44] B. Long and C. J. Yang, Phys. Rev. C 84, 057001 (2011). \",\"[45] S. Wu and B. Long, Phys. Rev. C 99, 024003 (2019). \",\"[46] Y.-H. Song, R. Lazauskas, and U. van Kolck, Phys. Rev. C 96, 024002 (2017). \",\"[47] Y.-H. Song, R. Lazauskas, and U. van Kolck, Phys. Rev. C 100, 019901(E) (2019). \",\"[48] S. Weinberg, The Quantum Theory of Fields. Vol. 2: Modern Applications (Cambridge University Press, Cambridge, 2013). \"]","page_idx":"11","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[66,47,290,61]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PENG, LYU, KONIG, AND LONG ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[651,49,930,61]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PHYSICAL REVIEW C 105, 054002 (2022) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[463,950,534,963]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"054002-12 ","text_format":null,"text_level":null,"type":"footer"}],"string":"[\n {\n \"bbox\": \"[125,114,870,133]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Constructing chiral effective field theory around unnatural leading-order interactions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[246,147,750,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Rui Peng,1 Songlin Lyu,1\\\\* Sebastian Konig,2 and Bingwei Long 1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[269,164,728,178]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"<sup>1</sup>College of Physics, Sichuan University, Chengdu, Sichuan 610065, China \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[205,178,791,191]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{2}$ Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[162,204,190,222]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0544/7d21f99ea4c33196e4c9f352729f6b7299229978888b4f1bb72e0b805e83416f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[193,205,835,220]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(Received 9 December 2021; revised 16 March 2022; accepted 30 March 2022; published 12 May 2022) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[154,237,840,339]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A momentum-dependent formulation based on a stationary spin-0 and isospin-1 dibaryon field is proposed to improve convergence of chiral effective field theory in the $^1 S_0$ channel of $NN$ scattering. Although the two-parameter leading-order interaction appears to be unnatural, it nevertheless has the necessary features of an effective field theory. A rapid order-by-order convergence is found in $^1 S_0$ . As an application beyond the two-body level, the triton binding energy is studied and compared to standard chiral effective field theory with partly perturbative pions. The consistency of the chiral Lagrangian for the new formulation is examined by working out the pionic radiative corrections, and consequences of nontrivial chiral-connection terms are discussed. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[154,349,390,363]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"DOI: 10.1103/PhysRevC.105.054002 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,400,346,412]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"I. INTRODUCTION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,421,485,768]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It is a lore about the nuclear force that it has attractive long-range and repulsive short-range components. This can be inferred phenomenologically from the $^1 S_0$ and $^3 S_1$ phase shifts, both showing strong attraction near threshold and vanishing around center-of-mass (c.m.) momentum $k \\\\sim 350 \\\\mathrm{MeV}$ . But nuclear forces derived from chiral effective field theory (EFT) are characteristically different in the two channels at leading order (LO): in $^3 S_1 - ^3 D_1$ , the tensor part of one-pion exchange (OPE) is singularly attractive, providing sufficiently strong attraction at long distances to generate the shallow deuteron bound state. A contact term in $^3 S_1$ provides repulsion at short distances to avoid a collapse of the two-nucleon system into an infinitely deep bound state. This mechanism is well understood to ensure renormalization [1,2]. In $^1 S_0$ , however, OPE turns out to be numerically weak, thus it can in principle be treated as a perturbation [3-5]. This implies that in $^1 S_0$ the short-range interaction alone needs to provide strong attraction at long distances and strong repulsion at short distances in order to produce the phenomenological behavior of the phase shift. A single $^1 S_0$ contact term at LO as proposed by Weinberg [6,7] is too simple to generate both features simultaneously, which is likely the reason why chiral forces have been found to converge rather slowly in $^1 S_0$ [8-11], unless a soft cutoff is carefully chosen [9]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,768,485,857]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As first calculated in Ref. [12] and then argued further in Ref. [13], the slow convergence can be attributed to the quite large value of the generalized effective range in $^{1}S_{0}$ , which is defined in an expansion similar to the effective-range expansion while incorporating iteration of OPE. To improve the convergence, a power counting based on a spin-0 and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,398,932,428]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"isospin-1 auxiliary dibaryon field [14-16] was suggested in Ref. [13], and subsequently developed in Ref. [17]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,429,932,744]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A mere reproduction of empirical phase shifts does not bring much to the discussion of nuclear forces, as there exist several phenomenological models that fit nucleon-nucleon scattering data very well [18-20]. We therefore use the following requirements as guidelines to reformulate power counting of chiral forces in order to address the slow $^{1}S_{0}$ convergence. First, as any other consistent EFT, the formulation sets up a controlled expansion, allowing for a highly unnatural LO that includes more than one low-energy constant (LEC) (two in Ref. [13] and three in Ref. [17]) in the $^{1}S_{0}$ channel. Second, renormalization-group (RG) invariance is enforced at each order. Third, the symmetries of the chiral Lagrangian are observed, in particular the nonlinearly realized chiral symmetry. The dibaryon formalism has been shown to meet all these requirements, and in particular it does not alter the well-established hierarchy of long-range chiral forces that follows from naive dimensional analysis (NDA) [6,7]: OPE is LO, two-pion-exchange (TPE) contributions are two powers down or more, and so on. This is in contrast to a recent proposal that TPE should be promoted to LO in order to address the convergence issue in $^{1}S_{0}$ [21]; see also Ref. [22] for a related discussion regarding the promotion of TPE. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,746,932,805]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Unfortunately, the resulting ${}^{1}S_{0}$ potential is energy-dependent, making it difficult to apply the overall interaction in many-body calculations. For example, the dibaryon-exchange potential, part of LO, is given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[651,825,932,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV _ {\\\\phi} (E) = \\\\sigma \\\\frac {y ^ {2}}{E + \\\\Delta}, \\\\tag {1}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,876,932,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $E$ is the center-of-mass (c.m.) energy, $\\\\Delta$ the dibaryon mass, $y$ the dibaryon coupling constant, and $\\\\sigma = \\\\pm 1$ . In order to facilitate many-body calculations, we discuss in Sec. II a separable, momentum-dependent force to replace the original \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[300,49,696,66]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PHYSICAL REVIEW C 105, 054002 (2022) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[73,905,208,920]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"* songlin@scu.edu.cn \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[74,921,213,934]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{\\\\dagger}$ bingwei@scu.edu.cn \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[66,950,290,964]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2469-9985/2022/105(5)/054002(12) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[473,950,533,963]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"054002-1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[716,950,932,965]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"©2022 American Physical Society \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[64,80,310,170]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0313/ef26c3c2ba026794bfd07cc25e08272799d3112a43fb8d115c22ff738050e6d7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[327,80,488,170]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"FIG. 1. Radiation-pion Feynman diagrams contributing to $\\\\\\\\mathrm{N}^2\\\\\\\\mathrm{LO}$ potentials. The solid (dashed) lines represent nucleons (pions), and the solid blobs are the $\\\\\\\\phi NN$ vertex function (10). (a) The pion line connects both nucleons either in the initial or in the final states. (b) The pion line connects one of the incoming nucleon lines to one of the final nucleon legs. Other variants due to permuting the pion line on different nucleon external lines are not shown. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0058/bdfb278a493713b981012bb3a3ef85892bed264d7b8884b52f01eab696c1357c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[64,301,307,318]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"dibaryon exchange potential in $^1 S_0$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[113,325,487,362]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV _ {\\\\mathrm {s p r}} \\\\left(p ^ {\\\\prime}, p\\\\right) = - \\\\frac {4 \\\\pi}{m _ {N}} \\\\frac {\\\\lambda}{\\\\sqrt {p ^ {\\\\prime 2} + m _ {N} \\\\Delta} \\\\sqrt {p ^ {2} + m _ {N} \\\\Delta}}, \\\\tag {2}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,369,485,470]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $p(p')$ is the incoming (outgoing) c.m. momentum. The potential (2) is clearly motivated by the energy-dependent dibaryon potential (1), and the two potentials (1) and (2) have the same functional dependence on the energy when the Born approximation is taken and the nucleons are on the energy shell, $E = p^{\\\\prime 2} / m_{N} = p^{2} / m_{N}$ (while still featuring different coupling constants). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,472,485,587]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Potentials of the same (or similar) form as in Eq. (2) were investigated elsewhere in the literature. Reference [23] used it to construct a model potential in the context of discussing pionless EFT. More recently, Ref. [24] derived a potential with similar square-root form factors based on the so-called UV/IR symmetry of the $S$ matrix, assuming a separable form as in Eq. (2). An attempt to derive a similar potential from the Low equation can be found in Ref. [25]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,588,485,789]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Radiative corrections to nucleon-nucleon contact terms generated by pions (see Fig. 1) appear suppressed by $Q^2 /M_{\\\\mathrm{hi}}^2$ relative to OPE in a given partial wave. If the contact vertex has a single parameter, e.g., a constant in $S$ waves, the radiative corrections can be shown to generate only terms which are polynomials in momenta or energies because the diagrams are dominated by static intermediate nucleons. Owing to this lack of nonanalytic structures, radiative pions are typically not included in chiral nuclear forces unless chiral extrapolations [26-28] or pion productions are concerned. This is still the case with the energy-dependent dibaryon exchange. However, as will be discussed in Sec. III, the pionic radiative corrections to the momentum-dependent potential (2) can no longer be trivially cast into pure contact form. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,790,485,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In Sec. IV we discuss two- and three-body observables calculated with the momentum-dependent potential (plus additional nucleon-nucleon channels) and compare our results to other calculations. As a matter of fact, several nuclear-structure calculations have already used potentials with a similar form to various orders [29-31]. The results in Ref. [29] suggest that some nuclei are not bound with the proposed potentials up to NLO, based on which the authors argue that some three-body forces need to be considered at LO. While the role of three-body forces may continue to be debated, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,80,933,125]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"we believe that efforts to improve the overall convergence based on two-body and three-body forces can complement each other. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,125,933,268]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The momentum-dependent dibaryon potential can alternatively be thought of as a way to partially resum derivative-coupled NNNN operators in the effective Lagrangian. With the nonlinearly realized chiral symmetry, derivatives acting on baryon fields must be \\\"chiral-covariant\\\" so that chiral symmetry and its spontaneous breaking are properly implemented. This results in, among other things, a nontrivial $\\\\pi \\\\pi$ NNNN vertex function. We discuss the construction of this vertex and its phenomenological impacts in Sec. V. Finally, we summarize and conclude in Sec. VI. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,287,923,301]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"II. MOMENTUM-DEPENDENT DIBARYON POTENTIAL \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,308,932,354]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We begin with the $^1 S_0$ power counting developed in Ref. [8]. Thus, OPE is the LO long-range force, and its $^1 S_0$ projection reads \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[597,358,932,393]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV _ {1 \\\\pi} \\\\left(p ^ {\\\\prime}, p\\\\right) = \\\\frac {g _ {A} ^ {2}}{4 f _ {\\\\pi} ^ {2}} \\\\left(1 - \\\\frac {m _ {\\\\pi} ^ {2}}{q ^ {2} + m _ {\\\\pi} ^ {2}}\\\\right), \\\\tag {3}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,398,933,470]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where the momentum transfer $\\\\vec{q} = \\\\vec{p}' - \\\\vec{p}$ , the pion mass $m_{\\\\pi} = 138.0$ MeV, the pion decay constant $f_{\\\\pi} = 92.4$ MeV, and the axial coupling $g_{A} = 1.29$ . Counting external momenta $Q, m_{\\\\pi}$ , and $f_{\\\\pi}$ collectively as the infrared mass scale $M_{\\\\mathrm{lo}}$ , OPE scales as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[617,474,932,508]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV _ {1 \\\\pi} \\\\left(p ^ {\\\\prime}, p\\\\right) \\\\sim \\\\frac {1}{f _ {\\\\pi} ^ {2}} \\\\sim \\\\frac {4 \\\\pi}{m _ {N}} \\\\frac {1}{M _ {\\\\mathrm {l o}}}, \\\\tag {4}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,516,932,575]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $m_N \\\\sim 4\\\\pi f_\\\\pi$ is used. The contact term $V_S^{(0)} = C_0$ enters also at LO. As argued in Ref. [8], RG invariance requires a nonvanishing NLO generated by a momentum-dependent contact term, one order earlier than estimated from NDA, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[604,580,932,612]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV _ {S} ^ {(1)} = \\\\frac {C _ {2}}{2} \\\\left(p ^ {\\\\prime 2} + p ^ {2}\\\\right) \\\\sim \\\\frac {4 \\\\pi}{m _ {N}} \\\\frac {1}{M _ {\\\\mathrm {h i}}}. \\\\tag {5}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,616,933,863]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Even with this promotion, chiral EFT still converges slowly in $^1 S_0$ (see, e.g., Ref. [8]). It was later proposed in Ref. [13] that the mass scale embedded in $C_2$ is actually quite small and can be identified with the inverse of the so-called generalized effective range $\\\\simeq 130 \\\\mathrm{MeV}$ that was first extracted in Ref. [12]. This light mass scale needs to enter the LO amplitude, and promoting the $C_2$ term to LO is a choice to achieve this. The simplistic treatment of taking the sum of the $C_0$ and $C_2$ terms as the LO short-range potential has several obstacles, including satisfying RG invariance [23,32] and overcoming the Wigner bound [23,33]. However, these constraints do not necessarily mean that building a highly unnatural LO interaction with two adjustable parameter is a no-go scenario. Indeed, the dibaryon formalism used in Ref. [13] has been shown to be a viable implementation, making use of the kinetic energy of the dibaryon field to provide the much needed energy dependence of the potential. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,863,933,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"On the other hand, no principle states that implementation of a two-parameter LO potential is unique. As long as a formulation incorporating both infrared scales satisfies the criteria introduced in Sec. I, it is acceptable. In fact, there is a clear practical motivation to search for other ways \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[64,47,293,63]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PENG, LYU, KÖNIG, AND LONG \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[651,49,933,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PHYSICAL REVIEW C 105, 054002 (2022) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[466,950,529,963]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"054002-2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[62,82,488,170]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"to improve the $^1 S_0$ convergence: one encounters difficulties when applying the energy-dependent dibaryon potential (1) to many-nucleon calculations. It is the goal of the present paper to show that the separable, momentum-dependent alternative (2) provides a satisfactory foundation to be expanded around upon. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,80,933,156]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We find it useful to cast the separable potential (2) into the form of a Lagrangian. An auxiliary dibaryon field $\\\\phi$ with spin-0 and isospin-1 is introduced, but $\\\\phi$ is stationary, namely, it does not have a kinetic term. The Lagrangian terms involving $\\\\phi$ are given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[229,194,935,239]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {L} _ {\\\\phi} = \\\\sigma \\\\Delta \\\\boldsymbol {\\\\phi} ^ {\\\\dagger} \\\\cdot \\\\boldsymbol {\\\\phi} - \\\\sqrt {\\\\frac {4 \\\\pi}{m _ {N}}} \\\\sum_ {m = 1} ^ {3} \\\\sum_ {n = 0} ^ {\\\\infty} \\\\frac {g _ {2 n}}{2} \\\\left[ \\\\phi_ {m} ^ {\\\\dagger} N ^ {T} \\\\mathcal {P} _ {m} \\\\left(\\\\frac {- \\\\overleftrightarrow {\\\\nabla} ^ {2}}{4 m _ {N} \\\\Delta}\\\\right) ^ {n} N + H. c. \\\\right] + \\\\dots , \\\\tag {6}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,268,112,280]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[213,285,485,319]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {P} _ {m} = \\\\frac {1}{\\\\sqrt {8}} \\\\tau_ {2} \\\\tau_ {m} \\\\sigma_ {2} \\\\tag {7}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,323,485,356]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"is the spin and isospin projector to ensure that $\\\\phi$ couples only to the $^1 S_0$ channel and $\\\\overleftrightarrow{\\\\nabla}$ is defined so that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[176,361,485,381]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nN ^ {T} \\\\overleftrightarrow {\\\\nabla} N \\\\equiv N ^ {T} (\\\\overleftarrow {\\\\nabla} - \\\\overrightarrow {\\\\nabla}) N. \\\\tag {8}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,387,488,431]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Here, $\\\\sigma$ is normalized to $\\\\pm 1$ by rescaling $\\\\phi$ , and it will be determined by fitting to scattering data. If $g_{2n}$ are correlated by the binomial coefficients as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[222,436,485,472]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\frac {g _ {2 n}}{g} = \\\\binom {- \\\\frac {1}{2}} {n}, \\\\tag {9}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,478,485,506]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"then we can obtain the $\\\\phi NN$ vertex function after summing over all powers of relative momenta, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[171,513,485,551]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {A} _ {\\\\phi N N} = - \\\\frac {\\\\sqrt {4 \\\\pi} g}{\\\\sqrt {p ^ {2} / \\\\Delta + m _ {N}}} \\\\mathcal {P} _ {m}. \\\\tag {10}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,558,485,588]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The desired separable ${}^{1}S_{0}$ potential then follows from the $s$ -channel exchange of $\\\\phi$ , \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[98,593,485,628]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV _ {\\\\operatorname {s p r}} ^ {(0)} \\\\left(p ^ {\\\\prime}, p\\\\right) = - \\\\frac {4 \\\\pi}{m _ {N}} \\\\frac {\\\\lambda}{\\\\sqrt {p ^ {\\\\prime 2} + m _ {N} \\\\Delta} \\\\sqrt {p ^ {2} + m _ {N} \\\\Delta}}, \\\\tag {11}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,633,215,650]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\lambda \\\\equiv \\\\sigma m_N g^2 / 4$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[64,650,485,679]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In order to justify summing the $g_{2n}$ terms, $\\\\lambda$ and $\\\\Delta$ must be identified as two independent infrared mass scales, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[205,685,485,705]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\sqrt {m _ {N} \\\\Delta} \\\\sim \\\\lambda \\\\sim M _ {\\\\mathrm {l o}}, \\\\tag {12}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,710,261,724]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"which in turn translates into \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[232,729,485,770]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\ng \\\\sim \\\\sqrt {\\\\frac {M _ {\\\\mathrm {l o}}}{M _ {\\\\mathrm {h i}}}}. \\\\tag {13}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,775,485,819]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We will see that the expected scaling of $\\\\lambda$ and $\\\\Delta$ is verified once their values are obtained from fitting to the $^1 S_0$ empirical phase shifts. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,819,485,934]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Summing an infinite sequence of derivative coupling terms prompts concerns regarding chiral symmetry. Derivatives acting on the nucleon field must be accompanied by so-called chiral-connection operators involving the pion fields so that chiral symmetry is nonlinearly realized by these hadronic degrees of freedom [34,35]. We will come back to this in Sec. V to discuss chiral-connection operators of the $\\\\phi NN$ transition vertex. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,268,932,299]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The LO ${}^{1}S_{0}$ amplitude is the resummation of $V_{\\\\mathrm{spr}}^{(0)}$ and $V_{Y}$ to all orders by way of the partial-wave LS equation, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[546,304,932,372]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} T \\\\left(p ^ {\\\\prime}, p; E\\\\right) = V _ {\\\\mathrm {L O}} \\\\left(p ^ {\\\\prime}, p\\\\right) + \\\\frac {1}{2 \\\\pi^ {2}} \\\\int d l l ^ {2} V _ {\\\\mathrm {L O}} \\\\left(p ^ {\\\\prime}, l\\\\right) \\\\\\\\ \\\\times \\\\frac {T (l , p ; E)}{E - l ^ {2} / m _ {N} + i \\\\epsilon} \\\\tag {14} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[511,377,546,390]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"with \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[590,397,932,417]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV _ {\\\\mathrm {L O}} \\\\left(p ^ {\\\\prime}, p\\\\right) = V _ {\\\\mathrm {s p r}} ^ {(0)} \\\\left(p ^ {\\\\prime}, p\\\\right) + V _ {Y} \\\\left(p ^ {\\\\prime}, p\\\\right), \\\\tag {15}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[599,421,932,455]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV _ {Y} \\\\left(p ^ {\\\\prime}, p\\\\right) = - \\\\frac {g _ {A} ^ {2}}{4 f _ {\\\\pi} ^ {2}} \\\\frac {m _ {\\\\pi} ^ {2}}{q ^ {2} + m _ {\\\\pi} ^ {2}}. \\\\tag {16}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,460,852,476]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The LS equation is often schematically written as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[631,481,932,500]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nT ^ {(0)} = V _ {\\\\mathrm {L O}} + V _ {\\\\mathrm {L O}} G _ {0} T ^ {(0)}, \\\\tag {17}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,505,932,564]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $G_{0}$ is the nonrelativistic free-particle propagator. When solving the LS equation, we regularize the ultraviolet part of the potentials with a separable regulator to ensure that the regularization in one partial wave does not interfere another: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[577,569,932,604]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV ^ {\\\\Lambda} \\\\left(\\\\vec {p} ^ {\\\\prime}, \\\\vec {p}\\\\right) = f _ {R} \\\\left(\\\\frac {p ^ {\\\\prime 2}}{\\\\Lambda^ {2}}\\\\right) V \\\\left(\\\\vec {p} ^ {\\\\prime}, \\\\vec {p}\\\\right) f _ {R} \\\\left(\\\\frac {p ^ {2}}{\\\\Lambda^ {2}}\\\\right). \\\\tag {18}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,609,932,637]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In particular, a Gaussian regulator is used in our numerical calculations: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[672,642,932,662]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nf _ {R} (x) = e ^ {- x ^ {2}}. \\\\tag {19}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,667,932,712]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Using the two-potential method [32], the $\\\\mathrm{LO}^{1}\\\\mathrm{S}_{0}$ amplitude can be rewritten to facilitate analysis. We start by defining the off-shell Yukawa amplitude \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[650,719,932,734]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nT _ {Y} = V _ {Y} + V _ {Y} G _ {0} T _ {Y}, \\\\tag {20}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,739,932,784]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and the origin value of its scattering wave function, dressed by the square-root dipole form factor of the $\\\\phi NN$ transition vertex (10): \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[541,789,932,864]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\chi (p; E) = \\\\frac {1}{\\\\sqrt {p ^ {2} + m _ {N} \\\\Delta}} + \\\\int \\\\frac {d ^ {3} l}{(2 \\\\pi) ^ {3}} \\\\left(l ^ {2} + m _ {N} \\\\Delta\\\\right) ^ {- \\\\frac {1}{2}} \\\\\\\\ \\\\times \\\\frac {T _ {Y} (l , p)}{E - l ^ {2} / m _ {N} + i \\\\epsilon}. \\\\tag {21} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,869,752,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The LO amplitude is then given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[528,888,932,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nT ^ {(0)} (k, k; E) = T _ {Y} (k, k) - \\\\frac {4 \\\\pi}{m _ {N}} \\\\frac {\\\\chi (k ; E) ^ {2}}{\\\\lambda^ {- 1} \\\\left(k ^ {2} + m _ {N} \\\\Delta\\\\right) + I (E)}, \\\\tag {22}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,47,463,63]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CONSTRUCTING CHIRAL EFFECTIVE FIELD THEORY ... \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[651,49,932,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PHYSICAL REVIEW C 105, 054002 (2022) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[466,950,529,963]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"054002-3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[64,97,488,181]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0499/9c68a85999c6b5deab68570760596919b4c6fc26902da21cae8e8a945d46da0b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Λ</td><td>Δ(0)</td><td>λ(0)</td></tr><tr><td>600</td><td>27.1</td><td>270</td></tr><tr><td>1200</td><td>24.6</td><td>223</td></tr><tr><td>2400</td><td>24.1</td><td>209</td></tr></table>\",\n \"table_caption\": \"[\\\"TABLE I. Running of $\\\\\\\\lambda$ (MeV) and $\\\\\\\\Delta$ (MeV) with $\\\\\\\\Lambda$ (MeV) at LO. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[64,214,112,227]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[74,242,485,280]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nI (E) \\\\equiv \\\\frac {4 \\\\pi}{m _ {N}} \\\\int \\\\frac {d ^ {3} l}{(2 \\\\pi) ^ {3}} \\\\left(l ^ {2} + m _ {N} \\\\Delta\\\\right) ^ {- \\\\frac {1}{2}} \\\\frac {\\\\chi (l ; E)}{E - l ^ {2} / m _ {N} + i \\\\epsilon}. \\\\tag {23}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,292,485,454]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Compared with the energy-dependent dibaryon potential, the factor $(p^2 + m_N\\\\Delta)^{-\\\\frac{1}{2}}$ brings so much UV suppression that the integral would be finite even without the regulator, and $\\\\Delta(\\\\Lambda)$ and $\\\\lambda(\\\\Lambda)$ approach finite values for $\\\\Lambda \\\\rightarrow \\\\infty$ . Table I shows their values as a function of $\\\\Lambda$ . The fitting to empirical $^1 S_0$ phase shifts will be explained in Sec. IV. Using these values, we have $\\\\sqrt{m_N\\\\Delta} \\\\simeq 150 \\\\mathrm{MeV}$ and $\\\\lambda \\\\simeq 200 \\\\mathrm{MeV}$ , which confirms the expected scaling given in Eq. (12). The inverse of $\\\\sqrt{m_N\\\\Delta}$ comes out close to the pion Compton wave length $\\\\simeq 1.4 \\\\mathrm{fm}$ , suggesting that the dibaryon potential has a range similar to that of OPE. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,80,932,125]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let us turn to higher orders. Although $\\\\lambda (\\\\Lambda)$ and $\\\\Delta (\\\\Lambda)$ appear at LO, their running with $\\\\Lambda$ can be modified at subleading orders: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[551,132,932,150]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\lambda (\\\\Lambda) = \\\\lambda^ {(0)} (\\\\Lambda) + \\\\lambda^ {(1)} (\\\\Lambda) + \\\\lambda^ {(2)} (\\\\Lambda) + \\\\dots , \\\\tag {24}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[544,160,932,179]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\Delta (\\\\Lambda) = \\\\Delta^ {(0)} (\\\\Lambda) + \\\\Delta^ {(1)} (\\\\Lambda) + \\\\Delta^ {(2)} (\\\\Lambda) + \\\\dots . \\\\tag {25}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,186,932,231]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The $\\\\lambda^{(\\\\nu)}$ and $\\\\Delta^{(\\\\nu)}$ are formally smaller than their LO value by $Q^{\\\\nu} / M_{\\\\mathrm{hi}}^{\\\\nu}$ . These modifications play a role at higher orders, which can be constructed by the generating function \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[524,234,932,290]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {F} _ {\\\\operatorname {s p r}} \\\\left(p ^ {\\\\prime}, p; x\\\\right) \\\\equiv - \\\\frac {4 \\\\pi}{m _ {N}} \\\\frac {\\\\lambda (x)}{\\\\sqrt {p ^ {\\\\prime 2} + m _ {N} \\\\Delta (x)} \\\\sqrt {p ^ {2} + m _ {N} \\\\Delta (x)}}, \\\\tag {26}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,297,932,311]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $x$ is an auxiliary variable to generate the expansion and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[595,318,932,337]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\lambda (x) = \\\\lambda^ {(0)} + x \\\\lambda^ {(1)} + x ^ {2} \\\\lambda^ {(2)} + \\\\dots , \\\\tag {27}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[589,347,932,364]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\Delta (x) = \\\\Delta^ {(0)} + x \\\\Delta^ {(1)} + x ^ {2} \\\\Delta^ {(2)} + \\\\dots . \\\\tag {28}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,372,911,387]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"From there, the dibaryon part at each order is generated by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[577,391,932,435]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\mathcal {F} _ {\\\\mathrm {s p r}} (p ^ {\\\\prime}, p; x) = V _ {\\\\mathrm {s p r}} ^ {(0)} (p ^ {\\\\prime}, p) + x V _ {\\\\mathrm {s p r}} ^ {(1)} (p ^ {\\\\prime}, p) \\\\\\\\ + x ^ {2} V _ {\\\\mathrm {s p r}} ^ {(2)} \\\\left(p ^ {\\\\prime}, p\\\\right) + \\\\dots \\\\tag {29} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,439,840,455]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"with the first two corrections explicitly given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[129,478,932,516]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV _ {\\\\mathrm {s p r}} ^ {(1)} \\\\left(p ^ {\\\\prime}, p\\\\right) = - \\\\frac {4 \\\\pi}{m _ {N}} \\\\frac {1}{\\\\sqrt {p ^ {2} + m _ {N} \\\\Delta^ {(0)}} \\\\sqrt {p ^ {\\\\prime 2} + m _ {N} \\\\Delta^ {(0)}}} \\\\left\\\\{\\\\lambda^ {(1)} - \\\\frac {m _ {N} \\\\lambda^ {(0)}}{2} \\\\left(\\\\frac {1}{p ^ {2} + m _ {N} \\\\Delta^ {(0)}} + \\\\frac {1}{p ^ {\\\\prime 2} + m _ {N} \\\\Delta^ {(0)}}\\\\right) \\\\Delta^ {(1)} \\\\right\\\\} \\\\tag {30}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,520,96,534]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[144,537,932,651]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} V _ {\\\\mathrm {s p r}} ^ {(2)} (p ^ {\\\\prime}, p) = - \\\\frac {4 \\\\pi}{m _ {N}} \\\\frac {1}{\\\\sqrt {(p ^ {2} + m _ {N} \\\\Delta^ {(0)})} \\\\sqrt {(p ^ {\\\\prime 2} + m _ {N} \\\\Delta^ {(0)})}} \\\\\\\\ \\\\times \\\\left\\\\{\\\\lambda^ {(2)} - \\\\frac {m _ {N}}{2} \\\\left[ \\\\frac {1}{\\\\left(p ^ {2} + m _ {N} \\\\Delta^ {(0)}\\\\right)} + \\\\frac {1}{\\\\left(p ^ {\\\\prime 2} + m _ {N} \\\\Delta^ {(0)}\\\\right)} \\\\right] \\\\left(\\\\lambda^ {(0)} \\\\Delta^ {(2)} + \\\\lambda^ {(1)} \\\\Delta^ {(1)}\\\\right) \\\\right. \\\\\\\\ + \\\\frac {m _ {N} ^ {2} \\\\lambda^ {(0)}}{8} \\\\left[ \\\\frac {3}{\\\\left(p ^ {2} + m _ {N} \\\\Delta^ {(0)}\\\\right) ^ {2}} + \\\\frac {2}{\\\\left(p ^ {2} + m _ {N} \\\\Delta^ {(0)}\\\\right) \\\\left(p ^ {\\\\prime 2} + m _ {N} \\\\Delta^ {(0)}\\\\right)} + \\\\frac {3}{\\\\left(p ^ {\\\\prime 2} + m _ {N} \\\\Delta^ {(0)}\\\\right) ^ {2}} \\\\right] \\\\Delta^ {(1) ^ {2}} \\\\}. \\\\tag {31} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,679,485,781]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If one expands the potential (11) in powers of momenta, a series of $^1 S_0$ contact terms emerges. Therefore, the values of $\\\\Delta$ and $\\\\lambda$ span a surface in the parameter space of $^1 S_0$ contact couplings. The deviation away from the surface can be described by residual values of $^1 S_0$ contact terms. Reference [13] has shown that higher-order short-range forces are parametrized by conventional four-nucleon operators \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[183,791,485,830]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV _ {S} = \\\\sum_ {n = 0} ^ {\\\\infty} \\\\frac {C _ {2 n}}{2} \\\\left(p ^ {\\\\prime 2 n} + p ^ {2 n}\\\\right) \\\\tag {32}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,839,303,854]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"with the following scaling for $C_{2n}$ : \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,863,485,898]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nC _ {2 n} \\\\sim \\\\frac {4 \\\\pi}{m _ {N}} \\\\frac {1}{M _ {\\\\mathrm {l o}} ^ {n} M _ {\\\\mathrm {h i}} ^ {n + 1}}. \\\\tag {33}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,905,485,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"NLO and higher-orders amplitudes are built as perturbations on top of LO, i.e., they are diagrammatically perturbative \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,679,923,695]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"insertions of $V_{\\\\mathrm{NLO}}$ , $V_{\\\\mathrm{N}^2\\\\mathrm{LO}}$ (and so on) into the LO amplitude: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[524,700,796,720]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nT ^ {(1)} = (1 + T ^ {(0)} G _ {0}) V _ {\\\\mathrm {N L O}} \\\\left(G _ {0} T ^ {(0)} + 1\\\\right),\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[526,724,916,765]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} T ^ {(2)} = (1 + T ^ {(0)} G _ {0}) [ V _ {\\\\mathrm {N} ^ {2} \\\\mathrm {L O}} + V _ {\\\\mathrm {N L O}} G _ {0} (1 + T ^ {(0)} G _ {0}) V _ {\\\\mathrm {N L O}} ] \\\\\\\\ \\\\times \\\\left(G _ {0} T ^ {(0)} + 1\\\\right). \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[558,773,930,801]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\dots . \\\\tag {34}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,811,930,842]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In particular, since there is no pion-exchanges at NLO, the $^1 S_0$ potential is given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[606,847,932,868]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV _ {\\\\mathrm {N L O}} \\\\left(p ^ {\\\\prime}, p\\\\right) = C _ {0} ^ {(0)} + V _ {\\\\mathrm {s p r}} ^ {(1)} \\\\left(p ^ {\\\\prime}, p\\\\right). \\\\tag {35}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[602,883,840,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"III. RADIATIVE CORRECTIONS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,905,932,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The scaling (12) has so far led us to have the momentum-dependent dibaryon potential (and its subleading corrections) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[64,47,293,63]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PENG, LYU, KÖNIG, AND LONG \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[651,49,932,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PHYSICAL REVIEW C 105, 054002 (2022) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[466,950,529,964]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"054002-4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[62,80,485,224]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"simply substitute the energy-dependent one. But there is an important difference at $\\\\mathrm{N}^2\\\\mathrm{LO}$ . Besides the leading two-pion exchange $V_{\\\\mathrm{TPE0}}$ [36], pionic radiative corrections to the dibaryon potential, depicted in Fig. 1, appear at this order. For a dynamically propagating dibaryon, the radiative corrections are zero-range interactions (much like the radiative corrections to pure $NN$ contact operators [37,38]); therefore, they do not change the form of the potentials in any nontrivial way. For the momentum-dependent dibaryon vertex, this is no longer the case because the vertex is finite-ranged. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[64,226,485,470]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In Fig. 1, $\\\\vec{p} (\\\\vec{p}^{\\\\prime})$ is the incoming (outgoing) nucleon c.m. momentum, and $k,n,r,$ and $s(a,b,c,$ and $d$ ) are spin (isospin) indexes. While Fig. 1(a) contributes only to $^1 S_0$ , the impact of Fig. 1(b) is confined to the triplet channels, as will be shown later in the section. Without the dibaryon field, the convergence in the triplet channels is already quite good [39,40]. Thus, it is important for the purpose of validating the dibaryon potential to examine how it affects the triplet channels through radiative corrections. If Fig. 1(b) interferes with the triplet channels so much that a satisfactory description of data is spoiled, we will have to give up the momentum-dependent dibaryon formalism even if it does improve $^1 S_0$ . Fortunately, it turns out that these radiative corrections for the most part only renormalize the $NN$ contact terms in $^3 S_1 - ^3 D_1$ and do not significantly change the on-shell amplitudes. Before turning to the phase shifts, we discuss calculation of the Feynman diagrams in Fig. 1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,472,485,617]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As mentioned previously, the diagram of Fig. 1(a) is expected to contribute only to ${}^{1}S_{0}$ , for it can be broken by cutting the dibaryon propagator. The $NN$ reducible part of the diagram is the contribution from picking up the nucleon pole when integrating out the zeroth component of the loop momentum, which is part of the LO amplitude and has been accounted for when iterating $V_{\\\\mathrm{LO}}$ in Eq. (14). What is counted as $\\\\mathrm{N}^2\\\\mathrm{LO}$ is the irreducible part of the diagram that results from picking up the pion pole and is given by the three-dimensional integral \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[83,625,485,708]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\mathcal {A} _ {\\\\mathrm {r a d}} ^ {(a)} = - \\\\frac {4 \\\\pi}{m _ {N}} \\\\frac {g _ {A} ^ {2}}{4 f _ {\\\\pi} ^ {2}} \\\\lambda^ {(0)} (\\\\Lambda) \\\\sum_ {m} [ (\\\\mathcal {P} _ {m} ^ {\\\\dagger}) _ {r s, a b} (\\\\mathcal {P} _ {m}) _ {k n, c d} ] \\\\\\\\ \\\\times \\\\int \\\\frac {d ^ {3} l}{(2 \\\\pi) ^ {3}} \\\\frac {l ^ {2}}{\\\\left(l ^ {2} + m _ {\\\\pi} ^ {2}\\\\right) ^ {\\\\frac {3}{2}}} \\\\mathcal {R} (| \\\\vec {p} ^ {\\\\prime} |, | \\\\vec {p} - \\\\vec {l} |; \\\\Lambda) \\\\tag {36} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,715,230,729]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"with the scalar function \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,734,485,776]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {R} (x, y; \\\\Lambda) \\\\equiv \\\\frac {f _ {R} \\\\left(\\\\frac {x ^ {2}}{\\\\Lambda^ {2}}\\\\right) f _ {R} \\\\left(\\\\frac {y ^ {2}}{\\\\Lambda^ {2}}\\\\right)}{\\\\sqrt {x ^ {2} + m _ {N} \\\\Delta^ {(0)} (\\\\Lambda)} \\\\sqrt {y ^ {2} + m _ {N} \\\\Delta^ {(0)} (\\\\Lambda)}}. \\\\tag {37}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,782,485,842]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\lambda^{(0)}(\\\\Lambda)$ and $\\\\Delta^{(0)}(\\\\Lambda)$ are the LO values, determined by fitting to empirical $^1 S_0$ phase shifts (see Table I). On the ground of satisfying unitarity up to this order, one must use the same regularization function adopted for the LO resummation (18). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,842,485,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The amplitude of the diagram in which the pion propagator connects the outgoing nucleon lines (not shown in Fig. 1) can be obtained by making the following replacements: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,895,485,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} (a, b) (c, d) \\\\rightarrow (c, d) (a, b); \\\\quad (r, s) (k, n) \\\\rightarrow (k, n) (r, s); \\\\\\\\ (\\\\bar {p}, \\\\bar {p} ^ {\\\\prime}) \\\\rightarrow (- \\\\bar {p} ^ {\\\\prime}, - \\\\bar {p}). \\\\tag {38} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,80,932,167]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The integrals are calculated numerically, and the trace formalism of Ref. [41] is used to obtain partial-wave projected amplitudes before the loop momentum is integrated over. With a bit of spin-isospin algebra, the contribution of Fig. 1(a) and its permutation to $^1 S_0$ is obtained by evaluating the following integral: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,174,932,239]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} V _ {\\\\text {r a d}} ^ {1 S _ {0}} = - \\\\frac {\\\\pi}{m _ {N}} \\\\frac {g _ {A} ^ {2}}{4 f _ {\\\\pi} ^ {2}} \\\\lambda^ {(0)} (\\\\Lambda) \\\\int \\\\frac {d ^ {3} l}{(2 \\\\pi) ^ {3}} \\\\frac {l ^ {2}}{\\\\left(l ^ {2} + m _ {\\\\pi} ^ {2}\\\\right) ^ {\\\\frac {3}{2}}} \\\\\\\\ \\\\times \\\\left[ \\\\mathcal {R} \\\\left(\\\\left| \\\\vec {p} ^ {\\\\prime} \\\\right|, \\\\left| \\\\vec {p} - \\\\vec {l} \\\\right|; \\\\Lambda\\\\right) + \\\\mathcal {R} \\\\left(\\\\left| \\\\vec {p} \\\\right|, \\\\left| \\\\vec {p} ^ {\\\\prime} + \\\\vec {l} \\\\right|; \\\\Lambda\\\\right) \\\\right]. \\\\tag {39} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,246,932,276]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The corrections to the triplet channels come from the diagrams in Fig. 1(b), \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[531,282,932,391]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\mathcal {A} _ {\\\\mathrm {r a d}} ^ {(b)} = \\\\frac {4 \\\\pi}{m _ {N}} \\\\frac {g _ {A} ^ {2}}{1 6 f _ {\\\\pi} ^ {2}} \\\\lambda^ {(0)} (\\\\Lambda) \\\\sum_ {e, m, \\\\alpha , \\\\beta} \\\\frac {1}{8} [ (\\\\tau_ {e} \\\\tau_ {2} \\\\tau_ {m}) _ {b a} (\\\\tau_ {2} \\\\tau_ {e} \\\\tau_ {m}) _ {c d} \\\\\\\\ \\\\times \\\\left(\\\\sigma_ {\\\\alpha} \\\\sigma_ {2}\\\\right) _ {r s} \\\\left(\\\\sigma_ {2} \\\\sigma_ {\\\\beta}\\\\right) _ {k n} ] \\\\int \\\\frac {d ^ {3} l}{(2 \\\\pi) ^ {3}} \\\\frac {l _ {\\\\alpha} l _ {\\\\beta}}{\\\\left(l ^ {2} + m _ {\\\\pi} ^ {2}\\\\right) ^ {\\\\frac {3}{2}}} \\\\\\\\ \\\\times \\\\mathcal {R} (| \\\\vec {p} _ {-} |, | \\\\vec {p} _ {+} ^ {\\\\prime} |; \\\\Lambda), \\\\tag {40} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,397,558,410]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[604,416,932,450]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\vec {p} _ {\\\\pm} \\\\equiv \\\\vec {p} \\\\pm \\\\frac {\\\\vec {l}}{2}, \\\\quad \\\\vec {p} _ {\\\\pm} ^ {\\\\prime} \\\\equiv \\\\vec {p} ^ {\\\\prime} \\\\pm \\\\frac {\\\\vec {l}}{2}. \\\\tag {41}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,457,933,516]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Projection of $\\\\mathcal{A}_{\\\\mathrm{rad}}^{(b)}$ is again performed with the trace formalism. After taking all the variants due to permutations of the pion line into account, the radiative corrections to the $^3 S_1 - ^3 D_1$ potential is given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[522,522,932,628]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} V _ {\\\\text {r a d}} ^ {3 S _ {1} - 3 D _ {1}} = - \\\\frac {\\\\pi}{m _ {N}} \\\\frac {g _ {A} ^ {2}}{1 6 f _ {\\\\pi} ^ {2}} \\\\lambda^ {(0)} (\\\\Lambda) \\\\int \\\\frac {d ^ {3} l}{(2 \\\\pi) ^ {3}} \\\\frac {l ^ {2}}{\\\\left(l ^ {2} + m _ {\\\\pi} ^ {2}\\\\right) ^ {\\\\frac {3}{2}}} \\\\\\\\ \\\\times \\\\mathcal {T} (\\\\hat {p}, \\\\hat {p} ^ {\\\\prime}, \\\\hat {l}) [ \\\\mathcal {R} (| \\\\vec {p} _ {-} |, | \\\\vec {p} _ {+} ^ {\\\\prime} |; \\\\Lambda) \\\\\\\\ + \\\\mathcal {R} (| \\\\vec {p} _ {-} |, | \\\\vec {p} _ {-} ^ {\\\\prime} |; \\\\Lambda) \\\\\\\\ + \\\\mathcal {R} (| \\\\bar {p} _ {+} |, | \\\\bar {p} _ {-} ^ {\\\\prime} |; \\\\Lambda) + \\\\mathcal {R} (| \\\\bar {p} _ {+} |, | \\\\bar {p} _ {-} ^ {\\\\prime} |; \\\\Lambda) ], \\\\tag {42} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,636,840,652]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where the $2 \\\\times 2$ matrix $\\\\mathcal{T}(\\\\hat{p},\\\\hat{p}^{\\\\prime},\\\\hat{l})$ is defined by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,659,640,676]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\langle^ {3} S _ {1} | \\\\mathcal {T} | ^ {3} S _ {1} \\\\rangle = 1,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[522,681,740,718]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\langle^ {3} S _ {1} | \\\\mathcal {T} | ^ {3} D _ {1} \\\\rangle = \\\\frac {3 (\\\\hat {p} \\\\cdot \\\\hat {l}) ^ {2}}{\\\\sqrt {2}} - \\\\frac {1}{\\\\sqrt {2}},\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[522,722,741,757]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\langle^ {3} D _ {1} | \\\\mathcal {T} | ^ {3} S _ {1} \\\\rangle = \\\\frac {3 (\\\\hat {p} ^ {\\\\prime} \\\\cdot \\\\hat {l}) ^ {2}}{\\\\sqrt {2}} - \\\\frac {1}{\\\\sqrt {2}},\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[519,761,932,825]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\langle^ {3} D _ {1} | \\\\mathcal {T} | ^ {3} D _ {1} \\\\rangle = \\\\frac {9}{2} (\\\\hat {p} \\\\cdot \\\\hat {l}) (\\\\hat {p} ^ {\\\\prime} \\\\cdot \\\\hat {l}) \\\\hat {p} \\\\cdot \\\\hat {p} ^ {\\\\prime} - \\\\frac {3}{2} [ (\\\\hat {p} ^ {\\\\prime} \\\\cdot \\\\hat {l}) ^ {2} + (\\\\hat {p} \\\\cdot \\\\hat {l}) ^ {2} ] \\\\\\\\ + \\\\frac {1}{2}. \\\\tag {43} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[521,840,921,869]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IV. NUCLEON-NUCLEON PHASE SHIFTS AND TRITON BINDING ENERGY \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,877,932,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this section we show how well the momentum-dependent dibaryon potential agrees with empirical phase shifts of $NN$ scattering and its prediction for the triton binding energy at LO and NLO. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[64,47,461,63]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CONSTRUCTING CHIRAL EFFECTIVE FIELD THEORY ... \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[651,49,932,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PHYSICAL REVIEW C 105, 054002 (2022) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[466,950,529,964]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"054002-5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[166,82,495,261]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0072/063531139f14c2447eba0e98d974df36f556a7c5775d3e62dafe663ecf8fd730.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[500,80,831,262]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0910/3957b1bb39eeb48e484d264a820e1ccca3a38237ee32f919608de98330033d80.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[337,266,663,448]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"FIG. 2. The $^1 S_0$ phase shifts as a function of c.m. momentum $k$ up to $\\\\\\\\mathrm{N}^2\\\\\\\\mathrm{LO}$ . The blue, orange and black bands represent LO, NLO, and $\\\\\\\\mathrm{N}^2\\\\\\\\mathrm{LO}$ respectively, and the bands show the variation with $\\\\\\\\Lambda$ from 600 to $2400\\\\\\\\mathrm{MeV}$ . The potentials used in (a), (b), and (c) are momentum-dependent dibaryon potentials, MMW scheme and dynamic dibaryon potentials, respectively. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0628/79becbdf2d4a10b40c8fbb5d21211d8e9a4b27b5b3dcb1ba5de0340f34899326.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[224,515,329,529]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A. ${}^{1}{S}_{0}$ channel \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[64,534,485,565]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Having computed the radiative corrections, we write the NNLO $^1 S_0$ potential explicitly as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[120,574,485,633]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} V _ {\\\\mathrm {N} ^ {2} \\\\mathrm {L O}} = C _ {0} ^ {(2)} + \\\\frac {C _ {2} ^ {(0)}}{2} \\\\left(p ^ {2} + p ^ {\\\\prime 2}\\\\right) + V _ {\\\\mathrm {s p r}} ^ {(2)} \\\\left(p ^ {\\\\prime}, p\\\\right) \\\\\\\\ + V _ {\\\\mathrm {T P E 0}} + V _ {\\\\mathrm {r a d}} ^ {1 S _ {0}} \\\\left(p ^ {\\\\prime}, p\\\\right). \\\\tag {44} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,643,485,847]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The $^1 S_0$ phase shifts up to $\\\\mathrm{N}^2\\\\mathrm{LO}$ are shown in Fig. 2(a). The bands represent the cutoff variation spanning from $\\\\Lambda = 600$ MeV to $2400\\\\mathrm{MeV}$ . The LECs are determined by fitting the EFT amplitudes to the empirical phase shifts provided by the partial-wave analysis (PWA) of the Nijmegen group [42,43] by a least-square procedure. For LO and NLO, PWA points with c.m. momentum $k \\\\lesssim 150\\\\mathrm{MeV}$ are used, and at $\\\\mathrm{N}^2\\\\mathrm{LO}$ inputs from $k = 150 - 300\\\\mathrm{MeV}$ are added. For comparison, the phase shifts up to $\\\\mathrm{N}^2\\\\mathrm{LO}$ obtained with the dynamic dibaryon potentials of Ref. [13] and the power counting of Ref. [8]—referred to as minimally modified Weinberg (MMW) in the current paper—are shown in Fig. 2(b) and 2(c). The LECs for this interaction were determined with the same set of PWA inputs. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,848,485,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The rather mild sensitivity to the cutoff $\\\\Lambda$ , manifest in the narrowness of the cutoff-variation bands, is somewhat expected based on the ultraviolet suppression afforded by the momentum-dependent $\\\\phi NN$ vertex. The rapid order-by-order convergence is also retained from the energy-dependent dibaryon potential, as illustrated in Ref. [13]. Moreover, the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,516,933,550]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"radiative correction $V_{\\\\mathrm{rad}}^{\\\\mathrm{ls}_0}$ does not spoil the cutoff independence or the convergence of the EFT expansion. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[640,566,804,580]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"B. Spin-triplet channels \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,583,933,688]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^3 S_1 - ^3 D_1$ is the spin-triplet channel that is most likely affected by the pion cloud because the centrifugal barrier in higher waves tends to suppress the radiated pions. In calculating the phase shifts of $^3 S_1 - ^3 D_1$ , we follow the power counting of Ref. [39], with OPE and one $S$ -wave counterterm at LO, NLO vanishing, and two more counterterms, TPE0, and $V_{\\\\mathrm{rad}}^{3S_1 - 3D_1}$ (42) at $\\\\mathrm{N}^2\\\\mathrm{LO}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,689,933,847]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The cutoff dependence has typically been more of a concern for the triplet channels because the singular attraction of OPE was a major source to upset NDA from the perspective of RG invariance. We determine the values of LECs by demanding that several PWA phase shifts are reproduced exactly. Specifically, the following PWA phase shifts are used: the $^3 S_1$ phase shift $\\\\delta_{^3 S_1}$ at $k = 118 \\\\mathrm{MeV}$ and $153 \\\\mathrm{MeV}$ and the mixing angle $\\\\epsilon_1$ at $153 \\\\mathrm{MeV}$ . Shown in Fig. 3, $^3 S_1 - ^3 D_1$ phase shifts and mixing angles for representative momenta ( $k = 100$ and $200 \\\\mathrm{MeV}$ ) become insensitive to the cutoff value $\\\\Lambda$ when $\\\\Lambda$ is sufficiently large. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,847,933,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 4 compares the $^3 S_1 - ^3 D_1$ phase shifts produced by the radiatively corrected dibaryon potential and the MMW scheme. The difference is minuscule: for the $^3 S_1$ phase shifts, the discrepancy is no more than about one degree, whereas the differences of the $^3 D_1$ phase shifts and the mixing angle is smaller than one degree. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[64,47,293,63]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PENG, LYU, KÖNIG, AND LONG \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[651,47,933,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PHYSICAL REVIEW C 105, 054002 (2022) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[466,950,534,964]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"054002-6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[169,80,395,306]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0722/e777b266aedb7d1c48e1104f565ff5897ea53686f2f1f891351cd517e2c254af.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[405,80,626,306]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0990/29ff20de74ddeb0ea575610a6d51e43fc0352d51fef34755cfa33656a114616b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[634,80,830,306]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"FIG. 3. The $^3 S_1 - ^3 D_1$ phase shifts and mixing angle at $k = 100 \\\\\\\\, \\\\\\\\mathrm{MeV}$ (red) and $200 \\\\\\\\, \\\\\\\\mathrm{MeV}$ (blue), as functions of momentum cutoff $\\\\\\\\Lambda$ . The dashed (solid) lines represent the LO ( $\\\\\\\\mathrm{N}^2\\\\\\\\mathrm{LO}$ ) result. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0937/4d28dcba5a5f2546fc83c33e68e20d0f89317313a2c4e52a536e94b55857b8d8.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[62,356,488,518]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, the values of $^3 S_1 - ^3 D_1$ counterterms are renormalized by these radiative corrections, varying up to $50\\\\%$ compared to their MMW values. Thus, the impact of the radiative corrections on the triplet channels appears to be almost entirely short-ranged. This is further confirmed by the numerically tiny contributions to higher partial waves such as $^3 P_0$ , $^3 P_1$ , and $^3 D_2$ . We have computed the phase shifts of these partial waves, using partially-perturbative-pion power counting, Ref. [44] for $^3 P_0$ and Ref. [45] for $^3 P_1$ and $^3 D_2$ . Within numerical precision of our calculations, the differences are found to be negligible. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[190,547,361,561]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"C. Triton binding energy \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,565,488,652]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The success of the momentum-dependent dibaryon potential in $^1 S_0$ was more or less expected because it is unitarily equivalent to the energy-dependent version in $^1 S_0$ , at least at tree level. A third particle can assess its impact beyond the two-nucleon system. The exchanged pion in the radiative corrections considered in Sec. III plays the role of a third \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,354,933,383]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"particle, but it is virtual. We therefore now assess what the theory predicts for the triton binding energy up to NLO. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,383,933,558]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The calculation is set up following the power counting of partially perturbative pions. At LO, we iterate to all orders the potential (11) plus OPE in $^1 S_0$ , and one contact term plus OPE in $^3 S_1 - ^3 D_1$ and $^3 P_0$ [1]. This is done by solving the Faddeev equations to obtain binding energies as LO. At NLO, in addition to the NLO $^1 S_0$ force, OPE is included in channels up to $D$ waves $(^1 P_1, ^3 P_1, ^3 P_2 - ^3 F_2, ^1 D_2, ^3 D_2,$ and $^3 D_3 - ^3 G_3)$ . Perturbative corrections to the binding energy are obtained by evaluating the NLO potentials between LO wave functions, obtained from the Faddeev equations along with the LO energies. For all calculations we include channels with angular momentum up to $j_{\\\\mathrm{max}} = 4$ in the Faddeev equations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,558,933,647]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The results for various cutoff are shown in Table II as columns of labeled \\\"SEP.\\\" For comparison, we also show the results for the MMW scheme. Since the triton is relatively shallow, with an average binding momentum $\\\\sqrt{2m_NB_{3\\\\mathrm{H}} / 3}\\\\simeq$ $73~\\\\mathrm{MeV}$ we do not expect the dibaryon potential to necessarily perform much better in reproducing the triton binding \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[169,674,398,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0090/67f08a0422487e5810e985544148cc782ab9666384a6de7f761fb10a3da26014.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[402,672,619,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/1008/acda9d4f235e92efd2ada28422c1524d4df14a286a55d5747c2c2a03a2f4b3ff.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[624,672,830,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"FIG. 4. The $^3 S_1 - ^3 D_1$ phase shifts and mixing angle as functions of the c.m. momentum $k$ , for cutoff $\\\\\\\\Lambda = 600 \\\\\\\\, \\\\\\\\mathrm{MeV}$ (red) and $2400 \\\\\\\\, \\\\\\\\mathrm{MeV}$ (green). The solid lines represent the results with radiative corrections to the dibaryon potential, and the dashed lines correspond to the MMW scheme. The circles are the PWA values. See the text for more detailed explanation. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0594/8b1c5a9057955edde8b9b2dce408c45e14b454addeeb3d49d42244797031e769.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[64,47,465,63]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CONSTRUCTING CHIRAL EFFECTIVE FIELD THEORY ... \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[651,47,933,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PHYSICAL REVIEW C 105, 054002 (2022) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[466,950,529,963]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"054002-7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[64,112,488,229]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0317/83927de3a84836a722f96664d078ab474b3a1e9731f0f3f7cf60d461088afc92.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=\\\"2\\\">Λ (MeV)</td><td colspan=\\\"2\\\">SEP</td><td colspan=\\\"2\\\">MMW</td></tr><tr><td>LO</td><td>NLO</td><td>LO</td><td>NLO</td></tr><tr><td>400</td><td>-8.67</td><td>-8.50</td><td>-11.02</td><td>-7.68</td></tr><tr><td>600</td><td>-6.10</td><td>-6.10</td><td>-6.46</td><td>-6.90</td></tr><tr><td>800</td><td>-5.57</td><td>-5.58</td><td>-5.30</td><td>-6.64</td></tr><tr><td>1600</td><td>-5.37</td><td>-5.51</td><td>-4.89</td><td>-6.49</td></tr></table>\",\n \"table_caption\": \"[\\\"TABLE II. The binding energy of the triton (MeV). See the text for more explanations. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[66,253,485,484]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"energy. In fact, the NLO of MMW has a smaller cutoff variation, and the large $\\\\Lambda$ limit is closer to the experimental value of $\\\\simeq 8.5\\\\mathrm{MeV}$ . However, cutoff variation at best should be taken as a lower bound for the full theoretical uncertainty. The NLO correction of SEP is much smaller than MMW, which might imply that the actual EFT truncation error is smaller with SEP than with MMW. While a more systematic comparison of the two schemes in few- or many-nucleon is definitely interesting, it is beyond the scope of the paper, as is a triton calculation involving the energy-dependent dibaryon potential. We are for now content with finding that the dibaryon potential gives a description of the three-nucleon system that is comparable to the MMW scheme. Both the SEP and MMW interactions yield the triton slightly more bound compared to earlier calculations using a similar perturbative power-counting scheme [46,47]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,484,488,602]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nuclear-structure calculations using the dibaryon interaction [29] or an interaction inspired by it [31] have been carried out previously. In Ref. [31], some of the light nuclei with $A = 3 - 6$ were investigated. A direct comparison between the triton binding energy calculated in Ref. [31] and this work is however difficult because different power-counting and regularization schemes have been used. We only note that results agree within $10\\\\%$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[185,621,366,633]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"V. CHIRAL SYMMETRY \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,642,488,702]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nonlinear realization of spontaneously broken chiral symmetry requires derivatives acting on hadronic fields to be chirally covariant. The chiral-covariant derivative $\\\\mathcal{D}_i$ for the nucleon, which is an isospin- $1 / 2$ field, is given as [48] \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[188,708,485,736]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathscr {D} _ {i} N \\\\equiv \\\\left(\\\\nabla_ {i} + \\\\frac {\\\\boldsymbol {\\\\tau}}{2} \\\\cdot \\\\boldsymbol {E} _ {i}\\\\right) N, \\\\tag {45}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,742,422,757]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where the so-called chiral connection $E_{i}$ is given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[215,763,485,794]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\boldsymbol {E} _ {i} \\\\equiv i \\\\frac {\\\\boldsymbol {\\\\pi}}{f _ {\\\\pi}} \\\\times \\\\boldsymbol {D} _ {i} \\\\tag {46}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,801,101,814]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"with \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[142,820,485,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\boldsymbol {D} _ {i} \\\\equiv D ^ {- 1} \\\\frac {\\\\nabla_ {i} \\\\boldsymbol {\\\\pi}}{2 f _ {\\\\pi}} \\\\quad \\\\text {a n d} \\\\quad D \\\\equiv 1 + \\\\frac {\\\\boldsymbol {\\\\pi} ^ {2}}{4 f _ {\\\\pi} ^ {2}}. \\\\tag {47}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,863,488,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The moral here is that derivatives acting on $N$ must be accompanied by composite chiral-connection terms consisting of $\\\\pi$ and $N$ , with two types of operators sharing the same set of LECs. Because the $\\\\phi NN$ vertex function (10) is constructed out of an infinite series of derivative couplings acting on $N$ , \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[638,84,806,191]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"FIG. 5. The transition vertex of $NN\\\\\\\\pi \\\\\\\\pi \\\\\\\\rightarrow \\\\\\\\phi$ . \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0829/8221006afbfca54a7be6315fb872ead9a8b009eb5f6f77cf02673e4b3423fad3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[507,234,932,306]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"it is less straightforward than usual to write down the corresponding chiral-connection operators. Furthermore, in light of the proposed two-parameter fine-tuning at LO in $^1 S_0$ , these chiral-connection operators could be enhanced in comparison with NDA. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,308,933,469]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Chiral-connection operators that include products of two pion fields, the minimal number of pion fields such operators expected to have, are normally the most phenomenologically important for low-energy nuclear physics. We therefore focus on the transition vertex of $NN\\\\pi \\\\pi \\\\rightarrow \\\\phi$ , depicted in Fig. 5, where $\\\\alpha_{1,2}$ denotes collectively the spin and isospin indices of the incoming nucleons, $\\\\vec{p} \\\\equiv (\\\\vec{p}_1 - \\\\vec{p}_2) / 2$ their relative momentum, $a, b, c$ the isospin indices of the pions and the isovector dibaryon, and $\\\\vec{k}_{1,2}$ the momentum of the incoming pions. Following the derivations in the Appendix, one finds the vertex function of $\\\\phi NN\\\\pi \\\\pi$ to be \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[558,476,932,555]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\mathcal {A} _ {\\\\phi N N \\\\pi \\\\pi} = \\\\frac {i g}{4 f _ {\\\\pi} ^ {2}} \\\\sqrt {\\\\frac {4 \\\\pi}{m _ {N}}} \\\\left\\\\{i (\\\\delta_ {b c} \\\\mathcal {P} _ {a} - \\\\delta_ {a c} \\\\mathcal {P} _ {b}) _ {\\\\alpha_ {2} \\\\alpha_ {1}} \\\\mathcal {B} _ {+} \\\\right. \\\\\\\\ \\\\left. + \\\\frac {1}{\\\\sqrt {8}} \\\\epsilon_ {a b c} \\\\left(\\\\sigma_ {2} \\\\tau_ {2}\\\\right) _ {\\\\alpha_ {2} \\\\alpha_ {1}} \\\\mathcal {B} _ {-} \\\\right\\\\}, \\\\tag {48} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,560,672,574]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where we have defined \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[570,578,930,628]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\mathcal {B} _ {\\\\pm} \\\\equiv u (| \\\\vec {p} + \\\\vec {k} _ {1} / 2 |, | \\\\vec {p} + \\\\vec {k} _ {2} / 2 |) \\\\\\\\ \\\\pm u \\\\left(\\\\left| \\\\vec {p} - \\\\vec {k} _ {1} / 2 \\\\right|, \\\\left| \\\\vec {p} - \\\\vec {k} _ {2} / 2 \\\\right|\\\\right), \\\\tag {49} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[548,628,867,666]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nu (x, y) \\\\equiv \\\\left(1 + \\\\frac {x ^ {2}}{m _ {N} \\\\Delta}\\\\right) ^ {- \\\\frac {1}{2}} - \\\\left(1 + \\\\frac {y ^ {2}}{m _ {N} \\\\Delta}\\\\right) ^ {- \\\\frac {1}{2}}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,670,930,699]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Using the scalings (12) and (13), one has the vertex function scale as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[631,703,932,738]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {A} _ {\\\\phi N N \\\\pi \\\\pi} \\\\sim \\\\frac {4 \\\\pi}{m _ {N}} \\\\frac {1}{\\\\sqrt {M _ {\\\\mathrm {h i}}}} \\\\frac {1}{f _ {\\\\pi}}. \\\\tag {50}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,750,933,808]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Combining then the scaling (50) with the standard counting rule for irreducible pion loops, we find that the $\\\\phi NN\\\\pi \\\\pi$ vertex contributes to the two-nucleon force at $\\\\mathrm{N}^2\\\\mathrm{LO}$ , illustrated in Fig. 6. However, the amplitude of this diagram vanishes, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[624,830,820,912]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"FIG. 6. Irreducible $NN$ diagram built out of a $\\\\\\\\phi NN\\\\\\\\pi \\\\\\\\pi$ vertex. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0948/b0908bd3c89d84750dd1a8c5f5bfc96f9c44aabcb75d958541437c794058e724.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[64,47,293,63]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PENG, LYU, KÖNIG, AND LONG \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[651,49,932,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PHYSICAL REVIEW C 105, 054002 (2022) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[466,950,529,964]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"054002-8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[64,83,249,165]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0273/2c13e89795402b742fff7c1dd7dd453362b51cd490897bed49affa2fd8fc1d49.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[305,82,487,165]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"FIG. 7. The Feynman diagrams contributing to three-body and four-body forces with the $\\\\\\\\phi NN\\\\\\\\pi \\\\\\\\pi$ vertex. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0591/ad6874bbcccf8de9f9299ce4478b5afcbaaba53f77d9c64b409a910d5b858e8a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[62,222,485,251]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"which can be seen by evaluating the isospin factors of $\\\\mathcal{A}_{\\\\phi NN\\\\pi \\\\pi}$ under exchange of the pion isospin index $a$ and $b$ : \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[147,258,485,273]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\epsilon_ {a a c} = 0 \\\\quad \\\\text {a n d} \\\\quad \\\\delta_ {a c} \\\\mathcal {P} _ {a} - \\\\delta_ {a c} \\\\mathcal {P} _ {a} = 0. \\\\tag {51}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,281,485,468]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As shown in Fig. 7, the $\\\\phi NN\\\\pi \\\\pi$ vertex (48) contributes to three-nucleon forces and four-nucleon forces. If we follow Weinberg's counting for long-range few-nucleon forces, these both enter at $\\\\mathrm{N}^4\\\\mathrm{LO}$ , four orders higher than the LO two-nucleon forces. If one ever ventures to describe two-pion production by nucleon-nucleon collision, the $\\\\phi NN\\\\pi \\\\pi$ will become relevant. These contributions are either quite high-order effects (3N or 4N forces) or become sizable only at such high momenta ( $NN\\\\rightarrow NN\\\\pi \\\\pi$ ), where the applicability of chiral EFT is questionable at best. In conclusion, the enhancement due to the momentum-dependent dibaryon vertex does not give rise to particularly significant extraneous contributions to nuclear structures or reactions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[142,488,407,500]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"VI. SUMMARY AND CONCLUSIONS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,508,485,594]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We have considered a new formulation of chiral EFT to improve the slow convergence of the $^1 S_0$ phase shifts. The key idea is to replace the energy-dependent dibaryon potential proposed in Ref. [13] with a momentum-dependent formulation that it is more amenable to many-body methods used for nuclear-structure calculations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[64,595,485,626]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The main ingredient is a transition form factor, from ${}^{1}{\\\\mathrm{S}}_{0}$ ${NN}$ states to the spin-0 and isospin-1 dibaryon: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[174,632,485,669]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {A} _ {\\\\phi N N} = - \\\\frac {\\\\sqrt {4 \\\\pi} g}{\\\\sqrt {p ^ {2} / \\\\Delta + m _ {N}}} \\\\mathcal {P} _ {m} \\\\tag {52}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,674,485,818]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"with two parameters $g$ and $\\\\Delta$ characterizing, respectively, the strength and momentum range of the transition. The vertex function (52) is interpreted as the sum of an infinite sequence of $\\\\phi NN$ derivative-coupling operators, correlated by $g$ and $\\\\Delta$ , which in turn correspond to two independent low-energy mass scales, as shown in Sec. II. With $g$ and $\\\\Delta$ varying, the resulting momentum-dependent potential traces out a two-dimensional surface in the EFT parameter space, in contrast to the one-dimensional line for the more conventional $^1 S_0$ LO chiral forces. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,819,485,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This phenomenologically inspired potential must demonstrate its consistency with the chiral Lagrangian. For instance, the $\\\\phi NN$ vertex can be radiatively corrected by the pion and could contribute non-trivial force to $^1 S_0$ at $\\\\mathrm{N}^2\\\\mathrm{LO}$ [see Fig. 1(a)]. When one of the incoming nucleons is connected to one of the outgoing nucleons by a radiation pion, triplet-channel amplitudes receive corrections as well [see Fig. 1(b)]. We examined these radiative corrections and found that they \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,80,932,125]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"turn out to modify the long-range chiral forces only modestly. In particular, they leave the already satisfactory convergence in the triplet channels intact. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,125,932,181]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We investigated further along this line, studying the case where a third nucleon is present. More specifically, the triton binding energy was calculated up to NLO using a power-counting scheme with partially perturbative pions [39,45]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,183,933,268]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Since the $\\\\phi NN$ transition form factor is interpreted as an infinite series of nucleonic derivative couplings, it is accompanied by a $\\\\phi NN\\\\pi \\\\pi$ vertex in order to satisfy chiral symmetry. We worked out the expression of this $\\\\phi NN\\\\pi \\\\pi$ vertex function and discussed its phenomenological impacts, concluding that it only modifies chiral nuclear forces at quite high orders. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,270,933,428]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Because of our practical motivation of nuclear-structure studies, we did not touch the issue of chiral extrapolation, analytical continuation of observables in the light quark mass $m_{u,d}$ . The chiral symmetry-breaking parts of $^1 S_0$ contact terms have been argued to defy NDA based on RG considerations [4]. We conjecture here that the UV-suppressing dibaryon vertex offers an intriguing opportunity to reduce the divergences proportional to $m_{\\\\pi}^{2}$ , and then this might change the degree to which RG invariance modifies the NDA-based power counting. However, it is unclear how this can be implemented in a model-independent fashion. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,429,933,515]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In closing we note that likely further versions of a multiparameter LO in the $^1 S_0$ channel can be constructed with yet another formulation. What was done in this paper for the momentum-dependent $^1 S_0$ dibaryon potential provides guidance for inspecting whether the specific choice of interaction can be incorporated into chiral EFT. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[634,537,806,549]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ACKNOWLEDGMENTS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,558,933,775]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We thank Bira van Kolck for valuable comments on the manuscript. B.L. and S.K. thank the Institute for Nuclear Theory at the University of Washington and the organizers of the program \\\"Nuclear Structure at the Crossroads\\\" for hospitality while part of this work was carried out. This work was supported by the National Natural Science Foundation of China (NSFC) under Grants No. 11775148 and No. 11735003, the Fundamental Research Funds for the Central Universities, and by the National Science Foundation under Grant No. PHY-2044632. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under the FRIB Theory Alliance, Award No. DE-SC0013617. Computational resources for parts of this work have been provided by the Jülich Supercomputing Center. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[546,797,896,811]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"APPENDIX: VERTEX FUNCTION OF $NN\\\\pi \\\\pi \\\\to \\\\phi$ \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,819,932,876]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In order to satisfy chiral symmetry, there must be pion-absorption vertices entering along with $\\\\mathcal{A}_{NN\\\\phi}$ defined in Eq. (10). In this Appendix, we work out the vertex function for the transition $NN\\\\pi \\\\pi \\\\rightarrow \\\\phi$ , discussed in Sec. V. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,877,933,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A nonlinearly realized chiral transformation acts on the nucleon field like an isospin rotation with an angle depending on the local pion field. Let us focus on the axial sector $SU(2)_A$ of chiral symmetry, parametrized by $\\\\theta^A$ with stereographic \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[64,49,463,61]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CONSTRUCTING CHIRAL EFFECTIVE FIELD THEORY ... \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[651,49,932,63]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PHYSICAL REVIEW C 105, 054002 (2022) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[466,950,529,963]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"054002-9 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[64,80,154,94]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"coordinates: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[144,99,353,133]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\delta_ {A} N = - i \\\\left(\\\\boldsymbol {\\\\theta} ^ {A} \\\\times \\\\frac {\\\\boldsymbol {\\\\pi}}{2 f _ {\\\\pi}}\\\\right) \\\\cdot \\\\frac {\\\\boldsymbol {\\\\tau}}{2} N,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[147,137,485,172]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\delta_ {A} \\\\boldsymbol {\\\\pi} = f _ {\\\\pi} \\\\boldsymbol {\\\\theta} ^ {A} \\\\left(1 - \\\\frac {\\\\boldsymbol {\\\\pi} ^ {2}}{4 f _ {\\\\pi} ^ {2}}\\\\right) + \\\\left(\\\\frac {\\\\boldsymbol {\\\\theta} ^ {A} \\\\cdot \\\\boldsymbol {\\\\pi}}{2 f _ {\\\\pi}}\\\\right) \\\\boldsymbol {\\\\pi}, \\\\tag {A1}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[130,176,351,212]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left(\\\\delta_ {A} \\\\boldsymbol {\\\\phi}\\\\right) _ {c} = \\\\left[ \\\\left(\\\\boldsymbol {\\\\theta} ^ {A} \\\\times \\\\frac {\\\\boldsymbol {\\\\pi}}{2 f _ {\\\\pi}}\\\\right) \\\\times \\\\boldsymbol {\\\\phi} \\\\right] _ {c}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,215,488,273]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We first seek the chiral-connection operator that has two pion fields, the fewest number of pion fields required by chiral symmetry, and then study its vertex function in momentum space. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,80,933,112]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As an illustration of our approach, we first derive the chiral-connection terms for the following operator: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[643,123,932,156]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\sum_ {m} \\\\phi_ {m} ^ {\\\\dagger} \\\\left[ N ^ {T} \\\\mathcal {P} _ {m} \\\\overleftrightarrow {\\\\nabla} ^ {2} N \\\\right]. \\\\tag {A2}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,167,933,275]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Unless noted otherwise, derivatives here and in the following act only on the fields within brackets. $\\\\phi_m^{\\\\dagger}$ in the above equation, for instance, is not acted upon. The most straightforward way to account for chiral symmetry is to replace the derivative $\\\\overleftrightarrow{\\\\nabla}$ with the chiral-covariant derivative $\\\\overleftrightarrow{\\\\mathcal{D}}$ defined in Eq. (45). Expanding in powers of $\\\\pi$ , we can read off the corresponding chiral-connection terms up to $\\\\mathcal{O}(\\\\pi^2 /f_\\\\pi^2)$ : \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[161,301,933,362]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\sum_ {b c d m} \\\\frac {i \\\\epsilon_ {b c d}}{4 f _ {\\\\pi} ^ {2}} \\\\phi_ {m} ^ {\\\\dagger} \\\\sum_ {i} \\\\left\\\\{\\\\left[ 2 (\\\\nabla_ {i} N) ^ {T} \\\\tau_ {d} ^ {T} \\\\mathcal {P} _ {m} \\\\pi_ {b} (\\\\nabla_ {i} \\\\pi_ {c}) N + N ^ {T} \\\\tau_ {d} ^ {T} \\\\mathcal {P} _ {m} \\\\pi_ {b} (\\\\nabla^ {2} \\\\pi_ {c}) N - 2 N ^ {T} \\\\tau_ {d} ^ {T} \\\\mathcal {P} _ {m} \\\\pi_ {b} (\\\\nabla_ {i} \\\\pi_ {c}) (\\\\nabla_ {i} N) \\\\right] \\\\right. \\\\\\\\ \\\\left. + \\\\left[ 2 N ^ {T} \\\\mathcal {P} _ {m} \\\\tau_ {d} \\\\pi_ {b} (\\\\nabla_ {i} \\\\pi_ {c}) (\\\\nabla_ {i} N) + N ^ {T} \\\\mathcal {P} _ {m} \\\\tau_ {d} \\\\pi_ {b} (\\\\nabla^ {2} \\\\pi_ {c}) N - 2 (\\\\nabla_ {i} N) ^ {T} \\\\mathcal {P} _ {m} \\\\tau_ {d} \\\\pi_ {b} (\\\\nabla_ {i} \\\\pi_ {c}) N \\\\right] \\\\right\\\\}. \\\\tag {A3} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,369,933,398]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, the expansion becomes cumbersome if we substitute the chiral-covariant derivatives in the following operator, which is part of the Lagrangian (6), when $n$ is large: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[400,406,932,440]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\sum_ {m} \\\\phi_ {m} ^ {\\\\dagger} \\\\left[ N ^ {T} \\\\mathcal {P} _ {m} (- i \\\\overleftrightarrow {\\\\bigvee}) ^ {2 n} N \\\\right]. \\\\tag {A4}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,448,806,464]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We therefore try a slightly different approach and consider the axial transform $\\\\delta_A$ of the operator in Eq. (A2): \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[183,470,933,510]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\sum_ {b c d m} \\\\phi_ {m} ^ {\\\\dagger} \\\\left[ N ^ {T} \\\\mathcal {P} _ {m} (\\\\overleftrightarrow {\\\\nabla} - \\\\overrightarrow {\\\\nabla}) ^ {2} \\\\left(- i \\\\epsilon_ {b c d} \\\\theta_ {b} \\\\frac {\\\\pi_ {c}}{4 f _ {\\\\pi}} \\\\tau_ {d} N\\\\right) + N ^ {T} \\\\left(- i \\\\epsilon_ {b c d} \\\\theta_ {b} \\\\frac {\\\\pi_ {c}}{4 f _ {\\\\pi}}\\\\right) \\\\tau_ {d} ^ {T} \\\\mathcal {P} _ {m} (\\\\overleftrightarrow {\\\\nabla} - \\\\overrightarrow {\\\\nabla}) ^ {2} N \\\\right]. \\\\tag {A5}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,518,414,537]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Noticing that to the lowest order in $\\\\pi^2 /f_\\\\pi^2$ we have \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[405,544,933,564]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\delta_ {A} \\\\boldsymbol {\\\\pi} = f _ {\\\\pi} \\\\boldsymbol {\\\\theta} ^ {A} + \\\\mathcal {O} \\\\left(\\\\boldsymbol {\\\\pi} ^ {2} / f _ {\\\\pi} ^ {2}\\\\right), \\\\tag {A6}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,571,760,587]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"we tentatively propose the following operator to cancel the preceding chiral-symmetry violation (A5): \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[269,594,933,659]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\sum_ {b c d m} \\\\frac {i}{4 f _ {\\\\pi} ^ {2}} \\\\epsilon_ {b c d} \\\\pi_ {b} \\\\phi_ {m} ^ {\\\\dagger} \\\\big \\\\{[ N ^ {T} \\\\mathcal {P} _ {m} \\\\tau_ {d} (\\\\overleftarrow {\\\\nabla} - \\\\overrightarrow {\\\\nabla}) ^ {2} \\\\pi_ {c} N - N ^ {T} \\\\mathcal {P} _ {m} \\\\tau_ {d} \\\\overleftarrow {\\\\nabla} ^ {2} \\\\pi_ {c} N ]. \\\\\\\\ + \\\\left[ N ^ {T} \\\\pi_ {c} \\\\tau_ {d} ^ {T} \\\\mathcal {P} _ {m} (\\\\overleftarrow {\\\\nabla} - \\\\overrightarrow {\\\\nabla}) ^ {2} N - N ^ {T} \\\\pi_ {c} \\\\tau_ {d} ^ {T} \\\\mathcal {P} _ {m} \\\\overrightarrow {\\\\nabla} ^ {2} N \\\\right] \\\\}. \\\\tag {A7} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,666,910,696]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It is straightforward to verify that the combination of the operators in Eqs. (A2) and (A7) is chiral invariant up to $\\\\mathcal{O}(\\\\pi^2 /f_\\\\pi^2)$ . Coming back to the more general case, we expand Eq. (A4) as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[159,705,933,755]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\sum_ {m} \\\\phi_ {m} ^ {\\\\dagger} \\\\left[ N ^ {T} \\\\mathcal {P} _ {m} (- i \\\\overleftrightarrow {\\\\nabla}) ^ {2 n} N \\\\right] = \\\\sum_ {m} \\\\sum_ {k + l + q = n} C (k, l, q) \\\\phi_ {m} ^ {\\\\dagger} \\\\left[ N ^ {T} \\\\mathcal {P} _ {m} \\\\left(\\\\frac {\\\\overleftarrow {\\\\nabla}}{i}\\\\right) ^ {2 k} \\\\left(- \\\\frac {\\\\overleftarrow {\\\\nabla}}{i} \\\\cdot \\\\frac {\\\\overrightarrow {\\\\nabla}}{i}\\\\right) ^ {l} \\\\left(\\\\frac {\\\\overrightarrow {\\\\nabla}}{i}\\\\right) ^ {2 q} N \\\\right], \\\\tag {A8}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,762,356,777]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $C(k,l,q)$ are binomial coefficients, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[354,786,933,821]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n(x + y) ^ {2 n} = \\\\sum_ {k + l + q = n} C (k, l, q) x ^ {2 k} (x y) ^ {l} y ^ {2 q}, \\\\tag {A9}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,829,137,844]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"satisfying \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[415,853,932,869]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nC (k, l, q) = C (q, l, k). \\\\tag {A10}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,878,567,895]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The chiral-connection operator for Eq. (A8), in analogy with Eq. (A7), is \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[342,904,932,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\sum_ {k + l + q = n} C (k, l, q) \\\\left[ \\\\mathcal {O} _ {B} (k, l, q) + \\\\mathcal {O} _ {C} (k, l, q) \\\\right], \\\\tag {A11}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,47,293,63]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PENG, LYU, KÖNIG, AND LONG \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[651,49,932,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PHYSICAL REVIEW C 105, 054002 (2022) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[463,950,534,964]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"054002-10 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[64,82,112,94]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[205,98,770,147]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {O} _ {B} (k, l, q) \\\\equiv \\\\sum_ {b c d m} \\\\frac {i}{4 f _ {\\\\pi} ^ {2}} \\\\epsilon_ {b c d} \\\\pi_ {b} \\\\phi_ {m} ^ {\\\\dagger} \\\\left[ N ^ {T} \\\\mathcal {P} _ {m} \\\\tau_ {d} \\\\left(\\\\frac {\\\\overleftarrow {\\\\nabla}}{i}\\\\right) ^ {2 k} \\\\left(- \\\\frac {\\\\overleftarrow {\\\\nabla}}{i} \\\\cdot \\\\frac {\\\\overrightarrow {\\\\nabla}}{i}\\\\right) ^ {l} \\\\left(\\\\frac {\\\\overrightarrow {\\\\nabla}}{i}\\\\right) ^ {2 q} \\\\pi_ {c} N \\\\right],\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[205,151,933,200]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {O} _ {C} (k, l, q) \\\\equiv \\\\sum_ {b c d m} \\\\frac {i}{4 f _ {\\\\pi} ^ {2}} \\\\epsilon_ {b c d} \\\\pi_ {b} \\\\phi_ {m} ^ {\\\\dagger} \\\\left[ N ^ {T} \\\\pi_ {c} \\\\tau_ {d} ^ {T} \\\\mathcal {P} _ {m} \\\\left(\\\\frac {\\\\overleftarrow {\\\\nabla}}{i}\\\\right) ^ {2 k} \\\\left(- \\\\frac {\\\\overleftarrow {\\\\nabla}}{i} \\\\cdot \\\\frac {\\\\overrightarrow {\\\\nabla}}{i}\\\\right) ^ {l} \\\\left(\\\\frac {\\\\overrightarrow {\\\\nabla}}{i}\\\\right) ^ {2 q} N \\\\right]. \\\\tag {A12}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,207,933,239]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For $\\\\mathcal{O}_B(k,l,q)$ , either $l$ or $q$ must be positive so that there is at least one $\\\\vec{\\\\nabla}$ acting on $\\\\pi_cN$ . Similarly, either $l$ or $k$ must be positive for $\\\\mathcal{O}_C(k,l,q)$ . Transposing the operator inside the square brackets, say, of $\\\\mathcal{O}_B$ and using $\\\\mathcal{P}_a^T = -\\\\mathcal{P}_a$ , we realize \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[407,244,932,261]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {O} _ {C} (k, l, q) = \\\\mathcal {O} _ {B} (q, l, k). \\\\tag {A13}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,267,563,281]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Combining this with Eq. (A10), one concludes that Eq. (A11) reduces to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[390,287,932,321]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n2 \\\\sum_ {k + l + q = n} C (k, l, q) \\\\mathcal {O} _ {B} (k, l, q). \\\\tag {A14}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,327,933,356]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We then consider the following matrix element of $\\\\mathcal{O}_B(k,l,q)$ between the free-particle states whose quantum numbers are specified in Fig. 5: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[83,364,932,463]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\int d ^ {4} x \\\\langle \\\\phi_ {c}, p _ {3} | \\\\mathcal {O} _ {B} (k, l, q; x) | k _ {1}, a; k _ {2}, b; p _ {1}, \\\\alpha_ {1}; p _ {2}, \\\\alpha_ {2} \\\\rangle \\\\\\\\ = \\\\frac {i}{4 f _ {\\\\pi} ^ {2}} \\\\sum_ {b ^ {\\\\prime} c ^ {\\\\prime} d ^ {\\\\prime} m} \\\\epsilon_ {b ^ {\\\\prime} c ^ {\\\\prime} d ^ {\\\\prime}} \\\\int d ^ {4} x \\\\left\\\\langle \\\\phi_ {c}, p _ {3} \\\\right| \\\\pi_ {b ^ {\\\\prime}} \\\\phi_ {m} ^ {\\\\dagger} \\\\left[ N ^ {T} \\\\mathcal {P} _ {m} \\\\tau_ {d ^ {\\\\prime}} \\\\left(\\\\frac {\\\\overleftarrow {\\\\nabla}}{i}\\\\right) ^ {2 k} \\\\left(- \\\\frac {\\\\overleftarrow {\\\\nabla}}{i} \\\\cdot \\\\frac {\\\\overrightarrow {\\\\nabla}}{i}\\\\right) ^ {l} \\\\left(\\\\frac {\\\\overrightarrow {\\\\nabla}}{i}\\\\right) ^ {2 q} \\\\left(\\\\pi_ {c ^ {\\\\prime}} N\\\\right) \\\\right] _ {x} | k _ {1}, a; k _ {2}, b; p _ {1}, \\\\alpha_ {1}; p _ {2}, \\\\alpha_ {2} \\\\rangle . \\\\tag {A15} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,472,933,502]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Here, $a$ , $b$ , $c$ are the isospin indexes of the external pions and intermediate dibaryon. After counting all contractions and stripping the $\\\\delta$ function that enforces momentum conservation we obtain \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[91,506,933,592]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} - \\\\frac {i}{4 f _ {\\\\pi} ^ {2}} \\\\left\\\\{\\\\left[ \\\\frac {1}{\\\\sqrt {8}} \\\\epsilon_ {a b c} \\\\sigma_ {2} \\\\tau_ {2} + i \\\\left(\\\\delta_ {b c} \\\\mathcal {P} _ {a} - \\\\delta_ {a c} \\\\mathcal {P} _ {b}\\\\right) \\\\right] _ {\\\\alpha_ {2}, \\\\alpha_ {1}} \\\\vec {p} _ {2} ^ {2 k} \\\\left\\\\{\\\\left[ - \\\\vec {p} _ {2} \\\\cdot (\\\\vec {p} _ {1} + \\\\vec {k} _ {1}) \\\\right] ^ {l} (\\\\vec {p} _ {1} + \\\\vec {k} _ {1}) ^ {2 q} - \\\\left[ - \\\\vec {p} _ {2} \\\\cdot (\\\\vec {p} _ {1} + \\\\vec {k} _ {2}) \\\\right] ^ {l} (\\\\vec {p} _ {1} + \\\\vec {k} _ {2}) ^ {2 q} \\\\right\\\\} \\\\right. \\\\\\\\ \\\\left. + \\\\left[ - \\\\frac {1}{\\\\sqrt {8}} \\\\epsilon_ {a b c} \\\\sigma_ {2} \\\\tau_ {2} + i \\\\left(\\\\delta_ {b c} \\\\mathcal {P} _ {a} - \\\\delta_ {a c} \\\\mathcal {P} _ {b}\\\\right) \\\\right] _ {\\\\alpha_ {2}, \\\\alpha_ {1}} \\\\vec {p} _ {1} ^ {2 k} \\\\left\\\\{\\\\left[ - \\\\vec {p} _ {1} \\\\cdot (\\\\vec {p} _ {2} + \\\\vec {k} _ {1}) \\\\right] ^ {l} (\\\\vec {p} _ {2} + \\\\vec {k} _ {1}) ^ {2 q} - \\\\left[ - \\\\vec {p} _ {1} \\\\cdot (\\\\vec {p} _ {2} + \\\\vec {k} _ {2}) \\\\right] ^ {l} (\\\\vec {p} _ {2} + \\\\vec {k} _ {2}) ^ {2 q} \\\\right\\\\} \\\\right\\\\}. \\\\tag {A16} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,597,930,625]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The dibaryon momentum $\\\\vec{p}_3$ does not appear in the above equation because the derivatives in Eq. (A12) act only on the fields inside the brackets. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,625,933,669]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To obtain the $\\\\phi NN\\\\pi \\\\pi$ vertex function $\\\\mathcal{A}_{\\\\phi NN\\\\pi \\\\pi}$ (48), we need to carry out two summations of the above matrix elements. The first is over all the combinations of $(k,l,q)$ prescribed by Eq. (A14), using Eq. (A10). The second is given by summing $n$ from 0 to $\\\\infty$ , as defined in the Lagrangian (6), using the identity \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[363,676,933,715]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\sum_ {n = 0} ^ {\\\\infty} g _ {2 n} t ^ {2 n} = g \\\\sum_ {n = 0} ^ {\\\\infty} \\\\binom {- \\\\frac {1}{2}} {n} t ^ {2 n} = g W (t) \\\\tag {A17}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,720,100,733]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"with \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[422,739,932,758]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nW (t) \\\\equiv (1 + t ^ {2}) ^ {- \\\\frac {1}{2}}. \\\\tag {A18}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[62,767,933,797]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We can apply these two summations to any individual term in the expression (A16). Take the following term as an example. The first summation is given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[252,805,933,840]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\sum_ {k + l + q = n} C (k, l, q) \\\\vec {p} _ {2} ^ {2 k} [ - \\\\vec {p} _ {2} \\\\cdot (\\\\vec {p} _ {1} + \\\\vec {k} _ {1}) ] ^ {l} (\\\\vec {p} _ {1} + \\\\vec {k} _ {1}) ^ {2 q} = (\\\\vec {p} _ {1} - \\\\vec {p} _ {2} + \\\\vec {k} _ {1}) ^ {2 n}, \\\\tag {A19}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,848,307,863]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"followed by the second summation \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[344,871,932,912]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\sum_ {n = 0} ^ {\\\\infty} g _ {2 n} \\\\left[ \\\\frac {(2 \\\\vec {p} + \\\\vec {k} _ {1}) ^ {2}}{4 m _ {N} \\\\Delta} \\\\right] ^ {n} = g W \\\\left(\\\\frac {| p + \\\\vec {k} _ {1} / 2 |}{\\\\sqrt {m _ {N} \\\\Delta}}\\\\right). \\\\tag {A20}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[64,920,687,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Adding up the contributions from every term in Eq. (A16), we eventually arrive at Eq. (48). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[64,49,463,63]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CONSTRUCTING CHIRAL EFFECTIVE FIELD THEORY ... \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[651,49,932,64]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PHYSICAL REVIEW C 105, 054002 (2022) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[463,950,534,964]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"054002-11 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[67,82,485,619]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[1] A. 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Long and C. J. Yang, Phys. Rev. C 84, 057001 (2011). \\\",\\\"[45] S. Wu and B. Long, Phys. Rev. C 99, 024003 (2019). \\\",\\\"[46] Y.-H. Song, R. Lazauskas, and U. van Kolck, Phys. Rev. C 96, 024002 (2017). \\\",\\\"[47] Y.-H. Song, R. Lazauskas, and U. van Kolck, Phys. Rev. C 100, 019901(E) (2019). \\\",\\\"[48] S. Weinberg, The Quantum Theory of Fields. Vol. 2: Modern Applications (Cambridge University Press, Cambridge, 2013). \\\"]\",\n \"page_idx\": \"11\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[66,47,290,61]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PENG, LYU, KONIG, AND LONG \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[651,49,930,61]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PHYSICAL REVIEW C 105, 054002 (2022) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[463,950,534,963]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"054002-12 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1103/physrevc.105.054002"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Physics"},"sha256":{"kind":"string","value":"b76da9e7a6841ad412efdb4cbbb625665a11b71b49c5cf8dd75089fea9f4faf1"},"title":{"kind":"string","value":"Constructing chiral effective field theory around unnatural leading-order interactions"}}},{"rowIdx":253,"cells":{"abstract":{"kind":"string","value":""},"author":{"kind":"string","value":"Robert Guggenberger|Kathrin Machetanz|Levan Berelidze|Marius Keute|Alireza Gharabaghi"},"content_list":{"kind":"list like","value":[{"bbox":"[58,219,813,261]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Neuro-cardiac coupling predicts transcutaneous auricular vagus nerve stimulation effects ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[840,221,890,259]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0673/7b19541e3276b35b8c33d097e50f60d7844d12760483c58a573944e2fdc73d91.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,272,692,307]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Marius Keute*, Kathrin Machetanz, Levan Berelidze, Robert Guggenberger, Alireza Gharabaghi** 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","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,422,161,431]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"24 November 2020 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,433,189,443]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Accepted 4 January 2021 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,443,223,453]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Available online 7 January 2021 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,467,112,477]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,479,171,489]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Auricular stimulation ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,490,257,510]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Transcutaneous auricular vagus nerve stimulation ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,511,257,522]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Non-invasive vagus nerve stimulation ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,522,171,532]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heart rate variability ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,533,201,543]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Autonomic nervous system ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,544,231,554]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Parasympathetic nervous system ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,554,183,564]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Neuro-cardiac coupling ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[334,363,453,375]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABSTRACT ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[332,388,937,461]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Background: Transcutaneous auricular Vagus Nerve Stimulation (taVNS) is a non-invasive neuromodulation technique that may constitute an effective treatment for a wide range of neurological, psychiatric, and medical conditions. One key challenge in taVNS research is the high interindividual response variability. To gain an understanding of this variability, reliable biomarkers for taVNS responsiveness would be highly desirable. In this study, we investigated physiological candidate biomarkers while systematically varying stimulation conditions and observing physiological state characteristics. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[332,461,937,534]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methods: Forty-four healthy young adults received taVNS and sham-stimulation. Subjects were pseudorandomly assigned to stimulation of the left or right ear. Each subject underwent six blocks of stimulation. Across blocks, respiration-locking (inhalation-locked taVNS vs. exhalation-locked taVNS vs. sham) and the electrode location (tragus vs. cymba conchae) were varied. We analyzed heart rate (HR), various heart rate variability (HRV) scores, and neuro-cardiac coupling (NCC), indexed by the relationship between electroencephalographic delta power and heartbeat length. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[332,534,937,582]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results: We observed an effect of taVNS on HR and HRV scores during, but not after stimulation. The direction of the effects was consistent with parasympathetic activation. We did not observe any systematic influence of the stimulation conditions that we varied. However, we found baseline NCC scores to be significant predictors for the individual effect of taVNS on HRV scores. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[332,582,937,617]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conclusion: Cardiac effects of taVNS indicate parasympathetic activation. These effects were short lived, which might explain that some previous studies were unable to detect them. We propose NCC as a novel candidate biomarker for responsiveness to taVNS. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[334,617,937,629]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"© 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[584,630,937,641]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"license (http://creativecommons.org/licenses/by-nc-nd/4.0/). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,691,149,704]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,717,487,810]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Recent years have seen a growing interest in transcutaneous auricular Vagus Nerve Stimulation (taVNS), on the part of both researchers and clinicians. TaVNS holds great promise as a low-risk and low-cost treatment in an impressively wide range of medical fields such as neurology, psychiatry, cardiology. However, empirical findings have been varied, and include a significant proportion of clinical non-responders [21], as well as non-replications of earlier ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,691,937,823]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"findings [11]. A concerted effort is therefore currently being made to determine biomarkers for taVNS responsiveness, i.e., physiological readouts that can reliably monitor taVNS effects and/or predict whether a subject will respond to taVNS. Any biomarkers that are reproducibly associated with – but not necessarily caused by – the condition of interest [31], could be used to titrate stimulation parameters (i.e., current intensity, pulse width, stimulation frequency), identify optimal stimulation targets within the auricle and/or detect susceptible physiological states, e.g., during the respiratory cycle [10,19,40]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,823,937,902]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Candidate taVNS biomarkers include cardiac, neurophysiological, and biochemical readouts [10]. Electrocardiographic (ECG) metrics are considered to be among the most promising candidate biomarkers [17,20], for two reasons: Firstly, ECG is inexpensive, and quickly and safely applicable in virtually all patient subpopulations, unlike, for example, magnetic resonance imaging-based ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[403,56,591,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Brain Stimulation 14 (2021) 209-216 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[58,85,166,157]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"header"},{"bbox":"[60,160,163,175]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ELSEVIER ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[366,89,635,102]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Contents lists available at ScienceDirect ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[401,119,601,139]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Brain Stimulation ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[215,158,786,172]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"journal homepage: http://www.journals.elsevier.com/brain-stimulation ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[838,81,937,174]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"BRAIN ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[57,847,485,868]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"* Corresponding author. Institute for Neuromodulation and Neurotechnology, University of Tuebingen, Otfried-Mueller-Str.45, 72076, Tuebingen, Germany. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[60,870,196,880]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"** Corresponding author. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[58,881,485,902]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"E-mail addresses: marius.keute@uni-tuebingen.de (M. Keute), alireza. gharabaghi@uni-tuebingen.de (A. Gharabaghi). ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[57,912,265,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1016/j.brs.2021.01.001 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[58,925,937,947]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1935-861X/© 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[60,80,484,185]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"biomarkers [32,45]. Secondly, there is a clear physiological rationale for a relationship between taVNS and cardiac readouts, since the vagus nerve is involved in the autonomic regulation of heart rate (HR), heart rate variability (HRV) and blood pressure (BP) [14,27]. Accordingly, animal studies have confirmed cardiac effects of (invasive) VNS [8,9,13,25,28,29]. Likewise, a growing number of human studies have shown effects of taVNS on HR and HRV, albeit the evidence is less consistent between studies $($ ; [6,17,18,43,44]). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,185,484,277]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This lack of consistency of physiological responses to taVNS could be due to individual trait and state characteristics, such as the auricular innervation pattern [36], pre-stimulation vagal tone [17], or the respiration cycle: a recent study found effects of taVNS on brainstem activations and HRV when taVNS was delivered during exhalation but not during inhalation [40]. In the present study, we aimed to replicate this respiratory dependency of taVNS effects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,278,484,566]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Several approaches have been proposed to control for individual baseline characteristics. While methods to map the individual auricular innervation pattern are still under development [26], it is relatively straightforward to take the baseline vagal tone into account, as indexed by ECG metrics [41]. On the other hand, taVNS response variability could be driven by characteristics of the stimulation protocol. To date, a generally accepted standard taVNS protocol does not exist, and stimulation parameters, including current intensity and pulse frequency, appear to exert complex, partly non-monotonic (e.g., U-shaped) and overall elusive influences on stimulation effects [1,7,23,46]. It has also been suggested that various stimulation locations within the auricle may activate different neural pathways, and that the ability to recruit the vagus nerve differs with the stimulation location, given the individual anatomical differences, respectively [12,36,45]. In addition, it has been claimed that taVNS at the left vs. right ear entails different cardiac effects. While no substantial evidence in support of this claim is currently available [16], there is, in general, clear evidence for a lateralization of vagal efferent functions [22,34]. In the present study, we systematically varied the stimulated ear and the electrode location within the auricle to test for an impact on cardiac tavNS effects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,568,484,659]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A recent study reported that beat-to-beat HR variations at rest are predicted by EEG delta power around each heartbeat, and that the strength of this association is correlated with HRV indices, suggesting that the coupling between delta power and heart rate can serve as a novel index of (vagally mediated) neuro-cardiac autonomic control [35], thereby rendering it a potentially promising predictor for taVNS responsiveness. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,660,484,856]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In sum, individual trait and state characteristics as well as characteristics of the stimulation protocol probably contribute to taVNS response variability. The number of different factors that might contribute to taVNS responsiveness, including mutual interactions, highlights the importance of biomarkers in determining the individual optima in this high-dimensional parameter space. In this study, we have three goals: Firstly, we intend to replicate cardiac effects of taVNS so as to further establish them as potential biomarkers. Secondly, we shall examine whether a variation in respiration-locking of taVNS (inhalation-vs. exhalation-locked), stimulation location (tragus vs. cymba conchae), and stimulated ear (left vs. right) systematically modulates cardiac effects of taVNS. Thirdly, we aim to ascertain whether and how the individual prestimulation strength of neuro-cardiac coupling (NCC) can predict the individual cardiac response to taVNS. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,81,571,92]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,107,657,119]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Subjects and procedure ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,132,936,250]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Forty-four healthy young [5] adults $(\\mathrm{M} = 28.2 \\pm 5.6$ years of age, 22 females) participated in this study. All were right-handed and had no history of neurological, neurosurgical, or psychiatric, or cardiological disease or treatment (all by self-report). Subjects covered a relatively wide range of height $(\\mathrm{M} = 173.5 \\pm 8.7$ cm; minimum: $160$ cm; maximum: $190$ cm), weight $(\\mathrm{M} = 69.4 \\pm 13.8$ kg; minimum: $48$ kg; maximum: $118$ kg) and body-mass indices (BMI, $\\mathrm{M} = 22.9 \\pm 3.6$ ; minimum: 17; maximum: 39.4). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,250,936,356]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Subjects were seated comfortably in a reclining chair in a dimly lit room. We prepared various physiological recordings: 59 channel EEG (10-5 montage, $1000\\mathrm{Hz}$ sampling frequency, BrainAmp, BrainProducts GmbH), ECG (two-lead chest montage), electromyography (from several arm muscles, EMG), electrogastrography (EGG), electrooculography (EOG), pupillometry (Pupil Core Eye-tracking Headset, pupil labs GmbH), and respiration (GoDirect respiration belt, Vernier, Inc.) were continuously measured. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,356,936,619]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Throughout the experiment, participants were at rest, with the instruction to follow a paced breathing rhythm, with 4 s of inhalation, 4 s of exhalation, and 2 s of rest per cycle. Subjects were instructed to focus on their breath, and try to ignore the stimulation. The breathing cycle was visually prompted by a waxing and waning blue circle on the screen, and monitored using a respiration belt (see Fig. 1C). Paced breathing was chosen over free breathing in an aim to control for the number of (respiration-locked) stimulation pulses delivered, and to minimize random fluctuations of respiratory sinus arrhythmia (RSA). The experiment was carried out in one session which was divided into six blocks. Across the blocks, stimulation conditions were systematically varied, see section 'Electrical Stimulation'. Each block consisted of a resting physiological measurement (2 min), an intervention (taVNS or sham, 5 min), and a post-intervention resting physiological measurement (2 min). The experiment was approved by the ethics committee of the medical faculty at the University of Tuebingen, and all procedures were carried out in accordance with the Declaration of Helsinki. All participants provided their informed written consent prior to the experiment. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,646,643,656]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electrical Stimulation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,670,936,829]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electrical stimulation was administered using a handheld bipolar stimulation electrode (Spes Medica Neurotools, see photograph in the Supplementary Material) which delivered rectangular biphasic square pulses with a pulse length of $100~\\mu \\mathrm{s}$ and a current intensity (peak-to-peak) of $2\\mathrm{mA}$ . Electrical stimulation was delivered in bursts of five pulses, with a pulse-onset asynchrony of $40~\\mathrm{ms}$ (i.e., intra-burst frequency of $25\\mathrm{Hz}$ ) and a burst-onset asynchrony of $1\\mathrm{s}$ (i.e., burst frequency of $1\\mathrm{Hz}$ , see Fig. 1B for illustration) using a programmable current stimulator (Multichannel Systems, Harvard Bioscience, Inc.). During the sham conditions, the electrode was held at the cymba conchae or tragus, respectively, but no current was delivered. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,831,936,868]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Across the six blocks, two stimulation parameters were systematically varied: respiration-locking of stimulation (stimulation during inhalation vs. stimulation during exhalation vs. sham, see ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,58,260,66]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"M. Keute, K. Machetanz, L. Berelidze et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[756,58,937,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Brain Stimulation 14 (2021) 209-216 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[489,945,507,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"210 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[171,80,467,257]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0743/98b571fa4beb3b56eb5882058f9223efa51b6d10a80617b6b15217b630e514fd.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[478,80,823,233]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0530/173b5e3d6359a035d2a2a36ddfc0b12a7a2d36f91d57f6facafb4605a83c166d.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[173,259,591,361]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0475/a316cf94a345562a0f2531584e60a3fe7ff79a1bfe1a9b89fe0af49d837a28db.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[611,239,763,424]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 1. A: Illustration of the ECG and EEG analysis process. B. Illustration of electrode locations and stimulation protocol. C: Illustration of the visual breathing cue and exemplary respiration belt data. Red and blue vertical lines illustrate stimulation bursts locked to inhalation and exhalation, respectively. D: Illustration of the condition assignment procedure. For each subject, the stimulated ear was selected pseudo-randomly (top row). For each block, electrode location (cymba vs. tragus) as well as respiration locking (red: inhalation-locked, blue: exhalation-locked, black: sham) were selected by pseudo-random permutation. All six possible combinations of location and respiration-locking were conducted with each subject. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) \"]","image_footnote":"[]","img_path":"images/0905/5993b9768e99e25a27b3da1d558799d306d7feb7f2921463db5ca2bcd2a809d4.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[55,510,485,563]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Fig. 1C), and electrode location (cymba conchae vs. inner tragus auricularis, see Fig. 1B and Supplementary Figures). As an additional between-subject factor, participants were pseudo-randomly assigned to stimulation of the left or right ear (22 subjects each). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,563,485,617]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Since stimulation was locked to the 4 s periods of inhalation and exhalation, respectively, four bursts were administered per respiration cycle, each followed by a 6-s interval without stimulation. The order of the six blocks was pseudo-randomized across subjects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,633,174,646]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ECG data analysis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,659,487,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"All HR-related scores were derived from ECG data using the BioSPPy package [15] and custom code written in Python 3. R-peaks were detected automatically and verified by visual inspection. The intervals between successive R-peaks (referred to as RRi, see Fig. 1 A) and instantaneous HR, i.e., the linearly interpolated inverse of RRi, were the basis for the subsequent calculation of all following metrics. We analyzed mean HR per subject, condition, and time (pre, stim, post). For statistical analyses, all scores were baseline adjusted to the pre-measurement, see section 'Statistical analyses'. To gain a better understanding about the temporal evolution of stimulation-related HR changes, we visually inspected instantaneous HR over the time course of stim and post. For visualization only (Fig. 2D), we smoothed the HR time course with a $20\\mathrm{~s}$ moving-average filter to suppress respiratory sinus arrhythmia (see section 'Statistical analyses') and to make any slower HR changes visible. To quantify RSA, we averaged instantaneous HR across the paced breathing cycles (10s, starting with the inhalation cue, see Supplementary Figures). Each epoch was mean-centered (to the overall mean of the recording), and multilevel regression models were used to test for an effect of taVNS, as described in the section 'Statistical analyses'. Furthermore, we calculated the following HRV ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,509,939,788]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"scores: Root mean squares of successive differences (RMSSD), i.e., the square root of the mean of squared differences between successive R Ri. We also calculated the conceptually similar Standard deviation of $RRi$ (SDNN). The PNN50 score is defined as the percentage of R Ri that differs from the preceding R Ri by more than 50 ms among all R Ri. These time-domain scores represent the global beat-to-beat variability of R Ri. Frequency domain scores, on the other hand, are obtained from a spectral analysis of instantaneous HR. They represent the strength of HR change over a given time window or at a given frequency. We take two frequency domain HRV scores into consideration. High-frequency HRV (HF) is the power spectral density (PSD) of HR changes at a frequency between 0.15 and 0.4 Hz. The LF/HF score is defined as the ratio between low- $(0.04 - 0.15\\mathrm{Hz})$ and high-frequency HRV. It is believed to reflect the current balance between sympathetic and parasympathetic activation. Finally, we calculated SD1/SD2, a nonlinear HRV score calculated from Poincare recurrence matrices, i.e., a matrix representation of each $\\mathsf{RRi}_{\\mathrm{t}}$ and its subsequent $\\mathsf{RRi}_{\\mathrm{t + 1}}$ . SD1/SD2 is defined as the ratio of the standard deviations of the two principal components of the Poincare recurrence matrix. It provides an estimation of signal unpredictability/complexity [41]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,805,660,819]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Neuro-cardiac coupling ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,831,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In accordance with the findings of a recent study [35], we determined the strength of NCC as the relationship between EEG delta power around each R-peak and occurrence of a long vs. short heartbeat. A heartbeat was defined as being long or short if the interval passing between the current and the subsequent R-peak (RRi) was in the upper or lower third of all RRi in the same recording, similar to the methodology described by Ref. [35]. EEG data were bandpass $(0.3 - 35\\mathrm{Hz}$ , 4th order Butterworth filter) and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,56,262,66]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"M. Keute, K. Machetanz, L. Berelidze et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[754,56,937,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Brain Stimulation 14 (2021) 209-216 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[487,945,507,955]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"211 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,81,440,344]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0175/a320bd9702d3471128bc30a3dc3340a042e65fd6e5e2150b06143e84bd930f0a.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[457,97,781,340]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0471/d2c1b8f4da2a5f7359b56aeab71b0c85d26daca736253cb436c01db6876305fc.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[186,346,357,601]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0960/9900365f9e1b91de7b64bf833b4c7c7c8fed2c1e55c8628926d8da575b453d1a.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[405,378,811,611]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 2. A. Mean HR per subject, time and condition. B. Change to baseline (pre) in beats per minute. C. Change to baseline, resolved by all fixed factors. D. Change to baseline, time-resolved and moving-average smoothed (window length: 20s). Ripples in the curves are the residual RSA. \"]","image_footnote":"[]","img_path":"images/0929/25eeaeeb06654b06d2c0b49178dfadda17ecdb43c3df4be422424448249d3876.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[60,664,487,930]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"notch (48–52 Hz, 4th order Butterworth filter) filtered. Corrupted channels were identified by visual inspection on the basis of intra-channel variance, and excluded from further analysis. Ocular and muscular artifacts were removed using independent component analysis (ICA) based on correlations between the ICA components and the vertical EOG, horizontal EOG, and envelope of the masseter EMG, respectively. To assess NCC, we divided the pre- and post-stimulation EEG data into 1.2 s epochs, starting 0.6 s before each of the R-peaks detected in the simultaneously recorded ECG. Segments with remaining artifacts were excluded on the basis of a threshold criterion $(\\pm 80~\\mu \\mathrm{V})$ . We determined power spectral density (PSD) for each segment using Fast Fourier Transform (FFT) with Hann-tapered windows, zero-padded to a total window length of 2000 samples (2s). PSD values were log-transformed and averaged across delta frequencies (0.5–4 Hz). We defined seven frontocentral electrodes (Fp1, Fp2, F3, F4, Fz, FC3, FC4) as region of interest (ROI), following the results reported by Ref. [35]. Delta power, averaged across the ROI and z-standardized, served as predictor in a logistic model, predicting for each R-peak whether the subsequent R-peak belongs to the lower (short heartbeat) or upper (long ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,664,937,706]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"heartbeat) third of all RRi. We used the subject-and-condition-wise regression weight, expressed in log-odds per standard deviation, as a measure for the strength and direction of NCC. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,726,633,738]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Statistical analyses ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,752,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"All scores were analyzed using linear multilevel regression models (LMM) with subject-wise random intercepts and by-subject random slopes for all within-subject effects to account for repeated measurements, i.e., a maximal random effects structure, as is recommended for the procurement of generalizable results [4]. SDNN, RMSSD, HF, LF/HF, and SD1/SD2 were log transformed prior to entering the LMM to approximate normal distributions. PNN50 was converted to log-odds. All scores were baseline-corrected to the respective pre-measurement. Fixed factors were time (on-intervention vs. post-intervention), taVNS (taVNS vs. sham), stimulated ear (left vs. right), electrode placement (tragus auricularis vs. cymba conchae), and a time $\\times$ taVNS interaction, reflecting an altered time course of HRV in taVNS conditions compared to sham. P-values were calculated from the model F- or t-values, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,56,262,66]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"M. Keute, K. Machetanz, L. Berelidze et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[754,56,937,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Brain Stimulation 14 (2021) 209-216 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[487,945,510,955]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"212 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[55,79,487,172]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"respectively, using Satterthwaite approximations for (denominator) degrees of freedom. Statistical modeling and testing were carried out in R using the packages lme4 and lmerTest. We conducted post-hoc comparisons by fitting and testing reduced LMM to subsets of the data (e.g., taVNS data only during intervention). To compare baseline characteristics between active and sham blocks, we used non-baseline-corrected values. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,190,225,205]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data and code availability ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[55,216,485,284]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Python and R code used for data analysis will be made available on Github (https://github.com/mkeute). The data will be available from the corresponding author upon request, as the ethics approval does not allow uploading the datasets to a publicly available repository. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,302,112,315]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[58,327,127,341]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heart rate ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,354,485,684]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HR changed significantly over time $(\\mathrm{F} = 41.03, \\mathrm{p} < .001)$ . Furthermore, there was a main effect of electrode location on HR $(\\mathrm{F} = 6.42, \\mathrm{p} = .016)$ , as well as a time $\\times$ taVNS interaction $(\\mathrm{F} = 4.54, \\mathrm{p} = .011)$ , but no main effects of taVNS or stimulated ear (both $\\mathrm{F} < 0.6$ , both $\\mathrm{p} > .4$ ). Post-hoc tests revealed that the main effect of time was driven by an increase in HR post-stimulation $(\\mathrm{t} = 5.16, \\mathrm{p} < .001)$ , but that HR did not differ significantly from baseline during stim $(\\mathrm{t} = 0.84, \\mathrm{p} = .403)$ . Conversely, HR change to baseline was significantly different between sham and taVNS during stim $(\\mathrm{t} = -2.24, \\mathrm{p} = .030)$ , but not post-stim $(\\mathrm{t} = 0.60, \\mathrm{p} = .549)$ . When considering taVNS data only and separately for stim and post, we found neither main effects of the location or side of stimulation, nor any interaction effects (see Supplementary Results). Baseline HR was not different between sham and taVNS blocks $(\\mathrm{t} = 0.01, \\mathrm{p} = .992)$ . Moreover, excluding inhalation locked and exhalation-locked taVNS data, respectively, did not lead to any substantial changes in the pattern of significant effects (see Supplementary Results). Visual inspection of the HR time course (Fig. 2D) revealed that the post-stim HR increase relative to baseline was driven by a transient rebound immediately upon stimulation offset and sham intervention offset, respectively. Furthermore, the relative HR decrease during taVNS was predominantly driven by an HR decrease in the first half of the stimulation period (i.e., about $2.5\\mathrm{min}$ ), whereas HR tended to return to the pre-stimulation level in the second half of the stimulation period. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,703,235,716]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Respiratory sinus arrythmia ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[55,728,485,809]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Overall, subjects adhered well to the paced breathing rhythm, with a mean phase locking value $\\mathrm{PLV} = .78 \\pm 0.16$ (see Supplementary Methods). Mean RSA (peak-to-peak) during the intervention was $15.59 \\pm 5.65$ bpm (see Supplementary Figures). There were no main effects of condition $(\\mathrm{F} = 2.02, \\mathrm{p} = .140)$ , ear $(\\mathrm{F} = 0.56, \\mathrm{p} = .460)$ , or of location $(\\mathrm{F} = 0.210, \\mathrm{p} = .647)$ on peak-to-peak RSA, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,854,485,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0560/ca843f65ed589625558c3276d46f2801a51b791af8c18cee530b0b6e15768bce.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":"<table><tr><td></td><td>HR</td><td>SDNN</td><td>RMSSD</td><td>PNN50</td><td>HF</td><td>LF/HF</td><td>SD1/SD2</td></tr><tr><td>time</td><td>41.03</td><td>2.35</td><td>8.69</td><td>13.62</td><td>4.80</td><td>1.05</td><td>10.14</td></tr><tr><td>taVNS</td><td>0.51</td><td>0.00</td><td>1.17</td><td>1.20</td><td>0.01</td><td>0.20</td><td>1.48</td></tr><tr><td>location</td><td>6.24</td><td>0.03</td><td>0.17</td><td>1.71</td><td>0.46</td><td>0.04</td><td>0.24</td></tr><tr><td>ear</td><td>0.06</td><td>0.30</td><td>0.23</td><td>0.16</td><td>0.00</td><td>0.02</td><td>0.04</td></tr><tr><td>time x taVNS</td><td>4.54</td><td>3.77</td><td>7.24</td><td>3.81</td><td>5.74</td><td>4.52</td><td>2.84</td></tr></table>","table_caption":"[\"Table 1 F-values for fixed effects. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[507,79,937,108]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"nor did condition interact with ear $(\\mathrm{F} = 2,30, \\mathrm{p} = .108)$ or with location $(\\mathrm{F} = 1.16, \\mathrm{p} = .316)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,119,648,134]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heart rate variability ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,146,937,412]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The results of the main statistical analysis are summarized in Tables 1 and 2. No main effects of taVNS, location, or ear were found for any of the HRV scores. A significant time $\\times$ taVNS interaction was, however, found for SDNN, RMSSD, PNN50, HF, and LF/HF, and a marginally significant interaction for SD1/SD2. Much like in HR (see above), we observed that most HRV scores significantly changed over time, across taVNS and sham. Post-hoc comparisons are summarized in Tables 3 and 4. During stimulation, we found the overall (across sham and taVNS) change to baseline to be significantly different from zero for all time-domain HRV scores, HF, and SD1/SD2. Moreover, we found significant differences between sham and taVNS during stimulation for RMSSD, PNN50, and SD1/SD2 (see Fig. 3A). Post-stimulation, we found differences to baseline for some scores, but no significant differences between taVNS and sham. We found no significant effects of respiration-locking, ear or location in the post-hoc comparisons. Baseline HRV scores were not significantly different between sham and taVNS blocks. In addition, the exclusion of inhalation-locked and exhalation-locked taVNS data, respectively, did not lead to any substantial changes in the pattern of significant effects (see Supplementary Results). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,424,660,438]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Neuro-cardiac coupling ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,451,937,622]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We could not establish any overall trend for a relationship between delta power and heartbeat length at baseline recordings (regression weights were, on the group level, not significantly different from zero, $t = 0.134$ , $p = .894$ ). Neither was NCC different between pre- and post-measurements, i.e., it was unaffected by the intervention ( $t = 1.523$ , $p = .128$ ). Finally, baseline NCC did not differ between sham and taVNS blocks ( $t = 1.159$ , $p = .253$ ). However, baseline NCC was a significant predictor for the change in SDNN between baseline and taVNS ( $t = 3.095$ , $p = .002$ , see Fig. 3 B), as well as for the change in HF ( $t = 2.28$ , $p = .024$ ) and SD1/SD2 ( $t = 2.396$ , $p = .017$ ), but not for any of the other HR/HRV metrics (all $|t| < 1.65$ , $p > .1$ ). All effects were positive, i.e., a higher (positive) NCC predicted a higher (positive) taVNS effect. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,636,586,649]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Discussion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,663,759,678]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Summary and interpretation of findings ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,689,937,809]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this study, we aimed to corroborate cardiac effects of taVNS, examine the modulation of such an effect by variations in respiration-locking, stimulation location, and the stimulated ear, as well as investigate the potential of individual neuro-cardiac baseline characteristics to predict the responses to taVNS. We identified cardiac taVNS effects, i.e., decreased HR and increased HRV scores RMSSD, PNN50, and SD1/SD2 (but not SDNN, HF, LF/HF), which is consistent with previous findings and, as an overall pattern, reflective of parasympathetic activation [17]. Overall, similar effects ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,854,937,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0347/f0c36a6072e6c7e1fda1527fd8c2a1d26f399517068ca4e40ef74c8e6308dd61.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":"<table><tr><td></td><td>HR</td><td>SDNN</td><td>RMSSD</td><td>PNN50</td><td>HF</td><td>LF/HF</td><td>SD1/SD2</td></tr><tr><td>time</td><td>.000</td><td>.104</td><td>.000</td><td>.000</td><td>.011</td><td>.352</td><td>.000</td></tr><tr><td>taVNS</td><td>.479</td><td>.984</td><td>.285</td><td>.279</td><td>.925</td><td>.654</td><td>.230</td></tr><tr><td>location</td><td>.016</td><td>.870</td><td>.680</td><td>.197</td><td>.499</td><td>.840</td><td>.624</td></tr><tr><td>ear</td><td>.806</td><td>.587</td><td>.630</td><td>.695</td><td>.953</td><td>.880</td><td>.837</td></tr><tr><td>time x taVNS</td><td>.011</td><td>.024</td><td>.001</td><td>.023</td><td>.003</td><td>.011</td><td>.059</td></tr></table>","table_caption":"[\"Table 2 p-values for fixed effects. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[58,56,262,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"M. Keute, K. Machetanz, L. Berelidze et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[754,56,937,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Brain Stimulation 14 (2021) 209-216 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[487,944,510,955]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"213 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[58,104,937,184]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0867/c040995c4bd4b0848cd59aa883fdc0fec5880486860ce12c94c7d243e4b6b6d9.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td></td><td>HR</td><td>SDNN</td><td>RMSSD</td><td>PNN50</td><td>HF</td><td>LF/HF</td><td>SD1/SD2</td></tr><tr><td>taVNS vs. sham during pre</td><td>0.01</td><td>0.38</td><td>-0.72</td><td>-0.54</td><td>0.2</td><td>-0.27</td><td>-1.59</td></tr><tr><td>taVNS vs. sham during stim</td><td>-2.24</td><td>1.50</td><td>2.68</td><td>2.54</td><td>1.84</td><td>-1.21</td><td>2.22</td></tr><tr><td>taVNS & sham vs. baseline during stim</td><td>0.84</td><td>-2.84</td><td>-3.77</td><td>-3.04</td><td>-3.51</td><td>1.86</td><td>-2.22</td></tr><tr><td>taVNS vs. sham during post</td><td>0.60</td><td>-0.91</td><td>-0.68</td><td>-0.15</td><td>-1.44</td><td>1.71</td><td>0.02</td></tr><tr><td>taVNS & sham vs. baseline during post</td><td>5.16</td><td>-0.84</td><td>-2.72</td><td>-3.60</td><td>-1.73</td><td>-0.14</td><td>-2.89</td></tr></table>","table_caption":"[\"Table 3 t-values for post-hoc comparisons. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[60,208,484,259]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"have already been reported, albeit some studies found no cardiac effects of taVNS [10]. This could be due to trait and state characteristics and the stimulation protocol, as detailed in the introduction. We found no effect of taVNS on peak-to-peak RSA. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,261,484,470]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In accordance with earlier findings, HR changes were visible soon after taVNS onset [24]. No cardiac effects extended beyond stimulation offset. This transient nature of cardiac taVNS effects may provide a further explanation for the inconsistencies between studies. Immediately upon stimulation offset, we detected a HR rebound that occurred across sham and taVNS conditions. This was surprising, since a HR rebound resulting from reinstatement of sympathetic activation after taVNS offset would not be expected to follow the sham stimulation. Very similar findings have, however, already been reported [2], and one possible interpretation is that the HR rebound is partially caused by a cognitive process (e.g., appraisal of the change between intervention and rest). Finally, we demonstrated that the use of a novel stimulation protocol, with intermittent stimulation bursts rather than continuous stimulation at, e.g., $25\\mathrm{Hz}$ , leads to similar cardiac effects as standard taVNS protocols while reducing the overall current delivered. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,472,484,655]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Moreover, we found no evidence for any systematic difference between inhalation-locked and exhalation exhalation-locked taVNS, which is surprising, since a recent study [40] showed a very prominent influence of taVNS respiration-locking on brainstem activations and HF-HRV, and exhalation-locked taVNS has been used in patient studies for several years [33]. Similarly, we found no evidence that taVNS effects were systematically modulated by variations in stimulation location (tragus vs. cymba conchae) or stimulated ear (right vs left). In sum, none of the stimulation conditions that were varied in this study provided a satisfactory explanation for cardiac response variance. With regard to the stimulated ear, this was anticipated based on anatomical considerations [16] and experimental evidence from left- and right-sided invasive VNS [37]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,656,484,786]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"With respect to stimulation locations (cymba conchae vs. tragus), on the other hand, the question as to whether both targets equally recruit the auricular branch of the vagus nerve is still under debate. In particular, the idea that the cymba conchae is more strongly or more consistently innervated by the vagus nerve than the tragus is mostly based on a single study [36], with partially inconsistent results [12]. Other studies suggest similar vagal innervation patterns for the tragus and cymba conchae [3], and several taVNS studies have shown comparable results for both stimulation targets [3,45], in line with our findings. In sum, the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,208,936,233]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"existing evidence supports a similar vagus nerve recruitment at both locations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,235,936,602]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, we calculated an index of neuro-cardiac autonomic control that was first described in a recent study [35]. On the group level, we were unable to replicate the reported relationship between EEG delta power and heartbeat length, possibly on account of a slightly different methodology than that used in the original study. In particular, to avoid EEG artifacts of previous or subsequent R-peaks, which could potentially introduce an artifact in the delta frequency range, we used a shorter window length for the spectral analysis (1.2 s rather than 4 s). Importantly, however, we found that individual NCC regression weights predicted stimulation-induced cardiac changes (SDNN, SD1/SD2 and HF). The relationship was positive, i.e., a higher positive NCC at baseline predicted a stronger taVNS effect, which is in agreement with the findings by Ref. [35]; who suggested that a stronger positive NCC reflects a stronger vagally mediated brain-heart communication. Interestingly, we found that NCC was related to SDNN and HF, two of the HRV scores that were not significantly modulated by taVNS on the group level (post-hoc contrast), i.e., where taVNS effects had higher interindividual variability, which in turn can be explained by the NCC. Crucially, NCC did not baseline-to-intervention changes for any HRV metric in the sham condition, i.e., its predictive value was specific to taVNS. In sum, we found tentative evidence that NCC, as assessed by baseline correlations between delta power and heartbeat length, may constitute a promising biomarker for responsiveness to taVNS, even though the precise physiological interpretation of the NCC score and its relationship to taVNS effects warrants further investigation, e.g., with longer baseline recording periods. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,624,581,635]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Limitations ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,650,936,807]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Our sample size was limited in the light of the experimental design, i.e., our study may well have been underpowered for the detection of subtle effects such as three- and four-way interaction effects between stimulation conditions. The stimulation paradigm that was used in our study (burst stimulation) is novel and has not yet been formally evaluated and compared to other, more established protocols. Moreover, we did not use an active sham condition (e.g., earlobe stimulation), but instead held the electrode at the stimulation sites without delivering current. The somatosensory quality may thus have differed between conditions. We cannot, therefore, fully rule out that the findings may be partially driven by somatosensory or cognitive processes. However, some HRV effects ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,854,937,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/1021/bf165d0960d1e6e3454e65601215c254e478820c4999750aa792aef913acb663.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td></td><td>HR</td><td>SDNN</td><td>RMSSD</td><td>PNN50</td><td>HF</td><td>LF/HF</td><td>SD1/SD2</td></tr><tr><td>taVNS vs. sham during pre</td><td>.992</td><td>.703</td><td>.476</td><td>.589</td><td>.845</td><td>.791</td><td>.116</td></tr><tr><td>taVNS vs. sham during stim</td><td>.030</td><td>.139</td><td>.010</td><td>.013</td><td>.071</td><td>.229</td><td>.031</td></tr><tr><td>taVNS & sham vs. baseline during stim</td><td>.403</td><td>.006</td><td>.000</td><td>.003</td><td>.001</td><td>.070</td><td>.029</td></tr><tr><td>taVNS vs. sham during post</td><td>.549</td><td>.366</td><td>.498</td><td>.883</td><td>.152</td><td>.092</td><td>.987</td></tr><tr><td>taVNS & sham vs. baseline during post</td><td>.000</td><td>.406</td><td>.009</td><td>.001</td><td>.086</td><td>.890</td><td>.006</td></tr></table>","table_caption":"[\"Table 4 p-values for post-hoc comparisons. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[60,58,260,66]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"M. Keute, K. Machetanz, L. Berelidze et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[756,58,937,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Brain Stimulation 14 (2021) 209-216 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[489,945,507,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"214 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[174,81,327,293]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0721/1f18302004264962c6771c54248f23a8fcc4eb9d88a4d0cbd3d802bba4231bdc.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[341,80,515,292]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0762/bc41d3022af9294bb74a72d88f1c574fe5b022097bdc483a98f5b75575e98bd3.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[519,97,665,291]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0134/8bc8d3ac4ef574465900d65e45a0fab23a1fa58a48fa0e2e880822758aadb7da.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[687,166,823,279]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 3. A. Regression weights and confidence intervals for the taVNS vs. sham post-hoc effect during intervention for all cardiac dependent variables. Significant effects are marked with asterisks. Positive regression weights indicate higher values during taVNS. B: Regression weights and confidence intervals for the prediction of cardiac taVNS effects by baseline NCC. It can be seen that the NCC was a significant predictor for the taVNS effect on HF, SD1/SD2, and SDNN, but for none of the sham effects. \"]","image_footnote":"[]","img_path":"images/0719/5a262c665740734c84b7c8d2d8adcacb9efe8bd9068a964c8d2a535b574f57d7.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,359,485,597]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"observed during and after the sham condition resembled the findings during the stimulation conditions. This suggests that the applied sham approach was at least sufficient to induce unspecific effects similar to those observed in the stimulation condition. However, taVNS also induced specific HRV effects which did not occur during the sham condition and which were predicted by NCC. Moreover, the paced breathing rhythm used in our experiment might limit the interpretation of frequency-domain HRV scores (HF and LF/HF), since the canonical frequency bands for HF $(0.15 - 0.4\\mathrm{Hz})$ do not contain the breathing frequency $(0.1\\mathrm{Hz})$ . To compensate for this limitation, we conducted an additional analysis of RSA, which is reported in the Supplementary Material. Finally, it is an open question what exactly NCC reflects, in particular with respect to causality, i.e., whether NCC indicates central nervous control of vagal and cardiac function, or rather a cortical response to cardiac changes induced by the autonomous nervous system. Furthermore, the mediating role of physiological covariates, especially respiration, warrant further investigation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,620,112,631]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Outlook ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,646,485,804]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It has already been shown that individual patient trait and state characteristics can be predictive of VNS effects, including resting-state brain connectivity [32] and HRV [30]. NCC, as a novel predictive biomarker, has the potential to bridge the gap between the central and autonomic effects of taVNS, branches of research for which no integrative model exists. This might be most relevant for diseases in which a clinical improvement manifests itself in brain and heart functioning alike, e.g., depression [42]. Moreover, a small but growing number of studies on closed-loop taVNS has emerged [38,39], with the aim to optimize the instantaneous autonomic status in real time by coupling taVNS administration to a physiological control signal. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,805,485,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The exact role that NCC could have in this context remains to be determined. In particular, it should be investigated whether intra-individual changes in NCC over longer periods, e.g., several days, reliably predict changes in taVNS responsiveness or whether the NCC-responsiveness relationship that we have reported rather reflects an individual trait that is relatively stable over time. In the latter case, NCC might have a role in selecting patients that are susceptible to taVNS therapy. In the former case, however, NCC could be used as a control signal to, e.g., find the most efficient time windows to deliver taVNS for a given patient. Moreover, it remains ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,359,937,398]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"an open question whether NCC can be manipulated, e.g., via breathing techniques, and if such a manipulation could enable patients to increase their own susceptibility to taVNS treatment. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,399,937,477]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Applying taVNS in such a closed-loop fashion requires the availability of wearable measurement and stimulation devices that work in a highly automatized way and that can be easily used by patients. The development of such devices is underway, even though they are not yet available on the market, to the best of our knowledge. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,503,589,515]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conclusion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,529,937,622]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"TaVNS, delivered with a burst protocol, led to HR and HRV changes during the stimulation. These effects could be similarly induced at the right and left ear, at the tragus and cymba conchae and during inhalation inhalation and exhalation. Baseline neurocardiac coupling in the EEG delta band may serve as a predictive biomarker for individual taVNS responsiveness; a finding that requires independent replication. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,648,729,660]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Author contributions statement ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,674,937,742]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MK was responsible for data analysis, interpretation of data, and writing of the manuscript. KM, LB and RB contributed to study design, data acquisition/analysis, and reviewing of the manuscript. AG was responsible for the conception and design of the study, interpretation of data, and writing of the manuscript. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,766,742,779]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Declaration of competing interest ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,791,937,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This research study was supported by the German Federal Ministry of Education and Research [BMBF 13GW0270B, INAUDITAS]. We also acknowledge support by the Open Access Publishing Fund of the University of Tuebingen. None of the authors has potential conflicts of interest to disclose. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,883,739,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Appendix A. Supplementary data ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,910,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Supplementary data to this article can be found online at https://doi.org/10.1016/j.brs.2021.01.001. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,56,262,66]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"M. Keute, K. Machetanz, L. Berelidze et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[754,56,937,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Brain Stimulation 14 (2021) 209-216 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[487,944,507,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"215 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[58,80,134,92]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[65,104,485,878]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[1] Badran BW, Mithoefer OJ, Summer CE, LaBate NT, Glusman CE, Badran AW, DeVries WH, Summers PM, Austelle CW, McTeague LM, Borckardt JJ, George MS. 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Quantifying acute physiological biomarkers of transcutaneous cervical vagal nerve stimulation in the context of psychological stress. Brain Stimul 2019;13(1):47-59. \",\"[20] Gurel NZ, Wittbrodt MT, Jung H, Ladd SL, Shah AJ, Vaccarino V, et al. Automatic detection of target engagement in transcutaneous cervical vagal nerve stimulation for traumatic stress triggers. IEEE J Biomed Health Inf 2020;24(7):1917-25. https://doi.org/10.1101/2020.01.27.20018689. \",\"[21] Hamer HM, Bauer S. Lessons learned from transcutaneous vagus nerve stimulation (tVNS). Epilepsy Res 2019;153:83-4. \",\"[22] Han W, Tellez LA, Perkins MH, Perez IO, Qu T, Ferreira J, Ferreira TL, Quinn D, Liu Z-W, Gao X-B, Kaelberer MM, Bohorquez DV, Shammah-Lagnado SJ, de Lartigue G, de Araujo IE. A neural circuit for gut-induced reward. Cell 2018;175:665-78. https://doi.org/10.1016/j.cell.2018.08.049. e23. \",\"[23] Hulsey DR, Riley JR, Loerwald KW, Rennaker II RL, Kilgard MP, Hays SA. Parametric characterization of neural activity in the locus coeruleus in response to vagus nerve stimulation. Exp Neurol 2017;289:21-30. \",\"[24] Iseger TA, Padberg F, Kenemans JL, Gervitz R, Arns M. Neuro-Cardiac-Guided TMS (NCG-TMS): probing DLPFC-sgACC-vagus nerve connectivity using heart rate – first results. Brain Stimulat 2017;10:1006–8. https://doi.org/10.1016/j.brs.2017.05.002. \"]","page_idx":"7","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[512,80,937,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[25] Iwao T, Yonemochi H, Nakagawa M, Takahashi N, Saikawa T, Ito M. Effect of constant and intermittent vagal stimulation on the heart rate and heart rate variability in rabbits. Jpn J Physiol 2000;50:33-9. https://doi.org/10.2170/jjphysiol.50.33. \",\"[26] Kaniusas E, Kampusch S, Tittgemeyer M, Panetsos F, Gines RF, Papa M, Kiss A, Podesser B, Cassara A, Tanghe E, others. Current directions in the auricular vagus nerve stimulation II—an engineering perspective. Front Neurosci 2019;13:772. \",\"[27] Karemaker JM. How the vagus nerve produces beat-to-beat heart rate variability; experiments in rabbits to mimic in vivo vagal patterns. J Clin Transl Res 2015;1:190-204. \",\"[28] Kuo TB, Lai CJ, Huang Y-T, Yang CC. Regression analysis between heart rate variability and baroreflex-related vagus nerve activity in rats. J Cardiovasc Electrophysiol 2005;16:864-9. \",\"[29] Levy MN, Martin PJ, Iano T, Zieske H. Paradoxical effect of vagus nerve stimulation on heart rate in dogs. Circ Res 1969;25:303-14. \",\"[30] Liu H-Y, Yang Z, Meng F-G, Guan Y-G, Ma Y-S, Liang S-L, Lin J-L, Pan L-S, Zhao M-M, Qu W, Hao H-W, Luan G-M, Zhang J-G, Li L-M. Preoperative heart rate variability as predictors of vagus nerve stimulation outcome in patients with drug-resistant epilepsy. Sci Rep 2018;8:3856. https://doi.org/10.1038/s41598-018-21669-3. \",\"[31] Mischak H, Allmaier G, Apweiler R, Attwood T, Baumann M, Benigni A, Bennett SE, Bischoff R, Bongcam-Rudloff E, Capasso G, others. Recommendations for biomarker identification and qualification in clinical proteomics. Sci Transl Med 2010;2:46ps42. 46ps42. \",\"[32] Mithani K, Mikhail M, Morgan BR, Wong S, Weil AG, Deschenes S, Wang S, Bernal B, Guillen MR, Ochi A, Otsubo H, Yau I, Lo W, Pang E, Holowka S, Snead OC, Donner E, Rutka JT, Go C, Widjaja E, Ibrahim GM. Connectomic profiling identifies responders to vagus nerve stimulation. Ann Neurol 2019;86:743-53. https://doi.org/10.1002/ana.25574. \",\"[33] Napadow V, Edwards RR, Cahalan CM, Mensing G, Greenbaum S, Valovska A, Wasan AD. Evoked pain analgesia in chronic pelvic pain patients using respiratory-gated auricular vagal afferent nerve stimulation. Pain Med 2012;13(6):777-89. \",\"[34] Neuser MP, Teckentrup V, Kühnel A, Hallschmid M, Walter M, Kroemer NB. Vagus nerve stimulation boosts the drive to work for rewards. Nat Commun 2020;11(1):1-11. \",\"[35] Patron E, Mennella R, Benvenuti SM, Thayer JF. The frontal cortex is a heart-brake: reduction in delta oscillations is associated with heart rate deceleration. Neuroimage 2019;188:403-10. \",\"[36] Peuker ET, Filler TJ. The nerve supply of the human auricle. Clin Anat 2002;15: 35-7. \",\"[37] Premchand RK, Sharma K, Mittal S, Monteiro R, Dixit S, Libbus I, KenKnight BH. Autonomic regulation therapy via left or right cervical vagus nerve stimulation in patients with chronic heart failure: results of the ANTHEM-HF trial. J Card Fail 2014;20(11):808-16. \",\"[38] Romero-Ugalde HM, Le Rolle V, Bonnet J-L, Henry C, Mabo P, Carrault G, Hernández Al. Closed-loop vagus nerve stimulation based on state transition models. IEEE Trans Biomed Eng 2018;65:1630-8. \",\"[39] Romero-Ugalde HM, Rolle VL, Bonnet J-L, Henry C, Bel A, Mabo P, Carrault G, Hernández Al. A novel controller based on state-transition models for closed-loop vagus nerve stimulation: application to heart rate regulation. PLoS One 2017;12:e0186068. https://doi.org/10.1371/journal.pone.0186068. \",\"[40] Sclocco R, Garcia RG, Kettner NW, Isenburg K, Fisher HP, Hubbard CS, Ay I, Polimeni JR, Goldstein J, Makris N, Toschi N, Barbieri R, Napadow V. The influence of respiration on brainstem and cardiovascular response to auricular vagus nerve stimulation: a multimodal ultrahigh-field (7T) fMRI study. Brain Stimulat 2019;12:911-21. https://doi.org/10.1016/j.brs.2019.02.003. \",\"[41] Shaffer F, Ginsberg J. An overview of heart rate variability metrics and norms. Front Publ Health 2017;5:258. \",\"[42] Sperling W, Reulbach U, Bleich S, Padberg F, Kornhuber J, Mueck-Weymann M. Cardiac effects of vagus nerve stimulation in patients with major depression. Pharmacopsychiatry 2010;43:7-11. https://doi.org/10.1055/s-0029-1237374. \",\"[43] Stavrakis S, Humphrey MB, Scherlag BJ, Hu Y, Jackman WM, Nakagawa H, Lockwood D, Lazzara R, Po SS. Low-level transcutaneous electrical vagus nerve stimulation suppresses atrial fibrillation. J Am Coll Cardiol 2015;65:867-75. https://doi.org/10.1016/j.jacc.2014.12.026. \",\"[44] Tobaldini E, Toschi-Dias E, Appratto de Souza L, Rabello Casali K, Vicenzi M, Sandrone G, Cogliati C, La Rovere MT, Pinna GD, Montano N. Cardiac and peripheral autonomic responses to orthostatic stress during transcutaneous vagus nerve stimulation in healthy subjects. J Clin Med 2019;8:496. \",\"[45] Yakunina N, Kim SS, Nam E-C. Optimization of transcutaneous vagus nerve stimulation using functional MRI. Neuromodulat Technol Neural Interface 2017;20:290-300. https://doi.org/10.1111/ner.12541. \",\"[46] Antonino D, Teixeira AL, Maia-Lopes PM, Souza MC, Sabino-Carvalho JL, Murray AR, Deuchars J, Vianna LC. Non-invasive vagus nerve stimulation acutely improves spontaneous cardiac baroreflex sensitivity in healthy young men: a randomized placebo-controlled trial. Brain Stimulat 2017;10:875-81. https://doi.org/10.1016/j.brs.2017.05.006. \"]","page_idx":"7","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[58,56,260,66]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"M. Keute, K. Machetanz, L. Berelidze et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[754,56,937,68]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Brain Stimulation 14 (2021) 209-216 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[487,945,510,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"216 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[58,219,813,261]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Neuro-cardiac coupling predicts transcutaneous auricular vagus nerve stimulation effects \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[840,221,890,259]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0673/7b19541e3276b35b8c33d097e50f60d7844d12760483c58a573944e2fdc73d91.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,272,692,307]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Marius Keute*, Kathrin Machetanz, Levan Berelidze, Robert Guggenberger, Alireza Gharabaghi** \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,312,794,335]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Institute for Neuromodulation and Neurotechnology, Department of Neurosurgery and Neurotechnology, And Tuebingen NeuroCampus, University of Tuebingen, Tuebingen, Germany \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,363,223,375]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ARTICLEINFO \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,388,136,399]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article history: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,399,191,409]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received 5 October 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,411,189,419]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received in revised form \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,422,161,431]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"24 November 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,433,189,443]\",\n \"code_body\": null,\n \"code_caption\": null,\n 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\"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,479,171,489]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Auricular stimulation \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,490,257,510]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Transcutaneous auricular vagus nerve stimulation \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,511,257,522]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Non-invasive vagus nerve stimulation \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,522,171,532]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heart rate variability \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,533,201,543]\",\n 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\"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Neuro-cardiac coupling \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[334,363,453,375]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABSTRACT \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[332,388,937,461]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Background: Transcutaneous auricular Vagus Nerve Stimulation (taVNS) is a non-invasive neuromodulation technique that may constitute an effective treatment for a wide range of neurological, psychiatric, and medical conditions. One key challenge in taVNS research is the high interindividual response variability. To gain an understanding of this variability, reliable biomarkers for taVNS responsiveness would be highly desirable. In this study, we investigated physiological candidate biomarkers while systematically varying stimulation conditions and observing physiological state characteristics. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[332,461,937,534]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methods: Forty-four healthy young adults received taVNS and sham-stimulation. Subjects were pseudorandomly assigned to stimulation of the left or right ear. Each subject underwent six blocks of stimulation. Across blocks, respiration-locking (inhalation-locked taVNS vs. exhalation-locked taVNS vs. sham) and the electrode location (tragus vs. cymba conchae) were varied. We analyzed heart rate (HR), various heart rate variability (HRV) scores, and neuro-cardiac coupling (NCC), indexed by the relationship between electroencephalographic delta power and heartbeat length. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[332,534,937,582]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results: We observed an effect of taVNS on HR and HRV scores during, but not after stimulation. The direction of the effects was consistent with parasympathetic activation. We did not observe any systematic influence of the stimulation conditions that we varied. However, we found baseline NCC scores to be significant predictors for the individual effect of taVNS on HRV scores. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[332,582,937,617]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conclusion: Cardiac effects of taVNS indicate parasympathetic activation. These effects were short lived, which might explain that some previous studies were unable to detect them. We propose NCC as a novel candidate biomarker for responsiveness to taVNS. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[334,617,937,629]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"© 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[584,630,937,641]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"license (http://creativecommons.org/licenses/by-nc-nd/4.0/). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,691,149,704]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,717,487,810]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Recent years have seen a growing interest in transcutaneous auricular Vagus Nerve Stimulation (taVNS), on the part of both researchers and clinicians. TaVNS holds great promise as a low-risk and low-cost treatment in an impressively wide range of medical fields such as neurology, psychiatry, cardiology. However, empirical findings have been varied, and include a significant proportion of clinical non-responders [21], as well as non-replications of earlier \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,691,937,823]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"findings [11]. A concerted effort is therefore currently being made to determine biomarkers for taVNS responsiveness, i.e., physiological readouts that can reliably monitor taVNS effects and/or predict whether a subject will respond to taVNS. Any biomarkers that are reproducibly associated with – but not necessarily caused by – the condition of interest [31], could be used to titrate stimulation parameters (i.e., current intensity, pulse width, stimulation frequency), identify optimal stimulation targets within the auricle and/or detect susceptible physiological states, e.g., during the respiratory cycle [10,19,40]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,823,937,902]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Candidate taVNS biomarkers include cardiac, neurophysiological, and biochemical readouts [10]. Electrocardiographic (ECG) metrics are considered to be among the most promising candidate biomarkers [17,20], for two reasons: Firstly, ECG is inexpensive, and quickly and safely applicable in virtually all patient subpopulations, unlike, for example, magnetic resonance imaging-based \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[403,56,591,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Brain Stimulation 14 (2021) 209-216 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[58,85,166,157]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[60,160,163,175]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ELSEVIER \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[366,89,635,102]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Contents lists available at ScienceDirect \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[401,119,601,139]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Brain Stimulation \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[215,158,786,172]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"journal homepage: http://www.journals.elsevier.com/brain-stimulation \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[838,81,937,174]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"BRAIN \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[57,847,485,868]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"* Corresponding author. Institute for Neuromodulation and Neurotechnology, University of Tuebingen, Otfried-Mueller-Str.45, 72076, Tuebingen, Germany. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[60,870,196,880]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"** Corresponding author. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[58,881,485,902]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"E-mail addresses: marius.keute@uni-tuebingen.de (M. Keute), alireza. gharabaghi@uni-tuebingen.de (A. Gharabaghi). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[57,912,265,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1016/j.brs.2021.01.001 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[58,925,937,947]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1935-861X/© 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[60,80,484,185]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"biomarkers [32,45]. Secondly, there is a clear physiological rationale for a relationship between taVNS and cardiac readouts, since the vagus nerve is involved in the autonomic regulation of heart rate (HR), heart rate variability (HRV) and blood pressure (BP) [14,27]. Accordingly, animal studies have confirmed cardiac effects of (invasive) VNS [8,9,13,25,28,29]. Likewise, a growing number of human studies have shown effects of taVNS on HR and HRV, albeit the evidence is less consistent between studies $($ ; [6,17,18,43,44]). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,185,484,277]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This lack of consistency of physiological responses to taVNS could be due to individual trait and state characteristics, such as the auricular innervation pattern [36], pre-stimulation vagal tone [17], or the respiration cycle: a recent study found effects of taVNS on brainstem activations and HRV when taVNS was delivered during exhalation but not during inhalation [40]. In the present study, we aimed to replicate this respiratory dependency of taVNS effects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,278,484,566]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Several approaches have been proposed to control for individual baseline characteristics. While methods to map the individual auricular innervation pattern are still under development [26], it is relatively straightforward to take the baseline vagal tone into account, as indexed by ECG metrics [41]. On the other hand, taVNS response variability could be driven by characteristics of the stimulation protocol. To date, a generally accepted standard taVNS protocol does not exist, and stimulation parameters, including current intensity and pulse frequency, appear to exert complex, partly non-monotonic (e.g., U-shaped) and overall elusive influences on stimulation effects [1,7,23,46]. It has also been suggested that various stimulation locations within the auricle may activate different neural pathways, and that the ability to recruit the vagus nerve differs with the stimulation location, given the individual anatomical differences, respectively [12,36,45]. In addition, it has been claimed that taVNS at the left vs. right ear entails different cardiac effects. While no substantial evidence in support of this claim is currently available [16], there is, in general, clear evidence for a lateralization of vagal efferent functions [22,34]. In the present study, we systematically varied the stimulated ear and the electrode location within the auricle to test for an impact on cardiac tavNS effects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,568,484,659]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A recent study reported that beat-to-beat HR variations at rest are predicted by EEG delta power around each heartbeat, and that the strength of this association is correlated with HRV indices, suggesting that the coupling between delta power and heart rate can serve as a novel index of (vagally mediated) neuro-cardiac autonomic control [35], thereby rendering it a potentially promising predictor for taVNS responsiveness. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,660,484,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In sum, individual trait and state characteristics as well as characteristics of the stimulation protocol probably contribute to taVNS response variability. The number of different factors that might contribute to taVNS responsiveness, including mutual interactions, highlights the importance of biomarkers in determining the individual optima in this high-dimensional parameter space. In this study, we have three goals: Firstly, we intend to replicate cardiac effects of taVNS so as to further establish them as potential biomarkers. Secondly, we shall examine whether a variation in respiration-locking of taVNS (inhalation-vs. exhalation-locked), stimulation location (tragus vs. cymba conchae), and stimulated ear (left vs. right) systematically modulates cardiac effects of taVNS. Thirdly, we aim to ascertain whether and how the individual prestimulation strength of neuro-cardiac coupling (NCC) can predict the individual cardiac response to taVNS. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,81,571,92]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,107,657,119]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Subjects and procedure \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,132,936,250]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Forty-four healthy young [5] adults $(\\\\mathrm{M} = 28.2 \\\\pm 5.6$ years of age, 22 females) participated in this study. All were right-handed and had no history of neurological, neurosurgical, or psychiatric, or cardiological disease or treatment (all by self-report). Subjects covered a relatively wide range of height $(\\\\mathrm{M} = 173.5 \\\\pm 8.7$ cm; minimum: $160$ cm; maximum: $190$ cm), weight $(\\\\mathrm{M} = 69.4 \\\\pm 13.8$ kg; minimum: $48$ kg; maximum: $118$ kg) and body-mass indices (BMI, $\\\\mathrm{M} = 22.9 \\\\pm 3.6$ ; minimum: 17; maximum: 39.4). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,250,936,356]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Subjects were seated comfortably in a reclining chair in a dimly lit room. We prepared various physiological recordings: 59 channel EEG (10-5 montage, $1000\\\\mathrm{Hz}$ sampling frequency, BrainAmp, BrainProducts GmbH), ECG (two-lead chest montage), electromyography (from several arm muscles, EMG), electrogastrography (EGG), electrooculography (EOG), pupillometry (Pupil Core Eye-tracking Headset, pupil labs GmbH), and respiration (GoDirect respiration belt, Vernier, Inc.) were continuously measured. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,356,936,619]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Throughout the experiment, participants were at rest, with the instruction to follow a paced breathing rhythm, with 4 s of inhalation, 4 s of exhalation, and 2 s of rest per cycle. Subjects were instructed to focus on their breath, and try to ignore the stimulation. The breathing cycle was visually prompted by a waxing and waning blue circle on the screen, and monitored using a respiration belt (see Fig. 1C). Paced breathing was chosen over free breathing in an aim to control for the number of (respiration-locked) stimulation pulses delivered, and to minimize random fluctuations of respiratory sinus arrhythmia (RSA). The experiment was carried out in one session which was divided into six blocks. Across the blocks, stimulation conditions were systematically varied, see section 'Electrical Stimulation'. Each block consisted of a resting physiological measurement (2 min), an intervention (taVNS or sham, 5 min), and a post-intervention resting physiological measurement (2 min). The experiment was approved by the ethics committee of the medical faculty at the University of Tuebingen, and all procedures were carried out in accordance with the Declaration of Helsinki. All participants provided their informed written consent prior to the experiment. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,646,643,656]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electrical Stimulation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,670,936,829]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electrical stimulation was administered using a handheld bipolar stimulation electrode (Spes Medica Neurotools, see photograph in the Supplementary Material) which delivered rectangular biphasic square pulses with a pulse length of $100~\\\\mu \\\\mathrm{s}$ and a current intensity (peak-to-peak) of $2\\\\mathrm{mA}$ . Electrical stimulation was delivered in bursts of five pulses, with a pulse-onset asynchrony of $40~\\\\mathrm{ms}$ (i.e., intra-burst frequency of $25\\\\mathrm{Hz}$ ) and a burst-onset asynchrony of $1\\\\mathrm{s}$ (i.e., burst frequency of $1\\\\mathrm{Hz}$ , see Fig. 1B for illustration) using a programmable current stimulator (Multichannel Systems, Harvard Bioscience, Inc.). During the sham conditions, the electrode was held at the cymba conchae or tragus, respectively, but no current was delivered. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,831,936,868]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Across the six blocks, two stimulation parameters were systematically varied: respiration-locking of stimulation (stimulation during inhalation vs. stimulation during exhalation vs. sham, see \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,58,260,66]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"M. Keute, K. Machetanz, L. Berelidze et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[756,58,937,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Brain Stimulation 14 (2021) 209-216 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[489,945,507,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"210 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[171,80,467,257]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0743/98b571fa4beb3b56eb5882058f9223efa51b6d10a80617b6b15217b630e514fd.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[478,80,823,233]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0530/173b5e3d6359a035d2a2a36ddfc0b12a7a2d36f91d57f6facafb4605a83c166d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[173,259,591,361]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0475/a316cf94a345562a0f2531584e60a3fe7ff79a1bfe1a9b89fe0af49d837a28db.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[611,239,763,424]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 1. A: Illustration of the ECG and EEG analysis process. B. Illustration of electrode locations and stimulation protocol. C: Illustration of the visual breathing cue and exemplary respiration belt data. Red and blue vertical lines illustrate stimulation bursts locked to inhalation and exhalation, respectively. D: Illustration of the condition assignment procedure. For each subject, the stimulated ear was selected pseudo-randomly (top row). For each block, electrode location (cymba vs. tragus) as well as respiration locking (red: inhalation-locked, blue: exhalation-locked, black: sham) were selected by pseudo-random permutation. All six possible combinations of location and respiration-locking were conducted with each subject. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0905/5993b9768e99e25a27b3da1d558799d306d7feb7f2921463db5ca2bcd2a809d4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[55,510,485,563]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Fig. 1C), and electrode location (cymba conchae vs. inner tragus auricularis, see Fig. 1B and Supplementary Figures). As an additional between-subject factor, participants were pseudo-randomly assigned to stimulation of the left or right ear (22 subjects each). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,563,485,617]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Since stimulation was locked to the 4 s periods of inhalation and exhalation, respectively, four bursts were administered per respiration cycle, each followed by a 6-s interval without stimulation. The order of the six blocks was pseudo-randomized across subjects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,633,174,646]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ECG data analysis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,659,487,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"All HR-related scores were derived from ECG data using the BioSPPy package [15] and custom code written in Python 3. R-peaks were detected automatically and verified by visual inspection. The intervals between successive R-peaks (referred to as RRi, see Fig. 1 A) and instantaneous HR, i.e., the linearly interpolated inverse of RRi, were the basis for the subsequent calculation of all following metrics. We analyzed mean HR per subject, condition, and time (pre, stim, post). For statistical analyses, all scores were baseline adjusted to the pre-measurement, see section 'Statistical analyses'. To gain a better understanding about the temporal evolution of stimulation-related HR changes, we visually inspected instantaneous HR over the time course of stim and post. For visualization only (Fig. 2D), we smoothed the HR time course with a $20\\\\mathrm{~s}$ moving-average filter to suppress respiratory sinus arrhythmia (see section 'Statistical analyses') and to make any slower HR changes visible. To quantify RSA, we averaged instantaneous HR across the paced breathing cycles (10s, starting with the inhalation cue, see Supplementary Figures). Each epoch was mean-centered (to the overall mean of the recording), and multilevel regression models were used to test for an effect of taVNS, as described in the section 'Statistical analyses'. Furthermore, we calculated the following HRV \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,509,939,788]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"scores: Root mean squares of successive differences (RMSSD), i.e., the square root of the mean of squared differences between successive R Ri. We also calculated the conceptually similar Standard deviation of $RRi$ (SDNN). The PNN50 score is defined as the percentage of R Ri that differs from the preceding R Ri by more than 50 ms among all R Ri. These time-domain scores represent the global beat-to-beat variability of R Ri. Frequency domain scores, on the other hand, are obtained from a spectral analysis of instantaneous HR. They represent the strength of HR change over a given time window or at a given frequency. We take two frequency domain HRV scores into consideration. High-frequency HRV (HF) is the power spectral density (PSD) of HR changes at a frequency between 0.15 and 0.4 Hz. The LF/HF score is defined as the ratio between low- $(0.04 - 0.15\\\\mathrm{Hz})$ and high-frequency HRV. It is believed to reflect the current balance between sympathetic and parasympathetic activation. Finally, we calculated SD1/SD2, a nonlinear HRV score calculated from Poincare recurrence matrices, i.e., a matrix representation of each $\\\\mathsf{RRi}_{\\\\mathrm{t}}$ and its subsequent $\\\\mathsf{RRi}_{\\\\mathrm{t + 1}}$ . SD1/SD2 is defined as the ratio of the standard deviations of the two principal components of the Poincare recurrence matrix. It provides an estimation of signal unpredictability/complexity [41]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,805,660,819]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Neuro-cardiac coupling \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,831,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In accordance with the findings of a recent study [35], we determined the strength of NCC as the relationship between EEG delta power around each R-peak and occurrence of a long vs. short heartbeat. A heartbeat was defined as being long or short if the interval passing between the current and the subsequent R-peak (RRi) was in the upper or lower third of all RRi in the same recording, similar to the methodology described by Ref. [35]. EEG data were bandpass $(0.3 - 35\\\\mathrm{Hz}$ , 4th order Butterworth filter) and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,56,262,66]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"M. Keute, K. Machetanz, L. Berelidze et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[754,56,937,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Brain Stimulation 14 (2021) 209-216 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[487,945,507,955]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"211 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,81,440,344]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0175/a320bd9702d3471128bc30a3dc3340a042e65fd6e5e2150b06143e84bd930f0a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[457,97,781,340]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0471/d2c1b8f4da2a5f7359b56aeab71b0c85d26daca736253cb436c01db6876305fc.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[186,346,357,601]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0960/9900365f9e1b91de7b64bf833b4c7c7c8fed2c1e55c8628926d8da575b453d1a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[405,378,811,611]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 2. A. Mean HR per subject, time and condition. B. Change to baseline (pre) in beats per minute. C. Change to baseline, resolved by all fixed factors. D. Change to baseline, time-resolved and moving-average smoothed (window length: 20s). Ripples in the curves are the residual RSA. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0929/25eeaeeb06654b06d2c0b49178dfadda17ecdb43c3df4be422424448249d3876.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[60,664,487,930]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"notch (48–52 Hz, 4th order Butterworth filter) filtered. Corrupted channels were identified by visual inspection on the basis of intra-channel variance, and excluded from further analysis. Ocular and muscular artifacts were removed using independent component analysis (ICA) based on correlations between the ICA components and the vertical EOG, horizontal EOG, and envelope of the masseter EMG, respectively. To assess NCC, we divided the pre- and post-stimulation EEG data into 1.2 s epochs, starting 0.6 s before each of the R-peaks detected in the simultaneously recorded ECG. Segments with remaining artifacts were excluded on the basis of a threshold criterion $(\\\\pm 80~\\\\mu \\\\mathrm{V})$ . We determined power spectral density (PSD) for each segment using Fast Fourier Transform (FFT) with Hann-tapered windows, zero-padded to a total window length of 2000 samples (2s). PSD values were log-transformed and averaged across delta frequencies (0.5–4 Hz). We defined seven frontocentral electrodes (Fp1, Fp2, F3, F4, Fz, FC3, FC4) as region of interest (ROI), following the results reported by Ref. [35]. Delta power, averaged across the ROI and z-standardized, served as predictor in a logistic model, predicting for each R-peak whether the subsequent R-peak belongs to the lower (short heartbeat) or upper (long \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,664,937,706]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"heartbeat) third of all RRi. We used the subject-and-condition-wise regression weight, expressed in log-odds per standard deviation, as a measure for the strength and direction of NCC. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,726,633,738]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Statistical analyses \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,752,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"All scores were analyzed using linear multilevel regression models (LMM) with subject-wise random intercepts and by-subject random slopes for all within-subject effects to account for repeated measurements, i.e., a maximal random effects structure, as is recommended for the procurement of generalizable results [4]. SDNN, RMSSD, HF, LF/HF, and SD1/SD2 were log transformed prior to entering the LMM to approximate normal distributions. PNN50 was converted to log-odds. All scores were baseline-corrected to the respective pre-measurement. Fixed factors were time (on-intervention vs. post-intervention), taVNS (taVNS vs. sham), stimulated ear (left vs. right), electrode placement (tragus auricularis vs. cymba conchae), and a time $\\\\times$ taVNS interaction, reflecting an altered time course of HRV in taVNS conditions compared to sham. P-values were calculated from the model F- or t-values, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,56,262,66]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"M. Keute, K. Machetanz, L. Berelidze et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[754,56,937,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Brain Stimulation 14 (2021) 209-216 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[487,945,510,955]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"212 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[55,79,487,172]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"respectively, using Satterthwaite approximations for (denominator) degrees of freedom. Statistical modeling and testing were carried out in R using the packages lme4 and lmerTest. We conducted post-hoc comparisons by fitting and testing reduced LMM to subsets of the data (e.g., taVNS data only during intervention). To compare baseline characteristics between active and sham blocks, we used non-baseline-corrected values. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,190,225,205]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data and code availability \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,216,485,284]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Python and R code used for data analysis will be made available on Github (https://github.com/mkeute). The data will be available from the corresponding author upon request, as the ethics approval does not allow uploading the datasets to a publicly available repository. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,302,112,315]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,327,127,341]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heart rate \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,354,485,684]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HR changed significantly over time $(\\\\mathrm{F} = 41.03, \\\\mathrm{p} < .001)$ . Furthermore, there was a main effect of electrode location on HR $(\\\\mathrm{F} = 6.42, \\\\mathrm{p} = .016)$ , as well as a time $\\\\times$ taVNS interaction $(\\\\mathrm{F} = 4.54, \\\\mathrm{p} = .011)$ , but no main effects of taVNS or stimulated ear (both $\\\\mathrm{F} < 0.6$ , both $\\\\mathrm{p} > .4$ ). Post-hoc tests revealed that the main effect of time was driven by an increase in HR post-stimulation $(\\\\mathrm{t} = 5.16, \\\\mathrm{p} < .001)$ , but that HR did not differ significantly from baseline during stim $(\\\\mathrm{t} = 0.84, \\\\mathrm{p} = .403)$ . Conversely, HR change to baseline was significantly different between sham and taVNS during stim $(\\\\mathrm{t} = -2.24, \\\\mathrm{p} = .030)$ , but not post-stim $(\\\\mathrm{t} = 0.60, \\\\mathrm{p} = .549)$ . When considering taVNS data only and separately for stim and post, we found neither main effects of the location or side of stimulation, nor any interaction effects (see Supplementary Results). Baseline HR was not different between sham and taVNS blocks $(\\\\mathrm{t} = 0.01, \\\\mathrm{p} = .992)$ . Moreover, excluding inhalation locked and exhalation-locked taVNS data, respectively, did not lead to any substantial changes in the pattern of significant effects (see Supplementary Results). Visual inspection of the HR time course (Fig. 2D) revealed that the post-stim HR increase relative to baseline was driven by a transient rebound immediately upon stimulation offset and sham intervention offset, respectively. Furthermore, the relative HR decrease during taVNS was predominantly driven by an HR decrease in the first half of the stimulation period (i.e., about $2.5\\\\mathrm{min}$ ), whereas HR tended to return to the pre-stimulation level in the second half of the stimulation period. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,703,235,716]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Respiratory sinus arrythmia \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,728,485,809]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Overall, subjects adhered well to the paced breathing rhythm, with a mean phase locking value $\\\\mathrm{PLV} = .78 \\\\pm 0.16$ (see Supplementary Methods). Mean RSA (peak-to-peak) during the intervention was $15.59 \\\\pm 5.65$ bpm (see Supplementary Figures). There were no main effects of condition $(\\\\mathrm{F} = 2.02, \\\\mathrm{p} = .140)$ , ear $(\\\\mathrm{F} = 0.56, \\\\mathrm{p} = .460)$ , or of location $(\\\\mathrm{F} = 0.210, \\\\mathrm{p} = .647)$ on peak-to-peak RSA, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,854,485,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0560/ca843f65ed589625558c3276d46f2801a51b791af8c18cee530b0b6e15768bce.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td></td><td>HR</td><td>SDNN</td><td>RMSSD</td><td>PNN50</td><td>HF</td><td>LF/HF</td><td>SD1/SD2</td></tr><tr><td>time</td><td>41.03</td><td>2.35</td><td>8.69</td><td>13.62</td><td>4.80</td><td>1.05</td><td>10.14</td></tr><tr><td>taVNS</td><td>0.51</td><td>0.00</td><td>1.17</td><td>1.20</td><td>0.01</td><td>0.20</td><td>1.48</td></tr><tr><td>location</td><td>6.24</td><td>0.03</td><td>0.17</td><td>1.71</td><td>0.46</td><td>0.04</td><td>0.24</td></tr><tr><td>ear</td><td>0.06</td><td>0.30</td><td>0.23</td><td>0.16</td><td>0.00</td><td>0.02</td><td>0.04</td></tr><tr><td>time x taVNS</td><td>4.54</td><td>3.77</td><td>7.24</td><td>3.81</td><td>5.74</td><td>4.52</td><td>2.84</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1 F-values for fixed effects. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[507,79,937,108]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"nor did condition interact with ear $(\\\\mathrm{F} = 2,30, \\\\mathrm{p} = .108)$ or with location $(\\\\mathrm{F} = 1.16, \\\\mathrm{p} = .316)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,119,648,134]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heart rate variability \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,146,937,412]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The results of the main statistical analysis are summarized in Tables 1 and 2. No main effects of taVNS, location, or ear were found for any of the HRV scores. A significant time $\\\\times$ taVNS interaction was, however, found for SDNN, RMSSD, PNN50, HF, and LF/HF, and a marginally significant interaction for SD1/SD2. Much like in HR (see above), we observed that most HRV scores significantly changed over time, across taVNS and sham. Post-hoc comparisons are summarized in Tables 3 and 4. During stimulation, we found the overall (across sham and taVNS) change to baseline to be significantly different from zero for all time-domain HRV scores, HF, and SD1/SD2. Moreover, we found significant differences between sham and taVNS during stimulation for RMSSD, PNN50, and SD1/SD2 (see Fig. 3A). Post-stimulation, we found differences to baseline for some scores, but no significant differences between taVNS and sham. We found no significant effects of respiration-locking, ear or location in the post-hoc comparisons. Baseline HRV scores were not significantly different between sham and taVNS blocks. In addition, the exclusion of inhalation-locked and exhalation-locked taVNS data, respectively, did not lead to any substantial changes in the pattern of significant effects (see Supplementary Results). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,424,660,438]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Neuro-cardiac coupling \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,451,937,622]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We could not establish any overall trend for a relationship between delta power and heartbeat length at baseline recordings (regression weights were, on the group level, not significantly different from zero, $t = 0.134$ , $p = .894$ ). Neither was NCC different between pre- and post-measurements, i.e., it was unaffected by the intervention ( $t = 1.523$ , $p = .128$ ). Finally, baseline NCC did not differ between sham and taVNS blocks ( $t = 1.159$ , $p = .253$ ). However, baseline NCC was a significant predictor for the change in SDNN between baseline and taVNS ( $t = 3.095$ , $p = .002$ , see Fig. 3 B), as well as for the change in HF ( $t = 2.28$ , $p = .024$ ) and SD1/SD2 ( $t = 2.396$ , $p = .017$ ), but not for any of the other HR/HRV metrics (all $|t| < 1.65$ , $p > .1$ ). All effects were positive, i.e., a higher (positive) NCC predicted a higher (positive) taVNS effect. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,636,586,649]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,663,759,678]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Summary and interpretation of findings \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,689,937,809]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this study, we aimed to corroborate cardiac effects of taVNS, examine the modulation of such an effect by variations in respiration-locking, stimulation location, and the stimulated ear, as well as investigate the potential of individual neuro-cardiac baseline characteristics to predict the responses to taVNS. We identified cardiac taVNS effects, i.e., decreased HR and increased HRV scores RMSSD, PNN50, and SD1/SD2 (but not SDNN, HF, LF/HF), which is consistent with previous findings and, as an overall pattern, reflective of parasympathetic activation [17]. Overall, similar effects \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,854,937,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0347/f0c36a6072e6c7e1fda1527fd8c2a1d26f399517068ca4e40ef74c8e6308dd61.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td></td><td>HR</td><td>SDNN</td><td>RMSSD</td><td>PNN50</td><td>HF</td><td>LF/HF</td><td>SD1/SD2</td></tr><tr><td>time</td><td>.000</td><td>.104</td><td>.000</td><td>.000</td><td>.011</td><td>.352</td><td>.000</td></tr><tr><td>taVNS</td><td>.479</td><td>.984</td><td>.285</td><td>.279</td><td>.925</td><td>.654</td><td>.230</td></tr><tr><td>location</td><td>.016</td><td>.870</td><td>.680</td><td>.197</td><td>.499</td><td>.840</td><td>.624</td></tr><tr><td>ear</td><td>.806</td><td>.587</td><td>.630</td><td>.695</td><td>.953</td><td>.880</td><td>.837</td></tr><tr><td>time x taVNS</td><td>.011</td><td>.024</td><td>.001</td><td>.023</td><td>.003</td><td>.011</td><td>.059</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2 p-values for fixed effects. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[58,56,262,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"M. Keute, K. Machetanz, L. Berelidze et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[754,56,937,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Brain Stimulation 14 (2021) 209-216 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[487,944,510,955]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"213 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[58,104,937,184]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0867/c040995c4bd4b0848cd59aa883fdc0fec5880486860ce12c94c7d243e4b6b6d9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td></td><td>HR</td><td>SDNN</td><td>RMSSD</td><td>PNN50</td><td>HF</td><td>LF/HF</td><td>SD1/SD2</td></tr><tr><td>taVNS vs. sham during pre</td><td>0.01</td><td>0.38</td><td>-0.72</td><td>-0.54</td><td>0.2</td><td>-0.27</td><td>-1.59</td></tr><tr><td>taVNS vs. sham during stim</td><td>-2.24</td><td>1.50</td><td>2.68</td><td>2.54</td><td>1.84</td><td>-1.21</td><td>2.22</td></tr><tr><td>taVNS & sham vs. baseline during stim</td><td>0.84</td><td>-2.84</td><td>-3.77</td><td>-3.04</td><td>-3.51</td><td>1.86</td><td>-2.22</td></tr><tr><td>taVNS vs. sham during post</td><td>0.60</td><td>-0.91</td><td>-0.68</td><td>-0.15</td><td>-1.44</td><td>1.71</td><td>0.02</td></tr><tr><td>taVNS & sham vs. baseline during post</td><td>5.16</td><td>-0.84</td><td>-2.72</td><td>-3.60</td><td>-1.73</td><td>-0.14</td><td>-2.89</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 3 t-values for post-hoc comparisons. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[60,208,484,259]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"have already been reported, albeit some studies found no cardiac effects of taVNS [10]. This could be due to trait and state characteristics and the stimulation protocol, as detailed in the introduction. We found no effect of taVNS on peak-to-peak RSA. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,261,484,470]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In accordance with earlier findings, HR changes were visible soon after taVNS onset [24]. No cardiac effects extended beyond stimulation offset. This transient nature of cardiac taVNS effects may provide a further explanation for the inconsistencies between studies. Immediately upon stimulation offset, we detected a HR rebound that occurred across sham and taVNS conditions. This was surprising, since a HR rebound resulting from reinstatement of sympathetic activation after taVNS offset would not be expected to follow the sham stimulation. Very similar findings have, however, already been reported [2], and one possible interpretation is that the HR rebound is partially caused by a cognitive process (e.g., appraisal of the change between intervention and rest). Finally, we demonstrated that the use of a novel stimulation protocol, with intermittent stimulation bursts rather than continuous stimulation at, e.g., $25\\\\mathrm{Hz}$ , leads to similar cardiac effects as standard taVNS protocols while reducing the overall current delivered. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,472,484,655]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Moreover, we found no evidence for any systematic difference between inhalation-locked and exhalation exhalation-locked taVNS, which is surprising, since a recent study [40] showed a very prominent influence of taVNS respiration-locking on brainstem activations and HF-HRV, and exhalation-locked taVNS has been used in patient studies for several years [33]. Similarly, we found no evidence that taVNS effects were systematically modulated by variations in stimulation location (tragus vs. cymba conchae) or stimulated ear (right vs left). In sum, none of the stimulation conditions that were varied in this study provided a satisfactory explanation for cardiac response variance. With regard to the stimulated ear, this was anticipated based on anatomical considerations [16] and experimental evidence from left- and right-sided invasive VNS [37]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,656,484,786]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"With respect to stimulation locations (cymba conchae vs. tragus), on the other hand, the question as to whether both targets equally recruit the auricular branch of the vagus nerve is still under debate. In particular, the idea that the cymba conchae is more strongly or more consistently innervated by the vagus nerve than the tragus is mostly based on a single study [36], with partially inconsistent results [12]. Other studies suggest similar vagal innervation patterns for the tragus and cymba conchae [3], and several taVNS studies have shown comparable results for both stimulation targets [3,45], in line with our findings. In sum, the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,208,936,233]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"existing evidence supports a similar vagus nerve recruitment at both locations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,235,936,602]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, we calculated an index of neuro-cardiac autonomic control that was first described in a recent study [35]. On the group level, we were unable to replicate the reported relationship between EEG delta power and heartbeat length, possibly on account of a slightly different methodology than that used in the original study. In particular, to avoid EEG artifacts of previous or subsequent R-peaks, which could potentially introduce an artifact in the delta frequency range, we used a shorter window length for the spectral analysis (1.2 s rather than 4 s). Importantly, however, we found that individual NCC regression weights predicted stimulation-induced cardiac changes (SDNN, SD1/SD2 and HF). The relationship was positive, i.e., a higher positive NCC at baseline predicted a stronger taVNS effect, which is in agreement with the findings by Ref. [35]; who suggested that a stronger positive NCC reflects a stronger vagally mediated brain-heart communication. Interestingly, we found that NCC was related to SDNN and HF, two of the HRV scores that were not significantly modulated by taVNS on the group level (post-hoc contrast), i.e., where taVNS effects had higher interindividual variability, which in turn can be explained by the NCC. Crucially, NCC did not baseline-to-intervention changes for any HRV metric in the sham condition, i.e., its predictive value was specific to taVNS. In sum, we found tentative evidence that NCC, as assessed by baseline correlations between delta power and heartbeat length, may constitute a promising biomarker for responsiveness to taVNS, even though the precise physiological interpretation of the NCC score and its relationship to taVNS effects warrants further investigation, e.g., with longer baseline recording periods. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,624,581,635]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Limitations \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,650,936,807]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Our sample size was limited in the light of the experimental design, i.e., our study may well have been underpowered for the detection of subtle effects such as three- and four-way interaction effects between stimulation conditions. The stimulation paradigm that was used in our study (burst stimulation) is novel and has not yet been formally evaluated and compared to other, more established protocols. Moreover, we did not use an active sham condition (e.g., earlobe stimulation), but instead held the electrode at the stimulation sites without delivering current. The somatosensory quality may thus have differed between conditions. We cannot, therefore, fully rule out that the findings may be partially driven by somatosensory or cognitive processes. However, some HRV effects \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,854,937,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/1021/bf165d0960d1e6e3454e65601215c254e478820c4999750aa792aef913acb663.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td></td><td>HR</td><td>SDNN</td><td>RMSSD</td><td>PNN50</td><td>HF</td><td>LF/HF</td><td>SD1/SD2</td></tr><tr><td>taVNS vs. sham during pre</td><td>.992</td><td>.703</td><td>.476</td><td>.589</td><td>.845</td><td>.791</td><td>.116</td></tr><tr><td>taVNS vs. sham during stim</td><td>.030</td><td>.139</td><td>.010</td><td>.013</td><td>.071</td><td>.229</td><td>.031</td></tr><tr><td>taVNS & sham vs. baseline during stim</td><td>.403</td><td>.006</td><td>.000</td><td>.003</td><td>.001</td><td>.070</td><td>.029</td></tr><tr><td>taVNS vs. sham during post</td><td>.549</td><td>.366</td><td>.498</td><td>.883</td><td>.152</td><td>.092</td><td>.987</td></tr><tr><td>taVNS & sham vs. baseline during post</td><td>.000</td><td>.406</td><td>.009</td><td>.001</td><td>.086</td><td>.890</td><td>.006</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 4 p-values for post-hoc comparisons. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[60,58,260,66]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"M. Keute, K. Machetanz, L. Berelidze et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[756,58,937,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Brain Stimulation 14 (2021) 209-216 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[489,945,507,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"214 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[174,81,327,293]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0721/1f18302004264962c6771c54248f23a8fcc4eb9d88a4d0cbd3d802bba4231bdc.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[341,80,515,292]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0762/bc41d3022af9294bb74a72d88f1c574fe5b022097bdc483a98f5b75575e98bd3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[519,97,665,291]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0134/8bc8d3ac4ef574465900d65e45a0fab23a1fa58a48fa0e2e880822758aadb7da.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[687,166,823,279]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 3. A. Regression weights and confidence intervals for the taVNS vs. sham post-hoc effect during intervention for all cardiac dependent variables. Significant effects are marked with asterisks. Positive regression weights indicate higher values during taVNS. B: Regression weights and confidence intervals for the prediction of cardiac taVNS effects by baseline NCC. It can be seen that the NCC was a significant predictor for the taVNS effect on HF, SD1/SD2, and SDNN, but for none of the sham effects. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0719/5a262c665740734c84b7c8d2d8adcacb9efe8bd9068a964c8d2a535b574f57d7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,359,485,597]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"observed during and after the sham condition resembled the findings during the stimulation conditions. This suggests that the applied sham approach was at least sufficient to induce unspecific effects similar to those observed in the stimulation condition. However, taVNS also induced specific HRV effects which did not occur during the sham condition and which were predicted by NCC. Moreover, the paced breathing rhythm used in our experiment might limit the interpretation of frequency-domain HRV scores (HF and LF/HF), since the canonical frequency bands for HF $(0.15 - 0.4\\\\mathrm{Hz})$ do not contain the breathing frequency $(0.1\\\\mathrm{Hz})$ . To compensate for this limitation, we conducted an additional analysis of RSA, which is reported in the Supplementary Material. Finally, it is an open question what exactly NCC reflects, in particular with respect to causality, i.e., whether NCC indicates central nervous control of vagal and cardiac function, or rather a cortical response to cardiac changes induced by the autonomous nervous system. Furthermore, the mediating role of physiological covariates, especially respiration, warrant further investigation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,620,112,631]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Outlook \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,646,485,804]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It has already been shown that individual patient trait and state characteristics can be predictive of VNS effects, including resting-state brain connectivity [32] and HRV [30]. NCC, as a novel predictive biomarker, has the potential to bridge the gap between the central and autonomic effects of taVNS, branches of research for which no integrative model exists. This might be most relevant for diseases in which a clinical improvement manifests itself in brain and heart functioning alike, e.g., depression [42]. Moreover, a small but growing number of studies on closed-loop taVNS has emerged [38,39], with the aim to optimize the instantaneous autonomic status in real time by coupling taVNS administration to a physiological control signal. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,805,485,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The exact role that NCC could have in this context remains to be determined. In particular, it should be investigated whether intra-individual changes in NCC over longer periods, e.g., several days, reliably predict changes in taVNS responsiveness or whether the NCC-responsiveness relationship that we have reported rather reflects an individual trait that is relatively stable over time. In the latter case, NCC might have a role in selecting patients that are susceptible to taVNS therapy. In the former case, however, NCC could be used as a control signal to, e.g., find the most efficient time windows to deliver taVNS for a given patient. Moreover, it remains \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,359,937,398]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"an open question whether NCC can be manipulated, e.g., via breathing techniques, and if such a manipulation could enable patients to increase their own susceptibility to taVNS treatment. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,399,937,477]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Applying taVNS in such a closed-loop fashion requires the availability of wearable measurement and stimulation devices that work in a highly automatized way and that can be easily used by patients. The development of such devices is underway, even though they are not yet available on the market, to the best of our knowledge. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,503,589,515]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conclusion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,529,937,622]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"TaVNS, delivered with a burst protocol, led to HR and HRV changes during the stimulation. These effects could be similarly induced at the right and left ear, at the tragus and cymba conchae and during inhalation inhalation and exhalation. Baseline neurocardiac coupling in the EEG delta band may serve as a predictive biomarker for individual taVNS responsiveness; a finding that requires independent replication. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,648,729,660]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Author contributions statement \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,674,937,742]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MK was responsible for data analysis, interpretation of data, and writing of the manuscript. KM, LB and RB contributed to study design, data acquisition/analysis, and reviewing of the manuscript. AG was responsible for the conception and design of the study, interpretation of data, and writing of the manuscript. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,766,742,779]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Declaration of competing interest \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,791,937,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This research study was supported by the German Federal Ministry of Education and Research [BMBF 13GW0270B, INAUDITAS]. We also acknowledge support by the Open Access Publishing Fund of the University of Tuebingen. None of the authors has potential conflicts of interest to disclose. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,883,739,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Appendix A. Supplementary data \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,910,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Supplementary data to this article can be found online at https://doi.org/10.1016/j.brs.2021.01.001. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,56,262,66]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"M. Keute, K. Machetanz, L. Berelidze et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[754,56,937,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Brain Stimulation 14 (2021) 209-216 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[487,944,507,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"215 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[58,80,134,92]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,104,485,878]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[1] Badran BW, Mithoefer OJ, Summer CE, LaBate NT, Glusman CE, Badran AW, DeVries WH, Summers PM, Austelle CW, McTeague LM, Borckardt JJ, George MS. 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Parametric characterization of neural activity in the locus coeruleus in response to vagus nerve stimulation. Exp Neurol 2017;289:21-30. \\\",\\\"[24] Iseger TA, Padberg F, Kenemans JL, Gervitz R, Arns M. Neuro-Cardiac-Guided TMS (NCG-TMS): probing DLPFC-sgACC-vagus nerve connectivity using heart rate – first results. Brain Stimulat 2017;10:1006–8. https://doi.org/10.1016/j.brs.2017.05.002. \\\"]\",\n \"page_idx\": \"7\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[512,80,937,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[25] Iwao T, Yonemochi H, Nakagawa M, Takahashi N, Saikawa T, Ito M. Effect of constant and intermittent vagal stimulation on the heart rate and heart rate variability in rabbits. Jpn J Physiol 2000;50:33-9. https://doi.org/10.2170/jjphysiol.50.33. \\\",\\\"[26] Kaniusas E, Kampusch S, Tittgemeyer M, Panetsos F, Gines RF, Papa M, Kiss A, Podesser B, Cassara A, Tanghe E, others. Current directions in the auricular vagus nerve stimulation II—an engineering perspective. Front Neurosci 2019;13:772. \\\",\\\"[27] Karemaker JM. How the vagus nerve produces beat-to-beat heart rate variability; experiments in rabbits to mimic in vivo vagal patterns. J Clin Transl Res 2015;1:190-204. \\\",\\\"[28] Kuo TB, Lai CJ, Huang Y-T, Yang CC. Regression analysis between heart rate variability and baroreflex-related vagus nerve activity in rats. J Cardiovasc Electrophysiol 2005;16:864-9. \\\",\\\"[29] Levy MN, Martin PJ, Iano T, Zieske H. Paradoxical effect of vagus nerve stimulation on heart rate in dogs. Circ Res 1969;25:303-14. \\\",\\\"[30] Liu H-Y, Yang Z, Meng F-G, Guan Y-G, Ma Y-S, Liang S-L, Lin J-L, Pan L-S, Zhao M-M, Qu W, Hao H-W, Luan G-M, Zhang J-G, Li L-M. Preoperative heart rate variability as predictors of vagus nerve stimulation outcome in patients with drug-resistant epilepsy. Sci Rep 2018;8:3856. https://doi.org/10.1038/s41598-018-21669-3. \\\",\\\"[31] Mischak H, Allmaier G, Apweiler R, Attwood T, Baumann M, Benigni A, Bennett SE, Bischoff R, Bongcam-Rudloff E, Capasso G, others. Recommendations for biomarker identification and qualification in clinical proteomics. Sci Transl Med 2010;2:46ps42. 46ps42. \\\",\\\"[32] Mithani K, Mikhail M, Morgan BR, Wong S, Weil AG, Deschenes S, Wang S, Bernal B, Guillen MR, Ochi A, Otsubo H, Yau I, Lo W, Pang E, Holowka S, Snead OC, Donner E, Rutka JT, Go C, Widjaja E, Ibrahim GM. Connectomic profiling identifies responders to vagus nerve stimulation. Ann Neurol 2019;86:743-53. https://doi.org/10.1002/ana.25574. \\\",\\\"[33] Napadow V, Edwards RR, Cahalan CM, Mensing G, Greenbaum S, Valovska A, Wasan AD. Evoked pain analgesia in chronic pelvic pain patients using respiratory-gated auricular vagal afferent nerve stimulation. Pain Med 2012;13(6):777-89. \\\",\\\"[34] Neuser MP, Teckentrup V, Kühnel A, Hallschmid M, Walter M, Kroemer NB. Vagus nerve stimulation boosts the drive to work for rewards. Nat Commun 2020;11(1):1-11. \\\",\\\"[35] Patron E, Mennella R, Benvenuti SM, Thayer JF. The frontal cortex is a heart-brake: reduction in delta oscillations is associated with heart rate deceleration. Neuroimage 2019;188:403-10. \\\",\\\"[36] Peuker ET, Filler TJ. The nerve supply of the human auricle. Clin Anat 2002;15: 35-7. \\\",\\\"[37] Premchand RK, Sharma K, Mittal S, Monteiro R, Dixit S, Libbus I, KenKnight BH. Autonomic regulation therapy via left or right cervical vagus nerve stimulation in patients with chronic heart failure: results of the ANTHEM-HF trial. J Card Fail 2014;20(11):808-16. \\\",\\\"[38] Romero-Ugalde HM, Le Rolle V, Bonnet J-L, Henry C, Mabo P, Carrault G, Hernández Al. Closed-loop vagus nerve stimulation based on state transition models. IEEE Trans Biomed Eng 2018;65:1630-8. \\\",\\\"[39] Romero-Ugalde HM, Rolle VL, Bonnet J-L, Henry C, Bel A, Mabo P, Carrault G, Hernández Al. A novel controller based on state-transition models for closed-loop vagus nerve stimulation: application to heart rate regulation. PLoS One 2017;12:e0186068. https://doi.org/10.1371/journal.pone.0186068. \\\",\\\"[40] Sclocco R, Garcia RG, Kettner NW, Isenburg K, Fisher HP, Hubbard CS, Ay I, Polimeni JR, Goldstein J, Makris N, Toschi N, Barbieri R, Napadow V. The influence of respiration on brainstem and cardiovascular response to auricular vagus nerve stimulation: a multimodal ultrahigh-field (7T) fMRI study. Brain Stimulat 2019;12:911-21. https://doi.org/10.1016/j.brs.2019.02.003. \\\",\\\"[41] Shaffer F, Ginsberg J. An overview of heart rate variability metrics and norms. Front Publ Health 2017;5:258. \\\",\\\"[42] Sperling W, Reulbach U, Bleich S, Padberg F, Kornhuber J, Mueck-Weymann M. Cardiac effects of vagus nerve stimulation in patients with major depression. Pharmacopsychiatry 2010;43:7-11. https://doi.org/10.1055/s-0029-1237374. \\\",\\\"[43] Stavrakis S, Humphrey MB, Scherlag BJ, Hu Y, Jackman WM, Nakagawa H, Lockwood D, Lazzara R, Po SS. Low-level transcutaneous electrical vagus nerve stimulation suppresses atrial fibrillation. J Am Coll Cardiol 2015;65:867-75. https://doi.org/10.1016/j.jacc.2014.12.026. \\\",\\\"[44] Tobaldini E, Toschi-Dias E, Appratto de Souza L, Rabello Casali K, Vicenzi M, Sandrone G, Cogliati C, La Rovere MT, Pinna GD, Montano N. Cardiac and peripheral autonomic responses to orthostatic stress during transcutaneous vagus nerve stimulation in healthy subjects. J Clin Med 2019;8:496. \\\",\\\"[45] Yakunina N, Kim SS, Nam E-C. Optimization of transcutaneous vagus nerve stimulation using functional MRI. Neuromodulat Technol Neural Interface 2017;20:290-300. https://doi.org/10.1111/ner.12541. \\\",\\\"[46] Antonino D, Teixeira AL, Maia-Lopes PM, Souza MC, Sabino-Carvalho JL, Murray AR, Deuchars J, Vianna LC. Non-invasive vagus nerve stimulation acutely improves spontaneous cardiac baroreflex sensitivity in healthy young men: a randomized placebo-controlled trial. Brain Stimulat 2017;10:875-81. https://doi.org/10.1016/j.brs.2017.05.006. \\\"]\",\n \"page_idx\": \"7\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[58,56,260,66]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"M. Keute, K. Machetanz, L. Berelidze et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[754,56,937,68]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Brain Stimulation 14 (2021) 209-216 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[487,945,510,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"216 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1016/j.brs.2021.01.001"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Medicine and Health Sciences"},"sha256":{"kind":"string","value":"200128fc0510f823e163dd96ec0a47c5f9bcd3364e1ad0bf2277b7620cb11d77"},"title":{"kind":"string","value":"Neuro-cardiac coupling predicts transcutaneous auricular vagus nerve stimulation effects"}}},{"rowIdx":254,"cells":{"abstract":{"kind":"string","value":""},"author":{"kind":"string","value":""},"content_list":{"kind":"list like","value":[{"bbox":"[62,206,714,248]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Applications of extended reality in spaceflight for human health and performance ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,261,776,310]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"M. Brent Woodlanda, Joshua Ongb, Nasif Zaman, Mohammad Hirzallahd,e,f, Ethan Waisberg 8\\*, Mouayad Masalkhi8, Sharif Amit KamranC, Andrew G. Leed,h,i,j,k,l,m,n Alireza Tavakkoli C ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,321,722,471]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"aBaylor College ofMedicine,Houston,TX, United tates \nb Michigan edicine,UniversityofMichigan,AnnArbor,MI,Unitedtates \nHuan-i \nCentere \neDepartmentof Neurology,Baylor Colegeof Medicine,Houston,TX,United tates \nfDepartmentofeurosrgryylorlgfedicineouto,Uee \ngUniversityollgeublinchoolofedicine,Belfield,Dublin,ed \nhDepartetostlt \nTheHoustoisthte,stistsialsoe \nDeprttllk \nk DepartmentfphthalmologyUniversityofTexas Medical Branch,Galveston,TXUnitedtates \nlUniversityofexasdersonCancerCenterHouston,Uitedtes \nm Texas A&MCollege of Medicine, Texas, United States \n\"DepartmentofOphthalmology,The UniversityofIowa Hospitalsand Clinics,Iowa City,IA,UnitedStates ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,501,157,513]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABSTRACT ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,527,939,634]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Vitaeaiie evalatiolatt decadeio coity teetecholisarb developedfoe vol itigate possiblebarstourasaceigdadeploosiscgsaceligsaedeurlard). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[63,673,378,686]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Introduction to virtual and augmented reality ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,699,484,778]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Virtual reality is a technology that immerses a user in a computergenerated environment, often using wearable devices such as a headmounted display (HMD),known colloquially as“VR goggles”or“VR headset.\"Visual,auditory,and other sensory inputs may be manipulated to give the user an enhanced sense that he or she is physically present within the virtual environment. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,780,484,818]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The concepts of the reality-virtuality (RV) continuum and “mixed reality”(MR) were concurrently introduced Paul Milgram and Fumio Kishino in their 1994 publication “A Taxonomy of Mixed Reality Visual ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,673,937,765]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Displays”[1].Visual displays for mixed reality (MR) entail the blending of actual and virtual worlds at some point along the“virtuality continuum,”which links entirely real settings to entirely virtual ones [1].The most well-known of these is perhaps augmented reality (AR),which is the term used to describe any instances in which a presentation of the real world is enhanced by the use of virtual (computer graphic) items [1]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,766,936,818]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Over the last thirty years,VR research in healthcare has grown exponentially [2].The technology has been applied in multiple disciplines,most prominently in surgical training,pain management,and psychiatric therapy [3].Laparoscopic,orthopedic,and microsurgical VR systems have been developed to help surgical trainees acquire the necessary skils to perform successful procedures in a safe,inexpensive, and iterative manner (2).VR has been combined with standard anesthetic protocols to help alleviate pain and may be an important part of pain management [3].VR has also shown promise in the treatment of psychiatric disease,particularly anxiety disorders.By implementing virtual exposure to anxiety-inducing stimuli,mental health professionals can aid patients in learning new responses to fear.This is especially useful when patients’fears are difficult to replicate in the office setting (crowds, heights,animals,etc.） [3]. Other common applications of VR in healthcare include neurological conditions (stroke, Parkinson disease,Alzheimer disease,dementia,multiple sclerosis), obesity,and cancer care [2]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,68,944,171]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Contents lists available at ScienceDirect ACTA ASTRONAUTIGA Acta Astronautica ELSEVIER journal homepage: www.elsevier.com/locate/actaastro ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[68,844,603,868]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"\\* Corresponding author.University Colege Dublin School of Medicine,Belfield, Dublin 4,Ireland. E-mail address: Ethan.waisberg@ucdconnect.ie (E. Waisberg). ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[60,882,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"nttps://ao1.org/1u.1u1b/j.actaastro.zuz3.11.025 Received 21 July 2023; Received in revised form 2 November 2023; Accepted 15 November 2023 Available online 23 November 2023 0094-5765/ $' { \\textcircled{ \\mathbf { C } } }$ 2023 The Authors. Published by Elsevier Ltdon behalf of IAA.Thisisan open accessarticle under the CC BY license (http://creativecommons.org/licenses/by/4.0/). ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[840,185,890,223]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Check for updates ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[394,45,605,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acta Astronautica 214 (2024) 748-756 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,66,485,237]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,238,485,355]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Because most VR technologies rely heavily on visual input for their effectiveness,ophthalmology is in a unique position to adopt virtual reality as a means of testing for and monitoring ophthalmic disease. These include visual evoked potentials [4-6],which can be used to evaluate visual pathway defects occurring from diseases such as multiple sclerosis or glaucoma,perimetry [7-14],binocular vision disorders [15-19]，amblyopia [20-22]，choroidal/retinal disease[23-28], contrast sensitivity [29],visual acuity [3O,31],and anterior chamber trauma [32]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,356,484,474]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Virtual reality slit lamp,direct ophthalmoscope,and indirect ophthalmoscope simulators have been developed to help trainees to obtain proficiency in visualizing ocular structures [33].These simulators have also been programmed to be able to display various eye pathologies so that the user may practice not only the technique but also learn to identifyabnormalities in the examination.The software has the capacity to evaluate the user on technical skill as well as diagnostic accuracy [33].VR has been developed to aid learners in developing skills in posterior segment procedures as well as cataract surgery. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,476,485,633]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In contrast to virtual reality (VR),which entirely submerges users in a digitally created virtual space,augmented reality (AR) is based on the realworld and improves itwith digital data [34].AR presentsa fresh method for medical treatments and training [35].This technology has been applied to several fields in medicine.One example is AccuVein (AccuVein Inc.,NY,USA),instrument that presents a map of blood vessels onto the skin [36]. Google Glass (GG),a head-mounted display (HMD) that superimposes images on top of the real-world environment and may include auditory,smell, taste,and haptic feedback features. Khor et al.[37] demonstrated prospects for having a variety of innovative effects on surgery,notably in the field of surgical training in a simulated operating environment. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,634,484,684]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Augmented reality combines the physical world with the virtual world by overlaying computer-generated images onto the user's visual field.This allows the user to see objects that are physically present in the environment while receiving additional input from the AR device. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,687,485,804]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Typically,these devices are also head-mounted displays but have a transparent material through which the wearer can see the real world while the artificial images are displayed in the field of view.VR and AR have important applications in medicine,particularly ophthalmology [38,39],as well as space exploration.Significant physiological changes and challenges during spaceflight include bone demineralization,loss of skeletal muscle mass,space motion sickness due to vestibular issues, anemias [4O-42] immunological dysfunction,among many other alterations [43]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,805,484,923]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Multiple ophthalmic clinical and imaging findings have been reported among astronauts following LDSF in a condition now termed space-associated neuro-ocular syndrome,or SANs.Those findings include optic disc edema [44],globe flattening,choroidal and retinal folds [45],hyperopic refractive error shifts greater than 0.75 diopters, and focal retinal ischemia [46].Not all signs are necessary to suggest the diagnosis,and not all astronauts experience the clinical manifestations of SANS [47],however,increased exposure to microgravity has been observed to increase the likelihood of SANS development [48]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,924,484,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Current on-board ophthalmic imaging modalities include optical coherence tomography (OCT),retinal fundoscopy，and orbital ultrasound which have been useful for understanding the imaging changes in this neuro-ophthalmic phenomenon [49]. OCT angiography (OCTA) was recently introduced to the ISS which will provide insight into the ocular vascular flow during spaceflight[46,5O].Additional modalities may be limited due to invasive procedural concerns, time,or mass and volume constraints. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,66,937,157]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,160,937,380]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"There are several limitations to spaceflight that astronauts face as they undertake missions farther and farther from Earth.One example is that missions in low Earth orbit (LEO),such as the ISS,focus on a protocol designed to stabilize the ill or injured crew member and return to Earth for definitive medical care [51].To ameliorate power issues, spacecraft such as Orion are being outfitted with solar panels.Missions to the moon follow a similar strategy but require an additional four to five days for transport [51].However,as the distance becomes even greater,such as the 50-milion-kilometer expedition to Mars, emergency return to Earth becomes impractical if not impossible to execute [52]. Crews to Mars will likely consist of a chief medical officer who is a trained physician to mitigate limitations of experience and expertise among crew members [51]. Still,the illnesses or injuries faced by the astronauts may be outside of the physician's scope of expertise,or the physician may be the injured crew member requiring medical attention. While spaceflight is inherently dangerous,research and development projects seek to attenuate the risks to an acceptable level. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,383,937,447]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Many of the limitations fall into general categories,such as mass/ power/volume constraints and isolation,but these barriers are often intertwined.As such,various space agencies across the globe are working to identify limitations and risks to long-duration spaceflight and provide innovative countermeasures for these obstacles. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,462,926,475]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.1.Current applications of VR/AR during spaceflight for human health ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[515,490,690,501]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.1.1．Physiological challenges ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,503,937,843]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Space is a harsh environment that presents a unique combination of challenges to crew members. The National Aeronautics and Space Administration (NASA) has identified over twenty individual risks by which astronauts'health and wellbeing may be affected during spaceflight, particularly those missions which involve travel to deep space (i. e.,Mars）[53].Current areas under investigation vary widely,but medical threats include risk of kidney stones,bone fracture,psychiatric disorders,sleep disturbances,altered vestibular function,inadequate food,and nutrition,decreased muscle mass/strength,and radiation exposure [53].While most of the risks outlined by NASA are also conditions found on Earth,the space environment is unique in that these threats are faced simultaneously. In addition, microgravity and absence of Earth's atmosphere may accelerate or accentuate these risks.NASA has sorted these dangers into four categories: exploration medical capability,human factors and behavioral performance,human health countermeasures,and space radiation [53].Deep space exploration poses greater risks because these missions necessitate further lengths of time in the harsh space conditions [54].Furthermore,the distance between the crew and Earth increases,resulting in delays in communication (up to $2 0 \\mathrm { { m i n } }$ one-way fora Mars mission [52]),decreased access to medical and technical experts,impracticality of return to Earth in emergency situations,confinement within small spacecraft,increased social isolation,and uncertainty regarding mission success (especially during pioneer missions).The following projects have been carried out to determine the efficacy and practicality of utilizing VR/AR technologies to advance space exploration. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,846,937,938]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Human Research Program (HRP) created at the Johnson Space Center (JSC) exerts great efforts and investment on analyzing and minimizing the greatest risks to astronaut health and function in support of planetary exploration.As such, the Health Research Roadmap page outlines the different health obstacles and risks facing astronauts during spaceflight.Furthermore,this roadmap represents a significant reference and starting point for inspiring novel tools and devices that aid astronauts and minimize the risk of adverse health effects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,44,176,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"M. Brent Woodland et al. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[754,44,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acta Astronautica 214 (2024) 748-756 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[490,953,509,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,66,408,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,93,242,104]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.1.2.Applications in medicine ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,105,485,249]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sensorimotor and Vestibular Function (10/2020-3/2022):Pilote [55] is an HMD VR system that investigates the complex interplay between haptics,proprioception,the vestibular system，visual input, movement,and microgravity.The technology requires astronauts to perform two game-like tasks by 1) controlling the orientation of and guiding virtual objects through a series of virtual paths as quickly and accurately as possible and 2) maneuvering a virtual robotic arm to attach it to a target object [55].These tests are performed on Earth as well as in microgravity with the goal of elucidating which combinations of tactile input,head position,visual input,and so on lead to the best combination for enhanced astronaut performance [55]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,252,485,433]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The role of sensorimotor/vestibular function in spaceflight is welldocumented in the HRP list as a critical player in the success of missions[55].While baselineknowledge exists on thesensorimotor/vestibular manifestation of spaceflight and G-transitions,the HRP outlines gaps in knowledge that necessitate further investigations such as:describing the impact of short-and long-duration weightlessness,with and without space radiation on postural control,gross and fine motor control, spatial disorientation [55].The investigation has the potential to get a greater understanding of how astronauts acclimatize their motor abilities and perception in a microgravity environment. If certain sensory or motor impairments in a microgravity settng are revealed,it has the potential to facilitate the advancement of countermeasures,encompassing customized training regimens or even pharmaceutical treatments. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,436,484,474]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Researchers aim to use Pilote and future advanced tools to optimize workspace design in microgravity and enhance telerobotics,where a remote operator directs robotic tasks. (Fig.1). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,475,484,513]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Immersive Exercise (10/2020-3/2022): Microgravity conditions create unique challenges for maintaining appropriate physical and mental health among astronauts.Muscle and bone mass are affected, and maintaining appropriate aerobic exercise is difficult. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,66,852,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,80,937,223]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The HRP well documents the risk of spaceflight conditions on the cardiovascular system,muscle and bone health,and aerobic capacity in astronauts.Some reported observations mentioned as part of the HRP list of health risks include alterations in bone strength and rate of fracture healing, changes in muscle mass resulting in decline in endurance, and cardiovascular deconditioning and remodeling associated with atherosclerosis-and ionizing radiation pathologies.As such the HRP outlines that more research is needed to investigate microgravity-related exercise physiology,benchmarking muscle mass during and post-flight, and designing specialized hardware to maintain muscle mass and mitigate muscle loss. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,224,937,290]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For bone health,knowledge deficits that need further investigation include understanding the impacts of space conditions on bone physiology,healing,and turnover,and developing tools for monitoring bone health during spaceflight,measuring the impact of different loads on fracture probability,to name a few. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,291,937,341]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lastly,for cardiovascular health,the HRP outlines that research is needed to identify the structural and functional effects of space conditions on the heart, the role of extra-terrestrial oxidative stress,and the development of suitable countermeasures. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,344,937,513]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The International Space Station (IsS) is equipped with three pieces of exercise equipment to counteract the effects of microgravity on the human body:the T2 treadmill,the Cycle Ergometer with Vibration Isolation and Stabilization (CEVIS),and the Advanced Resistive Exercise Device (ARED).These inventions have helped space crews curb musculoskeletal and cardiovascular degeneration while on missions. However,astronauts on long-duration space missions must exercise approximately $^ { 2 \\mathrm { h } }$ daily in addition to their regular workload consisting of experiments,maintenance,construction,and other mission objectives.The Immersive Exercise experiment [56] incorporates an HMD VR system into daily cycling routines to enhance motivation, performance, and enjoyment during exercise.While the merging of VR and exercise on the ISS has not yet been accomplished,preliminary terrestrial tests and questionnaires among crew members are being implemented to determine if this application of VR will be incorporated into a permanent exercise option aboard the ISS.If implemented,this system could potentially provide multiple outdoor virtual environments through which astronauts can cycle,virtual coaches and teammates,and competitions with other virtual riders to enhance motivation and performance [57]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[127,547,870,914]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.1.NASA astronaut Megan McArthur dons VR headset for Pilote experiment.Credits: NASA40. \"]","image_footnote":"[]","img_path":"images/1008/6fd5b713981380b3da242187a6a3b9877afe32d8a967a2be1ee38a4fe56ac443.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[754,44,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acta Astronautica 214 (2024) 748-756 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,44,176,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"M. Brent Woodland et al. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[490,953,509,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"750 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,66,484,157]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,158,485,354]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Augmented Reality Procedures (10/2020-3/2022):Ground-based communication with astronauts in Low-Earth Orbit (LEO) occurs in a nearly real-time manner；conversely,deep space exploration limits communication by introducing time delays of approximately $2 0 \\ \\mathrm { m i n }$ in one direction.In addition, current methods for routine maintenance in orbit comprise tablets or laptops with instruction manuals,which requires the astronaut to hold these devices while switching focus between the display and the task.This project utilizes the Sidekick AR technology to perform inspection and maintenance on the Combined Operational Load Bearing External Resistance Treadmill (COLBERT） [58]．By incorporating an HMD with voice and gesture commands,the user can perform inspection and maintenance on the treadmill in a hands-free manner.In addition,he or she can complete these tasks without delays in communication with terrestrial mission leaders (Fig.2) (see Fig. 3). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,356,485,513]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Time Perception in Microgravity (9/2017-10/2021): The purpose of this investigation is to gain an understanding of astronauts'perception of time while in orbit [59]. There are many factors that may affect how time is perceived on the ISS:variations in speed of movement within the ISS compared to in gravity,increased time required to complete tasks in space when compared to the same tasks on Earth,demanding workload and perturbed sleep cycle,and multiple references of time with respect to Earth (i.e.,time zone at Mission Control Center or other locations). The experiment itself incorporates a VR HMD that astronauts use to perform tasks such as evaluating the duration of a display in the headset, reaction times,and time reproduction. The results of these experiments will help clarify how astronauts perceive time in space and allow systems to be integrated to facilitate correction as needed. Microgravity affects astronauts’ability to gauge their own velocity onboard the ISs, which in turn impacts their perception of time [59].Moreover,tasks that may take a specific amount of time on Earth require more time to be completed in space,altering an astronaut's sense of how longan activity should last [59].This effect is potentially further compounded by the absence of normal day-night cycles in space,which leads to varying sleep habits among astronauts,disrupting their biological clock [59]. The study paves the way for system enhancements that can correct distorted time perceptions,ensuring that astronauts can perform tasks more effectively [59]. Findings could also be applicable in understanding time perception in other challenging environments,such as deep-sea exploration or high-altitude mountaineering [59]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,66,937,237]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,238,937,302]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The study paves the way for system enhancements that can correct distorted time perceptions,ensuring that astronauts can perform tasks more effectively.Findings could also be applicable in understanding time perception in other challenging environments,such as deep-sea exploration or high-altitude mountaineering. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,303,937,461]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sensation and Perception (various,6/2002-3/2023): These investigations use VR to explore the effects of microgravity on the body's sensory systems and how the body responds to these alterations in sensation and perception [6O].The GRIP [61] and GRASP [62] experiments examine how microgravity affects astronauts’performance on reaching for targets and on the grip forces used for tasks.The Neurocog [63] and VECTION [64] experiments explore how speed of body movement and proprioception alter perceptual understandings of motion in decreased or absent gravity.The information gained from these experiments will fine-tune the way in which equipment,vehicles,robots,and systems are developed to improve safety,ergonomics,and speed at which spaceflight missions can be accomplished. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,462,936,514]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ARAMIS (4/2017-2/2018): The Augmented Reality Application for Maintenance,Inventory，and Stowage (ARAMIS）project aimed to decrease the time spent on maintenance,inventory,and stowage tasks by incorporating a tablet-based AR program to guide astronauts in accomplishing these tasks [65]. One primary purpose was to determine whether AR applications had utility and validity for improving the speed and accuracy of astronauts’work in the aforementioned areas.This project differed from Sidekick and the T2 Treadmill AR Procedure in that no HMD was used.This decreases the usefulness of current AR technologies which allow the user to maintain head fixation on the task as well as free both hands for use in performing the actual objective. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[129,546,872,914]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.2.AstronautSchiogchipreparesformaintenanceproceduresonteTTeadmillileeingistructiosviRCedits:A. \"]","image_footnote":"[]","img_path":"images/0555/e0fb7e6b6c15e6729e0a67e466229c520cbd1438e26deb1957899b6f10e63a5d.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[754,44,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acta Astronautica 214 (2024) 748-756 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,44,176,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"M. Brent Woodland et al. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[490,953,507,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"751 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[129,68,870,382]","code_body":null,"code_caption":null,"image_caption":"[\"igd ipace Agency) astronaut Thomas Pesquet.57. \"]","image_footnote":"[]","img_path":"images/0995/2045e31e1366581e489254b2370ce680fce467a3ae9f9c4c658fb645e6c83f6a.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[62,432,484,523]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,524,485,655]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Healthcare Delivery (10/2021-9/2022): The term “holoportation\"is a combination of the words“holographic”and “teleportation.”The Holoportation Behavioral technology probes the feasibility of two-way communication between astronauts in orbit and ground-based mission control using ARHMDs [66].Each user wears the headset and sees the other user in their augmented reality display.Two functionalities are evaluated:a holoportation medical conference between a crew member and the flight surgeon as well as a family conference with the crew member's family to determine the capability of the technology to work outside of mission control [67]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,658,485,866]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Healthcare Delivery (3/2022-9/2022):MedChecker utilizes computer vision and AR to recognize and identify medications whose images have been captured through the device's camera [68].This technology will allow even non-medically trained astronauts to identify and administer medications during spaceflight.Additionally,the technology can assist crew members with inventory management by identifying medications,recording the supplies,and reducing errors with medication administration.A separate project, the Autonomous Medical Officer Support Software Demonstration (AMOs Demonstration), showed how software was effective in guiding astronauts in performing medical testing with no prior training in the task [69]; notably,there was no extended reality in this project.However,using this type of technology in conjunction with AR could potentially open an entire virtual library of medical techniques and tests available to guide crew members through administering medical care without the need for ground communication. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,881,275,892]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.1.3. Applications in ophthalmology ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,895,485,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"There are no currently no real-life applications of VR/AR during spaceflight for ophthalmology.However,a number of promising potential ideas and devices have been put forward and described in the last few years such as a head-mounted digital metamorphopsia suppression technique [7O],a dynamic visual acuity assessment device and stroboscopic countermeasure in a single head-mounted display [71,72],and wearable multi-modal visual assessment system for SANS [73],are several examples of this emerging novel technology designed for future spaceflight. This technology also hopes to be used terrestrially to help vision screening of underserved populations on Earth [74,75].Though not a completely exhaustive list,the examples displayed in Table 1 demonstrate the general categories in which VR and AR are used within the realm of spaceflight. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,432,937,563]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,578,581,590]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.1.4. Gait ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,591,937,682]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Microgravity is a unique environment that necessitates adaptation. Missions to the moon and Mars and returning to Earth would require astronauts to become accustomed to varying levels of gravitational exertion. Using VR,researchers are exploring how changes in sensory inputand gravity affect an individual's ability to adapt their gait to the new environments [76,77]. This has important implications for the success of spacewalks off Earth. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,697,673,707]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.1.5.Sensation/perception ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,709,937,800]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Normal internal constructs of gravity may change in microgravity, thus affecting the sensorimotor responses of astronauts.Investigators have employed VR methods to clarify the visual vestibular interplay in simulated conditions of altered gravity 76,77.VR hasalso been applied to spaceflight by evaluating the effects of spatial orientation on emergency egress from spacecraft 81 and improvements in ergonomics to enhance the fidelity of VR to the real world of space exploration.82. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,815,695,827]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.1.6.Vestibulo-ocular training ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,829,937,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The study explores the potential application of Stroboscopic Visual Training (SVT) in AR as a countermeasure for Space Motion Sickness (SMS) and SANS [71].The main objective was to explore how SVT could improve Dynamic Visual Acuity (DVA) and alleviate SMS symptoms in astronauts [71].Varjo XR-3,an AR headset,was used to implement a stroboscopic effect,altering vision at different frequencies $( 6 \\ \\mathrm { H z } , 3 \\ \\mathrm { H z }$ ， and $1 \\ \\mathrm { H z }$ ）[71].Four groups of participants were tested: healthy individuals without a headset, healthy individuals with a stroboscopic AR headset,individuals wearing minifying lenses to simulate gravitational changes,and a group wearing both minifying lenses and the stroboscopic AR headset.DVA was measured binocularly using Landolt C optotypes [71].Findings indicate that SVT may serve as an effective countermeasure for the vestibulo-ocular adaptations experienced by astronauts during spaceflight[71].The study showed that stroboscopic lighting may have the potential to improve DVA and reduce SMS [71]. The technology was also proposed as a potential terrestrial analog for vestibular dysfunctions and falls among the elderly,however,further investigations into the most effective strobe rates and long-term adaptation to better ascertain its efficacy as a countermeasure are needed [71]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,44,176,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"M. Brent Woodland et al. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[490,953,509,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"752 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[754,44,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acta Astronautica 214 (2024) 748-756 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[65,104,468,911]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0010/e4af5dc645c52d16823717ad67df6a3b29e3437631e08106a88adf6f80f01b6d.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td colspan=\"3\">sensation& perception,and exercise.</td></tr><tr><td>Group McHenry6 et al. (2020)</td><td>Investigation Design and development of AR</td><td>Category Navigation</td></tr><tr><td></td><td>visor display for eventual incorporation into spacesuits for EVA</td><td></td></tr><tr><td>Anandapadmanaban61 et al. (2018) Mulcahy83 et al. (2016)</td><td>AR navigation system for planetary exploration Evaluation of VR in mitigating fear</td><td>Navigation</td></tr><tr><td></td><td>of flying,particularly for commercial spaceflight operations</td><td>Psychology</td></tr><tr><td>Lyons6² et al. (2020)</td><td>Provided access to VR environments outside of a confined and isolated environment (H-SEAS analog)</td><td>Psychology</td></tr><tr><td>Eikema64 et al. (2016)</td><td>Used VR visual input to evaluate walking pattern adaptation in changing sensorimotor environments to mimic extreme changes astronauts face when</td><td>Gait</td></tr><tr><td>Leaes65 et al. (2006)</td><td>returning to Earth after prolonged time in microgravity Analysis of gait under simulated reduction in gravity with and</td><td>Gait</td></tr><tr><td>Helin et al. (2018)</td><td>without VR HMD Analyze the effectiveness of AR technology in performing tasks</td><td>Task Performance</td></tr><tr><td>Braly68 et al. (2019)</td><td>akin to those found on the ISS by using mock-ups Compare task performance using paper instructions versus AR</td><td>Task Performance</td></tr><tr><td>Nuernberger66 et al. (2020)</td><td>instructions Evaluated the utility of AR in completing a maintenance task at</td><td>Task Performance</td></tr><tr><td>Russomano et al. (2019)</td><td>Aquarius Description of how VR can be used to induce symptoms of space motion sickness (SMS) and allow</td><td>Space Motion Sickness</td></tr><tr><td>Jaekl7 et al. (2005)</td><td>ground teams to study VR-induces SMS-like symptomatology Used VR to exam the relationship between visual gain, head motion, and microgravity. One participant</td><td>Space Motion Sickness</td></tr><tr><td>Stroud1 et al. (2005)</td><td>performed testing in microgravity during a parabolic flight Tested subjects'performance on a VR task when beginning the procedure in various orientations</td><td>Space Motion Sickness</td></tr><tr><td>Chen7² et al. (2015)</td><td>compared to a single starting orientation Examined the role of orientation preferences and simulated space</td><td>Space Motion Sickness</td></tr><tr><td>Montgomery7 et al. (2001)</td><td>motion sickness using a virtual environment Development of a surgical assistance/training system with an HMD,tracked surgical instruments,</td><td>Training</td></tr><tr><td>Panait [78] et al. (2006)</td><td>and pre-programmed anatomy and surgical techniques Assessed performance on VR laparoscopic skils in terrestrial and</td><td>Training</td></tr><tr><td>Bruguera [79] et al. (2019)</td><td>microgravity conditions (parabolic flight) VR simulation of piloting techniques required for docking</td><td>Training</td></tr><tr><td>Harm [80] et al.(2008)</td><td>spacecraft in orbit Utilized VR to explore sensorimotor adaptation and visual-vestibular</td><td>Sensation &</td></tr><tr><td>Russo [81] et al. (2017)</td><td>interaction that may occur in the altered condition of microgravity Used an internal model of gravity to</td><td>Perception Sensation &</td></tr><tr><td></td><td>predict where a virtual ball would be intercepted based on direction</td><td>Perception</td></tr></table>","table_caption":"[\"Table 1 Extended reality-based investigations for spaceflight. Categories include navigation，psychology，gait, task performance,space motion sickness,training, \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[510,80,937,320]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0392/c49aad6c5942a97414c8dfe5a20729b366dd5d5d61d1dd664fa441bed55b0ce7.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td>Group</td><td>Investigation</td><td>Category</td></tr><tr><td>Yoshimitsu [82] et al. (2010)</td><td>Comparison of VR-based exercise to electrical muscle stimulation, includinga parabolic flight experiment, in preventing microgravity-induced muscle</td><td>Exercise</td></tr><tr><td>Keller [83] et al. (2021)</td><td>atrophy VR rowing game in conjunction with physical rowing machine to mimic technology and equipment available for future long-distance</td><td>Exercise</td></tr><tr><td>Aoki [84] et al.(2008)</td><td>spaceflight and improve exercise effectiveness VRHMD exploring variations in orientation while being guided through a virtual space station. Evaluated effects on a virtual</td><td>Other</td></tr><tr><td>Zhou [85] et al. (1998)</td><td>"emergency egress”situation Experimentation regarding improved ergonomics to improve fidelity of spaceflight virtual reality</td><td>Other</td></tr></table>","table_caption":"[\"Table 1 (continued) \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[514,339,937,496]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,498,937,721]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Previous studies using computational methods found a reduction in astronauts'dynamic visual acuity (DvA) following prolonged periods of space travel[72].The primary objective of this study was to establish the validity of a novel approach for evaluating dynamic visual acuity (DVA）by employing virtual reality (VR） technology [72].The researchers used various VR/AR headsets,including the HTC Vive Pro Eye system,and Epic's UnrealEngine 4 for the technical framework.The device also included eye-tracking features to monitor the eye's fixation [72].A preliminary investigation with a sample size of five individuals demonstrated a robust association between the virtual reality (VR) approach and conventional dynamic visual acuity (DvA) assessments conducted on a laptop [72].The observed Pearson correlation coefficient of O.91 substantiates this substantial correlation.The results indicate that utilizing virtual reality (VR) for dynamic visual acuity (DVA) evaluation shows potential as a viable alternative to traditional methods,particularly for monitoring astronauts in space missions that involve changes in gravity forces [72]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,735,801,747]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.1.7.VR/AR to address limitations of spaceflight ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,749,937,813]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Also VR/AR technologies continue to evolve they will become lighter and more powerful. The Apple Vision Pro (AVP) represents a new,and significantly improved mixed reality headset with a $^ { 4 \\mathrm { ~ k ~ } }$ display and spatial computing capabilities [86-88]．Table 2 summarizes the different studies pertaining to the current VR/AR limitations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,828,816,839]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.1.8.Mass and volume limitations and confinement ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,841,937,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Volume limitations and mass requirements are closely related and require important considerations.For instance,a long-duration mission to Mars does not allow for resupply from Earth as would be customary for ISS missions.All the oxygen, food,water,medical equipment,and othernecessities for the 2.5-year journey [52] must be carried with the crew.The limited availability of space for medications and medical supplies means that not every possible complication (illness,trauma, etc.) can be addressed; risk stratification is necessary to identify the most likely events and the severity of impact on the mission and crew health. Since the crew may accommodate up to four members,the number of life-sustaining supplies alone contributes considerably to the payload to Mars,competing for space and mass needed for experimental equipment,exercise machinery,and mission-critical technology.In addition, the vehicle that will deliver the crew is limited in size leading to limited mobility of astronauts,lack of privacy,and psychological distress.Fewer astronauts,in turn,limits the amount of experience and expertise available to the crew.Power constraints are influenced by factors such as electrical,chemical,and mechanical power available for vehicular function,flight operations,cabin lighting,and other on-board activities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[754,44,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acta Astronautica 214 (2024) 748-756 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[62,44,178,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"M. Brent Woodland et al. ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[490,953,509,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"753 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[60,92,484,290]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0362/479b636f48e32854c00f67eedf86e17c3bcfef1ec2c4f30c206bf5194e6e633f.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":"<table><tr><td>Spaceflight Limitation</td><td>Potential VR/AR Solution</td></tr><tr><td>Mass and volume constraints</td><td>HMDs tend to be lightweight, compact,and multi- functional</td></tr><tr><td>Emergency return to Earth may be impossible</td><td>Enhanced management of emergency situations</td></tr><tr><td>Communication delays</td><td>Improved autonomyvia preset procedures</td></tr><tr><td>Confinement</td><td>Expansive environment using virtual reality</td></tr><tr><td>Isolation</td><td>Holographic teleportation</td></tr><tr><td>Medical supplies and services</td><td>Medical officer support via augmented reality library</td></tr><tr><td>Increased cognitive demand</td><td>AR-guided procedures and processes</td></tr><tr><td>Microgravity</td><td>Enhanced preflight training of realistic microgravity environment</td></tr><tr><td>Spaceflight associated neuro- ocular syndrome</td><td>Close monitoring and computational reversal of visual distortions within VR headset</td></tr><tr><td>Exercise demands</td><td>Improved motivation and exercise efficacy via exergaming-type technology</td></tr></table>","table_caption":"[\"Table 2 Spaceflight limitations and potential solutions with virtual/augmented reality. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[62,308,485,465]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,466,485,663]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Similar to the CAL and COLBERT maintenance tasks detailed above, scientists are investigating how AR in particular can help astronauts execute assignments more efficiently.For instance,at the underwater Aquarius laboratory,researchers used AR to guide crew members in a daily maintenance task.These researchers found ways in which AR was beneficial,as well as ways in which it could be improved.For instance, their mission revealed that their AR only gave steps to the procedure one ata time (forwards or backwards).They noted that paper procedures were more easily searched and navigated 66.Other studies have used ISS mock-ups to evaluate the efficiency of AR67 or compared using paper instructions to AR instructions for spaceflight-like objectives 68. The latter group found that AR instructions significantly improved performance time when compared to paper instructions and found evidence to suggest that AR instruction methods may be more effective at transferring learning to new situations 68.68. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,678,236,689]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.1.9. VR/AR for stress relief ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,692,485,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Astronauts face considerable mental and emotional stress during space travel due to confinement, isolation,and high cognitive demands [53].In a space analog,Hawaii Space Exploration Analog and Simulation (HI-SEAS),VR was used to expose the inhabitants to environments outside of the dome [51].VR “travel\"to familiar or calming places (i.e., mountain ranges,beaches,etc.）has been shown to be an effective method for reducing objective and subjective stress [89].This measure could be incorporated into VR systems for deep space missions,allowing astronauts to “escape”to confines of the cabin and experience natural scenery from Earth.Astronauts must be proficient in using AR/XR systems.The time and effort required to train astronauts to adapt to new technologies can be substantial,considering the multifaceted skills astronauts already need to acquire.Furthermore,the efficacy of AR/XR for stress relief can be subjective and individual-specific.A lack of customization options may render the experiences less effective for some astronauts. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,66,655,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.1.10.VR/AR exercise ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,80,937,316]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Though crew members face multiple physiologic challenges in microgravity,muscle atrophy and bone deterioration have been specifically targeted by exercise equipment installed aboard the ISS. Resistance exercise,stationary cycling,and a modified treadmill provide cardiovascular and musculoskeletal training to help mitigate the effects on these systems while in space.However, the volume limitations for a deep space mission do not allow for all these machines to be installed on a Mars-bound vehicle.More likely,the only equipment available will be a specialized type of rowing machine [83].Research is being conducted to evaluate the usefulness of VR exercise games in helping motivate astronauts to complete the necessary exercise regimens [57,83,90]. In addition,VR-based exercise programs have been used in conjunction with other potential muscular strengthening systems (i.e.,electrical stimulation) in the evaluation of possible countermeasures to atrophy in space [77].AR/XR systems will draw from the spacecraft's power resources.Given the extended duration of deep space missions,efficient power management is essential,and AR/XR could strain available energyreserves. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,317,937,474]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In conclusion,AR and XR technology demonstrates significant potential in mitigatinga range of challenges associated with space travel. These technologies are gradually becoming important components of space missons,as they contribute to medical diagnosis,relieve psychological stresses,and improve learning and operational eficiency. The MedChecker application represents an excellent example of the innovative medical capabilities offered byaugmented reality (AR),as it enables anyone without medical training, such as astronauts, to recognize and dispense medications effectively and precisely.Additionally, this technology plays a crucial role in encouraging efficient inventory management and limiting drug delivery errors, hence contributing to the overall well-being of crew members during space missions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,476,937,592]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Froma psychological standpoint,virtual reality (VR)plays a pivotal role in providing vital assistance to astronauts who struggle with the profound isolation experienced during space missions. Its capacity to recreate peaceful terrestrial environments and provide relief from stress is crucial to preserving mental health throughout prolonged periods of isolation.As technology improves,multiple tests can be incorporated into a single VR headset, thus increasing speed and accuracy while decreasing the cost and size of the equipment required to obtain the necessary diagnostic data. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,607,566,619]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Funding ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,634,936,672]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"NASA Grant [80NSSC20K183]: A Non-intrusive Ocular Monitoring Framework to Model Ocular Structure and Functional Changes due to Long-term Spaceflight. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,687,731,698]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Declaration of competing interest ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,712,937,751]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,766,583,778]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[519,790,934,911]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"[1]P.Milgram,F.Kishino,A Taxonomy of mixed reality visual displays,Accessed: Jan. 11,2023. [Online]. Available: https://search.ieice.org/bin/summary.php?id=e77- d_12_1321. \n[2] A.W.K.Yeung,etal., Virtual and augmented reality applications in medicine: analysis of the scientific literature,J.Med.Internet Res.23 (2) (Feb.2021), e25499,https://doi.org/10.2196/25499. \n[3] L.Li, et al., Application of virtual reality technology in clinical medicine, Am. J. Transl. Res.9 (9) (Sep.2017) 3867-3880. \n[4]H.Arvind,A.Klistorner, S.L.Graham,J.R.Grigg,Multifocal visual evoked responses to dichoptic stimulation using virtual reality goggles: multifocal VER to dichoptic stimulation, Doc.Ophthalmol.112(3)(May 2006) 189-199,https://doi. 0rg/10.1007/s10633-006-0005-y. [5] H.Arvind,et al., Dichoptic stimulation improves detection of glaucoma with multifocal visual evoked potentials, Investig. Opthalmology Vis. Sci.48 (10) (Oct. 2007) 4590, https://doi.org/10.1167/iovs.07-0318. 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","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[489,953,509,962]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"756 ","text_format":null,"text_level":null,"type":"discarded"}],"string":"[\n {\n \"bbox\": \"[62,206,714,248]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Applications of extended reality in spaceflight for human health and performance \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,261,776,310]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"M. Brent Woodlanda, Joshua Ongb, Nasif Zaman, Mohammad Hirzallahd,e,f, Ethan Waisberg 8\\\\*, Mouayad Masalkhi8, Sharif Amit KamranC, Andrew G. Leed,h,i,j,k,l,m,n Alireza Tavakkoli C \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,321,722,471]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"aBaylor College ofMedicine,Houston,TX, United tates \\nb Michigan edicine,UniversityofMichigan,AnnArbor,MI,Unitedtates \\nHuan-i \\nCentere \\neDepartmentof Neurology,Baylor Colegeof Medicine,Houston,TX,United tates \\nfDepartmentofeurosrgryylorlgfedicineouto,Uee \\ngUniversityollgeublinchoolofedicine,Belfield,Dublin,ed \\nhDepartetostlt \\nTheHoustoisthte,stistsialsoe \\nDeprttllk \\nk DepartmentfphthalmologyUniversityofTexas Medical Branch,Galveston,TXUnitedtates \\nlUniversityofexasdersonCancerCenterHouston,Uitedtes \\nm Texas A&MCollege of Medicine, Texas, United States \\n\\\"DepartmentofOphthalmology,The UniversityofIowa Hospitalsand Clinics,Iowa City,IA,UnitedStates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,501,157,513]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABSTRACT \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,527,939,634]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Vitaeaiie evalatiolatt decadeio coity teetecholisarb developedfoe vol itigate possiblebarstourasaceigdadeploosiscgsaceligsaedeurlard). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[63,673,378,686]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction to virtual and augmented reality \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,699,484,778]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Virtual reality is a technology that immerses a user in a computergenerated environment, often using wearable devices such as a headmounted display (HMD),known colloquially as“VR goggles”or“VR headset.\\\"Visual,auditory,and other sensory inputs may be manipulated to give the user an enhanced sense that he or she is physically present within the virtual environment. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,780,484,818]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The concepts of the reality-virtuality (RV) continuum and “mixed reality”(MR) were concurrently introduced Paul Milgram and Fumio Kishino in their 1994 publication “A Taxonomy of Mixed Reality Visual \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,673,937,765]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Displays”[1].Visual displays for mixed reality (MR) entail the blending of actual and virtual worlds at some point along the“virtuality continuum,”which links entirely real settings to entirely virtual ones [1].The most well-known of these is perhaps augmented reality (AR),which is the term used to describe any instances in which a presentation of the real world is enhanced by the use of virtual (computer graphic) items [1]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,766,936,818]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Over the last thirty years,VR research in healthcare has grown exponentially [2].The technology has been applied in multiple disciplines,most prominently in surgical training,pain management,and psychiatric therapy [3].Laparoscopic,orthopedic,and microsurgical VR systems have been developed to help surgical trainees acquire the necessary skils to perform successful procedures in a safe,inexpensive, and iterative manner (2).VR has been combined with standard anesthetic protocols to help alleviate pain and may be an important part of pain management [3].VR has also shown promise in the treatment of psychiatric disease,particularly anxiety disorders.By implementing virtual exposure to anxiety-inducing stimuli,mental health professionals can aid patients in learning new responses to fear.This is especially useful when patients’fears are difficult to replicate in the office setting (crowds, heights,animals,etc.） [3]. Other common applications of VR in healthcare include neurological conditions (stroke, Parkinson disease,Alzheimer disease,dementia,multiple sclerosis), obesity,and cancer care [2]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,68,944,171]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Contents lists available at ScienceDirect ACTA ASTRONAUTIGA Acta Astronautica ELSEVIER journal homepage: www.elsevier.com/locate/actaastro \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[68,844,603,868]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\\\\* Corresponding author.University Colege Dublin School of Medicine,Belfield, Dublin 4,Ireland. E-mail address: Ethan.waisberg@ucdconnect.ie (E. Waisberg). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[60,882,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"nttps://ao1.org/1u.1u1b/j.actaastro.zuz3.11.025 Received 21 July 2023; Received in revised form 2 November 2023; Accepted 15 November 2023 Available online 23 November 2023 0094-5765/ $' { \\\\textcircled{ \\\\mathbf { C } } }$ 2023 The Authors. Published by Elsevier Ltdon behalf of IAA.Thisisan open accessarticle under the CC BY license (http://creativecommons.org/licenses/by/4.0/). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[840,185,890,223]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Check for updates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[394,45,605,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acta Astronautica 214 (2024) 748-756 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,66,485,237]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,238,485,355]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Because most VR technologies rely heavily on visual input for their effectiveness,ophthalmology is in a unique position to adopt virtual reality as a means of testing for and monitoring ophthalmic disease. These include visual evoked potentials [4-6],which can be used to evaluate visual pathway defects occurring from diseases such as multiple sclerosis or glaucoma,perimetry [7-14],binocular vision disorders [15-19]，amblyopia [20-22]，choroidal/retinal disease[23-28], contrast sensitivity [29],visual acuity [3O,31],and anterior chamber trauma [32]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,356,484,474]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Virtual reality slit lamp,direct ophthalmoscope,and indirect ophthalmoscope simulators have been developed to help trainees to obtain proficiency in visualizing ocular structures [33].These simulators have also been programmed to be able to display various eye pathologies so that the user may practice not only the technique but also learn to identifyabnormalities in the examination.The software has the capacity to evaluate the user on technical skill as well as diagnostic accuracy [33].VR has been developed to aid learners in developing skills in posterior segment procedures as well as cataract surgery. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,476,485,633]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In contrast to virtual reality (VR),which entirely submerges users in a digitally created virtual space,augmented reality (AR) is based on the realworld and improves itwith digital data [34].AR presentsa fresh method for medical treatments and training [35].This technology has been applied to several fields in medicine.One example is AccuVein (AccuVein Inc.,NY,USA),instrument that presents a map of blood vessels onto the skin [36]. Google Glass (GG),a head-mounted display (HMD) that superimposes images on top of the real-world environment and may include auditory,smell, taste,and haptic feedback features. Khor et al.[37] demonstrated prospects for having a variety of innovative effects on surgery,notably in the field of surgical training in a simulated operating environment. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,634,484,684]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Augmented reality combines the physical world with the virtual world by overlaying computer-generated images onto the user's visual field.This allows the user to see objects that are physically present in the environment while receiving additional input from the AR device. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,687,485,804]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Typically,these devices are also head-mounted displays but have a transparent material through which the wearer can see the real world while the artificial images are displayed in the field of view.VR and AR have important applications in medicine,particularly ophthalmology [38,39],as well as space exploration.Significant physiological changes and challenges during spaceflight include bone demineralization,loss of skeletal muscle mass,space motion sickness due to vestibular issues, anemias [4O-42] immunological dysfunction,among many other alterations [43]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,805,484,923]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Multiple ophthalmic clinical and imaging findings have been reported among astronauts following LDSF in a condition now termed space-associated neuro-ocular syndrome,or SANs.Those findings include optic disc edema [44],globe flattening,choroidal and retinal folds [45],hyperopic refractive error shifts greater than 0.75 diopters, and focal retinal ischemia [46].Not all signs are necessary to suggest the diagnosis,and not all astronauts experience the clinical manifestations of SANS [47],however,increased exposure to microgravity has been observed to increase the likelihood of SANS development [48]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,924,484,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Current on-board ophthalmic imaging modalities include optical coherence tomography (OCT),retinal fundoscopy，and orbital ultrasound which have been useful for understanding the imaging changes in this neuro-ophthalmic phenomenon [49]. OCT angiography (OCTA) was recently introduced to the ISS which will provide insight into the ocular vascular flow during spaceflight[46,5O].Additional modalities may be limited due to invasive procedural concerns, time,or mass and volume constraints. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,66,937,157]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,160,937,380]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"There are several limitations to spaceflight that astronauts face as they undertake missions farther and farther from Earth.One example is that missions in low Earth orbit (LEO),such as the ISS,focus on a protocol designed to stabilize the ill or injured crew member and return to Earth for definitive medical care [51].To ameliorate power issues, spacecraft such as Orion are being outfitted with solar panels.Missions to the moon follow a similar strategy but require an additional four to five days for transport [51].However,as the distance becomes even greater,such as the 50-milion-kilometer expedition to Mars, emergency return to Earth becomes impractical if not impossible to execute [52]. Crews to Mars will likely consist of a chief medical officer who is a trained physician to mitigate limitations of experience and expertise among crew members [51]. Still,the illnesses or injuries faced by the astronauts may be outside of the physician's scope of expertise,or the physician may be the injured crew member requiring medical attention. While spaceflight is inherently dangerous,research and development projects seek to attenuate the risks to an acceptable level. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,383,937,447]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Many of the limitations fall into general categories,such as mass/ power/volume constraints and isolation,but these barriers are often intertwined.As such,various space agencies across the globe are working to identify limitations and risks to long-duration spaceflight and provide innovative countermeasures for these obstacles. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,462,926,475]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.1.Current applications of VR/AR during spaceflight for human health \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,490,690,501]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.1.1．Physiological challenges \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,503,937,843]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Space is a harsh environment that presents a unique combination of challenges to crew members. The National Aeronautics and Space Administration (NASA) has identified over twenty individual risks by which astronauts'health and wellbeing may be affected during spaceflight, particularly those missions which involve travel to deep space (i. e.,Mars）[53].Current areas under investigation vary widely,but medical threats include risk of kidney stones,bone fracture,psychiatric disorders,sleep disturbances,altered vestibular function,inadequate food,and nutrition,decreased muscle mass/strength,and radiation exposure [53].While most of the risks outlined by NASA are also conditions found on Earth,the space environment is unique in that these threats are faced simultaneously. In addition, microgravity and absence of Earth's atmosphere may accelerate or accentuate these risks.NASA has sorted these dangers into four categories: exploration medical capability,human factors and behavioral performance,human health countermeasures,and space radiation [53].Deep space exploration poses greater risks because these missions necessitate further lengths of time in the harsh space conditions [54].Furthermore,the distance between the crew and Earth increases,resulting in delays in communication (up to $2 0 \\\\mathrm { { m i n } }$ one-way fora Mars mission [52]),decreased access to medical and technical experts,impracticality of return to Earth in emergency situations,confinement within small spacecraft,increased social isolation,and uncertainty regarding mission success (especially during pioneer missions).The following projects have been carried out to determine the efficacy and practicality of utilizing VR/AR technologies to advance space exploration. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,846,937,938]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Human Research Program (HRP) created at the Johnson Space Center (JSC) exerts great efforts and investment on analyzing and minimizing the greatest risks to astronaut health and function in support of planetary exploration.As such, the Health Research Roadmap page outlines the different health obstacles and risks facing astronauts during spaceflight.Furthermore,this roadmap represents a significant reference and starting point for inspiring novel tools and devices that aid astronauts and minimize the risk of adverse health effects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,44,176,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"M. Brent Woodland et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[754,44,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acta Astronautica 214 (2024) 748-756 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[490,953,509,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,66,408,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,93,242,104]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.1.2.Applications in medicine \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,105,485,249]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sensorimotor and Vestibular Function (10/2020-3/2022):Pilote [55] is an HMD VR system that investigates the complex interplay between haptics,proprioception,the vestibular system，visual input, movement,and microgravity.The technology requires astronauts to perform two game-like tasks by 1) controlling the orientation of and guiding virtual objects through a series of virtual paths as quickly and accurately as possible and 2) maneuvering a virtual robotic arm to attach it to a target object [55].These tests are performed on Earth as well as in microgravity with the goal of elucidating which combinations of tactile input,head position,visual input,and so on lead to the best combination for enhanced astronaut performance [55]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,252,485,433]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The role of sensorimotor/vestibular function in spaceflight is welldocumented in the HRP list as a critical player in the success of missions[55].While baselineknowledge exists on thesensorimotor/vestibular manifestation of spaceflight and G-transitions,the HRP outlines gaps in knowledge that necessitate further investigations such as:describing the impact of short-and long-duration weightlessness,with and without space radiation on postural control,gross and fine motor control, spatial disorientation [55].The investigation has the potential to get a greater understanding of how astronauts acclimatize their motor abilities and perception in a microgravity environment. If certain sensory or motor impairments in a microgravity settng are revealed,it has the potential to facilitate the advancement of countermeasures,encompassing customized training regimens or even pharmaceutical treatments. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,436,484,474]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Researchers aim to use Pilote and future advanced tools to optimize workspace design in microgravity and enhance telerobotics,where a remote operator directs robotic tasks. (Fig.1). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,475,484,513]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Immersive Exercise (10/2020-3/2022): Microgravity conditions create unique challenges for maintaining appropriate physical and mental health among astronauts.Muscle and bone mass are affected, and maintaining appropriate aerobic exercise is difficult. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,66,852,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,80,937,223]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The HRP well documents the risk of spaceflight conditions on the cardiovascular system,muscle and bone health,and aerobic capacity in astronauts.Some reported observations mentioned as part of the HRP list of health risks include alterations in bone strength and rate of fracture healing, changes in muscle mass resulting in decline in endurance, and cardiovascular deconditioning and remodeling associated with atherosclerosis-and ionizing radiation pathologies.As such the HRP outlines that more research is needed to investigate microgravity-related exercise physiology,benchmarking muscle mass during and post-flight, and designing specialized hardware to maintain muscle mass and mitigate muscle loss. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,224,937,290]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For bone health,knowledge deficits that need further investigation include understanding the impacts of space conditions on bone physiology,healing,and turnover,and developing tools for monitoring bone health during spaceflight,measuring the impact of different loads on fracture probability,to name a few. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,291,937,341]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lastly,for cardiovascular health,the HRP outlines that research is needed to identify the structural and functional effects of space conditions on the heart, the role of extra-terrestrial oxidative stress,and the development of suitable countermeasures. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,344,937,513]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The International Space Station (IsS) is equipped with three pieces of exercise equipment to counteract the effects of microgravity on the human body:the T2 treadmill,the Cycle Ergometer with Vibration Isolation and Stabilization (CEVIS),and the Advanced Resistive Exercise Device (ARED).These inventions have helped space crews curb musculoskeletal and cardiovascular degeneration while on missions. However,astronauts on long-duration space missions must exercise approximately $^ { 2 \\\\mathrm { h } }$ daily in addition to their regular workload consisting of experiments,maintenance,construction,and other mission objectives.The Immersive Exercise experiment [56] incorporates an HMD VR system into daily cycling routines to enhance motivation, performance, and enjoyment during exercise.While the merging of VR and exercise on the ISS has not yet been accomplished,preliminary terrestrial tests and questionnaires among crew members are being implemented to determine if this application of VR will be incorporated into a permanent exercise option aboard the ISS.If implemented,this system could potentially provide multiple outdoor virtual environments through which astronauts can cycle,virtual coaches and teammates,and competitions with other virtual riders to enhance motivation and performance [57]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[127,547,870,914]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.1.NASA astronaut Megan McArthur dons VR headset for Pilote experiment.Credits: NASA40. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/1008/6fd5b713981380b3da242187a6a3b9877afe32d8a967a2be1ee38a4fe56ac443.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[754,44,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acta Astronautica 214 (2024) 748-756 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,44,176,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"M. Brent Woodland et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[490,953,509,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"750 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,66,484,157]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,158,485,354]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Augmented Reality Procedures (10/2020-3/2022):Ground-based communication with astronauts in Low-Earth Orbit (LEO) occurs in a nearly real-time manner；conversely,deep space exploration limits communication by introducing time delays of approximately $2 0 \\\\ \\\\mathrm { m i n }$ in one direction.In addition, current methods for routine maintenance in orbit comprise tablets or laptops with instruction manuals,which requires the astronaut to hold these devices while switching focus between the display and the task.This project utilizes the Sidekick AR technology to perform inspection and maintenance on the Combined Operational Load Bearing External Resistance Treadmill (COLBERT） [58]．By incorporating an HMD with voice and gesture commands,the user can perform inspection and maintenance on the treadmill in a hands-free manner.In addition,he or she can complete these tasks without delays in communication with terrestrial mission leaders (Fig.2) (see Fig. 3). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,356,485,513]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Time Perception in Microgravity (9/2017-10/2021): The purpose of this investigation is to gain an understanding of astronauts'perception of time while in orbit [59]. There are many factors that may affect how time is perceived on the ISS:variations in speed of movement within the ISS compared to in gravity,increased time required to complete tasks in space when compared to the same tasks on Earth,demanding workload and perturbed sleep cycle,and multiple references of time with respect to Earth (i.e.,time zone at Mission Control Center or other locations). The experiment itself incorporates a VR HMD that astronauts use to perform tasks such as evaluating the duration of a display in the headset, reaction times,and time reproduction. The results of these experiments will help clarify how astronauts perceive time in space and allow systems to be integrated to facilitate correction as needed. Microgravity affects astronauts’ability to gauge their own velocity onboard the ISs, which in turn impacts their perception of time [59].Moreover,tasks that may take a specific amount of time on Earth require more time to be completed in space,altering an astronaut's sense of how longan activity should last [59].This effect is potentially further compounded by the absence of normal day-night cycles in space,which leads to varying sleep habits among astronauts,disrupting their biological clock [59]. The study paves the way for system enhancements that can correct distorted time perceptions,ensuring that astronauts can perform tasks more effectively [59]. Findings could also be applicable in understanding time perception in other challenging environments,such as deep-sea exploration or high-altitude mountaineering [59]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,66,937,237]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,238,937,302]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The study paves the way for system enhancements that can correct distorted time perceptions,ensuring that astronauts can perform tasks more effectively.Findings could also be applicable in understanding time perception in other challenging environments,such as deep-sea exploration or high-altitude mountaineering. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,303,937,461]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sensation and Perception (various,6/2002-3/2023): These investigations use VR to explore the effects of microgravity on the body's sensory systems and how the body responds to these alterations in sensation and perception [6O].The GRIP [61] and GRASP [62] experiments examine how microgravity affects astronauts’performance on reaching for targets and on the grip forces used for tasks.The Neurocog [63] and VECTION [64] experiments explore how speed of body movement and proprioception alter perceptual understandings of motion in decreased or absent gravity.The information gained from these experiments will fine-tune the way in which equipment,vehicles,robots,and systems are developed to improve safety,ergonomics,and speed at which spaceflight missions can be accomplished. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,462,936,514]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ARAMIS (4/2017-2/2018): The Augmented Reality Application for Maintenance,Inventory，and Stowage (ARAMIS）project aimed to decrease the time spent on maintenance,inventory,and stowage tasks by incorporating a tablet-based AR program to guide astronauts in accomplishing these tasks [65]. One primary purpose was to determine whether AR applications had utility and validity for improving the speed and accuracy of astronauts’work in the aforementioned areas.This project differed from Sidekick and the T2 Treadmill AR Procedure in that no HMD was used.This decreases the usefulness of current AR technologies which allow the user to maintain head fixation on the task as well as free both hands for use in performing the actual objective. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[129,546,872,914]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.2.AstronautSchiogchipreparesformaintenanceproceduresonteTTeadmillileeingistructiosviRCedits:A. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0555/e0fb7e6b6c15e6729e0a67e466229c520cbd1438e26deb1957899b6f10e63a5d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[754,44,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acta Astronautica 214 (2024) 748-756 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,44,176,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"M. Brent Woodland et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[490,953,507,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"751 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[129,68,870,382]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"igd ipace Agency) astronaut Thomas Pesquet.57. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0995/2045e31e1366581e489254b2370ce680fce467a3ae9f9c4c658fb645e6c83f6a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[62,432,484,523]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,524,485,655]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Healthcare Delivery (10/2021-9/2022): The term “holoportation\\\"is a combination of the words“holographic”and “teleportation.”The Holoportation Behavioral technology probes the feasibility of two-way communication between astronauts in orbit and ground-based mission control using ARHMDs [66].Each user wears the headset and sees the other user in their augmented reality display.Two functionalities are evaluated:a holoportation medical conference between a crew member and the flight surgeon as well as a family conference with the crew member's family to determine the capability of the technology to work outside of mission control [67]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,658,485,866]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Healthcare Delivery (3/2022-9/2022):MedChecker utilizes computer vision and AR to recognize and identify medications whose images have been captured through the device's camera [68].This technology will allow even non-medically trained astronauts to identify and administer medications during spaceflight.Additionally,the technology can assist crew members with inventory management by identifying medications,recording the supplies,and reducing errors with medication administration.A separate project, the Autonomous Medical Officer Support Software Demonstration (AMOs Demonstration), showed how software was effective in guiding astronauts in performing medical testing with no prior training in the task [69]; notably,there was no extended reality in this project.However,using this type of technology in conjunction with AR could potentially open an entire virtual library of medical techniques and tests available to guide crew members through administering medical care without the need for ground communication. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,881,275,892]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.1.3. Applications in ophthalmology \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,895,485,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"There are no currently no real-life applications of VR/AR during spaceflight for ophthalmology.However,a number of promising potential ideas and devices have been put forward and described in the last few years such as a head-mounted digital metamorphopsia suppression technique [7O],a dynamic visual acuity assessment device and stroboscopic countermeasure in a single head-mounted display [71,72],and wearable multi-modal visual assessment system for SANS [73],are several examples of this emerging novel technology designed for future spaceflight. This technology also hopes to be used terrestrially to help vision screening of underserved populations on Earth [74,75].Though not a completely exhaustive list,the examples displayed in Table 1 demonstrate the general categories in which VR and AR are used within the realm of spaceflight. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,432,937,563]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,578,581,590]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.1.4. Gait \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,591,937,682]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Microgravity is a unique environment that necessitates adaptation. Missions to the moon and Mars and returning to Earth would require astronauts to become accustomed to varying levels of gravitational exertion. Using VR,researchers are exploring how changes in sensory inputand gravity affect an individual's ability to adapt their gait to the new environments [76,77]. This has important implications for the success of spacewalks off Earth. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,697,673,707]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.1.5.Sensation/perception \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,709,937,800]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Normal internal constructs of gravity may change in microgravity, thus affecting the sensorimotor responses of astronauts.Investigators have employed VR methods to clarify the visual vestibular interplay in simulated conditions of altered gravity 76,77.VR hasalso been applied to spaceflight by evaluating the effects of spatial orientation on emergency egress from spacecraft 81 and improvements in ergonomics to enhance the fidelity of VR to the real world of space exploration.82. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,815,695,827]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.1.6.Vestibulo-ocular training \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,829,937,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The study explores the potential application of Stroboscopic Visual Training (SVT) in AR as a countermeasure for Space Motion Sickness (SMS) and SANS [71].The main objective was to explore how SVT could improve Dynamic Visual Acuity (DVA) and alleviate SMS symptoms in astronauts [71].Varjo XR-3,an AR headset,was used to implement a stroboscopic effect,altering vision at different frequencies $( 6 \\\\ \\\\mathrm { H z } , 3 \\\\ \\\\mathrm { H z }$ ， and $1 \\\\ \\\\mathrm { H z }$ ）[71].Four groups of participants were tested: healthy individuals without a headset, healthy individuals with a stroboscopic AR headset,individuals wearing minifying lenses to simulate gravitational changes,and a group wearing both minifying lenses and the stroboscopic AR headset.DVA was measured binocularly using Landolt C optotypes [71].Findings indicate that SVT may serve as an effective countermeasure for the vestibulo-ocular adaptations experienced by astronauts during spaceflight[71].The study showed that stroboscopic lighting may have the potential to improve DVA and reduce SMS [71]. The technology was also proposed as a potential terrestrial analog for vestibular dysfunctions and falls among the elderly,however,further investigations into the most effective strobe rates and long-term adaptation to better ascertain its efficacy as a countermeasure are needed [71]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,44,176,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"M. Brent Woodland et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[490,953,509,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"752 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[754,44,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acta Astronautica 214 (2024) 748-756 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[65,104,468,911]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0010/e4af5dc645c52d16823717ad67df6a3b29e3437631e08106a88adf6f80f01b6d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td colspan=\\\"3\\\">sensation& perception,and exercise.</td></tr><tr><td>Group McHenry6 et al. (2020)</td><td>Investigation Design and development of AR</td><td>Category Navigation</td></tr><tr><td></td><td>visor display for eventual incorporation into spacesuits for EVA</td><td></td></tr><tr><td>Anandapadmanaban61 et al. (2018) Mulcahy83 et al. (2016)</td><td>AR navigation system for planetary exploration Evaluation of VR in mitigating fear</td><td>Navigation</td></tr><tr><td></td><td>of flying,particularly for commercial spaceflight operations</td><td>Psychology</td></tr><tr><td>Lyons6² et al. (2020)</td><td>Provided access to VR environments outside of a confined and isolated environment (H-SEAS analog)</td><td>Psychology</td></tr><tr><td>Eikema64 et al. (2016)</td><td>Used VR visual input to evaluate walking pattern adaptation in changing sensorimotor environments to mimic extreme changes astronauts face when</td><td>Gait</td></tr><tr><td>Leaes65 et al. (2006)</td><td>returning to Earth after prolonged time in microgravity Analysis of gait under simulated reduction in gravity with and</td><td>Gait</td></tr><tr><td>Helin et al. (2018)</td><td>without VR HMD Analyze the effectiveness of AR technology in performing tasks</td><td>Task Performance</td></tr><tr><td>Braly68 et al. (2019)</td><td>akin to those found on the ISS by using mock-ups Compare task performance using paper instructions versus AR</td><td>Task Performance</td></tr><tr><td>Nuernberger66 et al. (2020)</td><td>instructions Evaluated the utility of AR in completing a maintenance task at</td><td>Task Performance</td></tr><tr><td>Russomano et al. (2019)</td><td>Aquarius Description of how VR can be used to induce symptoms of space motion sickness (SMS) and allow</td><td>Space Motion Sickness</td></tr><tr><td>Jaekl7 et al. (2005)</td><td>ground teams to study VR-induces SMS-like symptomatology Used VR to exam the relationship between visual gain, head motion, and microgravity. One participant</td><td>Space Motion Sickness</td></tr><tr><td>Stroud1 et al. (2005)</td><td>performed testing in microgravity during a parabolic flight Tested subjects'performance on a VR task when beginning the procedure in various orientations</td><td>Space Motion Sickness</td></tr><tr><td>Chen7² et al. (2015)</td><td>compared to a single starting orientation Examined the role of orientation preferences and simulated space</td><td>Space Motion Sickness</td></tr><tr><td>Montgomery7 et al. (2001)</td><td>motion sickness using a virtual environment Development of a surgical assistance/training system with an HMD,tracked surgical instruments,</td><td>Training</td></tr><tr><td>Panait [78] et al. (2006)</td><td>and pre-programmed anatomy and surgical techniques Assessed performance on VR laparoscopic skils in terrestrial and</td><td>Training</td></tr><tr><td>Bruguera [79] et al. (2019)</td><td>microgravity conditions (parabolic flight) VR simulation of piloting techniques required for docking</td><td>Training</td></tr><tr><td>Harm [80] et al.(2008)</td><td>spacecraft in orbit Utilized VR to explore sensorimotor adaptation and visual-vestibular</td><td>Sensation &</td></tr><tr><td>Russo [81] et al. (2017)</td><td>interaction that may occur in the altered condition of microgravity Used an internal model of gravity to</td><td>Perception Sensation &</td></tr><tr><td></td><td>predict where a virtual ball would be intercepted based on direction</td><td>Perception</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1 Extended reality-based investigations for spaceflight. Categories include navigation，psychology，gait, task performance,space motion sickness,training, \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[510,80,937,320]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0392/c49aad6c5942a97414c8dfe5a20729b366dd5d5d61d1dd664fa441bed55b0ce7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Group</td><td>Investigation</td><td>Category</td></tr><tr><td>Yoshimitsu [82] et al. (2010)</td><td>Comparison of VR-based exercise to electrical muscle stimulation, includinga parabolic flight experiment, in preventing microgravity-induced muscle</td><td>Exercise</td></tr><tr><td>Keller [83] et al. (2021)</td><td>atrophy VR rowing game in conjunction with physical rowing machine to mimic technology and equipment available for future long-distance</td><td>Exercise</td></tr><tr><td>Aoki [84] et al.(2008)</td><td>spaceflight and improve exercise effectiveness VRHMD exploring variations in orientation while being guided through a virtual space station. Evaluated effects on a virtual</td><td>Other</td></tr><tr><td>Zhou [85] et al. (1998)</td><td>"emergency egress”situation Experimentation regarding improved ergonomics to improve fidelity of spaceflight virtual reality</td><td>Other</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1 (continued) \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[514,339,937,496]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,498,937,721]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Previous studies using computational methods found a reduction in astronauts'dynamic visual acuity (DvA) following prolonged periods of space travel[72].The primary objective of this study was to establish the validity of a novel approach for evaluating dynamic visual acuity (DVA）by employing virtual reality (VR） technology [72].The researchers used various VR/AR headsets,including the HTC Vive Pro Eye system,and Epic's UnrealEngine 4 for the technical framework.The device also included eye-tracking features to monitor the eye's fixation [72].A preliminary investigation with a sample size of five individuals demonstrated a robust association between the virtual reality (VR) approach and conventional dynamic visual acuity (DvA) assessments conducted on a laptop [72].The observed Pearson correlation coefficient of O.91 substantiates this substantial correlation.The results indicate that utilizing virtual reality (VR) for dynamic visual acuity (DVA) evaluation shows potential as a viable alternative to traditional methods,particularly for monitoring astronauts in space missions that involve changes in gravity forces [72]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,735,801,747]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.1.7.VR/AR to address limitations of spaceflight \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,749,937,813]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Also VR/AR technologies continue to evolve they will become lighter and more powerful. The Apple Vision Pro (AVP) represents a new,and significantly improved mixed reality headset with a $^ { 4 \\\\mathrm { ~ k ~ } }$ display and spatial computing capabilities [86-88]．Table 2 summarizes the different studies pertaining to the current VR/AR limitations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,828,816,839]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.1.8.Mass and volume limitations and confinement \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,841,937,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Volume limitations and mass requirements are closely related and require important considerations.For instance,a long-duration mission to Mars does not allow for resupply from Earth as would be customary for ISS missions.All the oxygen, food,water,medical equipment,and othernecessities for the 2.5-year journey [52] must be carried with the crew.The limited availability of space for medications and medical supplies means that not every possible complication (illness,trauma, etc.) can be addressed; risk stratification is necessary to identify the most likely events and the severity of impact on the mission and crew health. Since the crew may accommodate up to four members,the number of life-sustaining supplies alone contributes considerably to the payload to Mars,competing for space and mass needed for experimental equipment,exercise machinery,and mission-critical technology.In addition, the vehicle that will deliver the crew is limited in size leading to limited mobility of astronauts,lack of privacy,and psychological distress.Fewer astronauts,in turn,limits the amount of experience and expertise available to the crew.Power constraints are influenced by factors such as electrical,chemical,and mechanical power available for vehicular function,flight operations,cabin lighting,and other on-board activities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[754,44,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acta Astronautica 214 (2024) 748-756 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[62,44,178,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"M. Brent Woodland et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[490,953,509,962]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"753 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[60,92,484,290]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0362/479b636f48e32854c00f67eedf86e17c3bcfef1ec2c4f30c206bf5194e6e633f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Spaceflight Limitation</td><td>Potential VR/AR Solution</td></tr><tr><td>Mass and volume constraints</td><td>HMDs tend to be lightweight, compact,and multi- functional</td></tr><tr><td>Emergency return to Earth may be impossible</td><td>Enhanced management of emergency situations</td></tr><tr><td>Communication delays</td><td>Improved autonomyvia preset procedures</td></tr><tr><td>Confinement</td><td>Expansive environment using virtual reality</td></tr><tr><td>Isolation</td><td>Holographic teleportation</td></tr><tr><td>Medical supplies and services</td><td>Medical officer support via augmented reality library</td></tr><tr><td>Increased cognitive demand</td><td>AR-guided procedures and processes</td></tr><tr><td>Microgravity</td><td>Enhanced preflight training of realistic microgravity environment</td></tr><tr><td>Spaceflight associated neuro- ocular syndrome</td><td>Close monitoring and computational reversal of visual distortions within VR headset</td></tr><tr><td>Exercise demands</td><td>Improved motivation and exercise efficacy via exergaming-type technology</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2 Spaceflight limitations and potential solutions with virtual/augmented reality. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[62,308,485,465]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,466,485,663]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Similar to the CAL and COLBERT maintenance tasks detailed above, scientists are investigating how AR in particular can help astronauts execute assignments more efficiently.For instance,at the underwater Aquarius laboratory,researchers used AR to guide crew members in a daily maintenance task.These researchers found ways in which AR was beneficial,as well as ways in which it could be improved.For instance, their mission revealed that their AR only gave steps to the procedure one ata time (forwards or backwards).They noted that paper procedures were more easily searched and navigated 66.Other studies have used ISS mock-ups to evaluate the efficiency of AR67 or compared using paper instructions to AR instructions for spaceflight-like objectives 68. The latter group found that AR instructions significantly improved performance time when compared to paper instructions and found evidence to suggest that AR instruction methods may be more effective at transferring learning to new situations 68.68. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,678,236,689]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.1.9. VR/AR for stress relief \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,692,485,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Astronauts face considerable mental and emotional stress during space travel due to confinement, isolation,and high cognitive demands [53].In a space analog,Hawaii Space Exploration Analog and Simulation (HI-SEAS),VR was used to expose the inhabitants to environments outside of the dome [51].VR “travel\\\"to familiar or calming places (i.e., mountain ranges,beaches,etc.）has been shown to be an effective method for reducing objective and subjective stress [89].This measure could be incorporated into VR systems for deep space missions,allowing astronauts to “escape”to confines of the cabin and experience natural scenery from Earth.Astronauts must be proficient in using AR/XR systems.The time and effort required to train astronauts to adapt to new technologies can be substantial,considering the multifaceted skills astronauts already need to acquire.Furthermore,the efficacy of AR/XR for stress relief can be subjective and individual-specific.A lack of customization options may render the experiences less effective for some astronauts. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,66,655,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.1.10.VR/AR exercise \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,80,937,316]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Though crew members face multiple physiologic challenges in microgravity,muscle atrophy and bone deterioration have been specifically targeted by exercise equipment installed aboard the ISS. Resistance exercise,stationary cycling,and a modified treadmill provide cardiovascular and musculoskeletal training to help mitigate the effects on these systems while in space.However, the volume limitations for a deep space mission do not allow for all these machines to be installed on a Mars-bound vehicle.More likely,the only equipment available will be a specialized type of rowing machine [83].Research is being conducted to evaluate the usefulness of VR exercise games in helping motivate astronauts to complete the necessary exercise regimens [57,83,90]. In addition,VR-based exercise programs have been used in conjunction with other potential muscular strengthening systems (i.e.,electrical stimulation) in the evaluation of possible countermeasures to atrophy in space [77].AR/XR systems will draw from the spacecraft's power resources.Given the extended duration of deep space missions,efficient power management is essential,and AR/XR could strain available energyreserves. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,317,937,474]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In conclusion,AR and XR technology demonstrates significant potential in mitigatinga range of challenges associated with space travel. These technologies are gradually becoming important components of space missons,as they contribute to medical diagnosis,relieve psychological stresses,and improve learning and operational eficiency. The MedChecker application represents an excellent example of the innovative medical capabilities offered byaugmented reality (AR),as it enables anyone without medical training, such as astronauts, to recognize and dispense medications effectively and precisely.Additionally, this technology plays a crucial role in encouraging efficient inventory management and limiting drug delivery errors, hence contributing to the overall well-being of crew members during space missions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,476,937,592]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Froma psychological standpoint,virtual reality (VR)plays a pivotal role in providing vital assistance to astronauts who struggle with the profound isolation experienced during space missions. Its capacity to recreate peaceful terrestrial environments and provide relief from stress is crucial to preserving mental health throughout prolonged periods of isolation.As technology improves,multiple tests can be incorporated into a single VR headset, thus increasing speed and accuracy while decreasing the cost and size of the equipment required to obtain the necessary diagnostic data. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,607,566,619]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Funding \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,634,936,672]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"NASA Grant [80NSSC20K183]: A Non-intrusive Ocular Monitoring Framework to Model Ocular Structure and Functional Changes due to Long-term Spaceflight. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,687,731,698]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Declaration of competing interest \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,712,937,751]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,766,583,778]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,790,934,911]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"[1]P.Milgram,F.Kishino,A Taxonomy of mixed reality visual displays,Accessed: Jan. 11,2023. 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Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[278,403,939,614]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Accurate building extraction from remotely sensed images is essential for topographic mapping, urban planning, disaster management, navigation, and many other applications [1]. The easily available very-high resolution 2D/3D dataset and the rapid development of image processing techniques, especially the convolutional neural networks (CNN) and deep learning techniques have further boosted the research on building-extraction-related topics. Especially in recent years, many research institutes and associations have provided open-source datasets and annotated training data to meet the demand for advanced artificial intelligence models, which brings new opportunities to develop advanced approaches for building extraction and monitoring. Hence, there are higher expectations of the efficiency, accuracy, and robustness of building extraction approaches. They should also meet the demand of processing large datasets at the city, national, and global levels. Moreover, challenges remain on transform learning and dealing with imperfect training data, as well as unexpected objects in urban scenes such as trees, clouds, and shadows. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[278,615,939,707]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As a follow-on Special Issue of \"Remote Sensing based Building Extraction\", this Special Issue \"Remote Sensing based Building Extraction II\" has further collected the cutting-edge approaches for automatic building segmentation [1-4], vectorization [5,6], and regularization [7], dense matching [8], 3D reconstruction [9-11], and road detection [12]. The proposed methods fall into two main categories depending on the use of the input data sources: 2D building extraction and 3D reconstruction/segmentation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[278,722,472,736]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.2D Building Extraction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[278,741,939,923]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Deep learning (DL) shows remarkable performance in extracting buildings from high-resolution remote sensing images. How to improve the performance of DL methods, especially the perception of spatial information, is worth further study. Paper [2] proposed a building extraction network (B-FGC-Net) with a feature highlighting, global awareness, and cross-level information fusion to achieve improved profitability of accurate extraction and information integration for both small- and large-scale buildings. Focusing on the promotion of the robustness of the interactive segmentation, Shu et al. [1] propose one Progress Guidance Representation Net (PGR-Net) to utilize the distance of newly added clicks to the boundary of the previous segmentation mask as an indication of the interactive segmentation progress, and this information is employed with the previous segmentation mask and positive and negative clicks to form a progress guidance map. This progress guidance map is then fed into a CNN with the original RGB image. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,778,151,803]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0647/92bf60d5548be27fe44aa5d0c8c19d5080a6caabd48d9a920fdb4e3afab5ae55.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,58,115,99]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"# ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[122,68,351,95]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"remote sensing ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[865,61,942,97]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MDPI ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[58,626,250,722]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Citation: Tian, J.; Yan, Q.; Awrangjeb, M.; Kallfelz, B.; Demir, N. Editorial for Special Issue: \"Remote Sensing based Building Extraction II\". Remote Sens. 2023, 15, 998. https://doi.org/10.3390/rs15040998 ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[58,733,208,772]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received: 28 November 2022 \nAccepted: 1 February 2023 \nPublished: 10 February 2023 ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[58,810,253,921]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[58,967,418,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remote Sens. 2023, 15, 998. https://doi.org/10.3390/rs15040998 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[702,967,939,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.mdpi.com/journal/remotesensing ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[273,107,939,381]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Furthermore, they propose an iterative training strategy for the training of the network and adopt an adaptive zoom-in technique during the inference stage for further performance promotion. Farmland constitutes an important resource for human survival and development. With complex ground features and scattered distribution, building extraction from farmland remains a challenging topic. To this end, Paper [3] proposes an attention-enhanced U-Net for building extraction from farmland based on Google and WorldView-2 remote sensing images. First, a Resnet unit is adopted as the infrastructure of the U-Net network encoding part, then the spatial and channel attention mechanism module is introduced between the Resnet unit and the maximum pool and the multi-scale fusion module is added to improve the U-Net network. Second, the buildings are extracted from WorldView-2 and Google images through farmland boundary constraints. Third, boundary optimization and fusion processing are carried out to further refine the building extraction results. In order to investigate the photovoltaic potential of urban buildings, Paper [4] proposed a pseudo-label-guided self-supervised learning (PGSSL) semantic segmentation network structure to extract building information from high-resolution remote sensing images. The pseudo-label-guided learning method allows the feature results extracted by the pretext task to be more applicable to the target task and ultimately improves segmentation accuracy. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[273,382,939,715]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To further close the gap between airborne images and vector representation, Van den Broeck and Goedemé [5] propose a fully automated end-to-end workflow for large-scale roof-part polygon extraction from UHR orthoimagery (0.03 m GSD). Their workflow comprised three steps: (1) An multitask fully convolutional network (FCN) was utilized for the semantic segmentation of roof-part objects and edges; (2) A bottom-up clustering algorithm was used, given the predicted roof-part edges, to derive individual roof-part clusters, where the predicted roof-part object area distinguish roof from non-roof; and (3) The roof-part clusters were vectorized and simplified into polygons. The methodology is trained and tested on a challenging dataset comprising of UHR aerial RGB orthoimagery (0.03 m GSD) and LiDAR-derived digital elevation models (DEMs) (0.25 m GSD) of three Belgian urban areas (including the famous touristic city of Bruges). Li et al. [6] explore the idea of combining three deep learning models, each model performing specific tasks, for automated extraction of building footprint polygons from very high-resolution aerial imagery. Their approach uses the U-Net, Cascade R-CNN, and Cascade CNN models to obtain building segmentation maps, building bounding boxes, and building corners, respectively, thus allowing for the direct production of building maps in a vector format. A polygon construction strategy based on Delaunay triangulation is designed to integrate the outputs from the deep learning models effectively, as well as to generate high-quality vector data. To solve the problem of edge discontinuity and incompleteness generated by semantic edge detection, Xia et al. [7] propose a multitask learning Dense D-LinkNet (DDLNet), which adopts full-scale skip connections and edge guidance module to ensure the effective combination of low-level information and high-level information. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[273,731,552,745]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.3D Reconstruction/Segmentation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[273,749,939,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The use of 3D building models is essential and provides realistic data for spatial and environmental analysis for various applications such as creating digital, generating simulations to predict and prepare for future scenarios, and creating various urban analytical processes, especially those that consider environmental impact, which is a growing global concern. To obtain a precise 3D model with lower cost, dense stereo matching has been studied persistently in the field of computer vision, remote sensing, and photogrammetry. Along with the development of deep learning, the Guided Aggregation Network (GA-Net) achieves state-of-the-art performance via the proposed Semi-Global Guided Aggregation layers and reduces the use of costly 3D convolutional layers. To solve the problem of GA-Net requiring large GPU memory consumption, Xia et al. [8] propose an efficient end-to-end network GA-Net-Pyramid for dense matching a pyramid architecture to modify the model. Starting from a downsampled stereo input, the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,60,211,72]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remote Sens. 2023, 15, 998 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[897,60,942,71]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 of 4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[273,107,939,350]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"disparity is estimated and continuously refined through the pyramid levels. Thus, the disparity search is only applied for a small size of stereo pair and then confined within a short residual range for minor correction, leading to highly reduced memory usage and runtime. Manual modelling of urban buildings is very time-consuming and costly. Due to the complexity of the dense urban regions, research oriented toward the automatic reconstruction of buildings is still an open topic. In the manuscript titled \"Parameter-Free Half-Spaces Based 3D Building Reconstruction Using Ground and Segmented Building Points from Airborne LiDAR Data with 2D Outlines\"[9], the authors propose a new half-spaces based algorithm for building reconstruction from airborne laser point clouds. In contrast to the related algorithms, which divide 2D outlines of buildings into smaller parts and then process them while taking only convex shapes into account, the proposed algorithm performs reconstruction without division, while also considering concave parts of the rooftops. The method works in two stages, where the input data is processed first to obtain the definition of the base model of each building and the corresponding half-spaces. In the second stage, a building shape is generated by performing 3D Boolean operations over the analysed half-spaces. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[273,351,939,609]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A major challenge of large-scale building reconstruction from airborne LiDAR point clouds is the reconstruction of missing vertical walls. Paper [10] provided a fully automatic building reconstruction approach to infer vertical walls based on the connection between planar segments of both roofs and walls. The reconstruction model is obtained by using an extended hypothesis-and-selection-based polygonal surface reconstruction framework. Experimental results demonstrated that the proposed method is superior to the state-of-the-art methods in terms of reconstruction accuracy and robustness. The study also generated a new dataset consisting of the point clouds and 3D models of $20\\mathrm{k}$ real-world buildings which can stimulate research in urban reconstruction and the use of 3D city models in urban applications. To further refine the extracted building boundaries, Hui et al. [11] propose a multi-constraints graph segmentation method for building extraction from airborne LiDAR data and achieve satisfactory results. The graph structure is generated using the three-dimensional spatial features of points. To reduce computational cost the point-based building extraction is transformed into an object-based building extraction and geometric morphological features are computed for each segmented object. Finally, a multi-scale progressively growing optimisation method is employed to recover the omitted building parts. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[273,609,939,731]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Besides buildings, digital maps of road networks are a vital part of digital cities and intelligent transportation. This study [12] provided a comprehensive review of road extraction based on various remote sensing data sources. It is divided into three parts. Part 1 provides an overview of the existing data acquisition techniques for road extraction, including data acquisition methods, typical sensors, application status, and prospects. Part 2 underlines the main road extraction methods based on four data sources. Part 3 presents the combined application of multisource data for road extraction. It can provide a comprehensive reference for research on existing road extraction technologies. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[273,745,939,787]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgments: We want to thank the authors who contributed to this Special Issue on \"Remote Sensing Based Building Extraction II\", as well as the reviewers who provided the authors with comments and very constructive feedback. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[273,794,704,807]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conflicts of Interest: The authors declare no conflict of interest. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,60,211,72]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remote Sens. 2023, 15, 998 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[897,60,942,71]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 of 4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[57,108,144,122]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[55,126,941,583]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1. Shu, Z.; Hu, X.; Dai, H.; Progress Guidance Representation for Robust Interactive Extraction of Buildings from Remotely Sensed Images. Remote Sens. 2021, 13, 5111. https://doi.org/10.3390/rs13245111. \",\"2. Wang, Y.; Zeng, X.; Liao, X.; Zhuang, D. B-FGC-Net: A Building Extraction Network from High Resolution Remote Sensing Imagery. Remote Sens. 2022, 14, 269. https://doi.org/10.3390/rs14020269. \",\"3. Li, C.; Fu, L.; Zhu, Q.; Zhu, J.; Fang, Z.; Xie, Y.; Guo, Y.; Gong, Y. Attention Enhanced U-Net for Building Extraction from Farmland Based on Google and WorldView-2 Remote Sensing Images. Remote Sens. 2021, 13, 4411. https://doi.org/10.3390/rs13214411. \",\"4. Chen, D.-Y.; Peng, L.; Zhang, W.-Y.; Wang, Y.-D.; Yang, L.-N. Research on Self-Supervised Building Information Extraction with High-Resolution Remote Sensing Images for Photovoltaic Potential Evaluation. Remote Sens. 2022, 14, 5350. https://doi.org/10.3390/rs14215350. \",\"5. Van den Broeck, W.A.J.; Goedemé, T. Combining Deep Semantic Edge and Object Segmentation for Large-Scale Roof-Part Polygon Extraction from Ultrahigh-Resolution Aerial Imagery. Remote Sens. 2022, 14, 4722. https://doi.org/10.3390/rs14194722. \",\"6. Li, Z.; Xin, Q.; Sun, Y.; Cao, M. A Deep Learning-Based Framework for Automated Extraction of Building Footprint Polygons from Very High-Resolution Aerial Imagery. Remote Sens. 2021, 13, 3630. https://doi.org/10.3390/rs13183630. \",\"7. Xia, L.; Zhang, J.; Zhang, X.; Yang, H.; Xu, M. Precise Extraction of Buildings from High-Resolution Remote-Sensing Images Based on Semantic Edges and Segmentation. Remote Sens. 2021, 13, 3083. https://doi.org/10.3390/rs13163083. \",\"8. Xia, Y.; d'Angelo, P.; Fraudorfer, F.; Tian, J.; Fuentes Reyes, M.; Reinartz, P. GA-Net-Pyramid: An Efficient End-to-End Network for Dense Matching. Remote Sens. 2022, 14, 1942. https://doi.org/10.3390/rs14081942. \",\"9. Bizjak, M.; Žalik, B.; Lukac, N. Parameter-Free Half-Spaces Based 3D Building Reconstruction Using Ground and Segmented Building Points from Airborne LiDAR Data with 2D Outlines. Remote Sens. 2021, 13, 4430. https://doi.org/10.3390/rs13214430. \",\"10. Huang, J.; Stoter, J.; Peters, R.; Nan, L. City3D: Large-Scale Building Reconstruction from Airborne LiDAR Point Clouds. Remote Sens. 2022, 14, 2254. https://doi.org/10.3390/rs14092254. \",\"11. Hui, Z.; Li, Z.; Cheng, P.; Ziggah, Y.Y.; Fan, J. Building Extraction from Airborne LiDAR Data Based on Multi-Constraints Graph Segmentation. Remote Sens. 2021, 13, 3766. https://doi.org/10.3390/rs13183766. \",\"12. Jia, J.; Sun, H.; Jiang, C.; Karila, K.; Karjalainen, M.; Ahokas, E.; Khoramshahi, E.; Hu, P.; Chen, C.; Xue, T.; et al. Review on Active and Passive Remote Sensing Techniques for Road Extraction. Remote Sens. 2021, 13, 4235. https://doi.org/10.3390/rs13214235. \"]","page_idx":"3","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[53,596,939,640]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Disclaimer/Publisher's Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,60,211,72]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remote Sens. 2023, 15, 998 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[897,60,941,71]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 of 4 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[58,123,121,136]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Editorial \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,141,889,193]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Editorial for Special Issue: \\\"Remote Sensing based Building Extraction II\\\" \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,211,820,225]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Jiaojiao Tian $^{1, *}$ , Qin Yan $^{2}$ , Mohammad Awrangjeb $^{3}$ , Beril Kallfelz (Sirmacek) $^{4}$ and Nusret Demir $^{5}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,247,880,337]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Remote Sensing Technology Institute, German Aerospace Center (DLR), 82234 Wessling, Germany \\\",\\\"$^{2}$ Chinese Academy of Surveying and Mapping, Beijing 100830, China \\\",\\\"3 Institute for Integrated and Intelligent Systems, Griffith University, Nathan, QLD 4111, Australia \\\",\\\"4 Independent Scientist, 7553 Hengelo, The Netherlands \\\",\\\"$^{5}$ Department of Space Science and Technologies, Remote Sensing Division, Akdeniz University, 07058 Antalya, Turkey \\\",\\\"* Correspondence: jiao jiao.tian@dlr.de \\\"]\",\n \"page_idx\": \"0\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[278,385,391,397]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,403,939,614]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Accurate building extraction from remotely sensed images is essential for topographic mapping, urban planning, disaster management, navigation, and many other applications [1]. The easily available very-high resolution 2D/3D dataset and the rapid development of image processing techniques, especially the convolutional neural networks (CNN) and deep learning techniques have further boosted the research on building-extraction-related topics. Especially in recent years, many research institutes and associations have provided open-source datasets and annotated training data to meet the demand for advanced artificial intelligence models, which brings new opportunities to develop advanced approaches for building extraction and monitoring. Hence, there are higher expectations of the efficiency, accuracy, and robustness of building extraction approaches. They should also meet the demand of processing large datasets at the city, national, and global levels. Moreover, challenges remain on transform learning and dealing with imperfect training data, as well as unexpected objects in urban scenes such as trees, clouds, and shadows. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,615,939,707]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As a follow-on Special Issue of \\\"Remote Sensing based Building Extraction\\\", this Special Issue \\\"Remote Sensing based Building Extraction II\\\" has further collected the cutting-edge approaches for automatic building segmentation [1-4], vectorization [5,6], and regularization [7], dense matching [8], 3D reconstruction [9-11], and road detection [12]. The proposed methods fall into two main categories depending on the use of the input data sources: 2D building extraction and 3D reconstruction/segmentation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,722,472,736]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2D Building Extraction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,741,939,923]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Deep learning (DL) shows remarkable performance in extracting buildings from high-resolution remote sensing images. How to improve the performance of DL methods, especially the perception of spatial information, is worth further study. Paper [2] proposed a building extraction network (B-FGC-Net) with a feature highlighting, global awareness, and cross-level information fusion to achieve improved profitability of accurate extraction and information integration for both small- and large-scale buildings. Focusing on the promotion of the robustness of the interactive segmentation, Shu et al. [1] propose one Progress Guidance Representation Net (PGR-Net) to utilize the distance of newly added clicks to the boundary of the previous segmentation mask as an indication of the interactive segmentation progress, and this information is employed with the previous segmentation mask and positive and negative clicks to form a progress guidance map. This progress guidance map is then fed into a CNN with the original RGB image. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,778,151,803]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0647/92bf60d5548be27fe44aa5d0c8c19d5080a6caabd48d9a920fdb4e3afab5ae55.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,58,115,99]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"# \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[122,68,351,95]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"remote sensing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[865,61,942,97]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MDPI \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[58,626,250,722]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Citation: Tian, J.; Yan, Q.; Awrangjeb, M.; Kallfelz, B.; Demir, N. Editorial for Special Issue: \\\"Remote Sensing based Building Extraction II\\\". Remote Sens. 2023, 15, 998. https://doi.org/10.3390/rs15040998 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[58,733,208,772]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received: 28 November 2022 \\nAccepted: 1 February 2023 \\nPublished: 10 February 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[58,810,253,921]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[58,967,418,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remote Sens. 2023, 15, 998. https://doi.org/10.3390/rs15040998 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[702,967,939,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.mdpi.com/journal/remotesensing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[273,107,939,381]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Furthermore, they propose an iterative training strategy for the training of the network and adopt an adaptive zoom-in technique during the inference stage for further performance promotion. Farmland constitutes an important resource for human survival and development. With complex ground features and scattered distribution, building extraction from farmland remains a challenging topic. To this end, Paper [3] proposes an attention-enhanced U-Net for building extraction from farmland based on Google and WorldView-2 remote sensing images. First, a Resnet unit is adopted as the infrastructure of the U-Net network encoding part, then the spatial and channel attention mechanism module is introduced between the Resnet unit and the maximum pool and the multi-scale fusion module is added to improve the U-Net network. Second, the buildings are extracted from WorldView-2 and Google images through farmland boundary constraints. Third, boundary optimization and fusion processing are carried out to further refine the building extraction results. In order to investigate the photovoltaic potential of urban buildings, Paper [4] proposed a pseudo-label-guided self-supervised learning (PGSSL) semantic segmentation network structure to extract building information from high-resolution remote sensing images. The pseudo-label-guided learning method allows the feature results extracted by the pretext task to be more applicable to the target task and ultimately improves segmentation accuracy. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,382,939,715]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To further close the gap between airborne images and vector representation, Van den Broeck and Goedemé [5] propose a fully automated end-to-end workflow for large-scale roof-part polygon extraction from UHR orthoimagery (0.03 m GSD). Their workflow comprised three steps: (1) An multitask fully convolutional network (FCN) was utilized for the semantic segmentation of roof-part objects and edges; (2) A bottom-up clustering algorithm was used, given the predicted roof-part edges, to derive individual roof-part clusters, where the predicted roof-part object area distinguish roof from non-roof; and (3) The roof-part clusters were vectorized and simplified into polygons. The methodology is trained and tested on a challenging dataset comprising of UHR aerial RGB orthoimagery (0.03 m GSD) and LiDAR-derived digital elevation models (DEMs) (0.25 m GSD) of three Belgian urban areas (including the famous touristic city of Bruges). Li et al. [6] explore the idea of combining three deep learning models, each model performing specific tasks, for automated extraction of building footprint polygons from very high-resolution aerial imagery. Their approach uses the U-Net, Cascade R-CNN, and Cascade CNN models to obtain building segmentation maps, building bounding boxes, and building corners, respectively, thus allowing for the direct production of building maps in a vector format. A polygon construction strategy based on Delaunay triangulation is designed to integrate the outputs from the deep learning models effectively, as well as to generate high-quality vector data. To solve the problem of edge discontinuity and incompleteness generated by semantic edge detection, Xia et al. [7] propose a multitask learning Dense D-LinkNet (DDLNet), which adopts full-scale skip connections and edge guidance module to ensure the effective combination of low-level information and high-level information. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,731,552,745]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.3D Reconstruction/Segmentation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,749,939,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The use of 3D building models is essential and provides realistic data for spatial and environmental analysis for various applications such as creating digital, generating simulations to predict and prepare for future scenarios, and creating various urban analytical processes, especially those that consider environmental impact, which is a growing global concern. To obtain a precise 3D model with lower cost, dense stereo matching has been studied persistently in the field of computer vision, remote sensing, and photogrammetry. Along with the development of deep learning, the Guided Aggregation Network (GA-Net) achieves state-of-the-art performance via the proposed Semi-Global Guided Aggregation layers and reduces the use of costly 3D convolutional layers. To solve the problem of GA-Net requiring large GPU memory consumption, Xia et al. [8] propose an efficient end-to-end network GA-Net-Pyramid for dense matching a pyramid architecture to modify the model. Starting from a downsampled stereo input, the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,60,211,72]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remote Sens. 2023, 15, 998 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[897,60,942,71]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 of 4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[273,107,939,350]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"disparity is estimated and continuously refined through the pyramid levels. Thus, the disparity search is only applied for a small size of stereo pair and then confined within a short residual range for minor correction, leading to highly reduced memory usage and runtime. Manual modelling of urban buildings is very time-consuming and costly. Due to the complexity of the dense urban regions, research oriented toward the automatic reconstruction of buildings is still an open topic. In the manuscript titled \\\"Parameter-Free Half-Spaces Based 3D Building Reconstruction Using Ground and Segmented Building Points from Airborne LiDAR Data with 2D Outlines\\\"[9], the authors propose a new half-spaces based algorithm for building reconstruction from airborne laser point clouds. In contrast to the related algorithms, which divide 2D outlines of buildings into smaller parts and then process them while taking only convex shapes into account, the proposed algorithm performs reconstruction without division, while also considering concave parts of the rooftops. The method works in two stages, where the input data is processed first to obtain the definition of the base model of each building and the corresponding half-spaces. In the second stage, a building shape is generated by performing 3D Boolean operations over the analysed half-spaces. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,351,939,609]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A major challenge of large-scale building reconstruction from airborne LiDAR point clouds is the reconstruction of missing vertical walls. Paper [10] provided a fully automatic building reconstruction approach to infer vertical walls based on the connection between planar segments of both roofs and walls. The reconstruction model is obtained by using an extended hypothesis-and-selection-based polygonal surface reconstruction framework. Experimental results demonstrated that the proposed method is superior to the state-of-the-art methods in terms of reconstruction accuracy and robustness. The study also generated a new dataset consisting of the point clouds and 3D models of $20\\\\mathrm{k}$ real-world buildings which can stimulate research in urban reconstruction and the use of 3D city models in urban applications. To further refine the extracted building boundaries, Hui et al. [11] propose a multi-constraints graph segmentation method for building extraction from airborne LiDAR data and achieve satisfactory results. The graph structure is generated using the three-dimensional spatial features of points. To reduce computational cost the point-based building extraction is transformed into an object-based building extraction and geometric morphological features are computed for each segmented object. Finally, a multi-scale progressively growing optimisation method is employed to recover the omitted building parts. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,609,939,731]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Besides buildings, digital maps of road networks are a vital part of digital cities and intelligent transportation. This study [12] provided a comprehensive review of road extraction based on various remote sensing data sources. It is divided into three parts. Part 1 provides an overview of the existing data acquisition techniques for road extraction, including data acquisition methods, typical sensors, application status, and prospects. Part 2 underlines the main road extraction methods based on four data sources. Part 3 presents the combined application of multisource data for road extraction. It can provide a comprehensive reference for research on existing road extraction technologies. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,745,939,787]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgments: We want to thank the authors who contributed to this Special Issue on \\\"Remote Sensing Based Building Extraction II\\\", as well as the reviewers who provided the authors with comments and very constructive feedback. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,794,704,807]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conflicts of Interest: The authors declare no conflict of interest. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,60,211,72]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remote Sens. 2023, 15, 998 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[897,60,942,71]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 of 4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,108,144,122]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,126,941,583]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1. Shu, Z.; Hu, X.; Dai, H.; Progress Guidance Representation for Robust Interactive Extraction of Buildings from Remotely Sensed Images. Remote Sens. 2021, 13, 5111. https://doi.org/10.3390/rs13245111. \\\",\\\"2. Wang, Y.; Zeng, X.; Liao, X.; Zhuang, D. B-FGC-Net: A Building Extraction Network from High Resolution Remote Sensing Imagery. Remote Sens. 2022, 14, 269. https://doi.org/10.3390/rs14020269. \\\",\\\"3. Li, C.; Fu, L.; Zhu, Q.; Zhu, J.; Fang, Z.; Xie, Y.; Guo, Y.; Gong, Y. Attention Enhanced U-Net for Building Extraction from Farmland Based on Google and WorldView-2 Remote Sensing Images. Remote Sens. 2021, 13, 4411. https://doi.org/10.3390/rs13214411. \\\",\\\"4. Chen, D.-Y.; Peng, L.; Zhang, W.-Y.; Wang, Y.-D.; Yang, L.-N. Research on Self-Supervised Building Information Extraction with High-Resolution Remote Sensing Images for Photovoltaic Potential Evaluation. Remote Sens. 2022, 14, 5350. https://doi.org/10.3390/rs14215350. \\\",\\\"5. Van den Broeck, W.A.J.; Goedemé, T. Combining Deep Semantic Edge and Object Segmentation for Large-Scale Roof-Part Polygon Extraction from Ultrahigh-Resolution Aerial Imagery. Remote Sens. 2022, 14, 4722. https://doi.org/10.3390/rs14194722. \\\",\\\"6. Li, Z.; Xin, Q.; Sun, Y.; Cao, M. A Deep Learning-Based Framework for Automated Extraction of Building Footprint Polygons from Very High-Resolution Aerial Imagery. Remote Sens. 2021, 13, 3630. https://doi.org/10.3390/rs13183630. \\\",\\\"7. Xia, L.; Zhang, J.; Zhang, X.; Yang, H.; Xu, M. Precise Extraction of Buildings from High-Resolution Remote-Sensing Images Based on Semantic Edges and Segmentation. Remote Sens. 2021, 13, 3083. https://doi.org/10.3390/rs13163083. \\\",\\\"8. Xia, Y.; d'Angelo, P.; Fraudorfer, F.; Tian, J.; Fuentes Reyes, M.; Reinartz, P. GA-Net-Pyramid: An Efficient End-to-End Network for Dense Matching. Remote Sens. 2022, 14, 1942. https://doi.org/10.3390/rs14081942. \\\",\\\"9. Bizjak, M.; Žalik, B.; Lukac, N. Parameter-Free Half-Spaces Based 3D Building Reconstruction Using Ground and Segmented Building Points from Airborne LiDAR Data with 2D Outlines. Remote Sens. 2021, 13, 4430. https://doi.org/10.3390/rs13214430. \\\",\\\"10. Huang, J.; Stoter, J.; Peters, R.; Nan, L. City3D: Large-Scale Building Reconstruction from Airborne LiDAR Point Clouds. Remote Sens. 2022, 14, 2254. https://doi.org/10.3390/rs14092254. \\\",\\\"11. Hui, Z.; Li, Z.; Cheng, P.; Ziggah, Y.Y.; Fan, J. Building Extraction from Airborne LiDAR Data Based on Multi-Constraints Graph Segmentation. Remote Sens. 2021, 13, 3766. https://doi.org/10.3390/rs13183766. \\\",\\\"12. Jia, J.; Sun, H.; Jiang, C.; Karila, K.; Karjalainen, M.; Ahokas, E.; Khoramshahi, E.; Hu, P.; Chen, C.; Xue, T.; et al. Review on Active and Passive Remote Sensing Techniques for Road Extraction. Remote Sens. 2021, 13, 4235. https://doi.org/10.3390/rs13214235. \\\"]\",\n \"page_idx\": \"3\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[53,596,939,640]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Disclaimer/Publisher's Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,60,211,72]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remote Sens. 2023, 15, 998 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[897,60,941,71]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 of 4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.3390/rs15040998"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Engineering and Manufacturing Science/Earth and Atmospheric Sciences"},"sha256":{"kind":"string","value":"ba5c5c0161d387202ea57e420bf3dd62e3a6ff1764e209ccc26a671a4487cbc0"},"title":{"kind":"string","value":"Editorial for Special Issue: “Remote Sensing Based Building Extraction II”"}}},{"rowIdx":256,"cells":{"abstract":{"kind":"string","value":"Constant current (CC) and constant voltage (CV) charging of batteries is a crucial research area in the practical implementation of wireless power transfer (WPT) systems. The typical charging process of a battery starts from the constant current mode. As the battery's voltage increases, the charging mode switches to the constant voltage mode. During charging, the equivalent load resistance of the battery will vary with the charging time, and the equivalent load resistance will affect the charging current or voltage and system's efficiency. In this study, an adaptive wireless charging method of CC-CV is proposed based on sinusoidal pulse width modulation (SPWM) inverter control. The proposed WPT circuit detects the load variation by measuring the parameters of load voltage and load current, and accurately controls the system output current or voltage by adjusting the modulation depth of the SPWM inverter on the primary side. When there is relative motion between the transmitting coil and the receiving coil, the sharp change in coupling coefficient directly affects the system's output voltage and output current, leading to output fluctuations and instability. To solve this problem, a method for estimating the coupling coefficient is proposed which estimates the coupling coefficient during the charging process by measuring system parameters. Then, the controller on the primary side adjusts the modulation depth of the SPWM inverter circuit based on the estimated new coupling coefficient, so that the system can still achieve constant current and constant voltage charging under displacement or distance changes. In this study, the CC mode output current during battery charging was set to 0.75 A, and the CV mode output voltage was set to 12 V. Simulation and experimental results demonstrate the validity and accuracy of the proposed control method."},"author":{"kind":"string","value":"Sun, Kang|Niu, Wangqiang"},"content_list":{"kind":"list like","value":[{"bbox":"[58,123,107,135]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,137,867,185]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"SPWM Inverter Control for Wireless Constant Current and Voltage Charging ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,198,334,214]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Kang Sun $\\textcircled{1}$ and Wangqiang Niu $\\ast \\textcircled { \\scriptsize { \\parallel } }$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,596,242,678]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Citation: Sun, K.; Niu, W. SPWM Inverter Control for Wireless Constant Current and Voltage Charging. World Electr. Veh. J. 2023, 14, 111. https://doi.org/ 10.3390/wevj14040111 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,689,247,700]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Academic Editor: Ghanim A. Putrus ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,712,188,765]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received: 5 March 2023 \nRevised: 23 March 2023 \nAccepted: 7 April 2023 \nPublished: 14 April 2023 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,240,789,277]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Key Laboratory of Transport Industry of Marine Technology and Control Engineering, \nShanghai Maritime University, Shanghai 201306, China \n\\* Correspondence: wqniu@shmtu.edu.cn ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,294,941,601]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract: Constant current (CC) and constant voltage (CV) charging of batteries is a crucial research area in the practical implementation of wireless power transfer (WPT) systems. The typical charging process of a battery starts from the constant current mode. As the battery’s voltage increases, the charging mode switches to the constant voltage mode. During charging, the equivalent load resistance of the battery will vary with the charging time, and the equivalent load resistance will affect the charging current or voltage and system’s efficiency. In this study, an adaptive wireless charging method of CC-CV is proposed based on sinusoidal pulse width modulation (SPWM) inverter control. The proposed WPT circuit detects the load variation by measuring the parameters of load voltage and load current, and accurately controls the system output current or voltage by adjusting the modulation depth of the SPWM inverter on the primary side. When there is relative motion between the transmitting coil and the receiving coil, the sharp change in coupling coefficient directly affects the system’s output voltage and output current, leading to output fluctuations and instability. To solve this problem, a method for estimating the coupling coefficient is proposed which estimates the coupling coefficient during the charging process by measuring system parameters. Then, the controller on the primary side adjusts the modulation depth of the SPWM inverter circuit based on the estimated new coupling coefficient, so that the system can still achieve constant current and constant voltage charging under displacement or distance changes. In this study, the CC mode output current during battery charging was set to $0 . 7 5 \\mathrm { A } .$ , and the CV mode output voltage was set to 12 V. Simulation and experimental results demonstrate the validity and accuracy of the proposed control method. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[273,618,941,646]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: wireless power transfer (WPT); constant current/constant voltage charging (CC/CV); SPWM inverter; estimation of coupling coefficient; self-adaption ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,692,393,706]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,711,941,799]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electricity transmission is crucial for human production and daily life. Wireless power transfer (WPT) technology enables the transmission of electric energy from a power source to a load without direct electrical contact. WPT technology has rapidly developed with the advancements in modern industry and technology and is widely utilized in various fields, such as biomedical equipment, aerospace, consumer electronics, manufacturing facilities, and electric vehicles [1–4]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,800,941,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As a sustainable transportation option, electric vehicles (EVs) are becoming increasingly popular worldwide. With the increasing demand for electric vehicles, it is important to develop efficient and reliable charging techniques for their lithium-ion batteries. There are three commonly used charging methods: constant current–constant voltage (CC-CV) charging [5], constant power charging [6,7], and pulse charging [8,9]. CC-CV charging involves controlling the charging current and voltage to keep the battery at a constant current or voltage during the charging process. Constant current charging can charge the battery faster in the early stages of charging, and constant voltage charging can fill the battery faster in the later stages of charging. Therefore, by combining constant currentconstant voltage charging, charging efficiency and speed can be maximized. This charging and constant voltage charging, charging efficiency and speed can be maximized. Thismethod performs well in terms of charging speed and efficiency and can prevent overcharging method performs well in terms of charging speed and efficiency and can preventcharging and over-discharging, thereby extending the battery’s lifespan. overcharging and over-discharging, thereby extending the battery’s lifespan.In contrast, constant power charging and pulse charging have faster char ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,778,154,804]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CC BY ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[57,57,270,99]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electric Vehicle Journal ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[57,966,489,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111. https://doi.org/10.3390/wevj14040111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[865,65,939,98]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MDPI ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[705,966,939,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://www.mdpi.com/journal/wevj ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[57,569,147,592]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"check for updates ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[57,809,257,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Copyright: $^ ©$ 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[277,111,941,172]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,173,941,262]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In contrast, constant power charging and pulse charging have faster charging speeds but are more prone to overcharging or over-discharging the battery, which can reduce itslifespan. Constant power charging involves continuously adjusting the charging current lifespan. Constant power charging involves continuously adjusting the charging current and voltage to maintain a constant charging power during the charging process. Pulse charging applies periodic high-voltage and high-current pulse signals to the battery during charging to increase the charging speed. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[278,262,941,321]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Although constant power charging and pulse charging allow faster charging speeds, they require more complex control strategies to avoid negative impacts on the battery. In comparison, CC-CV charging has a simpler and more reliable control strategy, can adapt to different types of batteries, and can effectively protect the battery.to different types of batteries, and can effectively protect the batte ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,322,941,381]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Therefore, in many applications, CC-CV charging is still one of the most commonlyTherefore, in many applications, CC-CV charging is still one of the most commonly used charging methods, especially in the electric vehicle and renewable energy storageused charging methods, especially in the electric vehicle and renewable energy storage fields. By accurately controlling the charging current and voltage, CC-CV charging canfields. By accurately controlling the charging current and voltage, CC-CV charging can achieve efficient, safe, and reliable battery charging.achieve efficient, safe, and reliable battery charging. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,381,941,530]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Over the years, electric vehicles known for their eco-friendliness and high efficiencyOver the years, electric vehicles known for their eco-friendliness and high efficiency have been increasingly replacing traditional fuel-based vehicles, leading to a surge in thehave been increasingly replacing traditional fuel-based vehicles, leading to a surge in the interest in wireless charging technologies for electric vehicles. Lithium-ion batteries areinterest in wireless charging technologies for electric vehicles. Lithium-ion batteries are now widely used as energy storage units in electric vehicles [10]. Figure 1 illustrates thenow widely used as energy storage units in electric vehicles [10]. Figure 1 illustrates the charging process of a lithium battery, which begins with the CC mode and switches to thecharging process of a lithium battery, which begins with the CC mode and switches to the CV mode as the battery voltage increases [11]. The dynamic changes in the equivalentCV mode as the battery voltage increases [11]. The dynamic changes in the equivalent load resistance of the battery during the charging process can affect the charging current,load resistance of the battery during the charging process can affect the charging current, charging voltage, and system transmission efficiency. Hence, a closed-loop control schemecharging voltage, and system transmission efficiency. Hence, a closed-loop control is crucial for achieving precise control of CC and CV charging in the wireless chargingscheme is crucial for achieving precise control of CC and CV charging in the wireless system [12].charging sys ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[280,548,742,741]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 1. CC-CV charging curve of battery.Figure 1. CC-CV charging curve of battery. \"]","image_footnote":"[]","img_path":"images/0538/37e51b9f501d7e02a3a984230733e64acfbce48e896b9f8556392fac18962907.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,776,942,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The output of a WPT system is influenced by compensation parameters, operating The output of a WPT system is influenced by compensation parameters, operating frefrequency, and load conditions. Typically, compensation parameters and operating fre-quency, and load conditions. Typically, compensation parameters and operating frequency quency are constant, while the system output varies with load conditions. The use of DC-are constant, while the system output varies with load conditions. The use of DC-DC con-DC converter, a variable frequency or phase-shifted full-bridge inverter, or an impedance verter, a variable frequency or phase-shifted full-bridge inverter, or an impedance matching matching network are the main control methods for CC and CV wireless charging systemsnetwork are the main control methods for CC and CV wireless charging systems [13–15]. [13–15]. Using a buck/boost converter for DC-DC conversion can potentially have a nega-Using a buck/boost converter for DC-DC conversion can potentially have a negative impact tive impact on the system transmission efficiency and may also result in increased weight on the system transmission efficiency and may also result in increased weight or cost [13]. If the operating frequency of the system deviates significantly from the optimal frequency, adjusting the frequency may result in a reduction in the system’s power transmission capacity [14]. Phase-shift control is a technique that modifies the duty cycle of the inverter output voltage by varying the phase difference between the front and rear sections of the inverter, thereby adjusting the system output. This method is effective at compensating for the reactive power of the system when it operates at the resonant frequency. However, when using impedance matching, a large array of capacitors or inductors is required, which can increase the weight, size, and control complexity of the system [15]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[277,112,941,187]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,187,941,395]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In two papers [14,15], the system in question utilizes a DC-DC converter on the primary side and employs frequency conversion or phase-shift control for the full bridge inverter on the primary side to achieve CV output through impedance-matching control. In another two studies [16,17], to achieve CV output, a chopper control link such as a buck or boost converter is added to the secondary circuit. While these systems have achieved good CV output, the addition of extra circuits reduces the transmission efficiency of the system and increases the control complexity. In the studies [18,19], phase shift control was utilized to achieve CV output, but the circuit may fail to meet the output voltage requirements when the load varies significantly. Another study [20] utilized a PWM scheme with a phase-locked loop (PLL) control method. However, the circuit-input impedance needs to be inductive throughout the entire load variation range, which results in an increase in reactive power loss. In the studies [21,22], the system achieved CC and CV output through frequency-conversion control at two different operating frequencies. However, changing the frequency increases the complexity of hardware circuit design. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,397,941,650]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Many practical applications of WPT systems suffer from misalignment or variations in transmission distance between the transmitting and receiving coils. This can cause a significant change in the coupling coefficient, leading to instability in the output voltage and current. To address this issue, many researchers have investigated methods to identify the coupling coefficient. One such method proposed in [23] uses a switched capacitor, but its implementation in practical applications is challenging. In [24], a dynamic method that only requires parameters from the receiving end was analyzed, but its measurement complexity and uncertainty are high due to the high harmonics of the rectified current. In [25], the coupling coefficient was estimated by analyzing the relationship between the duty cycle of the buck–boost circuit and the coupling-coefficient change. However, this method results in two solutions for the coupling coefficient, and obtaining the true value from the two solutions using the duty cycle of the buck circuit is inefficient. Another method proposed in [26] identifies the coupling coefficient using the input impedance equation, which offers a single solution and avoids the double-solution problem encountered in [25]. This paper proposes a method for estimating the coupling coefficient when the coil is misaligned or the transmission distance changes during charging, and designs a CC/CV output adaptive control flow based on the coupling-coefficient estimation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,650,941,769]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The SPWM inverter is a type of inverter used to convert DC voltage into AC voltage. It works by generating a sequence of high-frequency pulses whose widths are modulated in such a way that the average voltage waveform obtained is a sine wave. This makes the SPWM inverter an ideal solution for applications that require a high-quality sine wave input. One of the main advantages of SPWM inverters over other types of inverters is that they provide a high-quality sine wave output with low harmonic distortion, which is essential for many electrical devices. Additionally, SPWM inverters are efficient, reliable, and can be easily controlled, making them ideal for use in various applications. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,770,941,872]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This paper proposes a WPT system based on SS compensation with an SPWM inverter circuit. To achieve CC/CV output, the modulation depth of the inverter circuit is controlled within a certain range as the load varies. Specifically, the system operates in CC mode with an output current of 0.75 A when the load voltage is below the maximum charging voltage of $1 2 \\mathrm { V } .$ Once the load voltage reaches $1 2 \\mathrm { V } ,$ the system switches to CV mode, and charging ends when the load current is less than the charging end current. The contributions of this paper are as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[273,873,939,904]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(1) A method to realize CC/CV output of WPT system under the control of SPWM inverter is proposed. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[275,112,941,231]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2) A mathematical model between load voltage $u _ { L }$ (and load current $I _ { L }$ ) and the modulation depth m of SPWM inverter was built. (3) An adaptive control flow of CC/CV output was designed. (4) A method for coupling-coefficient estimation during charging is proposed. (5) A CC/CV adaptive output strategy for WPT systems with coupling-coefficient estimation was designed. (6) An experimental circuit of WPT with S-S compensation with CC/CV output was built, and the proposed model and method were verified. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,233,942,322]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This paper is organized as follows. Section 2 presents an analysis of the proposed WPT circuit, including the derivation of the relationship between modulation depth and CC/CV output condition, estimating coupling coefficients and the controlling scheme. In Section 3, the proposed control scheme is validated through simulations. Section 4 evaluates the effectiveness of the proposed method through experimental results. Finally, Section 5 provides the conclusions of this study. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,334,425,348]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. System Analysis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[280,349,568,363]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.1. Theoretical Model of S-S WPT Circuit ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,368,941,428]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The WPT system comprises a transmitter and a receiver, which are connected through magnetic coupling to transfer energy via an alternating magnetic field. The transmitter employs a full bridge inverter circuit to convert DC voltage to AC voltage, and the receiver uses a full bridge rectifier circuit to convert AC voltage back to DC voltage. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,428,941,562]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To efficiently transfer electrical energy in the WPT system using an alternating magnetic field, compensation elements (usually capacitors) are added to the transmitting and receiving coil ends to reduce reactive power [11,27–35]. The basic compensation topology of the WPT system can be classified into four types based on the series or parallel connection between the capacitor and the transmitting/receiving coil. These four types are: series– series (S-S), series–parallel (S-P), parallel–parallel (P-P), and parallel–series (P-S) [27–29]. Among them, the S-S compensation circuit is widely used due to its simple structure, and the selection of capacitance is not affected by load and coupling conditions when the system operates at resonance frequency, hence the popularity of this circuit [11,29–31]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,563,941,740]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 2 illustrates the typical circuit diagram of S-S WPT [11,29,31], which consists of a full bridge inverter circuit $\\left( Q _ { 1 } – Q _ { 4 } \\right)$ , a transmission coil $( L _ { 1 } )$ , a receiving coil $( L _ { 2 } ) _ { \\mathrm { ~ ~ } }$ , a full bridge rectifier circuit $\\left( D _ { 1 } – D _ { 4 } \\right)$ , and two compensation capacitors ( $C _ { 1 }$ and $C _ { 2 }$ ). The transmitter coil $L _ { 1 }$ and the compensation capacitor $C _ { 1 }$ form the primary-side resonant circuit, and the receiver coil $L _ { 2 }$ and the compensation capacitor $C _ { 2 }$ form the secondary-side resonant circuit. $M$ is the mutual inductance between the transmitter coil $L _ { 1 }$ and the receiver coil $L _ { 2 }$ . $I _ { 1 }$ and $I _ { 2 }$ are the rms values of the resonant current on the primary side and the secondary side, respectively. $R _ { 1 }$ and $R _ { 2 }$ are the internal resistance of the transmitter coil $L _ { 1 }$ and the receiver coil $L _ { 2 } ,$ , respectively, and $C _ { r }$ is the filter capacitor. The DC voltage $V _ { D C }$ is the input voltage of the full-bridge inverter circuit. $U _ { 1 }$ is the rms value of the output voltage of the full-bridge inverter circuit. $U _ { 2 }$ is the rms value of the input voltage of full-bridge rectifier circuit. $I _ { L }$ is the load current. $U _ { L }$ is the load voltage. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[278,109,910,401]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 2. S-S-compensated WPT circuit.Figure 2. S-S-compensated WPT circuit. \"]","image_footnote":"[]","img_path":"images/0097/c4637a56cfc9d27ae1eda7fe210b2d06fdec2d66106dbfd8f4c55eb78ef5a82a.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[310,434,910,449]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The following equations can be derived based on Kirchhoff’s voltage law (KVL): ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[524,458,692,499]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0437/afc70d955ab83a8e23f8c043ec7e390b59c913a5f57bd539105ec702d063eb1b.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left\\{ \\begin{array} { l } { \\dot { U } _ { 1 } = Z _ { 1 } \\dot { I } _ { 1 } - j \\omega M \\dot { I } _ { 2 } } \\\\ { 0 = Z _ { 2 } \\dot { I } _ { 2 } - j \\omega M \\dot { I } _ { 1 } } \\end{array} \\right.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[527,508,687,557]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0772/9877e47daa41c415f5a285d75fd245aa02009f9a76a6c830fd57174a9ca06444.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left\\{ \\begin{array} { l } { \\dot { I } _ { 1 } = \\frac { Z _ { 2 } } { Z _ { 1 } Z _ { 2 } + \\omega ^ { 2 } M ^ { 2 } } \\dot { U } _ { 1 } } \\\\ { \\dot { I } _ { 2 } = \\frac { j \\omega M } { Z _ { 1 } Z _ { 2 } + \\omega ^ { 2 } M ^ { 2 } } \\dot { U } _ { 1 } } \\end{array} \\right.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,560,941,606]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\omega$ ⎩ ????1????2 + is the operating angle frequency of the system satisfying $\\omega = 2 \\pi f$ . $f$ is the operatwhere is the operating anging frequency of the system. $Z _ { 1 }$ requand $Z _ { 2 }$ cy of the system satisfying = 2????????. is the op-are the equivalent impedances of the transmitting erating frequency of the system.and the receiving, respectively: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[487,615,727,658]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0687/84e37b889227a3d8c479fcece7bac804eddd4c981e7704670f70d3775fb876fc.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left\\{ \\begin{array} { c } { Z _ { 1 } = R _ { 1 } + j \\Big ( \\omega L _ { 1 } - \\frac { 1 } { \\omega C _ { 1 } } \\Big ) } \\\\ { Z _ { 2 } = R _ { 2 } + R _ { r } + j \\big ( \\omega L _ { 2 } - \\frac { 1 } { \\omega C _ { 2 } } \\big ) } \\end{array} \\right.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[275,667,941,741]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Typically, $Z _ { 1 }$ and $Z _ { 2 }$ ⎩ ????2 = ????2 + ???????? + ????( ????2 − ???? )are complex numbers. However, when the system operates at the resonant frequency, $Z _ { 1 }$ and $Z _ { 2 }$ can be represented as pure resistance, with $Z _ { 1 } = R _ { 1 } , Z _ { 2 } =$ $R _ { 2 } + R _ { r } ,$ ???? where $R _ { r }$ ????2 is the equivalent AC resistance between the rectifier bridge circuit and ????1 ????2 the DC load. According to the fundamental equivalent principle, $R _ { r }$ and $R _ { L }$ ????1 =are satisfied ????1, ????2 = ????2 with [34]: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[563,739,653,768]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0300/463f863e318aa8e9c44e42b15b2d1d8914180c8ea8d083b59b3add113226409f.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nR _ { r } = { \\frac { 8 } { \\pi ^ { 2 } } } R _ { L }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[561,778,655,810]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0233/494863ff021ae8f7b75795916525ca62910d8cc891c03f0617cf532806219564.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nI _ { L } = \\frac { 2 \\sqrt { 2 } } { \\pi } I _ { 2 }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[551,821,667,852]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0986/c19b5b173e85624c5d9a5dd847100470708e734e6dc2af97a195e4b2d561017e.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nU _ { L } = \\frac { \\pi } { 2 \\sqrt { 2 } } I _ { 2 } R _ { r }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[268,856,941,887]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"????It can be intuitively inferred that if the DC load $R _ { L }$ is known, the corresponding DC load voltage $U _ { L }$ or current $I _ { L }$ ???? 2√2 2 ???? can be adjusted by controlling $U _ { 1 }$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. World Electr. Veh. J.2023 2023,,1414, x FO, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"f 5 of 23 24 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[277,112,645,127]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.2. Analysis of SPWM Single-Phase Inverter Circuit2.2. Analysis of SPWM Single-Phase Inverter Circuit ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,130,941,265]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the single-phase inverter circuit, PWM modulation is often used to control then the single-phase inverter circuit, PWM modulation is often used to control the switchesswitches ( $\\left( Q _ { 1 } – Q _ { 4 } \\right)$ . There are square wave modulation and SPWM modulation amongThere are square wave modulation and SPWM modulation among the the PWM modulation methods. Although the square-wave modulation has a high DCPWM modulation methods. Although the square-wave modulation has a high DC utiliutilization rate, the harmonic content of output voltage is also high. The output voltagezation rate, the harmonic content of output voltage is also high. The output voltage wavewaveform of the inverter circuit using SPWM modulation is a series of rectangular pulsesorm of the inverter circuit using SPWM modulation is a series of rectangular pulses with with the same amplitude and unequal width. The pulse width varies according to the sinehe same amplitude and unequal width. The pulse width varies according to the sine law. law. When it acts on the inertial component, the output is equivalent to a sine wave. ItsWhen it acts on the inertial component, the output is equivalent to a sine wave. Its benefits benefits include a reduced level of harmonic distortion and a high degree of linearity innclude a reduced level of harmonic distortion and a high degree of linearity in voltage voltage regulation.regulation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,266,941,370]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The SPWM single-phase inverter circuit is shown in Figure 3. The SPWM signal ishe SPWM single-phase inverter circuit is shown in Figure 3. The SPWM signal is generated by comparing the sine wave of the modulation wave with the triangle wavegenerated by comparing the sine wave of the modulation wave with the triangle wave of of the carrier wave. In the part where the sine wave is larger than the triangle wave, thehe carrier wave. In the part where the sine wave is larger than the triangle wave, the switches switches $Q _ { 1 }$ and and $Q _ { 4 }$ are on. At the time where the sine wave is smaller than the triangleare on. At the time where the sine wave is smaller than the triangle wave, the switching devices wave, the switching devices $Q _ { 2 }$ and and $Q _ { 3 }$ are on. The output voltage are on. The output voltag $U _ { 1 }$ of the inverter circuitof the inverter ciris continuously switched between positive and negative cuit is continuously switched between positive and negati $V _ { D C }$ as the switches turn on atas the switches turn on carrier frequency.at carrier frequenc ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[278,386,915,546]","code_body":null,"code_caption":null,"image_caption":"[\"igure 3. The SPWM single-phase inverter circuit.Figure 3. The SPWM single-phase inverter circuit. \"]","image_footnote":"[]","img_path":"images/0982/146916723f72fd7ef7030b6003a6568eb38752b461badaf9c7bf4e29a0f41bf5.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,581,941,626]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"When the amplitude of the sine wave is When the amplitude of the sine wave is $U _ { s } ,$ he amplitude of the triangle wave is the amplitude of the triangle wave is $U _ { c } ,$ the modulation depth is defined as ???? the modulation depth is defined as $\\begin{array} { r } { m = \\frac { U _ { s } } { U _ { c } } . } \\end{array}$ ????nd 0 < , and $0 < m \\leq 1 .$ ????en the output voltage of in-, then the output voltage of inverter circuit can be expressed as: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[546,637,672,669]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0527/132781c422b472d35d749c3444225b73358ac6cbd0a6ec466b262ba50d5f29f5.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nU _ { 1 } = \\frac { \\sqrt { 2 } } { 2 } V _ { D C } { \\cdot } m\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,677,941,722]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where where $U _ { 1 }$ is the rms value of the voltage of the inverter circuit. It can be seen intuitively is the rms value of the voltage of the inverter circuit. It can be seen intuitively that hat the output voltthe output voltage $U _ { 1 }$ ???? of the inverter circuit can be adjusted by controlling the mod-of the inverter circuit can be adjusted by controlling the modulation ulationdepth $m$ e. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,724,941,768]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"n practical applications, microcontrollers (such asIn practical applications, microcontrollers (such as $\\mathsf { s t m 3 2 }$ 2 series controllers) are usu- series controllers) are usually ally used to generate a SPWM signal, and the external drive circuit drives the on–off of used to generate a SPWM signal, and the external drive circuit drives the on–off of switches $Q _ { 1 } – Q _ { 4 }$ s. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,778,495,794]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.3. Analysis of CC/CV Output ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,797,941,872]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"When the WPT system operates in the resonant frequency, the impedance angle is zero—that is, the imaginary part of the impedance is zero. The impedance can be represented as pure resistance, with $Z _ { 1 } = R _ { 1 } , Z _ { 2 } = R _ { 2 } + R _ { r }$ . Therefore, the resonant 1 1 2 2 ???? frequency of the resonant circuits on the primary side and secondary side are designed to be same, and the system is operated at the resonant frequency $f _ { 0 }$ —that is: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[489,883,729,915]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0920/1612ce98269fe9adc78b45b8312513cc5803b8f8f9770f368b95b20fcef1933f.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\omega _ { 0 } = 2 \\pi f _ { 0 } = \\frac { 1 } { \\sqrt { L _ { 1 } C _ { 1 } } } = \\frac { 1 } { \\sqrt { L _ { 2 } C _ { 2 } } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[58,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 World Electr. Veh. J. 2023, 14, x FO ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 of 23 of 24 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[275,112,941,142]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"When the WPT system is operated in CC mode, the relationship between load current $I _ { L }$ and modulation depth $m$ in the SPWM inverter is: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[489,152,727,185]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0833/0d2f332198f9bf5771ce26242ebca222b555ba0c71f361be133bcdc51cf94fc7.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nI _ { L } = \\frac { 2 \\omega M V _ { D C } } { \\pi [ R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\omega ^ { 2 } M ^ { 2 } ] } m\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[278,195,564,209]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Further, it can be expressed as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[470,219,749,254]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0891/c80f224afee584efe4cbfa1ca86a87e27a104ad8fcb74798158ff1fb39f62abb.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nm _ { C C } = \\frac { \\pi [ R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\omega ^ { 2 } M ^ { 2 } ] } { 2 \\omega M V _ { D C } } I _ { L , r e q }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[275,263,941,338]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $I _ { L , r e q }$ is the output current required in CC mode, and $m _ { C C }$ is the modulation depth in CC mode. From Equation (10), when the load $R _ { L }$ varies, the modulation depth $m$ can be adjusted so that the system output current $I _ { L }$ tracks the output current $I _ { L , r e q }$ required by the CC mode, and $m$ increases as $R _ { L }$ increases. When the coil internal resistance $R _ { 1 }$ and $R _ { 2 }$ are ignored, Equation (10) can be further simplified to: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[537,348,680,380]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0041/c86a9c4acd5895c7cd55cf0fa5d2280601d47c98216f9a11318f72de1696ea90.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nm _ { C C } = \\frac { \\pi \\omega M } { 2 V _ { D C } } I _ { L , r e q }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[278,388,941,434]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It can be seen in Equation (11) that when the internal resistance of the coil is ignored and the system operates at resonant frequency, the WPT circuit with S-S compensation can realize CC charging independent of load [32]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[278,435,939,463]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"When the WPT system is operated in CV mode, the relationship between load voltage $U _ { L }$ and modulation depth $m$ of SPWM inverter is as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[489,474,729,506]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0492/336f24b00c270e17f84b48969d823e3f58a81f3e7e15f2a0400928a2506845de.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nU _ { L } = \\frac { \\pi \\omega M R _ { r } V _ { D C } } { 4 [ R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\omega ^ { 2 } M ^ { 2 } ] } m\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,517,564,531]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Further, it can be expressed as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[467,542,751,576]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0160/9265ce6e81317b7ad3f1c2b6e92d71229f98707feae3f20d2ae061c20776aceb.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nm _ { C V } = \\frac { 4 [ R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\omega ^ { 2 } M ^ { 2 } ] } { \\pi \\omega M R _ { r } V _ { D C } } U _ { L , r e q }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,585,941,630]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $U _ { L , r e q }$ is the output voltage required in CV mode, and $m _ { C V }$ is the modulation depth in CV mode. Similarly, when the coil’s internal resistances, $R _ { 1 }$ and $R _ { 2 }$ , are ignored, Equation (13) can be further simplified to: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[522,640,694,673]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0588/f6c3ec9c9c55e819f64d34314e84bcac6c8200d00a37f41908e218f0ebd5dd43.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nm _ { C V } = \\frac { 4 \\omega M } { \\pi R _ { r } V _ { D C } } U _ { L , r e q }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[275,681,941,725]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"From Equations (13) and (14), when the load $R _ { L }$ varies, the modulation depth $m$ can be adjusted so that the system output voltage $U _ { L }$ tracks the output voltage $U _ { L , r e q }$ required by the CV mode, and $m$ decreases as $R _ { L }$ increases. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[314,726,521,740]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The system’s load power is: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[561,739,657,772]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0300/ea26affd35db88607fa07e00255af63ad0998adbfc978761e9c3e4133f9e6e90.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP _ { l o a d } = { \\frac { { U _ { L } } ^ { 2 } } { R _ { L } } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[314,777,529,793]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The system’s input power is: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,802,714,837]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0183/548a8290adf1b0121b77d8da2d407b591725b7e21ad167c981fcc8278c006d3b.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP _ { i n } = \\frac { { U _ { 1 } } ^ { 2 } ( R _ { 2 } + R _ { r } ) } { R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\omega ^ { 2 } M ^ { 2 } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[312,846,752,862]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The system’s transmission efficiency $\\eta$ can be expressed as: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[455,872,761,915]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0817/7c54794c2d1f2c9710696dbe9fc2e7aa9fb06c6f67723407d31c0de433a10002.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\eta = \\frac { P _ { l o a d } } { P _ { i n } } = \\frac { { U _ { L } } ^ { 2 } [ R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\omega ^ { 2 } M ^ { 2 } ] } { { U _ { 1 } } ^ { 2 } ( R _ { 2 } + R _ { r } ) R _ { L } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[57,65,247,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,65,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[275,112,937,141]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If the coil internal resistances $R _ { 1 }$ and $R _ { 2 }$ are ignored, transmission efficiency, $\\eta$ , can be simplified as: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[484,140,734,175]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0400/2939f03a22a1fbf90b37cdfe7f3e32667934a3786dd7608d6969c49e441ff147.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\eta = { \\frac { \\pi ^ { 2 } \\omega ^ { 2 } { M ^ { 2 } } { U _ { L } } ^ { 2 } } { 4 { V _ { \\mathrm { D C } } } ^ { 2 } { m ^ { 2 } } { R _ { L } } ^ { 2 } } } = { \\frac { \\pi ^ { 2 } \\omega ^ { 2 } { M ^ { 2 } } { I _ { L } } ^ { 2 } } { 4 { V _ { \\mathrm { D C } } } ^ { 2 } { m ^ { 2 } } } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,179,941,299]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In Equation (18), the DC input voltage $V _ { D C } ,$ mutual inductance $M _ { ☉ }$ , and operating angle frequency $\\omega$ of the WPT system are fixed. Therefore, when the system operates in CC mode, the transmission efficiency $\\eta$ is determined by the modulation depth $m$ and the system output current ${ \\cal I } _ { L } ,$ where $I _ { L }$ is constant. Equation (11) indicates that the modulation depth $m$ is constant when the system operates in CC mode, resulting in an almost constant efficiency $\\eta$ . When the system operates in CV mode, the transmission efficiency $\\eta$ is determined by the modulation depth $m$ , the system output voltage $U _ { L } ,$ and the load $R _ { L } ,$ where $U _ { L }$ is constant. Taking partial derivatives of $\\eta$ with respect to $m$ and $R _ { L }$ yields: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[524,310,692,346]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0289/5d4e70c76130785d995bce384cd21c97dae1fed2ffee588e332be5a1b2123748.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n{ \\frac { \\partial \\eta } { \\partial m } } = - { \\frac { \\pi ^ { 2 } \\omega ^ { 2 } M ^ { 2 } { U _ { L } } ^ { 2 } } { 2 { V _ { D C } } ^ { 2 } { m ^ { 3 } } { R _ { L } } ^ { 2 } } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[522,356,695,393]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0570/704f839e3ad4371406b8505849b4c48ee422c70cd2216fbb16f497f17759c988.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\frac { \\partial \\eta } { \\partial R _ { L } } = - \\frac { \\pi ^ { 2 } \\omega ^ { 2 } M ^ { 2 } { U _ { L } } ^ { 2 } } { 2 V _ { D C } { } ^ { 2 } m ^ { 2 } { R _ { L } } ^ { 3 } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[310,397,796,412]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Compare the absolute values of two partial derivatives, yielding: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[546,422,672,455]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0704/0b23c17f29534252b2214bf05b20c205ce1016a66eefa2124ceabc35d1ee8b0d.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\frac { | \\partial \\eta / \\partial m | } { | \\partial \\eta / \\partial R _ { L } | } = { \\frac { m } { R _ { L } } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[277,464,941,524]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As $m$ is less than or equal to 1, and $R _ { L }$ is typically greater than 1, Equation (21) is less than 1, which means $\\vert \\partial \\eta / \\partial m \\vert < \\vert \\partial \\eta / \\partial R _ { L } \\vert$ . Therefore, $R _ { L }$ dominates in the denominator of Equation (18). As a result, the efficiency $\\eta$ in CV mode gradually decreases with an increase in $R _ { L }$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,535,732,551]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.4. Adaptive Control Strategy for CC-CV Output of WPT System ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,555,941,750]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"During battery charging, the WPT system operates in CC mode if the battery voltage is lower than the set voltage, causing the voltage to rise. Once the battery voltage reaches the preset level, the system switches from CC mode to CV mode, resulting in a decrease in charging current. Charging ends once the charging current falls below the preset end current. The equivalent load resistance of the battery changes over time during the charging process, which can affect the charging voltage or current. As noted in literature [36], a properly designed WPT system should ensure output stability. Therefore, in the event of a variation in the equivalent load resistance, a well-designed WPT system should be capable of automatically adjusting the system’s parameters to enable the output current in CC mode to follow the required $I _ { L , r e q }$ and the output voltage in CV mode to follow the required $U _ { L , r e q }$ . In this study, the modulation depth $m$ of the SPWM inverter circuit is controlled to enable $U _ { L }$ to track $U _ { L , r e q }$ or $I _ { L }$ to track $I _ { L , r e q }$ . The closed-loop control structure is depicted in Figure 4. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,66,247,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,65,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[280,111,721,265]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 4. The closed-loop control structure of WPT system with CC/CV output.Figure 4. The closed-loop control structure of WPT system with CC/CV output. \"]","image_footnote":"[]","img_path":"images/0412/3458baac11288cf5ff421500430af6e6be92510deb02ec242787eeb2f109fd17.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,300,941,450]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The ARM (Advanced RISC Machine) controller is a type of microcontroller based on the ARM architecture. The ARM processor is designed to be 32-bit, but it also supports a 16-bit instruction set. In addition, the ARM processor has advantages such as low power consumption, high performance, high reliability, easy development, and good flexibility. The STM32F103ZET6 is a microcontroller based on the ARM Cortex-M3 core, developed by ST Microelectronics. It has the advantages of high performance, low power consumption, high reliability, and easy development. The microcontroller has 512 KB of built-in flash memory and 64 KB of SRAM memory, and is equipped with multiple timers, an ADC, a DAC, and other modules. Therefore, in this study, the STM32F103ZET6 was chosen as the controller. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,450,941,525]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In Figure $^ { 4 , }$ the ARM controller at the receiver calculates the load $R _ { L }$ by detecting the load current $I _ { L }$ and voltage $U _ { L }$ . Then, the $R _ { L }$ is fed back to the ARM controller at the transmitter through wireless communication. The transmitter ARM controller tracks the required output current $I _ { L , r e q }$ or the required output voltage $U _ { L , r e q }$ by calculating the modulation depth $m$ of SPWM inverter circuit through Equation (10) or Equation (13). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[275,525,939,555]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The flow of the control scheme proposed in this paper is shown in Figure 5, including the following steps: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[275,560,942,753]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(1) Make the WPT circuit operate at the resonant frequency $f = f _ { 0 } .$ ; \n(2) Detect whether $U _ { L } < U _ { L , r e q } ;$ if $U _ { L } < U _ { L , r e q } ,$ start the control procedure. Otherwise, close the S-S WPT circuit. \n(3) Detect $U _ { L }$ and ${ \\cal I } _ { L } ,$ and calculate $R _ { L }$ . \n(4) According to Equation (10), adjust the modulation depth $m$ , so that $I _ { L } = I _ { L , r e q } ,$ and the control system operates in CC mode. \n(5) Judge whether $U _ { L } = U _ { L , r e q }$ is true; if it is true, execute step (6); if not true, repeat steps (3)–(4). \n(6) Re-detect $U _ { L }$ and ${ \\cal I } _ { L } ,$ and calculate $R _ { L }$ . \n(7) According to Equation (13), adjust the modulation depth $m _ { \\iota }$ , so that $U _ { L } = U _ { L , r e q } ,$ and the control system operates in CV mode. \n(8) Repeat steps (6) and (7) until $I _ { L } \\leq I _ { L , e n d }$ . \n(9) When $I _ { L } \\leq I _ { L , e n d } ,$ , the charging is completed, and close the S-S WPT circuit. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[899,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"9 of 23 ntrol ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[278,105,559,706]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 5. Adaptive the control flow chart of the CC-CV output of the WPT system. \"]","image_footnote":"[]","img_path":"images/0879/d0c04abb505cfca9f70c704cbf1945124e48364f4d748a42398692e890416858.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[278,737,529,752]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.5. Coupling-Coefficient Estimation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,756,942,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"oupling-Coefficient EstimationThe WPT system exhibits loose coupling, which means that variations in the alignment The WPT system exhibits loose coupling, which means that variations in the align-of the transmitting and receiving coils, or changes in transmission distance, can lead to ment of the transmitting and receiving coils, or chansignificant fluctuations in the coupling coefficient $k$ s in transmission dista. These fluctuations in $\\mathbf { k }$ e, can lead can directly o significant fluctuations in the coupling coefficient k. These fluctuations in k can directly impact the output voltage or current of the system, resulting in unstable performance. To mpact the output voltage or current of the system, resulting in unstable permaintain CC/CV output, it is essential to estimate the coupling coefficient $k$ rmance. To . This section maintain CC/CV output, it is essential to estimate the coupling coefficient k. This section examines the method of estimating the coupling coefficient based on circuit parameters, xamines the method of estimatiutilizing Figure 2 as a reference. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[312,860,783,876]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The rms value of voltage of receiving coil $U _ { 2 }$ can be derived as: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[485,885,732,917]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0475/5e78b828f00713b365157f133ddc4098778a6fc8f2b5964b0f605942b8cfc33d.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nU _ { 2 } = \\frac { \\omega M } { R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\omega ^ { 2 } M ^ { 2 } } U _ { 1 } R _ { r }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[58,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"orld Electr. Veh. J. World Electr. Veh. J.2023 2023, 14, 14, x FO, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10 of 23 of 24 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[277,111,941,171]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Assuming that $R _ { L }$ is constant, and combined with Equation (4), it can be seen that $R _ { r }$ is also constant. However, any changes in the mutual inductance M would cause a variation in the ratio of $U _ { 2 } / U _ { 1 }$ . Therefore, combining Equations (4) and (22) can estimate mutual inductance $M$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[314,172,521,187]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$U _ { 2 } / U _ { 1 }$ can be calculated as: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,196,714,228]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0383/c245777ed3d56129e934825ca4b71871fa10e24b3dd3cd78fca5fb86449c90bd.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n{ \\frac { U _ { 2 } } { U _ { 1 } } } = { \\frac { \\omega M R _ { r } } { R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\omega ^ { 2 } M ^ { 2 } } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[314,237,613,253]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mutual inductance $M$ can be derived as: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[462,260,754,316]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0402/abbbc25b5a91fee350a1188833a531b89feaa1d092142865362c6ab71e30935a.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nM = \\frac { R _ { r } \\pm \\sqrt { { R _ { r } } ^ { 2 } - 4 \\big ( \\frac { U _ { 2 } } { U _ { 1 } } \\big ) ^ { 2 } R _ { 1 } \\big ( R _ { 2 } + R _ { r } \\big ) } } { 2 \\omega \\frac { U _ { 2 } } { U _ { 1 } } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[310,323,803,338]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Combining Equation (5) with Equation (6), it can be deduced that: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[556,349,662,381]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0691/967b81a0fbc7b62102af71fd22813a8d8762817180f4e389220ca71fbdbaee1b.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nU _ { 2 } = \\frac { 2 \\sqrt { 2 } } { \\pi } U _ { L }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[275,391,939,419]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Substituting Equation (25) into Equation (24), mutual inductance $M$ can be further deduced as: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[442,414,774,470]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0295/ce9115c47b8881a1d088e89832c39b67a07d4fcfa38baffc70271060efd58cd5.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nM = \\frac { \\pi R _ { r } \\pm \\sqrt { \\pi ^ { 2 } { R _ { r } } ^ { 2 } - 3 2 \\big ( \\frac { U _ { L } } { U _ { 1 } } \\big ) ^ { 2 } R _ { 1 } \\big ( R _ { 2 } + R _ { r } \\big ) } } { 4 \\sqrt { 2 } \\omega \\frac { U _ { L } } { U _ { 1 } } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[312,474,941,489]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The relationship between mutual inductance $M$ and coupling coefficient $k$ is as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[563,499,655,532]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0783/4e5f59bed3b2dec65439a8fbc0d553b76a7eb2c56f9a8724f356dfc11170be37.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nk = \\frac { M } { \\sqrt { L _ { 1 } L _ { 2 } } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[275,541,942,661]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Equation (27) reveals that the coupling coefficient $k$ is influenced by both the selfinductance of the transmitting and receiving coils and their mutual inductance. Specifically, the coupling coefficient $k$ is directly proportional to the mutual inductance $M$ and inversely proportional to the self-inductance $L _ { 1 }$ or $L _ { 2 }$ of the coils. Thus, when the sizes, dimensions, and numbers of turns of the transmitting and receiving coils are fixed, the coupling coefficient $k$ depends solely on the mutual inductance $M$ between the coils. In other words, as the mutual inductance $M$ increases, so does the coupling coefficient $k$ . Therefore, the coupling coefficient $k$ can be derived as: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[447,670,769,726]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0215/281c013693803f609ec73703afbddfc9a5dfe4c362607f3ba4afae5f489ae538.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nk = \\frac { \\pi R _ { r } \\pm \\sqrt { \\pi ^ { 2 } { R _ { r } } ^ { 2 } - 3 2 \\big ( \\frac { U _ { L } } { U _ { 1 } } \\big ) ^ { 2 } R _ { 1 } \\big ( R _ { 2 } + R _ { r } \\big ) } } { 4 \\omega \\frac { U _ { L } } { U _ { 1 } } \\sqrt { 2 L _ { 1 } L _ { 2 } } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[275,734,941,778]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"When the coil is misaligned or the transmission distance changes, the $\\mathrm { C C } / \\mathrm { C V }$ output of the WPT system can be achieved by utilizing the coupling coefficient $k$ calculated using Equation (28). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[278,780,941,821]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If the internal resistances $R _ { 1 }$ and $R _ { 2 }$ of the transmitting and receiving coils are ignored, then one solution of Equations (26) and (28) is 0, and the other solution can be expressed as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[549,819,667,857]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0631/f030b522685be38e87d1a8184ba089a97fcfe14006173543c0a10fc078d8ad8d.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nM = \\frac { \\pi R _ { r } } { 2 \\sqrt { 2 } \\omega \\frac { U _ { L } } { U _ { 1 } } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[537,862,680,898]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0731/75f3912db36c6bc3048e57050a37838cd16888b7d58f6c0b4df60da7b9993f16.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nk = \\frac { \\pi R _ { r } } { 2 \\omega \\frac { U _ { L } } { U _ { 1 } } \\sqrt { 2 L _ { 1 } L _ { 2 } } }\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[312,902,924,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Thus, the sign $\" \\pm { } \\prime \\prime$ in Equations (26) and (28) should be interpreted as $\" + \"$ instead. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,65,247,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,65,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"11 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[277,112,710,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.6. Control Strategy Based on Coupling-Coefficient Estimation2.6. Control Strategy Based on Coupling-Coefficient Estimation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,130,942,221]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"When the coils are misaligned or the transmission distance varies, the coupling coef-When the coils are misaligned or the transmission distance varies, the coupling coefficientficient $k$ will change accordingly, making it impossible for the system to achieve CC/CVwill change accordingly, making it impossible for the system to achieve CC/CV output. To address this issue, as depicted by Equation (28), we can estimate the couplingoutput. To address this issue, as depicted by Equation (28), we can estimate the coupling coefficient coefficient $k$ by measuring the output parameters of the circuit and known system parame-by measuring the output parameters of the circuit and known system paramters, and then use this estimated value to adjust the desired modulation depth eters, and then use this estimated value to adjust the desired modulation depth $m$ for thefor the CC/CV mode, as shown in Equation (10) or Equation (13) after substitution.CC/CV mode, as shown in Equation (10) or Equation (13) after substitution. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,221,941,341]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 6 illustrates the CC/CV control process utilizing coupling-coefficient estima-Figure 6 illustrates the CC/CV control process utilizing coupling-coefficient estimation. After establishing communication between the transmitter and receiver, the receivertion. After establishing communication between the transmitter and receiver, the receiver controller calculates the load resistance controller calculates the load resistanc $R _ { L }$ by measuring the load voltage by measuring the load volt $U _ { L }$ and the load ???? and the current load cur ${ \\cal I } _ { L } ,$ and also detects changes in t ???? , and also detects changes $U _ { L }$ and ???? an $R _ { L }$ . Any changes detected are then fed???? . Any changes detected are then fed back to the transmitter controller. Using Equation (28), the transmitter determines theback to the transmitter controller. Using Equation (28), the transmitter determines the coucoupling coefficient pling coefficient k a $k$ and subsequently determines thed subsequently determines the C $\\mathrm { C C } / \\mathrm { C V }$ modulation depth odulation depth $m$ usingusing Equation (10) or (13). The transmitter controller automatically adjusts Equation (10) or (13). The transmitter controller automatically adjusts $m$ to ensure that to ensure that $I _ { L }$ tracks tracks $I _ { L , r e q }$ or or $U _ { L }$ tracks tracks $U _ { L , r e q }$ .. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[284,357,885,567]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 6. CC/CV output control strategy based on coupling-coefficient estimation. Figure 6. CC/CV output control strategy based on coupling-coefficient estimation. \"]","image_footnote":"[]","img_path":"images/0591/e3340e378c22261481896bd27d583b4d22ceb3d1f7a026634271fedf0701a29c.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,605,941,738]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Based on Equation (9), as the coupling coefficienBased on Equation (9), as the coupling coefficient $k$ k varies, the output currevaries, the output current $I _ { L }$ in in CC CC mode also varies. Therefore, at this stage, the WPT system fails to achieve the required mode also varies. Therefore, at this stage, the WPT system fails to achieve the required output current output current $I _ { L , r e q }$ in CC mode. Equation (10) indicates that the system can achieve the in CC mode. Equation (10) indicates that the system can achieve required output current the required output current $I _ { L , r e q }$ CC mode by adjusting the modulation depth m. Tin CC mode by adjusting the modulation depth $m$ ad-. To ????,???????? just the modulation depth m,adjust the modulation depth $m$ he first step is to estimate the coupling coefficient , the first step is to estimate the coupling coefficient $k$ of the of the system when the coils are misaligned or the transmission distance varies. Subsequently, system when the coils are misaligned or the transmission distance varies. Subsequently, by by substituting the newly acquired coupling coefficisubstituting the newly acquired coupling coefficient $k$ t k into Equation (10), the modula-into Equation (10), the modulation tion ddepth $m$ th m that satisfies the requirement of the CC mode for the output cthat satisfies the requirement of the CC mode for the output current $I _ { L , r e q }$ t can be determined. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,739,942,873]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 7 illustrates the process for adjusting the modulation depth $m$ in CC mode when there is a misalignment of the coil or a change in transmission distance. The circuit should be connected based on the ideal circuit, and when the coupling coefficient $k$ changes, measurements of the output voltage $U _ { L } ,$ output current ${ \\cal I } _ { L } ,$ and input voltage $U _ { 1 }$ of the ???????? ????????transmitting coil should be taken. From these measurements, the load $R _ { L }$ ????1can be calculated. Using Equation (28), the coupling coefficient $k$ ???????? can be estimated. Next, the required modulation depth m can be calculated using Equation (10), and the controller can adjust the quired modulation depth m can be calculated using Eqmodulation depth m to ensure that the output current $I _ { L }$ tion (10), and the controlletracks the required current $I _ { L , r e q }$ for CC mode. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"12 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[280,115,843,462]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 7. Flow chart of modulation depth adjustment based on coupling-coefficient estimation in Figure 7. Flow chart of modulation depth adjustment based on coupling-coefficient estimation in CC mode.CC mode. \"]","image_footnote":"[]","img_path":"images/0325/d98cd9657eeaab9a9bc9881e9225a5a6696ec0e4d45a5634549f22a300cce0ee.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,514,941,649]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Equation (12) implies that changes in the coupling coefficient Equation (12) implies that changes in the coupling coefficient $k$ will cause a corre-will cause a corresponding change in the output voltage sponding change in the output voltage $U _ { L }$ in CV mode, making it impossible for the WPT in CV mode, making it impossible for the WPT system to meet the required output voltage system to meet the required output voltage $U _ { L , r e q }$ in CV mode. However, Equation (13) in CV mode. However, Equation (13) shows that adjusting the modulation depth shows that adjusting the modulation depth $m$ can enable the system to satisfy the required can enable the system to satisfy the required output voltageoutput voltage $U _ { L , r e q }$ in CV mode. To determine how to adjust the modulation dein CV mode. To determine how to adjust the modulation depth $m _ { \\iota }$ h m, , the the first step is to estimate the coupling coefficfirst step is to estimate the coupling coefficient $k$ nt k of the system when there is misalign-of the system when there is misalignment ment of the coils or variations in transmission distance. Then, this new coupling coeffof the coils or variations in transmission distance. Then, this new coupling coefficient $k$ ent can k can be substituted into Equation (13) to obtain the modulatbe substituted into Equation (13) to obtain the modulation depth $m$ n depth m required to required to achieve the achieve the outoutput voltage $U _ { L , r e q }$ oltage iin CV mode. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,650,941,783]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 8 illustrates the process for adjusting the modulation depth $m$ in CV mode when there is a misalignment or a change in transmission distance of the coil. The first step is to connect the circuit based on the ideal circuit. Then, when there is a change in the step is to connect the circuit based on the ideal circuit. Then, when there is a change in the coupling coefficient $k ,$ the output voltage $U _ { L } ,$ output current ${ \\cal I } _ { L } ,$ and input voltage $U _ { 1 }$ ???? ????of the transmitting coil are measured. Using the output voltage $U _ { L }$ 1 and output current ${ \\cal I } _ { L } ,$ the load $R _ { L }$ is calculated, and the coupling coefficient $k$ ???????? ???????? is estimated at this time using ???? Equation (28). Equation (13) is used to calculate the required modulation depth $m ,$ and the controller adjusts the modulation depth $m$ to ensure that the output voltage $U _ { L }$ tracks the $U _ { L , r e q }$ required for the CV mode. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"13 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[280,114,845,462]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 8. Flow chart of modulation depth adjustment based on coupling-coefficient estimation in Figure 8. Flow chart of modulation depth adjustment based on coupling-coefficient estimation in CV mode.CV mode. \"]","image_footnote":"[]","img_path":"images/0141/b5711ef8738bcde2a10cfe122d5e69347ff938845e859e753818048a272c4c46.jpg","list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,511,638,526]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. Simulation of the Wireless Charging System3. Simulation of the Wireless Charging System ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,530,941,575]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The circuit model of the WPT system was established in MATLAB/Simulink, and the The circuit model of the WPT system was established in MATLAB/Simulink, and the CC-CV charging was simulated under the condition of coupling coefficiCC-CV charging was simulated under the condition of coupling coefficient $k = 0 . 5 0 3 2$ and and the lthe load $R _ { L }$ d of $1 0 { - } 2 5 \\Omega$ 25 Ω. The system parameters are shown in Ta. The system parameters are shown in Table 1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,611,941,718]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0920/d255896b485ee72fb38eb8367c790d311df03c6e52167338426b78ceae7e3511.jpg","list_items":null,"page_idx":"13","sub_type":null,"table_body":"<table><tr><td>Parameters</td><td>Values</td><td>Parameters</td><td>Values</td></tr><tr><td>VDC</td><td>12 V</td><td>C2</td><td>0.2 μF</td></tr><tr><td>L1</td><td>67.89 μH</td><td>R2</td><td>0.5Ω</td></tr><tr><td>C1</td><td>0.2 μF</td><td>f</td><td>43.2 kHz</td></tr><tr><td>R1</td><td>0.5Ω</td><td>RL</td><td>10-25 Ω</td></tr><tr><td>f1</td><td>43.2 kHz</td><td>UL,req</td><td>12V</td></tr><tr><td>L2</td><td>66.15 μH</td><td>IL,req</td><td>0.75 A</td></tr></table>","table_caption":"[\"Table 1. WPT system parameters.Table 1. WPT system parameters. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[277,734,941,810]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The MATLAB/Simulink model established includes an SPWM inverter circuit, a The MATLAB/Simulink model established includes an SPWM inverter circuit, a res-resonant circuit, a rectifier circuit, a sinusoidal signal generator, a triangular wave-signal onant circuit, a rectifier circuit, a sinusoidal signal generator, a triangular wave-signal generator, an amplitude comparator, and a signal inverter, as shown in Figure 9. During generator, an amplitude comparator, and a signal inverter, as shothe model operation, the CC output is conducted when the load $R _ { L }$ in is $1 0 { - } 1 5 \\ \\Omega$ During and the the modrequired $I _ { L , r e q }$ eration, the CC outpis 0.75 A. When the $R _ { L }$ is is $1 6 { - } 2 5 \\Omega _ { \\iota }$ ed w, the $U _ { L , r e q }$ he load ???? is 10–15 Ω anrequired for CV output is $1 2 \\mathrm { V } .$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. World Electr. Veh. J. 2023 2023,, 1414, x F, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"414 of 23 of 24 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[282,112,840,789]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 9. The Simulink circuit model of the WPT Figure 9. The Simulink circuit model of the WPT system. \"]","image_footnote":"[]","img_path":"images/0878/72ddf68c7f98dc15d42689f02ac7e7a940ab82c1c2b6af73c9c903acc3ec36a9.jpg","list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,821,941,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The amplitude of the triangle wave signal generator was set as unit 1. The amplituThe amplitude of the triangle wave signal generator was set as unit 1. The amplitude of the sinusoidal signal generator was calculated by Equations (10) and (13) accordingof the sinusoidal signal generator was calculated by Equations (10) and (13) according to the value of the load $R _ { L }$ . The signals generated by the sinusoidal signal generator and the triangle wave signal generator were compared by the amplitude comparator to generate the SPWM signal, which controlled the switches $Q _ { 1 }$ and $Q _ { 4 }$ . The signal reverser reverses the generated SPWM signal and controls the switches $Q _ { 2 }$ and $Q _ { 3 }$ . The DC power $V _ { D C }$ is first converted to high-frequency AC power by the SPWM inverter circuit. This high-frequency ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"15 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[277,112,941,200]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"AC power is then fed into the transmitting coilquency AC power is then fed into the transmit $L _ { 1 }$ via the compensation capacitor g coil ????1 via the compensation $C _ { 1 } ,$ whichacitor generates a high-frequency alternating magnetic field when excited. The receiving coil ????1, which generates a high-frequency alternating magnetic field when excited. The rece $L _ { 2 }$ and compensation capacitor ing coil ????2 and compensati $C _ { 2 }$ generate AC power through magnetic coupling induced bycapacitor ????2 generate AC power through magnetic couthis high-frequency alternating magnetic field. The generated AC power is then rectifiedpling induced by this high-frequency alternating magnetic field. The generated AC power by the rectifier circuit, converting it to DC power. In this way, the wireless power transferis then rectified by the rectifier circuit, converting it to DC power. In this way, the wireless is achieved.power trans ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,203,941,336]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 10 shows that the Figure 10 shows that the ???? $R _ { L }$ increases from 10 toncreases from 10 to 2 $2 5 \\ \\Omega ,$ and simulation results ofnd simulation results of ???? $I _ { L }$ and d ???????? $U _ { L }$ are compared with the theoretical values. The simulation results are in goode compared with the theoretical values. The simulation results are in good agreement with the theoretical values, indicating that the system has good CC and CVagreement with the theoretical values, indicating that the system has good CC and CV output performance, which verifies the accuracy of the model and method. In CC mode,output performance, which verifies the accuracy of the model and method. In CC mode, $I _ { L }$ tracks tracks $I _ { L , r e q } ,$ and and $U _ { L }$ increases with increases of increases with increases of $R _ { L }$ . In CV mode, . In CV mode, $U _ { L }$ tracks tracks $U _ { L , r e q } ,$ andand $I _ { L }$ decreases as decreases as $R _ { L }$ increases. The simulation results of increases. The simulation results of $U _ { L }$ and and $I _ { L }$ are slightly lower thanare slightly lower than the theoretical values, because the impedance of the rectification bridge circuit and load isthe theoretical values, because the impedance of the rectification bridge circuit and load equivalent to a pure resistance, which will produce error in the design of system parameters.is equivalent to a pure resistance, which will produce error in the design of system pa-Overall, the error is within the acceptable range.rameters. Overall, the error is within the accepta ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[280,353,727,575]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 10. Comparison between simulation results and theoretical values of CC-CV output of the Figure 10. Comparison between simulation results and theoretical values of CC-CV output of the WPT system based on Simulink.WPT system based on Simulink. \"]","image_footnote":"[]","img_path":"images/0720/40efef48ae59ae44cd1e7db522e465a3fcca6ece5d6b0c4c4875b4a8e5cf191a.jpg","list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,623,492,637]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. Experimental Verification ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,640,941,879]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To further verify the method, a resonant WPT experimental circuit based on S-S compensated was designed and built, as shown in Figure 11. The system’s parameters are shown in Table 1. The parameters of coils and the compensation capacitor are measured by a LCR meter (GW Instek: LCR821). The ratio of coil turns at the transmitting and receiving ends is 17:17. The inner diameter and outer diameter of coil are 12 and $2 2 . 5 \\mathrm { c m } ,$ ceiving ends is 17:17. The inner diameter and outer drespectively. The operating frequency of the system is $4 3 . 2 \\mathrm { k H z } ,$ f coil are 12 and 22.5 cm, , and the DC input voltage $V _ { D C }$ is $1 2 \\mathrm { V } .$ The 0.75 A constant current output is achieved when the load $R _ { L }$ varies from ???????????? is10 to $1 5 \\ \\Omega ,$ The 0.75 and the $1 2 \\mathrm { ~ V ~ }$ nstant current output is achieved when the load ???????? v constant voltage output is achieved when the load $R _ { L }$ s from varies 10 to 15 Ω, from 16 to $2 5 \\Omega$ he 12 V constant voltage output is achieved when the load ???????? varies from . Initially, the CC-CV charging strategy based on SPWM inverter control 16 to 25 Ω. Initially, the CC-CV charging was tested at a transmission distance of $3 \\mathrm { \\ c m }$ gy based on SPWM inverter control was between the transmitting and receiving tested at a transmission distance of 3 cm between the transmitting and receiving coils. coils. Subsequently, the proposed CC-CV charging strategy based on coupling-coefficient Subsequently, the proposed CC-CV charging strategy baestimation was evaluated at a transmission distance of $4 \\mathrm { { c m } }$ n coupling-coefficient esti-. The coupling coefficient mation was evaluated at a transmission distance of 4 cm. The coupling coefficient between between the coils was calculated to be 0.5032 using Inca [37] software at a transmission the coils wdistance of $3 \\mathrm { c m }$ culated to be 0.5032 using Inca [37] software at a transmission distance of , based on the coil parameters in Table 1. When the transmission distance was increased to $4 \\mathrm { c m } _ { \\cdot }$ , the proposed coupling-coefficient-estimation method was used to estimate the new coupling coefficient, which was found to be 0.4257. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"16 of 23verses ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[282,114,689,329]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 11. The WPT experimental circuit based on S-S compensation.Figure 11. The WPT experimental circuit based on S-S compensation. \"]","image_footnote":"[]","img_path":"images/0790/9dcdba15b53cee6dd382ee3d51eda535dd93b953551aefbb30643ef15beb1eb7.jpg","list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[278,363,505,376]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.1. System Experimental Device4.1. System Experimental Device ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,381,941,650]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The experimental WPT system is shown in Figure 11. The system adopts STM32F103ZET6 inverter circuit, a resonant circuit, a rectifier filter circuit, and a DC-voltage-acquisition as the main control chip. The system circuit mainly includes a full-bridge inverter circuit, a circuit. The amplitude of a control signal generated by the microcontroller is only 5 V, so resonant circuit, a rectifier filter circuit, and a DC-voltage-acquisition circuit. The amplitude the driver circuit is required to amplify the control signal so that it cof a control signal generated by the microcontroller is only $5 \\mathrm { V } ,$ ve the MOS so the driver circuit is transistors to operate normally. Two half-bridge drive chips IR2110 are used in the drive required to amplify the control signal so that it can drive the MOS transistors to operate circuit to form a full-bridge driver. The full bridge inverter circuit converts DC power into normally. Two half-bridge drive chips IR2110 are used in the drive circuit to form a full-bridge driver. The full bridge inverter circuit converts DC power into AC power to provide a high-frequency excitation source for the transmitter. The MOS transistors adopt into the DC power to charge the DC load. The diode adopts HER508, which has high volt-FQPF5N60C, which has the characteristics of a high voltage resistance value and high age resistance, low turn-on voltage, low impedance, and other characteristics. The DC-switching frequency. The full-bridge rectifier circuit converts AC power into the DC power voltage-acquisition circuit collects the voltage across the DC load. STM32F103ZET6 has to charge the DC load. The diode adopts HER508, which has high voltage resistance, low its own analog-to-digital converter (ADC), which can collect analog voltage signals and turn-on voltage, low impedance, and other characteristics. The DC-voltage-acquisition convert them into digital signals for processing. However, the ADC input voltage of circuit collects the voltage across the DC load. STM32F103ZET6 has its own analog-todigital converter (ADC), which can collect analog voltage signals and convert them into V voltage to below 3.3 V, so that the STM32F103ZET6 ADC can be used to sample and digital signals for processing. However, the ADC input voltage of STM32F103ZET6 is 0 to $3 . 3 \\mathrm { V } ,$ ss. and the CV output voltage of the WPT circuit designed in this study is $1 2 \\mathrm { V } .$ Therefore, The core of the system software is the compilation of the SPWa DC-DC conversion circuit is required to step down the $1 2 \\mathrm { V }$ ve program and voltage to below $3 . 3 \\mathrm { V } ,$ so ADC sampling program. The software of SPWM wave design is to form an athat the STM32F103ZET6 ADC can be used to sample and process. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,650,941,755]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"rated by the software of the SPWM data table, and the data are stored in the micro-The core of the system software is the compilation of the SPWM wave program and controller and generate the SPWM wave by calling the array. The advanced timer TIMER1 ADC sampling program. The software of SPWM wave design is to form an array of data timer TIMER3 controls the sine wave period. Within each sine wave cycle, the generated generated by the software of the SPWM data table, and the data are stored in the microconsine table is assigned to the TIM1_CCR1 register in order to generate SPWM wave.troller and generate the SPWM wave by calling the array. The advanced timer TIMER1 of The time from the STM32 controller’s ADC sampling to the SPWM control signal STM32F103ZET6 generates two sets of complementary PWM signals. The ordinary timer output is in the milliseconds, about 10–20 ms, and the change time of the equivalent re-TIMER3 controls the sine wave period. Within each sine wave cycle, the generated sine sistance during battery charging is typically above the second level [38]. This means that table is assigned to the TIM1_CCR1 register in order to generate SPWM wave. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,755,941,873]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ng battery charging, the changing speed of the battery equivalent resistance is much The time from the STM32 controller’s ADC sampling to the SPWM control signal output is in the milliseconds, about $1 0 { - } 2 0 ~ \\mathrm { m s } ,$ and the change time of the equivalent resistance during battery charging is typically above the second level [38]. This means that during battery charging, the changing speed of the battery equivalent resistance is much slower than the STM32 controller’s processing speed, from ADC sampling to the SPWM control signal output. Therefore, during the battery charging process, the STM32 controller can capture the change trend of the equivalent resistance by continuously sampling and storing data, and then use these data for more accurate control. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"17 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[280,112,620,127]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.2. S Verification of the Proposed Control Methodand storing data, and then use these data for more accur ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[275,129,870,145]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.2.1. Validation of CC-CV Charging Strategy Based on SPWM Inverter Control ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,147,941,311]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"With the ideal alignment, the experiment was carried out with the transmission distance of $3 \\ \\mathrm { c m } ,$ and the circuit was operated at the resonant frequency $f = f _ { 0 }$ . We prepared 10 to $2 5 ~ \\Omega$ resistors with an interval of $1 \\Omega$ . When the $R _ { L }$ was $1 0 { - } 1 5 \\ \\Omega$ , we adjusted the modulation depth 10 to 25 Ω resistors with an interval of 1 $m$ according to Equation (10) so that 0 When the was 10 Ω–15 Ω, we adjusted t $I _ { L } = I _ { L , r e q } ,$ and the control system was operated in CC mode. When the modulation depth m according to Equation (10) so that ???? = ???? , a $R _ { L }$ wasthe co $1 6 { - } 2 5 \\ \\Omega ,$ we adjusted the modulation depthwas operated in CC m $m$ according to Equation (13) so that . When the ???????? was 16–25 Ω, we adjusted ${ U } _ { L } = { U } _ { L , r e q } ,$ and the control systemn depth was operated in CV mode. Figure 12 shows the adjustment process of modulation depthm according to Equation (13) so that ???????? = ????????,????????????, and the control system was operated in m varying with the load CV mode. Figure 12 shows the $R _ { L }$ . In Figure 12, when the system operates in CC mode, thestment process of modulation depth ???? varying with modulation depth ???????? $m$ gradually increases as the load $R _ { L }$ increases; and when in CV mode, the modulation depth depth decreases as the lo $m$ decreases as the load ???? increases. These result $R _ { L }$ increases. These results agree with theree with the theoretical analtheoretical analysis of (10) and (13).ysis of (10) and (13). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[280,326,650,493]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 12. Adjustment process of modulation depth $m$ with $R _ { L }$ \"]","image_footnote":"[]","img_path":"images/0021/e6ad304ab8097747971c9dc7ffc6c4ef0165cffa2decfa844c9c1be81aac26e9.jpg","list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,527,941,617]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"he experimental waveforms for the current ???? of the The experimental waveforms for the current $I _ { 1 }$ nsmitting coil and the cur-of the transmitting coil and the current $I _ { 2 }$ t ???? of the receiving coil are illustrated in Figure 13. As is evident in Figure 13, In CC of the receiving coil are illustrated in Figure 13. As is evident in Figure 13, In CC mode, mode, the curthe current $I _ { 1 }$ t ????1 of the transmitting coil increases as the load ???????? inof the transmitting coil increases as the load $R _ { L }$ ses, and the increases, and the current $I _ { 2 }$ ????2 ????1of the receiving coil remains basically unchanged. In CV mode, the current $I _ { 1 }$ of the 2 decreases as the load increases. transmitting coil remains basically constant, but the current EER REVIEW $I _ { 2 }$ of the receiving coil decreases19 of 24 as the load $R _ { L }$ ???? increases. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[282,632,653,800]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 13. The current ????1 ofFigure 13. The current $I _ { 1 }$ e transmitting coil and the current ????2 of the receof the transmitting coil and the current $I _ { 2 }$ ng coil.of the receiving coil. \"]","image_footnote":"[]","img_path":"images/0696/1200113876b1e9c3c9eb72490de153faa3dc7f2eba15096430a183c673e02d1f.jpg","list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,835,941,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"igure 14 shows the comparison between the experimental results and the theoretical Figure 14 shows the comparison between the experimental results and the theoretical ???????? CV mode, tracks requivalues. In CC mode, $I _ { L }$ ????????,???????????? , and decreasetracks the required $I _ { L , r e q } ,$ incr and $U _ { L }$ ???????? s. The experimeincreases as $R _ { L }$ increases. In CV results vmode, $U _ { L }$ ????y the validity of thtracks required $U _ { L , r e q } ,$ ???? sed m and $I _ { L }$ ???? hod. The resultdecreases as $R _ { L }$ ow that the proposed increases. The experimental results method is suitable for battery charging, and the adjustment of modulation depth m is cru-verify the validity of the proposed method. The results show that the proposed method is cial for ???????? tracking ????????,???????????? in CC charging mode and ???????? tracking ????????,???????????? in CV charginsuitable for battery charging, and the adjustment of modulation depth $m$ is crucial for $I _ { L }$ mode.tracking $I _ { L , r e q }$ in CC charging mode and $U _ { L }$ tracking $U _ { L , r e q }$ in CV charging mode. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"18 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[278,111,682,312]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 14. Comparison between experimental results and theoretical values.Figure 14. Comparison between experimental results and theoretical values. \"]","image_footnote":"[]","img_path":"images/0645/1fa9cf7da233443f8e3a23ab42e20abfc0a9c33fb8cfd137dd671d2d071db0e3.jpg","list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,346,941,494]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In Figure 14, it can be observed that although there are deviations between the ex-In Figure 14, it can be observed that although there are deviations between the experimental results and theoretical values, the overall trend is consistent, which confirms perimental results and theoretical values, the overall trend is consistent, which confirms the accuracy of the model and method used. The experimental values of ???? and the accuracy of the model and method used. The experimental values of $U _ { L }$ re and $I _ { L }$ are slightly lower than the theoretical values due to the fact that the rectifier bridge circuit slightly lower than the theoretical values due to the fact that the rectifier bridge circuit and and load impedance can be approximated as a pure resistance ???????? load impedance can be approximated as a pure resistance $R _ { r }$ ording to Equation according to Equation (4), (4), which can introduce errors in the design of system parameters [39,40]. Additionally, which can introduce errors in the design of system parameters [39,40]. Additionally, the the power electronic system is not ideal; and switches, inductors, capacitors, and other power electronic system is not ideal; and switches, inductors, capacitors, and other resonant devices can also introduce some errors in controlling the WPT system during operation. However, these errors are considered acceptable. Regardless, the ADC sampling of the STM32 controller will also introduce a certain error. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,495,941,585]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"harging process. It can be observed that the system transmission efficiency, denoted Figure 15 presents the system efficiency measured from the input to the load during the charging process. It can be observed that the system transmission efficiency, denoted as as $\\eta .$ , remains relatively stable throughout the CC charging process, whereas it graduallyremains relatively stable throughout the CC charging process, whereas it gradually decreases as the load resistance decreases as the load resistance $R _ { L }$ increases during the CV charging process. These resultsreases during the CV charging process. These reare consistent with the previous theoretical analysis given by Equation (18). The overallsults are consistent with the previous theoretical analysis given by Equation (18). The transmission efficiency of the system falls betweenoverall transmission efficiency of the system falls between $8 0 \\%$ andand 9 $9 2 \\%$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[280,599,712,793]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 15. Transmission efficiency. \"]","image_footnote":"[]","img_path":"images/0999/81d4f4c394e71410a8e446fc4b36dd5fc87d282c911f26028083becfa593a33a.jpg","list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[275,824,932,839]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.2.2. Validation of CC-CV Charging Strategy Based on Coupling Coefficient Estimation ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,841,941,932]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Equation (28) reveals that the coupling coefficient $k$ can be estimated by the ratio of $U _ { L }$ and $U _ { 1 }$ . The transmission distance between the transmitting coil and the receiving coil ???? 1was varied from 1.5 to 5.5 was varied from 1.5 to $5 . 5 \\mathrm { c m }$ ure 16 illustrates a comparison between the estimated . Figure 16 illustrates a comparison between the estimated coupling coefficient k acoupling coefficient $k$ the Inca-calculated value at different transmission distances. As and the Inca-calculated value at different transmission distances. As depicted in Figure 16, the estimated coupling coefficient k obtaindepicted in Figure 16, the estimated coupling coefficient $k$ using Equation (28) is obtained using Equation (28) is largely consistent with the Inca-calculated value, indicating that estimating the coupling largely consistent with the Inca-calculated value, indicating that estimating the coupling coefficient through the ratio of coefficient through the ratio of ???? $U _ { L }$ and d ???? $U _ { 1 }$ is practical and highly accurate. This satisfies theractical and highly accurate. This satisfies design requirements completely.he design requirements completely. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[894,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"19 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[277,112,939,142]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[282,159,710,350]","code_body":null,"code_caption":null,"image_caption":"[\"igure 16. Comparison between the estimated value of coupling coefficient k and Inca vFigure 16. Comparison between the estimated value of coupling coefficient $k$ e at dif-and Inca value at erent transmission distances.different transmission distances. \"]","image_footnote":"[]","img_path":"images/0398/b248267beabb86c51134fad6365f3872201644fd653cf7062d6a6eaff49f802b.jpg","list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,401,941,536]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"hen the transmission distance between the transmitting and receiving coils was When the transmission distance between the transmitting and receiving coils was ncreased from 3 to 4 cm,increased from 3 to $4 \\ \\mathrm { c m } ,$ upling coefficient k was esti the coupling coefficient $k$ ted to be 0.4257 using Equa-was estimated to be 0.4257 using Equation (28). This new value of $k$ was then used to recalculate and adjust the required modulation depth ation depth m for the $m$ for the system to operate in stem to operate in CC/CV mode $\\mathrm { C C } / \\mathrm { C V }$ mode, by substituting it into ituting it into either either Equation (10) or (13). The experimental and theoretical values of the system’s outputquation (10) or (13). The experimental and theoretical values of the system’s output curcurrent ent ???? an $I _ { L }$ and output voltage output voltage ???? wer $U _ { L }$ were compared and presented in Figure 17. As evincedmpared and presented in Figure 17. As evinced in in Figure 17, the required output current Figure 17, the required output current ????????,???????????? of $I _ { L , r e q }$ of the system in CC mode isystem in CC mode is 0.75 A, and $0 . 7 5 \\mathrm { A } ,$ and the required output voltage required output voltage ????????,???????? $U _ { L , r e q }$ in CV mode isV mode is 12 V. T $1 2 \\mathrm { V } .$ The system operates in CC mode forstem operates in CC mode for loads between 10 andoads between 10 and 15 $1 5 \\Omega$ , and shifts to CV mode for loads between 16 and shifts to CV mode for loads between 16 and 25 Ω. $2 5 \\Omega$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[278,550,749,784]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 17. Comparison between experimental results and theoretical values of CC-CV output based Figure 17. Comparison between experimental results and theoretical values of CC-CV output based n coupling-coefficient estimation.on coupling-coefficient estimation. \"]","image_footnote":"[]","img_path":"images/0440/3023d7e0ccce2305de264024d5d941396c076958e871be78e343ef1df69308da.jpg","list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[277,832,393,846]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":". Conclusions5. Conclusions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[277,851,941,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"his paper presents a wireless charging system that can adapt to changes in load by This paper presents a wireless charging system that can adapt to changes in load by ontrolling the modulation depth of the SPWM inverter circuit. The system uses an S-S controlling the modulation depth of the SPWM inverter circuit. The system uses an S-S basic asic compensation structure to achieve both CC and CV charging when the load changes,compensation structure to achieve both CC and CV charging when the load changes, and nd this is determined by detecting the load voltage and current. The modulation depth this is determined by detecting the load voltage and current. The modulation depth of the inverter circuit is adjusted to achieve the desired CC or CV output. In addition, we proposed a method for estimating the coupling coefficient and designed a CC/CV control strategy that employs this estimation method. If external disturbances result in coil misalignment or changes in the transmission distance, which affect the mutual inductance between the coils, the proposed coupling-coefficient-estimation method is utilized to estimate the new coupling coefficient. The controller then adjusts the modulation depth of the SPWM inverter to achieve CC/CV output for the system. The proposed method is mathematically simple and easy to implement—requiring no additional topology. The feasibility of the method was demonstrated through theoretical analysis and simulation, and its effectiveness and accuracy were further verified through experiments. The study also analyzed the sources of error in the system. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[892,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"20 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[277,112,941,261]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,275,942,344]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Author Contributions: Conceptualization, K.S. and W.N.; methodology, K.S. and W.N.; software, K.S.; validation, K.S. and W.N.; formal analysis, K.S. and W.N.; investigation, K.S. and W.N.; resources, K.S.; data curation, K.S.; writing—original draft preparation, K.S.; writing—review and editing, W.N.; visualization, K.S.; supervision, W.N. All authors have read and agreed to the published version of the manuscript. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,353,631,366]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Funding: This research received no external funding. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[278,374,579,387]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data Availability Statement: Not applicable. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,395,702,407]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conflicts of Interest: The authors declare no conflict of interest. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[277,424,388,437]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nomenclature ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[273,451,791,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"WPT Wireless power transfer \nCC Constant current \nCV Constant voltage \nSPWM Sinusoidal pulse width modulation \n$m$ SPWM inverter circuit modulation depth \n$Q _ { 1 } – Q _ { 4 }$ Switches of SPWM inverter \n$D _ { 1 } { - } D _ { 4 }$ Diodes of full-bridge rectifier \n$L _ { 1 }$ Transmitting coil (H) \n$L _ { 2 }$ Receiving coil (H) \n$C _ { 1 }$ Resonant capacitor of the transmitting coil (F) \n$C _ { 2 }$ Resonant capacitor of the receiving coil (F) \n$k$ Coupling coefficient \n$M$ Mutual inductance (H) \n$\\omega$ System operating angle frequency (rad/s) \n$\\omega _ { 0 }$ Resonant angle frequency (rad/s) \n$f _ { 0 }$ Resonant frequency (Hz) \n$f$ Operating frequency $\\left( \\mathrm { H z } \\right)$ \n$V _ { D C }$ DC input voltage of SPWM inverter (V) \n$U _ { 1 }$ The rms value of voltage of transmitting coil (V) \n$I _ { 1 }$ The rms value of current of transmitting coil (A) \n$U _ { 2 }$ The rms value of voltage of receiving coil (V) \n$I _ { 2 }$ The rms value of current of receiving coil (A) \n$U _ { L }$ Load voltage (V) \n$I _ { L }$ Load current (A) \n$Z _ { 1 }$ Impedance of transmitting coil $( \\Omega )$ \n$Z _ { 2 }$ Impedance of receiving coil $( \\Omega )$ \n$R _ { 1 }$ The transmission coil internal resistance is $( \\Omega )$ \n$R _ { 2 }$ Internal resistance of receiving coil $( \\Omega )$ \n$R _ { r }$ Equivalent resistance of the rectifier bridge circuit and the load $( \\Omega )$ \nRL Load resistance $( \\Omega )$ \n$\\eta$ Transmission efficiency \nUL,req Charging voltage required for CV mode (V) \nIL,req Charging current required for CC mode (A) \nIL,end End of charge current (A) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,66,247,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[892,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"21 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[57,112,144,126]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,136,942,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Zhang, Y.; Chen, S.; Li, X.; Tang, Y. 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Bosshard, R.; Kolar, J.W.; Mühlethaler, J.; Stevanovi´c, I.; Wunsch, B.; Canales, F. Modeling and η- $_ { \\cdot \\alpha }$ -pareto Optimization of Inductive Power Transfer Coils for Electric Vehicles. IEEE J. Emerg. Sel. Top. Power Electron. 2015, 3, 50–64. [CrossRef] \n31. Zheng, C.; Lai, J.S.; Chen, R.; Faraci, W.E.; Zahid, Z.U.; Gu, B.; Zhang, L.; Lisi, G.; Anderson, D. High-Efficiency Contactless Power Transfer System for Electric Vehicle Battery Charging Application. IEEE J. Emerg. Sel. Top. Power Electron. 2015, 3, 65–74. [CrossRef] \n32. Qu, X.; Han, H.; Wong, S.C.; Tse, C.K.; Chen, W. Hybrid IPT Topologies With Constant Current or Constant Voltage Output for Battery Charging Applications. IEEE Trans. Power Electron. 2015, 30, 6329–6337. [CrossRef] \n33. Mai, R.; Chen, Y.; Li, Y.; Zhang, Y.; Cao, G.; He, Z. Inductive Power Transfer for Massive Electric Bicycles Charging Based on Hybrid Topology Switching With a Single Inverter. IEEE Trans. Power Electron. 2017, 32, 5897–5906. [CrossRef] \n34. Song, K.; Li, Z.; Jiang, J.; Zhu, C. Constant Current/Voltage Charging Operation for Series–Series and Series–Parallel Compensated Wireless Power Transfer Systems Employing Primary-Side Controller. IEEE Trans. Power Electron. 2018, 33, 8065–8080. [CrossRef] \n35. Buja, G.; Bertoluzzo, M.; Mude, K.N. Design and Experimentation of WPT Charger for Electric City Car. IEEE Trans. Ind. Electron. 2015, 62, 7436–7447. [CrossRef] \n36. Li, H.; Li, J.; Wang, K.; Chen, W.; Yang, X. A Maximum Efficiency Point Tracking Control Scheme for Wireless Power Transfer Systems Using Magnetic Resonant Coupling. IEEE Trans. Power Electron. 2015, 30, 3998–4008. [CrossRef] \n37. Niu, W.Q.; Chu, J.X.; Gu, W.; Shen, A.D. Exact Analysis of Frequency Splitting Phenomena of Contactless Power Transfer Systems. IEEE Trans. Circuits Syst. I Regul. Pap. 2013, 60, 1670–1677. [CrossRef] \n38. Shi, J.; Tian, M.; Han, S.; Wu, T.-Y.; Tang, Y. Electric vehicle battery remaining charging time estimation considering charging accuracy and charging profile prediction. J. Energy Storage 2022, 49, 104132. [CrossRef] \n39. Zhu, Q.; Wang, L.; Guo, Y.; Liao, C.; Li, F. Applying LCC Compensation Network to Dynamic Wireless EV Charging System. IEEE Trans. Ind. Electron. 2016, 63, 6557–6567. [CrossRef] \n40. Wang, Z.H.; Xiao, L.; Sun, Y.; Dai, X.; Li, Y. A simple approach for load identification in current-fed inductive power transfer system. In Proceedings of the 2012 IEEE International Conference on Power System Technology (POWERCON), Auckland, New Zealand, 30 October–2 November 2012; pp. 1–5. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,65,247,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[892,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"22 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[55,112,942,554]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,65,247,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"World Electr. Veh. J. 2023, 14, 111 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[892,66,939,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"23 of 23 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[57,569,942,609]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. ","text_format":null,"text_level":null,"type":"discarded"}],"string":"[\n {\n \"bbox\": \"[58,123,107,135]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,137,867,185]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"SPWM Inverter Control for Wireless Constant Current and Voltage Charging \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,198,334,214]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Kang Sun $\\\\textcircled{1}$ and Wangqiang Niu $\\\\ast \\\\textcircled { \\\\scriptsize { \\\\parallel } }$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,596,242,678]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Citation: Sun, K.; Niu, W. SPWM Inverter Control for Wireless Constant Current and Voltage Charging. World Electr. Veh. J. 2023, 14, 111. https://doi.org/ 10.3390/wevj14040111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,689,247,700]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Academic Editor: Ghanim A. Putrus \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,712,188,765]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received: 5 March 2023 \\nRevised: 23 March 2023 \\nAccepted: 7 April 2023 \\nPublished: 14 April 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,240,789,277]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Key Laboratory of Transport Industry of Marine Technology and Control Engineering, \\nShanghai Maritime University, Shanghai 201306, China \\n\\\\* Correspondence: wqniu@shmtu.edu.cn \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,294,941,601]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract: Constant current (CC) and constant voltage (CV) charging of batteries is a crucial research area in the practical implementation of wireless power transfer (WPT) systems. The typical charging process of a battery starts from the constant current mode. As the battery’s voltage increases, the charging mode switches to the constant voltage mode. During charging, the equivalent load resistance of the battery will vary with the charging time, and the equivalent load resistance will affect the charging current or voltage and system’s efficiency. In this study, an adaptive wireless charging method of CC-CV is proposed based on sinusoidal pulse width modulation (SPWM) inverter control. The proposed WPT circuit detects the load variation by measuring the parameters of load voltage and load current, and accurately controls the system output current or voltage by adjusting the modulation depth of the SPWM inverter on the primary side. When there is relative motion between the transmitting coil and the receiving coil, the sharp change in coupling coefficient directly affects the system’s output voltage and output current, leading to output fluctuations and instability. To solve this problem, a method for estimating the coupling coefficient is proposed which estimates the coupling coefficient during the charging process by measuring system parameters. Then, the controller on the primary side adjusts the modulation depth of the SPWM inverter circuit based on the estimated new coupling coefficient, so that the system can still achieve constant current and constant voltage charging under displacement or distance changes. In this study, the CC mode output current during battery charging was set to $0 . 7 5 \\\\mathrm { A } .$ , and the CV mode output voltage was set to 12 V. Simulation and experimental results demonstrate the validity and accuracy of the proposed control method. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,618,941,646]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: wireless power transfer (WPT); constant current/constant voltage charging (CC/CV); SPWM inverter; estimation of coupling coefficient; self-adaption \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,692,393,706]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,711,941,799]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electricity transmission is crucial for human production and daily life. Wireless power transfer (WPT) technology enables the transmission of electric energy from a power source to a load without direct electrical contact. WPT technology has rapidly developed with the advancements in modern industry and technology and is widely utilized in various fields, such as biomedical equipment, aerospace, consumer electronics, manufacturing facilities, and electric vehicles [1–4]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,800,941,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As a sustainable transportation option, electric vehicles (EVs) are becoming increasingly popular worldwide. With the increasing demand for electric vehicles, it is important to develop efficient and reliable charging techniques for their lithium-ion batteries. There are three commonly used charging methods: constant current–constant voltage (CC-CV) charging [5], constant power charging [6,7], and pulse charging [8,9]. CC-CV charging involves controlling the charging current and voltage to keep the battery at a constant current or voltage during the charging process. Constant current charging can charge the battery faster in the early stages of charging, and constant voltage charging can fill the battery faster in the later stages of charging. Therefore, by combining constant currentconstant voltage charging, charging efficiency and speed can be maximized. This charging and constant voltage charging, charging efficiency and speed can be maximized. Thismethod performs well in terms of charging speed and efficiency and can prevent overcharging method performs well in terms of charging speed and efficiency and can preventcharging and over-discharging, thereby extending the battery’s lifespan. overcharging and over-discharging, thereby extending the battery’s lifespan.In contrast, constant power charging and pulse charging have faster char \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,778,154,804]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CC BY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[57,57,270,99]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electric Vehicle Journal \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[57,966,489,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111. https://doi.org/10.3390/wevj14040111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[865,65,939,98]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MDPI \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[705,966,939,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://www.mdpi.com/journal/wevj \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[57,569,147,592]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"check for updates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[57,809,257,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Copyright: $^ ©$ 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[277,111,941,172]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,173,941,262]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In contrast, constant power charging and pulse charging have faster charging speeds but are more prone to overcharging or over-discharging the battery, which can reduce itslifespan. Constant power charging involves continuously adjusting the charging current lifespan. Constant power charging involves continuously adjusting the charging current and voltage to maintain a constant charging power during the charging process. Pulse charging applies periodic high-voltage and high-current pulse signals to the battery during charging to increase the charging speed. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,262,941,321]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Although constant power charging and pulse charging allow faster charging speeds, they require more complex control strategies to avoid negative impacts on the battery. In comparison, CC-CV charging has a simpler and more reliable control strategy, can adapt to different types of batteries, and can effectively protect the battery.to different types of batteries, and can effectively protect the batte \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,322,941,381]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Therefore, in many applications, CC-CV charging is still one of the most commonlyTherefore, in many applications, CC-CV charging is still one of the most commonly used charging methods, especially in the electric vehicle and renewable energy storageused charging methods, especially in the electric vehicle and renewable energy storage fields. By accurately controlling the charging current and voltage, CC-CV charging canfields. By accurately controlling the charging current and voltage, CC-CV charging can achieve efficient, safe, and reliable battery charging.achieve efficient, safe, and reliable battery charging. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,381,941,530]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Over the years, electric vehicles known for their eco-friendliness and high efficiencyOver the years, electric vehicles known for their eco-friendliness and high efficiency have been increasingly replacing traditional fuel-based vehicles, leading to a surge in thehave been increasingly replacing traditional fuel-based vehicles, leading to a surge in the interest in wireless charging technologies for electric vehicles. Lithium-ion batteries areinterest in wireless charging technologies for electric vehicles. Lithium-ion batteries are now widely used as energy storage units in electric vehicles [10]. Figure 1 illustrates thenow widely used as energy storage units in electric vehicles [10]. Figure 1 illustrates the charging process of a lithium battery, which begins with the CC mode and switches to thecharging process of a lithium battery, which begins with the CC mode and switches to the CV mode as the battery voltage increases [11]. The dynamic changes in the equivalentCV mode as the battery voltage increases [11]. The dynamic changes in the equivalent load resistance of the battery during the charging process can affect the charging current,load resistance of the battery during the charging process can affect the charging current, charging voltage, and system transmission efficiency. Hence, a closed-loop control schemecharging voltage, and system transmission efficiency. Hence, a closed-loop control is crucial for achieving precise control of CC and CV charging in the wireless chargingscheme is crucial for achieving precise control of CC and CV charging in the wireless system [12].charging sys \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[280,548,742,741]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 1. CC-CV charging curve of battery.Figure 1. CC-CV charging curve of battery. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0538/37e51b9f501d7e02a3a984230733e64acfbce48e896b9f8556392fac18962907.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,776,942,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The output of a WPT system is influenced by compensation parameters, operating The output of a WPT system is influenced by compensation parameters, operating frefrequency, and load conditions. Typically, compensation parameters and operating fre-quency, and load conditions. Typically, compensation parameters and operating frequency quency are constant, while the system output varies with load conditions. The use of DC-are constant, while the system output varies with load conditions. The use of DC-DC con-DC converter, a variable frequency or phase-shifted full-bridge inverter, or an impedance verter, a variable frequency or phase-shifted full-bridge inverter, or an impedance matching matching network are the main control methods for CC and CV wireless charging systemsnetwork are the main control methods for CC and CV wireless charging systems [13–15]. [13–15]. Using a buck/boost converter for DC-DC conversion can potentially have a nega-Using a buck/boost converter for DC-DC conversion can potentially have a negative impact tive impact on the system transmission efficiency and may also result in increased weight on the system transmission efficiency and may also result in increased weight or cost [13]. If the operating frequency of the system deviates significantly from the optimal frequency, adjusting the frequency may result in a reduction in the system’s power transmission capacity [14]. Phase-shift control is a technique that modifies the duty cycle of the inverter output voltage by varying the phase difference between the front and rear sections of the inverter, thereby adjusting the system output. This method is effective at compensating for the reactive power of the system when it operates at the resonant frequency. However, when using impedance matching, a large array of capacitors or inductors is required, which can increase the weight, size, and control complexity of the system [15]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[277,112,941,187]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,187,941,395]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In two papers [14,15], the system in question utilizes a DC-DC converter on the primary side and employs frequency conversion or phase-shift control for the full bridge inverter on the primary side to achieve CV output through impedance-matching control. In another two studies [16,17], to achieve CV output, a chopper control link such as a buck or boost converter is added to the secondary circuit. While these systems have achieved good CV output, the addition of extra circuits reduces the transmission efficiency of the system and increases the control complexity. In the studies [18,19], phase shift control was utilized to achieve CV output, but the circuit may fail to meet the output voltage requirements when the load varies significantly. Another study [20] utilized a PWM scheme with a phase-locked loop (PLL) control method. However, the circuit-input impedance needs to be inductive throughout the entire load variation range, which results in an increase in reactive power loss. In the studies [21,22], the system achieved CC and CV output through frequency-conversion control at two different operating frequencies. However, changing the frequency increases the complexity of hardware circuit design. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,397,941,650]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Many practical applications of WPT systems suffer from misalignment or variations in transmission distance between the transmitting and receiving coils. This can cause a significant change in the coupling coefficient, leading to instability in the output voltage and current. To address this issue, many researchers have investigated methods to identify the coupling coefficient. One such method proposed in [23] uses a switched capacitor, but its implementation in practical applications is challenging. In [24], a dynamic method that only requires parameters from the receiving end was analyzed, but its measurement complexity and uncertainty are high due to the high harmonics of the rectified current. In [25], the coupling coefficient was estimated by analyzing the relationship between the duty cycle of the buck–boost circuit and the coupling-coefficient change. However, this method results in two solutions for the coupling coefficient, and obtaining the true value from the two solutions using the duty cycle of the buck circuit is inefficient. Another method proposed in [26] identifies the coupling coefficient using the input impedance equation, which offers a single solution and avoids the double-solution problem encountered in [25]. This paper proposes a method for estimating the coupling coefficient when the coil is misaligned or the transmission distance changes during charging, and designs a CC/CV output adaptive control flow based on the coupling-coefficient estimation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,650,941,769]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The SPWM inverter is a type of inverter used to convert DC voltage into AC voltage. It works by generating a sequence of high-frequency pulses whose widths are modulated in such a way that the average voltage waveform obtained is a sine wave. This makes the SPWM inverter an ideal solution for applications that require a high-quality sine wave input. One of the main advantages of SPWM inverters over other types of inverters is that they provide a high-quality sine wave output with low harmonic distortion, which is essential for many electrical devices. Additionally, SPWM inverters are efficient, reliable, and can be easily controlled, making them ideal for use in various applications. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,770,941,872]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This paper proposes a WPT system based on SS compensation with an SPWM inverter circuit. To achieve CC/CV output, the modulation depth of the inverter circuit is controlled within a certain range as the load varies. Specifically, the system operates in CC mode with an output current of 0.75 A when the load voltage is below the maximum charging voltage of $1 2 \\\\mathrm { V } .$ Once the load voltage reaches $1 2 \\\\mathrm { V } ,$ the system switches to CV mode, and charging ends when the load current is less than the charging end current. The contributions of this paper are as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,873,939,904]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(1) A method to realize CC/CV output of WPT system under the control of SPWM inverter is proposed. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[275,112,941,231]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2) A mathematical model between load voltage $u _ { L }$ (and load current $I _ { L }$ ) and the modulation depth m of SPWM inverter was built. (3) An adaptive control flow of CC/CV output was designed. (4) A method for coupling-coefficient estimation during charging is proposed. (5) A CC/CV adaptive output strategy for WPT systems with coupling-coefficient estimation was designed. (6) An experimental circuit of WPT with S-S compensation with CC/CV output was built, and the proposed model and method were verified. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,233,942,322]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This paper is organized as follows. Section 2 presents an analysis of the proposed WPT circuit, including the derivation of the relationship between modulation depth and CC/CV output condition, estimating coupling coefficients and the controlling scheme. In Section 3, the proposed control scheme is validated through simulations. Section 4 evaluates the effectiveness of the proposed method through experimental results. Finally, Section 5 provides the conclusions of this study. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,334,425,348]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. System Analysis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[280,349,568,363]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.1. Theoretical Model of S-S WPT Circuit \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,368,941,428]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The WPT system comprises a transmitter and a receiver, which are connected through magnetic coupling to transfer energy via an alternating magnetic field. The transmitter employs a full bridge inverter circuit to convert DC voltage to AC voltage, and the receiver uses a full bridge rectifier circuit to convert AC voltage back to DC voltage. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,428,941,562]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To efficiently transfer electrical energy in the WPT system using an alternating magnetic field, compensation elements (usually capacitors) are added to the transmitting and receiving coil ends to reduce reactive power [11,27–35]. The basic compensation topology of the WPT system can be classified into four types based on the series or parallel connection between the capacitor and the transmitting/receiving coil. These four types are: series– series (S-S), series–parallel (S-P), parallel–parallel (P-P), and parallel–series (P-S) [27–29]. Among them, the S-S compensation circuit is widely used due to its simple structure, and the selection of capacitance is not affected by load and coupling conditions when the system operates at resonance frequency, hence the popularity of this circuit [11,29–31]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,563,941,740]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 2 illustrates the typical circuit diagram of S-S WPT [11,29,31], which consists of a full bridge inverter circuit $\\\\left( Q _ { 1 } – Q _ { 4 } \\\\right)$ , a transmission coil $( L _ { 1 } )$ , a receiving coil $( L _ { 2 } ) _ { \\\\mathrm { ~ ~ } }$ , a full bridge rectifier circuit $\\\\left( D _ { 1 } – D _ { 4 } \\\\right)$ , and two compensation capacitors ( $C _ { 1 }$ and $C _ { 2 }$ ). The transmitter coil $L _ { 1 }$ and the compensation capacitor $C _ { 1 }$ form the primary-side resonant circuit, and the receiver coil $L _ { 2 }$ and the compensation capacitor $C _ { 2 }$ form the secondary-side resonant circuit. $M$ is the mutual inductance between the transmitter coil $L _ { 1 }$ and the receiver coil $L _ { 2 }$ . $I _ { 1 }$ and $I _ { 2 }$ are the rms values of the resonant current on the primary side and the secondary side, respectively. $R _ { 1 }$ and $R _ { 2 }$ are the internal resistance of the transmitter coil $L _ { 1 }$ and the receiver coil $L _ { 2 } ,$ , respectively, and $C _ { r }$ is the filter capacitor. The DC voltage $V _ { D C }$ is the input voltage of the full-bridge inverter circuit. $U _ { 1 }$ is the rms value of the output voltage of the full-bridge inverter circuit. $U _ { 2 }$ is the rms value of the input voltage of full-bridge rectifier circuit. $I _ { L }$ is the load current. $U _ { L }$ is the load voltage. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[278,109,910,401]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 2. S-S-compensated WPT circuit.Figure 2. S-S-compensated WPT circuit. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0097/c4637a56cfc9d27ae1eda7fe210b2d06fdec2d66106dbfd8f4c55eb78ef5a82a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[310,434,910,449]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The following equations can be derived based on Kirchhoff’s voltage law (KVL): \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[524,458,692,499]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0437/afc70d955ab83a8e23f8c043ec7e390b59c913a5f57bd539105ec702d063eb1b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left\\\\{ \\\\begin{array} { l } { \\\\dot { U } _ { 1 } = Z _ { 1 } \\\\dot { I } _ { 1 } - j \\\\omega M \\\\dot { I } _ { 2 } } \\\\\\\\ { 0 = Z _ { 2 } \\\\dot { I } _ { 2 } - j \\\\omega M \\\\dot { I } _ { 1 } } \\\\end{array} \\\\right.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[527,508,687,557]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0772/9877e47daa41c415f5a285d75fd245aa02009f9a76a6c830fd57174a9ca06444.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left\\\\{ \\\\begin{array} { l } { \\\\dot { I } _ { 1 } = \\\\frac { Z _ { 2 } } { Z _ { 1 } Z _ { 2 } + \\\\omega ^ { 2 } M ^ { 2 } } \\\\dot { U } _ { 1 } } \\\\\\\\ { \\\\dot { I } _ { 2 } = \\\\frac { j \\\\omega M } { Z _ { 1 } Z _ { 2 } + \\\\omega ^ { 2 } M ^ { 2 } } \\\\dot { U } _ { 1 } } \\\\end{array} \\\\right.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,560,941,606]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\omega$ ⎩ ????1????2 + is the operating angle frequency of the system satisfying $\\\\omega = 2 \\\\pi f$ . $f$ is the operatwhere is the operating anging frequency of the system. $Z _ { 1 }$ requand $Z _ { 2 }$ cy of the system satisfying = 2????????. is the op-are the equivalent impedances of the transmitting erating frequency of the system.and the receiving, respectively: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[487,615,727,658]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0687/84e37b889227a3d8c479fcece7bac804eddd4c981e7704670f70d3775fb876fc.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left\\\\{ \\\\begin{array} { c } { Z _ { 1 } = R _ { 1 } + j \\\\Big ( \\\\omega L _ { 1 } - \\\\frac { 1 } { \\\\omega C _ { 1 } } \\\\Big ) } \\\\\\\\ { Z _ { 2 } = R _ { 2 } + R _ { r } + j \\\\big ( \\\\omega L _ { 2 } - \\\\frac { 1 } { \\\\omega C _ { 2 } } \\\\big ) } \\\\end{array} \\\\right.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[275,667,941,741]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Typically, $Z _ { 1 }$ and $Z _ { 2 }$ ⎩ ????2 = ????2 + ???????? + ????( ????2 − ???? )are complex numbers. However, when the system operates at the resonant frequency, $Z _ { 1 }$ and $Z _ { 2 }$ can be represented as pure resistance, with $Z _ { 1 } = R _ { 1 } , Z _ { 2 } =$ $R _ { 2 } + R _ { r } ,$ ???? where $R _ { r }$ ????2 is the equivalent AC resistance between the rectifier bridge circuit and ????1 ????2 the DC load. According to the fundamental equivalent principle, $R _ { r }$ and $R _ { L }$ ????1 =are satisfied ????1, ????2 = ????2 with [34]: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[563,739,653,768]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0300/463f863e318aa8e9c44e42b15b2d1d8914180c8ea8d083b59b3add113226409f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nR _ { r } = { \\\\frac { 8 } { \\\\pi ^ { 2 } } } R _ { L }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[561,778,655,810]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0233/494863ff021ae8f7b75795916525ca62910d8cc891c03f0617cf532806219564.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nI _ { L } = \\\\frac { 2 \\\\sqrt { 2 } } { \\\\pi } I _ { 2 }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[551,821,667,852]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0986/c19b5b173e85624c5d9a5dd847100470708e734e6dc2af97a195e4b2d561017e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nU _ { L } = \\\\frac { \\\\pi } { 2 \\\\sqrt { 2 } } I _ { 2 } R _ { r }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[268,856,941,887]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"????It can be intuitively inferred that if the DC load $R _ { L }$ is known, the corresponding DC load voltage $U _ { L }$ or current $I _ { L }$ ???? 2√2 2 ???? can be adjusted by controlling $U _ { 1 }$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. World Electr. Veh. J.2023 2023,,1414, x FO, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"f 5 of 23 24 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[277,112,645,127]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2. Analysis of SPWM Single-Phase Inverter Circuit2.2. Analysis of SPWM Single-Phase Inverter Circuit \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,130,941,265]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the single-phase inverter circuit, PWM modulation is often used to control then the single-phase inverter circuit, PWM modulation is often used to control the switchesswitches ( $\\\\left( Q _ { 1 } – Q _ { 4 } \\\\right)$ . There are square wave modulation and SPWM modulation amongThere are square wave modulation and SPWM modulation among the the PWM modulation methods. Although the square-wave modulation has a high DCPWM modulation methods. Although the square-wave modulation has a high DC utiliutilization rate, the harmonic content of output voltage is also high. The output voltagezation rate, the harmonic content of output voltage is also high. The output voltage wavewaveform of the inverter circuit using SPWM modulation is a series of rectangular pulsesorm of the inverter circuit using SPWM modulation is a series of rectangular pulses with with the same amplitude and unequal width. The pulse width varies according to the sinehe same amplitude and unequal width. The pulse width varies according to the sine law. law. When it acts on the inertial component, the output is equivalent to a sine wave. ItsWhen it acts on the inertial component, the output is equivalent to a sine wave. Its benefits benefits include a reduced level of harmonic distortion and a high degree of linearity innclude a reduced level of harmonic distortion and a high degree of linearity in voltage voltage regulation.regulation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,266,941,370]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The SPWM single-phase inverter circuit is shown in Figure 3. The SPWM signal ishe SPWM single-phase inverter circuit is shown in Figure 3. The SPWM signal is generated by comparing the sine wave of the modulation wave with the triangle wavegenerated by comparing the sine wave of the modulation wave with the triangle wave of of the carrier wave. In the part where the sine wave is larger than the triangle wave, thehe carrier wave. In the part where the sine wave is larger than the triangle wave, the switches switches $Q _ { 1 }$ and and $Q _ { 4 }$ are on. At the time where the sine wave is smaller than the triangleare on. At the time where the sine wave is smaller than the triangle wave, the switching devices wave, the switching devices $Q _ { 2 }$ and and $Q _ { 3 }$ are on. The output voltage are on. The output voltag $U _ { 1 }$ of the inverter circuitof the inverter ciris continuously switched between positive and negative cuit is continuously switched between positive and negati $V _ { D C }$ as the switches turn on atas the switches turn on carrier frequency.at carrier frequenc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,386,915,546]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"igure 3. The SPWM single-phase inverter circuit.Figure 3. The SPWM single-phase inverter circuit. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0982/146916723f72fd7ef7030b6003a6568eb38752b461badaf9c7bf4e29a0f41bf5.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,581,941,626]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"When the amplitude of the sine wave is When the amplitude of the sine wave is $U _ { s } ,$ he amplitude of the triangle wave is the amplitude of the triangle wave is $U _ { c } ,$ the modulation depth is defined as ???? the modulation depth is defined as $\\\\begin{array} { r } { m = \\\\frac { U _ { s } } { U _ { c } } . } \\\\end{array}$ ????nd 0 < , and $0 < m \\\\leq 1 .$ ????en the output voltage of in-, then the output voltage of inverter circuit can be expressed as: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[546,637,672,669]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0527/132781c422b472d35d749c3444225b73358ac6cbd0a6ec466b262ba50d5f29f5.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nU _ { 1 } = \\\\frac { \\\\sqrt { 2 } } { 2 } V _ { D C } { \\\\cdot } m\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,677,941,722]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where where $U _ { 1 }$ is the rms value of the voltage of the inverter circuit. It can be seen intuitively is the rms value of the voltage of the inverter circuit. It can be seen intuitively that hat the output voltthe output voltage $U _ { 1 }$ ???? of the inverter circuit can be adjusted by controlling the mod-of the inverter circuit can be adjusted by controlling the modulation ulationdepth $m$ e. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,724,941,768]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"n practical applications, microcontrollers (such asIn practical applications, microcontrollers (such as $\\\\mathsf { s t m 3 2 }$ 2 series controllers) are usu- series controllers) are usually ally used to generate a SPWM signal, and the external drive circuit drives the on–off of used to generate a SPWM signal, and the external drive circuit drives the on–off of switches $Q _ { 1 } – Q _ { 4 }$ s. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,778,495,794]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.3. Analysis of CC/CV Output \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,797,941,872]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"When the WPT system operates in the resonant frequency, the impedance angle is zero—that is, the imaginary part of the impedance is zero. The impedance can be represented as pure resistance, with $Z _ { 1 } = R _ { 1 } , Z _ { 2 } = R _ { 2 } + R _ { r }$ . Therefore, the resonant 1 1 2 2 ???? frequency of the resonant circuits on the primary side and secondary side are designed to be same, and the system is operated at the resonant frequency $f _ { 0 }$ —that is: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[489,883,729,915]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0920/1612ce98269fe9adc78b45b8312513cc5803b8f8f9770f368b95b20fcef1933f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\omega _ { 0 } = 2 \\\\pi f _ { 0 } = \\\\frac { 1 } { \\\\sqrt { L _ { 1 } C _ { 1 } } } = \\\\frac { 1 } { \\\\sqrt { L _ { 2 } C _ { 2 } } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[58,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 World Electr. Veh. J. 2023, 14, x FO \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 of 23 of 24 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[275,112,941,142]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"When the WPT system is operated in CC mode, the relationship between load current $I _ { L }$ and modulation depth $m$ in the SPWM inverter is: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[489,152,727,185]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0833/0d2f332198f9bf5771ce26242ebca222b555ba0c71f361be133bcdc51cf94fc7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nI _ { L } = \\\\frac { 2 \\\\omega M V _ { D C } } { \\\\pi [ R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\\\omega ^ { 2 } M ^ { 2 } ] } m\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[278,195,564,209]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Further, it can be expressed as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[470,219,749,254]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0891/c80f224afee584efe4cbfa1ca86a87e27a104ad8fcb74798158ff1fb39f62abb.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nm _ { C C } = \\\\frac { \\\\pi [ R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\\\omega ^ { 2 } M ^ { 2 } ] } { 2 \\\\omega M V _ { D C } } I _ { L , r e q }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[275,263,941,338]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $I _ { L , r e q }$ is the output current required in CC mode, and $m _ { C C }$ is the modulation depth in CC mode. From Equation (10), when the load $R _ { L }$ varies, the modulation depth $m$ can be adjusted so that the system output current $I _ { L }$ tracks the output current $I _ { L , r e q }$ required by the CC mode, and $m$ increases as $R _ { L }$ increases. When the coil internal resistance $R _ { 1 }$ and $R _ { 2 }$ are ignored, Equation (10) can be further simplified to: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[537,348,680,380]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0041/c86a9c4acd5895c7cd55cf0fa5d2280601d47c98216f9a11318f72de1696ea90.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nm _ { C C } = \\\\frac { \\\\pi \\\\omega M } { 2 V _ { D C } } I _ { L , r e q }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[278,388,941,434]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It can be seen in Equation (11) that when the internal resistance of the coil is ignored and the system operates at resonant frequency, the WPT circuit with S-S compensation can realize CC charging independent of load [32]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,435,939,463]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"When the WPT system is operated in CV mode, the relationship between load voltage $U _ { L }$ and modulation depth $m$ of SPWM inverter is as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[489,474,729,506]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0492/336f24b00c270e17f84b48969d823e3f58a81f3e7e15f2a0400928a2506845de.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nU _ { L } = \\\\frac { \\\\pi \\\\omega M R _ { r } V _ { D C } } { 4 [ R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\\\omega ^ { 2 } M ^ { 2 } ] } m\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,517,564,531]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Further, it can be expressed as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[467,542,751,576]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0160/9265ce6e81317b7ad3f1c2b6e92d71229f98707feae3f20d2ae061c20776aceb.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nm _ { C V } = \\\\frac { 4 [ R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\\\omega ^ { 2 } M ^ { 2 } ] } { \\\\pi \\\\omega M R _ { r } V _ { D C } } U _ { L , r e q }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,585,941,630]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $U _ { L , r e q }$ is the output voltage required in CV mode, and $m _ { C V }$ is the modulation depth in CV mode. Similarly, when the coil’s internal resistances, $R _ { 1 }$ and $R _ { 2 }$ , are ignored, Equation (13) can be further simplified to: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[522,640,694,673]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0588/f6c3ec9c9c55e819f64d34314e84bcac6c8200d00a37f41908e218f0ebd5dd43.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nm _ { C V } = \\\\frac { 4 \\\\omega M } { \\\\pi R _ { r } V _ { D C } } U _ { L , r e q }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[275,681,941,725]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"From Equations (13) and (14), when the load $R _ { L }$ varies, the modulation depth $m$ can be adjusted so that the system output voltage $U _ { L }$ tracks the output voltage $U _ { L , r e q }$ required by the CV mode, and $m$ decreases as $R _ { L }$ increases. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[314,726,521,740]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The system’s load power is: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[561,739,657,772]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0300/ea26affd35db88607fa07e00255af63ad0998adbfc978761e9c3e4133f9e6e90.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP _ { l o a d } = { \\\\frac { { U _ { L } } ^ { 2 } } { R _ { L } } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[314,777,529,793]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The system’s input power is: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,802,714,837]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0183/548a8290adf1b0121b77d8da2d407b591725b7e21ad167c981fcc8278c006d3b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP _ { i n } = \\\\frac { { U _ { 1 } } ^ { 2 } ( R _ { 2 } + R _ { r } ) } { R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\\\omega ^ { 2 } M ^ { 2 } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[312,846,752,862]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The system’s transmission efficiency $\\\\eta$ can be expressed as: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[455,872,761,915]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0817/7c54794c2d1f2c9710696dbe9fc2e7aa9fb06c6f67723407d31c0de433a10002.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\eta = \\\\frac { P _ { l o a d } } { P _ { i n } } = \\\\frac { { U _ { L } } ^ { 2 } [ R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\\\omega ^ { 2 } M ^ { 2 } ] } { { U _ { 1 } } ^ { 2 } ( R _ { 2 } + R _ { r } ) R _ { L } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[57,65,247,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,65,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[275,112,937,141]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If the coil internal resistances $R _ { 1 }$ and $R _ { 2 }$ are ignored, transmission efficiency, $\\\\eta$ , can be simplified as: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[484,140,734,175]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0400/2939f03a22a1fbf90b37cdfe7f3e32667934a3786dd7608d6969c49e441ff147.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\eta = { \\\\frac { \\\\pi ^ { 2 } \\\\omega ^ { 2 } { M ^ { 2 } } { U _ { L } } ^ { 2 } } { 4 { V _ { \\\\mathrm { D C } } } ^ { 2 } { m ^ { 2 } } { R _ { L } } ^ { 2 } } } = { \\\\frac { \\\\pi ^ { 2 } \\\\omega ^ { 2 } { M ^ { 2 } } { I _ { L } } ^ { 2 } } { 4 { V _ { \\\\mathrm { D C } } } ^ { 2 } { m ^ { 2 } } } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,179,941,299]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In Equation (18), the DC input voltage $V _ { D C } ,$ mutual inductance $M _ { ☉ }$ , and operating angle frequency $\\\\omega$ of the WPT system are fixed. Therefore, when the system operates in CC mode, the transmission efficiency $\\\\eta$ is determined by the modulation depth $m$ and the system output current ${ \\\\cal I } _ { L } ,$ where $I _ { L }$ is constant. Equation (11) indicates that the modulation depth $m$ is constant when the system operates in CC mode, resulting in an almost constant efficiency $\\\\eta$ . When the system operates in CV mode, the transmission efficiency $\\\\eta$ is determined by the modulation depth $m$ , the system output voltage $U _ { L } ,$ and the load $R _ { L } ,$ where $U _ { L }$ is constant. Taking partial derivatives of $\\\\eta$ with respect to $m$ and $R _ { L }$ yields: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[524,310,692,346]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0289/5d4e70c76130785d995bce384cd21c97dae1fed2ffee588e332be5a1b2123748.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n{ \\\\frac { \\\\partial \\\\eta } { \\\\partial m } } = - { \\\\frac { \\\\pi ^ { 2 } \\\\omega ^ { 2 } M ^ { 2 } { U _ { L } } ^ { 2 } } { 2 { V _ { D C } } ^ { 2 } { m ^ { 3 } } { R _ { L } } ^ { 2 } } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[522,356,695,393]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0570/704f839e3ad4371406b8505849b4c48ee422c70cd2216fbb16f497f17759c988.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\frac { \\\\partial \\\\eta } { \\\\partial R _ { L } } = - \\\\frac { \\\\pi ^ { 2 } \\\\omega ^ { 2 } M ^ { 2 } { U _ { L } } ^ { 2 } } { 2 V _ { D C } { } ^ { 2 } m ^ { 2 } { R _ { L } } ^ { 3 } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[310,397,796,412]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Compare the absolute values of two partial derivatives, yielding: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[546,422,672,455]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0704/0b23c17f29534252b2214bf05b20c205ce1016a66eefa2124ceabc35d1ee8b0d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\frac { | \\\\partial \\\\eta / \\\\partial m | } { | \\\\partial \\\\eta / \\\\partial R _ { L } | } = { \\\\frac { m } { R _ { L } } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[277,464,941,524]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As $m$ is less than or equal to 1, and $R _ { L }$ is typically greater than 1, Equation (21) is less than 1, which means $\\\\vert \\\\partial \\\\eta / \\\\partial m \\\\vert < \\\\vert \\\\partial \\\\eta / \\\\partial R _ { L } \\\\vert$ . Therefore, $R _ { L }$ dominates in the denominator of Equation (18). As a result, the efficiency $\\\\eta$ in CV mode gradually decreases with an increase in $R _ { L }$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,535,732,551]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.4. Adaptive Control Strategy for CC-CV Output of WPT System \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,555,941,750]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"During battery charging, the WPT system operates in CC mode if the battery voltage is lower than the set voltage, causing the voltage to rise. Once the battery voltage reaches the preset level, the system switches from CC mode to CV mode, resulting in a decrease in charging current. Charging ends once the charging current falls below the preset end current. The equivalent load resistance of the battery changes over time during the charging process, which can affect the charging voltage or current. As noted in literature [36], a properly designed WPT system should ensure output stability. Therefore, in the event of a variation in the equivalent load resistance, a well-designed WPT system should be capable of automatically adjusting the system’s parameters to enable the output current in CC mode to follow the required $I _ { L , r e q }$ and the output voltage in CV mode to follow the required $U _ { L , r e q }$ . In this study, the modulation depth $m$ of the SPWM inverter circuit is controlled to enable $U _ { L }$ to track $U _ { L , r e q }$ or $I _ { L }$ to track $I _ { L , r e q }$ . The closed-loop control structure is depicted in Figure 4. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,66,247,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,65,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[280,111,721,265]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 4. The closed-loop control structure of WPT system with CC/CV output.Figure 4. The closed-loop control structure of WPT system with CC/CV output. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0412/3458baac11288cf5ff421500430af6e6be92510deb02ec242787eeb2f109fd17.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,300,941,450]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The ARM (Advanced RISC Machine) controller is a type of microcontroller based on the ARM architecture. The ARM processor is designed to be 32-bit, but it also supports a 16-bit instruction set. In addition, the ARM processor has advantages such as low power consumption, high performance, high reliability, easy development, and good flexibility. The STM32F103ZET6 is a microcontroller based on the ARM Cortex-M3 core, developed by ST Microelectronics. It has the advantages of high performance, low power consumption, high reliability, and easy development. The microcontroller has 512 KB of built-in flash memory and 64 KB of SRAM memory, and is equipped with multiple timers, an ADC, a DAC, and other modules. Therefore, in this study, the STM32F103ZET6 was chosen as the controller. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,450,941,525]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In Figure $^ { 4 , }$ the ARM controller at the receiver calculates the load $R _ { L }$ by detecting the load current $I _ { L }$ and voltage $U _ { L }$ . Then, the $R _ { L }$ is fed back to the ARM controller at the transmitter through wireless communication. The transmitter ARM controller tracks the required output current $I _ { L , r e q }$ or the required output voltage $U _ { L , r e q }$ by calculating the modulation depth $m$ of SPWM inverter circuit through Equation (10) or Equation (13). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[275,525,939,555]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The flow of the control scheme proposed in this paper is shown in Figure 5, including the following steps: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[275,560,942,753]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(1) Make the WPT circuit operate at the resonant frequency $f = f _ { 0 } .$ ; \\n(2) Detect whether $U _ { L } < U _ { L , r e q } ;$ if $U _ { L } < U _ { L , r e q } ,$ start the control procedure. Otherwise, close the S-S WPT circuit. \\n(3) Detect $U _ { L }$ and ${ \\\\cal I } _ { L } ,$ and calculate $R _ { L }$ . \\n(4) According to Equation (10), adjust the modulation depth $m$ , so that $I _ { L } = I _ { L , r e q } ,$ and the control system operates in CC mode. \\n(5) Judge whether $U _ { L } = U _ { L , r e q }$ is true; if it is true, execute step (6); if not true, repeat steps (3)–(4). \\n(6) Re-detect $U _ { L }$ and ${ \\\\cal I } _ { L } ,$ and calculate $R _ { L }$ . \\n(7) According to Equation (13), adjust the modulation depth $m _ { \\\\iota }$ , so that $U _ { L } = U _ { L , r e q } ,$ and the control system operates in CV mode. \\n(8) Repeat steps (6) and (7) until $I _ { L } \\\\leq I _ { L , e n d }$ . \\n(9) When $I _ { L } \\\\leq I _ { L , e n d } ,$ , the charging is completed, and close the S-S WPT circuit. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[899,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"9 of 23 ntrol \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[278,105,559,706]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 5. Adaptive the control flow chart of the CC-CV output of the WPT system. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0879/d0c04abb505cfca9f70c704cbf1945124e48364f4d748a42398692e890416858.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[278,737,529,752]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.5. Coupling-Coefficient Estimation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,756,942,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"oupling-Coefficient EstimationThe WPT system exhibits loose coupling, which means that variations in the alignment The WPT system exhibits loose coupling, which means that variations in the align-of the transmitting and receiving coils, or changes in transmission distance, can lead to ment of the transmitting and receiving coils, or chansignificant fluctuations in the coupling coefficient $k$ s in transmission dista. These fluctuations in $\\\\mathbf { k }$ e, can lead can directly o significant fluctuations in the coupling coefficient k. These fluctuations in k can directly impact the output voltage or current of the system, resulting in unstable performance. To mpact the output voltage or current of the system, resulting in unstable permaintain CC/CV output, it is essential to estimate the coupling coefficient $k$ rmance. To . This section maintain CC/CV output, it is essential to estimate the coupling coefficient k. This section examines the method of estimating the coupling coefficient based on circuit parameters, xamines the method of estimatiutilizing Figure 2 as a reference. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[312,860,783,876]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The rms value of voltage of receiving coil $U _ { 2 }$ can be derived as: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[485,885,732,917]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0475/5e78b828f00713b365157f133ddc4098778a6fc8f2b5964b0f605942b8cfc33d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nU _ { 2 } = \\\\frac { \\\\omega M } { R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\\\omega ^ { 2 } M ^ { 2 } } U _ { 1 } R _ { r }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[58,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"orld Electr. Veh. J. World Electr. Veh. J.2023 2023, 14, 14, x FO, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10 of 23 of 24 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[277,111,941,171]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Assuming that $R _ { L }$ is constant, and combined with Equation (4), it can be seen that $R _ { r }$ is also constant. However, any changes in the mutual inductance M would cause a variation in the ratio of $U _ { 2 } / U _ { 1 }$ . Therefore, combining Equations (4) and (22) can estimate mutual inductance $M$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[314,172,521,187]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$U _ { 2 } / U _ { 1 }$ can be calculated as: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,196,714,228]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0383/c245777ed3d56129e934825ca4b71871fa10e24b3dd3cd78fca5fb86449c90bd.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n{ \\\\frac { U _ { 2 } } { U _ { 1 } } } = { \\\\frac { \\\\omega M R _ { r } } { R _ { 1 } ( R _ { 2 } + R _ { r } ) + \\\\omega ^ { 2 } M ^ { 2 } } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[314,237,613,253]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mutual inductance $M$ can be derived as: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[462,260,754,316]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0402/abbbc25b5a91fee350a1188833a531b89feaa1d092142865362c6ab71e30935a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nM = \\\\frac { R _ { r } \\\\pm \\\\sqrt { { R _ { r } } ^ { 2 } - 4 \\\\big ( \\\\frac { U _ { 2 } } { U _ { 1 } } \\\\big ) ^ { 2 } R _ { 1 } \\\\big ( R _ { 2 } + R _ { r } \\\\big ) } } { 2 \\\\omega \\\\frac { U _ { 2 } } { U _ { 1 } } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[310,323,803,338]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Combining Equation (5) with Equation (6), it can be deduced that: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[556,349,662,381]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0691/967b81a0fbc7b62102af71fd22813a8d8762817180f4e389220ca71fbdbaee1b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nU _ { 2 } = \\\\frac { 2 \\\\sqrt { 2 } } { \\\\pi } U _ { L }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[275,391,939,419]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Substituting Equation (25) into Equation (24), mutual inductance $M$ can be further deduced as: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[442,414,774,470]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0295/ce9115c47b8881a1d088e89832c39b67a07d4fcfa38baffc70271060efd58cd5.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nM = \\\\frac { \\\\pi R _ { r } \\\\pm \\\\sqrt { \\\\pi ^ { 2 } { R _ { r } } ^ { 2 } - 3 2 \\\\big ( \\\\frac { U _ { L } } { U _ { 1 } } \\\\big ) ^ { 2 } R _ { 1 } \\\\big ( R _ { 2 } + R _ { r } \\\\big ) } } { 4 \\\\sqrt { 2 } \\\\omega \\\\frac { U _ { L } } { U _ { 1 } } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[312,474,941,489]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The relationship between mutual inductance $M$ and coupling coefficient $k$ is as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[563,499,655,532]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0783/4e5f59bed3b2dec65439a8fbc0d553b76a7eb2c56f9a8724f356dfc11170be37.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nk = \\\\frac { M } { \\\\sqrt { L _ { 1 } L _ { 2 } } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[275,541,942,661]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Equation (27) reveals that the coupling coefficient $k$ is influenced by both the selfinductance of the transmitting and receiving coils and their mutual inductance. Specifically, the coupling coefficient $k$ is directly proportional to the mutual inductance $M$ and inversely proportional to the self-inductance $L _ { 1 }$ or $L _ { 2 }$ of the coils. Thus, when the sizes, dimensions, and numbers of turns of the transmitting and receiving coils are fixed, the coupling coefficient $k$ depends solely on the mutual inductance $M$ between the coils. In other words, as the mutual inductance $M$ increases, so does the coupling coefficient $k$ . Therefore, the coupling coefficient $k$ can be derived as: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[447,670,769,726]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0215/281c013693803f609ec73703afbddfc9a5dfe4c362607f3ba4afae5f489ae538.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nk = \\\\frac { \\\\pi R _ { r } \\\\pm \\\\sqrt { \\\\pi ^ { 2 } { R _ { r } } ^ { 2 } - 3 2 \\\\big ( \\\\frac { U _ { L } } { U _ { 1 } } \\\\big ) ^ { 2 } R _ { 1 } \\\\big ( R _ { 2 } + R _ { r } \\\\big ) } } { 4 \\\\omega \\\\frac { U _ { L } } { U _ { 1 } } \\\\sqrt { 2 L _ { 1 } L _ { 2 } } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[275,734,941,778]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"When the coil is misaligned or the transmission distance changes, the $\\\\mathrm { C C } / \\\\mathrm { C V }$ output of the WPT system can be achieved by utilizing the coupling coefficient $k$ calculated using Equation (28). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,780,941,821]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If the internal resistances $R _ { 1 }$ and $R _ { 2 }$ of the transmitting and receiving coils are ignored, then one solution of Equations (26) and (28) is 0, and the other solution can be expressed as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[549,819,667,857]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0631/f030b522685be38e87d1a8184ba089a97fcfe14006173543c0a10fc078d8ad8d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nM = \\\\frac { \\\\pi R _ { r } } { 2 \\\\sqrt { 2 } \\\\omega \\\\frac { U _ { L } } { U _ { 1 } } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[537,862,680,898]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0731/75f3912db36c6bc3048e57050a37838cd16888b7d58f6c0b4df60da7b9993f16.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nk = \\\\frac { \\\\pi R _ { r } } { 2 \\\\omega \\\\frac { U _ { L } } { U _ { 1 } } \\\\sqrt { 2 L _ { 1 } L _ { 2 } } }\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[312,902,924,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Thus, the sign $\\\" \\\\pm { } \\\\prime \\\\prime$ in Equations (26) and (28) should be interpreted as $\\\" + \\\"$ instead. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,65,247,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,65,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"11 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[277,112,710,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.6. Control Strategy Based on Coupling-Coefficient Estimation2.6. Control Strategy Based on Coupling-Coefficient Estimation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,130,942,221]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"When the coils are misaligned or the transmission distance varies, the coupling coef-When the coils are misaligned or the transmission distance varies, the coupling coefficientficient $k$ will change accordingly, making it impossible for the system to achieve CC/CVwill change accordingly, making it impossible for the system to achieve CC/CV output. To address this issue, as depicted by Equation (28), we can estimate the couplingoutput. To address this issue, as depicted by Equation (28), we can estimate the coupling coefficient coefficient $k$ by measuring the output parameters of the circuit and known system parame-by measuring the output parameters of the circuit and known system paramters, and then use this estimated value to adjust the desired modulation depth eters, and then use this estimated value to adjust the desired modulation depth $m$ for thefor the CC/CV mode, as shown in Equation (10) or Equation (13) after substitution.CC/CV mode, as shown in Equation (10) or Equation (13) after substitution. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,221,941,341]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 6 illustrates the CC/CV control process utilizing coupling-coefficient estima-Figure 6 illustrates the CC/CV control process utilizing coupling-coefficient estimation. After establishing communication between the transmitter and receiver, the receivertion. After establishing communication between the transmitter and receiver, the receiver controller calculates the load resistance controller calculates the load resistanc $R _ { L }$ by measuring the load voltage by measuring the load volt $U _ { L }$ and the load ???? and the current load cur ${ \\\\cal I } _ { L } ,$ and also detects changes in t ???? , and also detects changes $U _ { L }$ and ???? an $R _ { L }$ . Any changes detected are then fed???? . Any changes detected are then fed back to the transmitter controller. Using Equation (28), the transmitter determines theback to the transmitter controller. Using Equation (28), the transmitter determines the coucoupling coefficient pling coefficient k a $k$ and subsequently determines thed subsequently determines the C $\\\\mathrm { C C } / \\\\mathrm { C V }$ modulation depth odulation depth $m$ usingusing Equation (10) or (13). The transmitter controller automatically adjusts Equation (10) or (13). The transmitter controller automatically adjusts $m$ to ensure that to ensure that $I _ { L }$ tracks tracks $I _ { L , r e q }$ or or $U _ { L }$ tracks tracks $U _ { L , r e q }$ .. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[284,357,885,567]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 6. CC/CV output control strategy based on coupling-coefficient estimation. Figure 6. CC/CV output control strategy based on coupling-coefficient estimation. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0591/e3340e378c22261481896bd27d583b4d22ceb3d1f7a026634271fedf0701a29c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,605,941,738]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Based on Equation (9), as the coupling coefficienBased on Equation (9), as the coupling coefficient $k$ k varies, the output currevaries, the output current $I _ { L }$ in in CC CC mode also varies. Therefore, at this stage, the WPT system fails to achieve the required mode also varies. Therefore, at this stage, the WPT system fails to achieve the required output current output current $I _ { L , r e q }$ in CC mode. Equation (10) indicates that the system can achieve the in CC mode. Equation (10) indicates that the system can achieve required output current the required output current $I _ { L , r e q }$ CC mode by adjusting the modulation depth m. Tin CC mode by adjusting the modulation depth $m$ ad-. To ????,???????? just the modulation depth m,adjust the modulation depth $m$ he first step is to estimate the coupling coefficient , the first step is to estimate the coupling coefficient $k$ of the of the system when the coils are misaligned or the transmission distance varies. Subsequently, system when the coils are misaligned or the transmission distance varies. Subsequently, by by substituting the newly acquired coupling coefficisubstituting the newly acquired coupling coefficient $k$ t k into Equation (10), the modula-into Equation (10), the modulation tion ddepth $m$ th m that satisfies the requirement of the CC mode for the output cthat satisfies the requirement of the CC mode for the output current $I _ { L , r e q }$ t can be determined. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,739,942,873]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 7 illustrates the process for adjusting the modulation depth $m$ in CC mode when there is a misalignment of the coil or a change in transmission distance. The circuit should be connected based on the ideal circuit, and when the coupling coefficient $k$ changes, measurements of the output voltage $U _ { L } ,$ output current ${ \\\\cal I } _ { L } ,$ and input voltage $U _ { 1 }$ of the ???????? ????????transmitting coil should be taken. From these measurements, the load $R _ { L }$ ????1can be calculated. Using Equation (28), the coupling coefficient $k$ ???????? can be estimated. Next, the required modulation depth m can be calculated using Equation (10), and the controller can adjust the quired modulation depth m can be calculated using Eqmodulation depth m to ensure that the output current $I _ { L }$ tion (10), and the controlletracks the required current $I _ { L , r e q }$ for CC mode. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"12 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[280,115,843,462]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 7. Flow chart of modulation depth adjustment based on coupling-coefficient estimation in Figure 7. Flow chart of modulation depth adjustment based on coupling-coefficient estimation in CC mode.CC mode. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0325/d98cd9657eeaab9a9bc9881e9225a5a6696ec0e4d45a5634549f22a300cce0ee.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,514,941,649]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Equation (12) implies that changes in the coupling coefficient Equation (12) implies that changes in the coupling coefficient $k$ will cause a corre-will cause a corresponding change in the output voltage sponding change in the output voltage $U _ { L }$ in CV mode, making it impossible for the WPT in CV mode, making it impossible for the WPT system to meet the required output voltage system to meet the required output voltage $U _ { L , r e q }$ in CV mode. However, Equation (13) in CV mode. However, Equation (13) shows that adjusting the modulation depth shows that adjusting the modulation depth $m$ can enable the system to satisfy the required can enable the system to satisfy the required output voltageoutput voltage $U _ { L , r e q }$ in CV mode. To determine how to adjust the modulation dein CV mode. To determine how to adjust the modulation depth $m _ { \\\\iota }$ h m, , the the first step is to estimate the coupling coefficfirst step is to estimate the coupling coefficient $k$ nt k of the system when there is misalign-of the system when there is misalignment ment of the coils or variations in transmission distance. Then, this new coupling coeffof the coils or variations in transmission distance. Then, this new coupling coefficient $k$ ent can k can be substituted into Equation (13) to obtain the modulatbe substituted into Equation (13) to obtain the modulation depth $m$ n depth m required to required to achieve the achieve the outoutput voltage $U _ { L , r e q }$ oltage iin CV mode. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,650,941,783]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 8 illustrates the process for adjusting the modulation depth $m$ in CV mode when there is a misalignment or a change in transmission distance of the coil. The first step is to connect the circuit based on the ideal circuit. Then, when there is a change in the step is to connect the circuit based on the ideal circuit. Then, when there is a change in the coupling coefficient $k ,$ the output voltage $U _ { L } ,$ output current ${ \\\\cal I } _ { L } ,$ and input voltage $U _ { 1 }$ ???? ????of the transmitting coil are measured. Using the output voltage $U _ { L }$ 1 and output current ${ \\\\cal I } _ { L } ,$ the load $R _ { L }$ is calculated, and the coupling coefficient $k$ ???????? ???????? is estimated at this time using ???? Equation (28). Equation (13) is used to calculate the required modulation depth $m ,$ and the controller adjusts the modulation depth $m$ to ensure that the output voltage $U _ { L }$ tracks the $U _ { L , r e q }$ required for the CV mode. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"13 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[280,114,845,462]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 8. Flow chart of modulation depth adjustment based on coupling-coefficient estimation in Figure 8. Flow chart of modulation depth adjustment based on coupling-coefficient estimation in CV mode.CV mode. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0141/b5711ef8738bcde2a10cfe122d5e69347ff938845e859e753818048a272c4c46.jpg\",\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,511,638,526]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. Simulation of the Wireless Charging System3. Simulation of the Wireless Charging System \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,530,941,575]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The circuit model of the WPT system was established in MATLAB/Simulink, and the The circuit model of the WPT system was established in MATLAB/Simulink, and the CC-CV charging was simulated under the condition of coupling coefficiCC-CV charging was simulated under the condition of coupling coefficient $k = 0 . 5 0 3 2$ and and the lthe load $R _ { L }$ d of $1 0 { - } 2 5 \\\\Omega$ 25 Ω. The system parameters are shown in Ta. The system parameters are shown in Table 1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,611,941,718]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0920/d255896b485ee72fb38eb8367c790d311df03c6e52167338426b78ceae7e3511.jpg\",\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Parameters</td><td>Values</td><td>Parameters</td><td>Values</td></tr><tr><td>VDC</td><td>12 V</td><td>C2</td><td>0.2 μF</td></tr><tr><td>L1</td><td>67.89 μH</td><td>R2</td><td>0.5Ω</td></tr><tr><td>C1</td><td>0.2 μF</td><td>f</td><td>43.2 kHz</td></tr><tr><td>R1</td><td>0.5Ω</td><td>RL</td><td>10-25 Ω</td></tr><tr><td>f1</td><td>43.2 kHz</td><td>UL,req</td><td>12V</td></tr><tr><td>L2</td><td>66.15 μH</td><td>IL,req</td><td>0.75 A</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. WPT system parameters.Table 1. WPT system parameters. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[277,734,941,810]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The MATLAB/Simulink model established includes an SPWM inverter circuit, a The MATLAB/Simulink model established includes an SPWM inverter circuit, a res-resonant circuit, a rectifier circuit, a sinusoidal signal generator, a triangular wave-signal onant circuit, a rectifier circuit, a sinusoidal signal generator, a triangular wave-signal generator, an amplitude comparator, and a signal inverter, as shown in Figure 9. During generator, an amplitude comparator, and a signal inverter, as shothe model operation, the CC output is conducted when the load $R _ { L }$ in is $1 0 { - } 1 5 \\\\ \\\\Omega$ During and the the modrequired $I _ { L , r e q }$ eration, the CC outpis 0.75 A. When the $R _ { L }$ is is $1 6 { - } 2 5 \\\\Omega _ { \\\\iota }$ ed w, the $U _ { L , r e q }$ he load ???? is 10–15 Ω anrequired for CV output is $1 2 \\\\mathrm { V } .$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. World Electr. Veh. J. 2023 2023,, 1414, x F, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"414 of 23 of 24 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[282,112,840,789]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 9. The Simulink circuit model of the WPT Figure 9. The Simulink circuit model of the WPT system. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0878/72ddf68c7f98dc15d42689f02ac7e7a940ab82c1c2b6af73c9c903acc3ec36a9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,821,941,927]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The amplitude of the triangle wave signal generator was set as unit 1. The amplituThe amplitude of the triangle wave signal generator was set as unit 1. The amplitude of the sinusoidal signal generator was calculated by Equations (10) and (13) accordingof the sinusoidal signal generator was calculated by Equations (10) and (13) according to the value of the load $R _ { L }$ . The signals generated by the sinusoidal signal generator and the triangle wave signal generator were compared by the amplitude comparator to generate the SPWM signal, which controlled the switches $Q _ { 1 }$ and $Q _ { 4 }$ . The signal reverser reverses the generated SPWM signal and controls the switches $Q _ { 2 }$ and $Q _ { 3 }$ . The DC power $V _ { D C }$ is first converted to high-frequency AC power by the SPWM inverter circuit. This high-frequency \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"15 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[277,112,941,200]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"AC power is then fed into the transmitting coilquency AC power is then fed into the transmit $L _ { 1 }$ via the compensation capacitor g coil ????1 via the compensation $C _ { 1 } ,$ whichacitor generates a high-frequency alternating magnetic field when excited. The receiving coil ????1, which generates a high-frequency alternating magnetic field when excited. The rece $L _ { 2 }$ and compensation capacitor ing coil ????2 and compensati $C _ { 2 }$ generate AC power through magnetic coupling induced bycapacitor ????2 generate AC power through magnetic couthis high-frequency alternating magnetic field. The generated AC power is then rectifiedpling induced by this high-frequency alternating magnetic field. The generated AC power by the rectifier circuit, converting it to DC power. In this way, the wireless power transferis then rectified by the rectifier circuit, converting it to DC power. In this way, the wireless is achieved.power trans \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,203,941,336]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 10 shows that the Figure 10 shows that the ???? $R _ { L }$ increases from 10 toncreases from 10 to 2 $2 5 \\\\ \\\\Omega ,$ and simulation results ofnd simulation results of ???? $I _ { L }$ and d ???????? $U _ { L }$ are compared with the theoretical values. The simulation results are in goode compared with the theoretical values. The simulation results are in good agreement with the theoretical values, indicating that the system has good CC and CVagreement with the theoretical values, indicating that the system has good CC and CV output performance, which verifies the accuracy of the model and method. In CC mode,output performance, which verifies the accuracy of the model and method. In CC mode, $I _ { L }$ tracks tracks $I _ { L , r e q } ,$ and and $U _ { L }$ increases with increases of increases with increases of $R _ { L }$ . In CV mode, . In CV mode, $U _ { L }$ tracks tracks $U _ { L , r e q } ,$ andand $I _ { L }$ decreases as decreases as $R _ { L }$ increases. The simulation results of increases. The simulation results of $U _ { L }$ and and $I _ { L }$ are slightly lower thanare slightly lower than the theoretical values, because the impedance of the rectification bridge circuit and load isthe theoretical values, because the impedance of the rectification bridge circuit and load equivalent to a pure resistance, which will produce error in the design of system parameters.is equivalent to a pure resistance, which will produce error in the design of system pa-Overall, the error is within the acceptable range.rameters. Overall, the error is within the accepta \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[280,353,727,575]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 10. Comparison between simulation results and theoretical values of CC-CV output of the Figure 10. Comparison between simulation results and theoretical values of CC-CV output of the WPT system based on Simulink.WPT system based on Simulink. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0720/40efef48ae59ae44cd1e7db522e465a3fcca6ece5d6b0c4c4875b4a8e5cf191a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,623,492,637]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. Experimental Verification \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,640,941,879]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To further verify the method, a resonant WPT experimental circuit based on S-S compensated was designed and built, as shown in Figure 11. The system’s parameters are shown in Table 1. The parameters of coils and the compensation capacitor are measured by a LCR meter (GW Instek: LCR821). The ratio of coil turns at the transmitting and receiving ends is 17:17. The inner diameter and outer diameter of coil are 12 and $2 2 . 5 \\\\mathrm { c m } ,$ ceiving ends is 17:17. The inner diameter and outer drespectively. The operating frequency of the system is $4 3 . 2 \\\\mathrm { k H z } ,$ f coil are 12 and 22.5 cm, , and the DC input voltage $V _ { D C }$ is $1 2 \\\\mathrm { V } .$ The 0.75 A constant current output is achieved when the load $R _ { L }$ varies from ???????????? is10 to $1 5 \\\\ \\\\Omega ,$ The 0.75 and the $1 2 \\\\mathrm { ~ V ~ }$ nstant current output is achieved when the load ???????? v constant voltage output is achieved when the load $R _ { L }$ s from varies 10 to 15 Ω, from 16 to $2 5 \\\\Omega$ he 12 V constant voltage output is achieved when the load ???????? varies from . Initially, the CC-CV charging strategy based on SPWM inverter control 16 to 25 Ω. Initially, the CC-CV charging was tested at a transmission distance of $3 \\\\mathrm { \\\\ c m }$ gy based on SPWM inverter control was between the transmitting and receiving tested at a transmission distance of 3 cm between the transmitting and receiving coils. coils. Subsequently, the proposed CC-CV charging strategy based on coupling-coefficient Subsequently, the proposed CC-CV charging strategy baestimation was evaluated at a transmission distance of $4 \\\\mathrm { { c m } }$ n coupling-coefficient esti-. The coupling coefficient mation was evaluated at a transmission distance of 4 cm. The coupling coefficient between between the coils was calculated to be 0.5032 using Inca [37] software at a transmission the coils wdistance of $3 \\\\mathrm { c m }$ culated to be 0.5032 using Inca [37] software at a transmission distance of , based on the coil parameters in Table 1. When the transmission distance was increased to $4 \\\\mathrm { c m } _ { \\\\cdot }$ , the proposed coupling-coefficient-estimation method was used to estimate the new coupling coefficient, which was found to be 0.4257. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"16 of 23verses \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[282,114,689,329]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 11. The WPT experimental circuit based on S-S compensation.Figure 11. The WPT experimental circuit based on S-S compensation. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0790/9dcdba15b53cee6dd382ee3d51eda535dd93b953551aefbb30643ef15beb1eb7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[278,363,505,376]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.1. System Experimental Device4.1. System Experimental Device \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,381,941,650]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The experimental WPT system is shown in Figure 11. The system adopts STM32F103ZET6 inverter circuit, a resonant circuit, a rectifier filter circuit, and a DC-voltage-acquisition as the main control chip. The system circuit mainly includes a full-bridge inverter circuit, a circuit. The amplitude of a control signal generated by the microcontroller is only 5 V, so resonant circuit, a rectifier filter circuit, and a DC-voltage-acquisition circuit. The amplitude the driver circuit is required to amplify the control signal so that it cof a control signal generated by the microcontroller is only $5 \\\\mathrm { V } ,$ ve the MOS so the driver circuit is transistors to operate normally. Two half-bridge drive chips IR2110 are used in the drive required to amplify the control signal so that it can drive the MOS transistors to operate circuit to form a full-bridge driver. The full bridge inverter circuit converts DC power into normally. Two half-bridge drive chips IR2110 are used in the drive circuit to form a full-bridge driver. The full bridge inverter circuit converts DC power into AC power to provide a high-frequency excitation source for the transmitter. The MOS transistors adopt into the DC power to charge the DC load. The diode adopts HER508, which has high volt-FQPF5N60C, which has the characteristics of a high voltage resistance value and high age resistance, low turn-on voltage, low impedance, and other characteristics. The DC-switching frequency. The full-bridge rectifier circuit converts AC power into the DC power voltage-acquisition circuit collects the voltage across the DC load. STM32F103ZET6 has to charge the DC load. The diode adopts HER508, which has high voltage resistance, low its own analog-to-digital converter (ADC), which can collect analog voltage signals and turn-on voltage, low impedance, and other characteristics. The DC-voltage-acquisition convert them into digital signals for processing. However, the ADC input voltage of circuit collects the voltage across the DC load. STM32F103ZET6 has its own analog-todigital converter (ADC), which can collect analog voltage signals and convert them into V voltage to below 3.3 V, so that the STM32F103ZET6 ADC can be used to sample and digital signals for processing. However, the ADC input voltage of STM32F103ZET6 is 0 to $3 . 3 \\\\mathrm { V } ,$ ss. and the CV output voltage of the WPT circuit designed in this study is $1 2 \\\\mathrm { V } .$ Therefore, The core of the system software is the compilation of the SPWa DC-DC conversion circuit is required to step down the $1 2 \\\\mathrm { V }$ ve program and voltage to below $3 . 3 \\\\mathrm { V } ,$ so ADC sampling program. The software of SPWM wave design is to form an athat the STM32F103ZET6 ADC can be used to sample and process. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,650,941,755]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"rated by the software of the SPWM data table, and the data are stored in the micro-The core of the system software is the compilation of the SPWM wave program and controller and generate the SPWM wave by calling the array. The advanced timer TIMER1 ADC sampling program. The software of SPWM wave design is to form an array of data timer TIMER3 controls the sine wave period. Within each sine wave cycle, the generated generated by the software of the SPWM data table, and the data are stored in the microconsine table is assigned to the TIM1_CCR1 register in order to generate SPWM wave.troller and generate the SPWM wave by calling the array. The advanced timer TIMER1 of The time from the STM32 controller’s ADC sampling to the SPWM control signal STM32F103ZET6 generates two sets of complementary PWM signals. The ordinary timer output is in the milliseconds, about 10–20 ms, and the change time of the equivalent re-TIMER3 controls the sine wave period. Within each sine wave cycle, the generated sine sistance during battery charging is typically above the second level [38]. This means that table is assigned to the TIM1_CCR1 register in order to generate SPWM wave. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,755,941,873]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ng battery charging, the changing speed of the battery equivalent resistance is much The time from the STM32 controller’s ADC sampling to the SPWM control signal output is in the milliseconds, about $1 0 { - } 2 0 ~ \\\\mathrm { m s } ,$ and the change time of the equivalent resistance during battery charging is typically above the second level [38]. This means that during battery charging, the changing speed of the battery equivalent resistance is much slower than the STM32 controller’s processing speed, from ADC sampling to the SPWM control signal output. Therefore, during the battery charging process, the STM32 controller can capture the change trend of the equivalent resistance by continuously sampling and storing data, and then use these data for more accurate control. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"17 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[280,112,620,127]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.2. S Verification of the Proposed Control Methodand storing data, and then use these data for more accur \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[275,129,870,145]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.2.1. Validation of CC-CV Charging Strategy Based on SPWM Inverter Control \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,147,941,311]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"With the ideal alignment, the experiment was carried out with the transmission distance of $3 \\\\ \\\\mathrm { c m } ,$ and the circuit was operated at the resonant frequency $f = f _ { 0 }$ . We prepared 10 to $2 5 ~ \\\\Omega$ resistors with an interval of $1 \\\\Omega$ . When the $R _ { L }$ was $1 0 { - } 1 5 \\\\ \\\\Omega$ , we adjusted the modulation depth 10 to 25 Ω resistors with an interval of 1 $m$ according to Equation (10) so that 0 When the was 10 Ω–15 Ω, we adjusted t $I _ { L } = I _ { L , r e q } ,$ and the control system was operated in CC mode. When the modulation depth m according to Equation (10) so that ???? = ???? , a $R _ { L }$ wasthe co $1 6 { - } 2 5 \\\\ \\\\Omega ,$ we adjusted the modulation depthwas operated in CC m $m$ according to Equation (13) so that . When the ???????? was 16–25 Ω, we adjusted ${ U } _ { L } = { U } _ { L , r e q } ,$ and the control systemn depth was operated in CV mode. Figure 12 shows the adjustment process of modulation depthm according to Equation (13) so that ???????? = ????????,????????????, and the control system was operated in m varying with the load CV mode. Figure 12 shows the $R _ { L }$ . In Figure 12, when the system operates in CC mode, thestment process of modulation depth ???? varying with modulation depth ???????? $m$ gradually increases as the load $R _ { L }$ increases; and when in CV mode, the modulation depth depth decreases as the lo $m$ decreases as the load ???? increases. These result $R _ { L }$ increases. These results agree with theree with the theoretical analtheoretical analysis of (10) and (13).ysis of (10) and (13). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[280,326,650,493]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 12. Adjustment process of modulation depth $m$ with $R _ { L }$ \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0021/e6ad304ab8097747971c9dc7ffc6c4ef0165cffa2decfa844c9c1be81aac26e9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,527,941,617]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"he experimental waveforms for the current ???? of the The experimental waveforms for the current $I _ { 1 }$ nsmitting coil and the cur-of the transmitting coil and the current $I _ { 2 }$ t ???? of the receiving coil are illustrated in Figure 13. As is evident in Figure 13, In CC of the receiving coil are illustrated in Figure 13. As is evident in Figure 13, In CC mode, mode, the curthe current $I _ { 1 }$ t ????1 of the transmitting coil increases as the load ???????? inof the transmitting coil increases as the load $R _ { L }$ ses, and the increases, and the current $I _ { 2 }$ ????2 ????1of the receiving coil remains basically unchanged. In CV mode, the current $I _ { 1 }$ of the 2 decreases as the load increases. transmitting coil remains basically constant, but the current EER REVIEW $I _ { 2 }$ of the receiving coil decreases19 of 24 as the load $R _ { L }$ ???? increases. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[282,632,653,800]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 13. The current ????1 ofFigure 13. The current $I _ { 1 }$ e transmitting coil and the current ????2 of the receof the transmitting coil and the current $I _ { 2 }$ ng coil.of the receiving coil. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0696/1200113876b1e9c3c9eb72490de153faa3dc7f2eba15096430a183c673e02d1f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,835,941,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"igure 14 shows the comparison between the experimental results and the theoretical Figure 14 shows the comparison between the experimental results and the theoretical ???????? CV mode, tracks requivalues. In CC mode, $I _ { L }$ ????????,???????????? , and decreasetracks the required $I _ { L , r e q } ,$ incr and $U _ { L }$ ???????? s. The experimeincreases as $R _ { L }$ increases. In CV results vmode, $U _ { L }$ ????y the validity of thtracks required $U _ { L , r e q } ,$ ???? sed m and $I _ { L }$ ???? hod. The resultdecreases as $R _ { L }$ ow that the proposed increases. The experimental results method is suitable for battery charging, and the adjustment of modulation depth m is cru-verify the validity of the proposed method. The results show that the proposed method is cial for ???????? tracking ????????,???????????? in CC charging mode and ???????? tracking ????????,???????????? in CV charginsuitable for battery charging, and the adjustment of modulation depth $m$ is crucial for $I _ { L }$ mode.tracking $I _ { L , r e q }$ in CC charging mode and $U _ { L }$ tracking $U _ { L , r e q }$ in CV charging mode. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"18 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[278,111,682,312]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 14. Comparison between experimental results and theoretical values.Figure 14. Comparison between experimental results and theoretical values. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0645/1fa9cf7da233443f8e3a23ab42e20abfc0a9c33fb8cfd137dd671d2d071db0e3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,346,941,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In Figure 14, it can be observed that although there are deviations between the ex-In Figure 14, it can be observed that although there are deviations between the experimental results and theoretical values, the overall trend is consistent, which confirms perimental results and theoretical values, the overall trend is consistent, which confirms the accuracy of the model and method used. The experimental values of ???? and the accuracy of the model and method used. The experimental values of $U _ { L }$ re and $I _ { L }$ are slightly lower than the theoretical values due to the fact that the rectifier bridge circuit slightly lower than the theoretical values due to the fact that the rectifier bridge circuit and and load impedance can be approximated as a pure resistance ???????? load impedance can be approximated as a pure resistance $R _ { r }$ ording to Equation according to Equation (4), (4), which can introduce errors in the design of system parameters [39,40]. Additionally, which can introduce errors in the design of system parameters [39,40]. Additionally, the the power electronic system is not ideal; and switches, inductors, capacitors, and other power electronic system is not ideal; and switches, inductors, capacitors, and other resonant devices can also introduce some errors in controlling the WPT system during operation. However, these errors are considered acceptable. Regardless, the ADC sampling of the STM32 controller will also introduce a certain error. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,495,941,585]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"harging process. It can be observed that the system transmission efficiency, denoted Figure 15 presents the system efficiency measured from the input to the load during the charging process. It can be observed that the system transmission efficiency, denoted as as $\\\\eta .$ , remains relatively stable throughout the CC charging process, whereas it graduallyremains relatively stable throughout the CC charging process, whereas it gradually decreases as the load resistance decreases as the load resistance $R _ { L }$ increases during the CV charging process. These resultsreases during the CV charging process. These reare consistent with the previous theoretical analysis given by Equation (18). The overallsults are consistent with the previous theoretical analysis given by Equation (18). The transmission efficiency of the system falls betweenoverall transmission efficiency of the system falls between $8 0 \\\\%$ andand 9 $9 2 \\\\%$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[280,599,712,793]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 15. Transmission efficiency. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0999/81d4f4c394e71410a8e446fc4b36dd5fc87d282c911f26028083becfa593a33a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[275,824,932,839]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.2.2. Validation of CC-CV Charging Strategy Based on Coupling Coefficient Estimation \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,841,941,932]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Equation (28) reveals that the coupling coefficient $k$ can be estimated by the ratio of $U _ { L }$ and $U _ { 1 }$ . The transmission distance between the transmitting coil and the receiving coil ???? 1was varied from 1.5 to 5.5 was varied from 1.5 to $5 . 5 \\\\mathrm { c m }$ ure 16 illustrates a comparison between the estimated . Figure 16 illustrates a comparison between the estimated coupling coefficient k acoupling coefficient $k$ the Inca-calculated value at different transmission distances. As and the Inca-calculated value at different transmission distances. As depicted in Figure 16, the estimated coupling coefficient k obtaindepicted in Figure 16, the estimated coupling coefficient $k$ using Equation (28) is obtained using Equation (28) is largely consistent with the Inca-calculated value, indicating that estimating the coupling largely consistent with the Inca-calculated value, indicating that estimating the coupling coefficient through the ratio of coefficient through the ratio of ???? $U _ { L }$ and d ???? $U _ { 1 }$ is practical and highly accurate. This satisfies theractical and highly accurate. This satisfies design requirements completely.he design requirements completely. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[894,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"19 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[277,112,939,142]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[282,159,710,350]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"igure 16. Comparison between the estimated value of coupling coefficient k and Inca vFigure 16. Comparison between the estimated value of coupling coefficient $k$ e at dif-and Inca value at erent transmission distances.different transmission distances. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0398/b248267beabb86c51134fad6365f3872201644fd653cf7062d6a6eaff49f802b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,401,941,536]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"hen the transmission distance between the transmitting and receiving coils was When the transmission distance between the transmitting and receiving coils was ncreased from 3 to 4 cm,increased from 3 to $4 \\\\ \\\\mathrm { c m } ,$ upling coefficient k was esti the coupling coefficient $k$ ted to be 0.4257 using Equa-was estimated to be 0.4257 using Equation (28). This new value of $k$ was then used to recalculate and adjust the required modulation depth ation depth m for the $m$ for the system to operate in stem to operate in CC/CV mode $\\\\mathrm { C C } / \\\\mathrm { C V }$ mode, by substituting it into ituting it into either either Equation (10) or (13). The experimental and theoretical values of the system’s outputquation (10) or (13). The experimental and theoretical values of the system’s output curcurrent ent ???? an $I _ { L }$ and output voltage output voltage ???? wer $U _ { L }$ were compared and presented in Figure 17. As evincedmpared and presented in Figure 17. As evinced in in Figure 17, the required output current Figure 17, the required output current ????????,???????????? of $I _ { L , r e q }$ of the system in CC mode isystem in CC mode is 0.75 A, and $0 . 7 5 \\\\mathrm { A } ,$ and the required output voltage required output voltage ????????,???????? $U _ { L , r e q }$ in CV mode isV mode is 12 V. T $1 2 \\\\mathrm { V } .$ The system operates in CC mode forstem operates in CC mode for loads between 10 andoads between 10 and 15 $1 5 \\\\Omega$ , and shifts to CV mode for loads between 16 and shifts to CV mode for loads between 16 and 25 Ω. $2 5 \\\\Omega$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,550,749,784]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 17. Comparison between experimental results and theoretical values of CC-CV output based Figure 17. Comparison between experimental results and theoretical values of CC-CV output based n coupling-coefficient estimation.on coupling-coefficient estimation. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0440/3023d7e0ccce2305de264024d5d941396c076958e871be78e343ef1df69308da.jpg\",\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[277,832,393,846]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \". Conclusions5. Conclusions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,851,941,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"his paper presents a wireless charging system that can adapt to changes in load by This paper presents a wireless charging system that can adapt to changes in load by ontrolling the modulation depth of the SPWM inverter circuit. The system uses an S-S controlling the modulation depth of the SPWM inverter circuit. The system uses an S-S basic asic compensation structure to achieve both CC and CV charging when the load changes,compensation structure to achieve both CC and CV charging when the load changes, and nd this is determined by detecting the load voltage and current. The modulation depth this is determined by detecting the load voltage and current. The modulation depth of the inverter circuit is adjusted to achieve the desired CC or CV output. In addition, we proposed a method for estimating the coupling coefficient and designed a CC/CV control strategy that employs this estimation method. If external disturbances result in coil misalignment or changes in the transmission distance, which affect the mutual inductance between the coils, the proposed coupling-coefficient-estimation method is utilized to estimate the new coupling coefficient. The controller then adjusts the modulation depth of the SPWM inverter to achieve CC/CV output for the system. The proposed method is mathematically simple and easy to implement—requiring no additional topology. The feasibility of the method was demonstrated through theoretical analysis and simulation, and its effectiveness and accuracy were further verified through experiments. The study also analyzed the sources of error in the system. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[892,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"20 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[277,112,941,261]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,275,942,344]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Author Contributions: Conceptualization, K.S. and W.N.; methodology, K.S. and W.N.; software, K.S.; validation, K.S. and W.N.; formal analysis, K.S. and W.N.; investigation, K.S. and W.N.; resources, K.S.; data curation, K.S.; writing—original draft preparation, K.S.; writing—review and editing, W.N.; visualization, K.S.; supervision, W.N. All authors have read and agreed to the published version of the manuscript. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,353,631,366]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Funding: This research received no external funding. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[278,374,579,387]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data Availability Statement: Not applicable. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,395,702,407]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conflicts of Interest: The authors declare no conflict of interest. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[277,424,388,437]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nomenclature \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[273,451,791,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"WPT Wireless power transfer \\nCC Constant current \\nCV Constant voltage \\nSPWM Sinusoidal pulse width modulation \\n$m$ SPWM inverter circuit modulation depth \\n$Q _ { 1 } – Q _ { 4 }$ Switches of SPWM inverter \\n$D _ { 1 } { - } D _ { 4 }$ Diodes of full-bridge rectifier \\n$L _ { 1 }$ Transmitting coil (H) \\n$L _ { 2 }$ Receiving coil (H) \\n$C _ { 1 }$ Resonant capacitor of the transmitting coil (F) \\n$C _ { 2 }$ Resonant capacitor of the receiving coil (F) \\n$k$ Coupling coefficient \\n$M$ Mutual inductance (H) \\n$\\\\omega$ System operating angle frequency (rad/s) \\n$\\\\omega _ { 0 }$ Resonant angle frequency (rad/s) \\n$f _ { 0 }$ Resonant frequency (Hz) \\n$f$ Operating frequency $\\\\left( \\\\mathrm { H z } \\\\right)$ \\n$V _ { D C }$ DC input voltage of SPWM inverter (V) \\n$U _ { 1 }$ The rms value of voltage of transmitting coil (V) \\n$I _ { 1 }$ The rms value of current of transmitting coil (A) \\n$U _ { 2 }$ The rms value of voltage of receiving coil (V) \\n$I _ { 2 }$ The rms value of current of receiving coil (A) \\n$U _ { L }$ Load voltage (V) \\n$I _ { L }$ Load current (A) \\n$Z _ { 1 }$ Impedance of transmitting coil $( \\\\Omega )$ \\n$Z _ { 2 }$ Impedance of receiving coil $( \\\\Omega )$ \\n$R _ { 1 }$ The transmission coil internal resistance is $( \\\\Omega )$ \\n$R _ { 2 }$ Internal resistance of receiving coil $( \\\\Omega )$ \\n$R _ { r }$ Equivalent resistance of the rectifier bridge circuit and the load $( \\\\Omega )$ \\nRL Load resistance $( \\\\Omega )$ \\n$\\\\eta$ Transmission efficiency \\nUL,req Charging voltage required for CV mode (V) \\nIL,req Charging current required for CC mode (A) \\nIL,end End of charge current (A) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,66,247,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[892,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"21 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[57,112,144,126]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,136,942,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. 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In Proceedings of the 2012 IEEE International Conference on Power System Technology (POWERCON), Auckland, New Zealand, 30 October–2 November 2012; pp. 1–5. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,65,247,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"World Electr. Veh. 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Veh. J. 2023, 14, 111 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[892,66,939,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"23 of 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[57,569,942,609]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.3390/wevj14040111"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Engineering and Manufacturing Science"},"sha256":{"kind":"string","value":"a18d83dd9565f1c393811508787b53ccd84ef455155bec462cc8c5da65506030"},"title":{"kind":"string","value":"SPWM Inverter Control for Wireless Constant Current and Voltage Charging"}}},{"rowIdx":257,"cells":{"abstract":{"kind":"string","value":"The purpose of this study was to examine the intermediary role of physical health quality of life and ability to participate social roles and activities in the relationship between pain intensity and mental health quality of life in veterans with mental illnesses. This is a cross-sectional correlational design study. Our participants are 156 veterans with self-reported mental illness (Mage = 37.85; SDage = 10.74). Descriptive, correlation, and mediation analyses were conducted for the current study. Pain intensity was negatively correlated with physical health QOL, ability to participate in social roles and activities, and mental health QOL. Physical health QOL and ability to participate in social roles and activities were positively associated with mental health QOL, respectively. Physical health QOL was positively correlated with a ability to participate in social roles and activities. Study results indicate that the effect of pain intensity on mental health QOL can be explained by physical health QOL and ability to participate. Specific recommendations for practitioners include implementing treatment goals that simultaneously focus on physical health and ability to participate in social roles and activities for clients who present with both physical pain and low mental health QOL."},"author":{"kind":"string","value":"Jessica M. Brooks|Beatrice Lee|Diana Villegas|Emre Umucu|Chung-Yi Chiu|Carolina Valencia|Thenral Mangadu|Paul Carrola|Karen L. Fortuna|Antonio Reyes"},"content_list":{"kind":"list like","value":[{"bbox":"[80,130,843,200]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Pain intensity and mental health quality of life in veterans with mental illnesses: the intermediary role of physical health and the ability to participate in activities ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[78,218,826,251]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Emre Umucu<sup>1</sup> $\\cdot$ Antonio Reyes<sup>2</sup> $\\cdot$ Paul Carrola<sup>3</sup> $\\cdot$ Thenral Mangadu<sup>4</sup> $\\cdot$ Beatrice Lee<sup>1</sup> $\\cdot$ Jessica M. Brooks<sup>5</sup> $\\cdot$ Karen L. Fortuna<sup>6</sup> $\\cdot$ Diana Villegas<sup>1</sup> $\\cdot$ Chung-Yi Chiu<sup>7</sup> $\\cdot$ Carolina Valencia<sup>1</sup> ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,273,252,284]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Accepted: 12 September 2020 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,286,300,300]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\odot$ Springer Nature Switzerland AG 2020 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,321,152,335]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[80,337,917,383]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Purpose The purpose of this study was to examine the intermediary role of physical health quality of life and ability to participate social roles and activities in the relationship between pain intensity and mental health quality of life in veterans with mental illnesses. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,384,917,494]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methods This is a cross-sectional correlational design study. Our participants are 156 veterans with self-reported mental illness $(M_{\\mathrm{age}} = 37.85; \\mathrm{SD}_{\\mathrm{age}} = 10.74)$ . Descriptive, correlation, and mediation analyses were conducted for the current study. Results Pain intensity was negatively correlated with physical health QOL, ability to participate in social roles and activities, and mental health QOL. Physical health QOL and ability to participate in social roles and activities were positively associated with mental health QOL, respectively. Physical health QOL was positively correlated with a ability to participate in social roles and activities. Study results indicate that the effect of pain intensity on mental health QOL can be explained by physical health QOL and ability to participate. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,496,915,541]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conclusions Specific recommendations for practitioners include implementing treatment goals that simultaneously focus on physical health and ability to participate in social roles and activities for clients who present with both physical pain and low mental health QOL. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,558,576,574]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords Quality of life $\\cdot$ Veterans $\\cdot$ Mental illness $\\cdot$ Participation $\\cdot$ Pain ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,606,915,856]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Due to the intense experiences associated with deployment and combat, Veterans are at high risk of developing a mental illness [1]. More than 1.7 million Veterans received treatment in a Department of Veterans Affairs (VA) mental health specialty program in fiscal year 2018 [2], and this number may not fully reflect the problem of mental illness among Veterans given that many do not seek treatment through the VA [1]. Mental illness is associated with poorer mental health quality of life, which is comprised of a combination of the perception of mental health and functional effects of mental illness [3]. Mental health quality of life provides a useful understanding of the burden of mental illness because it appreciates that the impact of mental illness may be variable among individuals. Additional research is needed to better understand predictors of mental health quality of life and well-being for Veterans with a mental illness [4, 5]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,859,915,906]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Veterans are also at high risk of developing chronic pain due to the extraordinary physical stress associated with military service [6]. Studies indicate that $66\\%$ of veterans ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,39,213,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Quality of Life Research ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[82,53,331,67]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1007/s11136-020-02642-y ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[862,81,915,120]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Check for updates ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[82,615,188,627]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Emre Umucu ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[105,629,216,641]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"eumucu@utep.edu ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[82,651,426,691]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{1}$ Department of Rehabilitation Sciences, The University of Texas at El Paso, 500 W University Ave, El Paso, TX 79968, USA ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[82,696,433,724]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 Division of Special Education and Counseling, CA State University - Los Angeles, Los Angeles, CA, USA ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[82,727,460,755]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{3}$ Department of Educational Psychology and Special Services, The University of Texas at El Paso, El Paso, TX, USA ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[82,759,421,786]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{4}$ Department of Public Health Sciences, The University of Texas at El Paso, El Paso, TX, USA ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[82,789,440,829]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 Department of Psychiatry, School of Medicine and Public Health, University of Wisconsin - Madison, Madison, WI, USA ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[82,835,436,863]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 The Geisel School of Medicine at Dartmouth, Dartmouth College, Concord, NH, USA ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[82,865,440,906]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{7}$ Department of Kinesiology and Community Health, University of Illinois Urbana Champaign, Champaign, IL, USA ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[80,929,302,944]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Published online: 24 September 2020 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[840,927,915,945]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[82,69,485,305]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"report experiencing pain with $9\\%$ reporting severe pain [7]. Over $50\\%$ of Veterans who receive care at the VA are diagnosed with musculoskeletal pain [8] and a survey of Veterans found a high prevalence of headaches $(54\\%)$ , joint pain $(45\\%)$ , back pain, $(44\\%)$ , muscle pain $(33\\%)$ , and abdominal pain $(23\\%)$ [9]. Researchers argue that addressing and treating pain, including addressing opioid use disorder (OUD) risk, is an increasingly important challenge for the VA due to the aging population and growth in number of Veterans with chronic pain related to recent military service [10]. Prior studies also indicate that veterans with chronic pain and comorbid psychiatric disorders are more likely to receive opioids than pain patients without comorbid psychopathology, these diagnoses are also associated with prescription of high opioid doses [11]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,307,485,621]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For Veterans who experience pain, the effects can extend to every aspect of their life. Pain can interfere with participation in daily activities and is associated with higher levels of emotional distress [12]. Thus, it is not surprising that pain and mental illnesses are commonly comorbid for Veterans [13]. Research suggests that pain is strongly associated with symptoms of anxiety, depressive disorders, suicidal ideation, and PTSD [13-15]. Poundja et al. [16] found that both pain severity and pain interference are negatively correlated with mental health quality of life in Canadian veterans suffering from traumatic stress. Boakye et al. [17] examined health-related quality of life in veterans with spinal cord injury (SCI) and found that a visual analog pain score was the most important predictor of worsened mental health quality of life scores. Likewise, Kazis et al. [18] reported that chronic low back pain is negatively associated with mental health quality of life in patients served by the VA. These studies and others highlight the importance of better understanding the underlying mechanisms by which pain intensity impacts mental health quality of life for Veterans. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,622,485,889]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mental health quality of life and pain are also associated with physical health quality of life (i.e., ratings of physical health and the ability to carry out physical activities) and participation in social roles and activities. The ability to participate in social roles and activities improves mental health while decreasing mental health symptoms [19]. Social participation is also strongly associated with social support, which has long been known to play an important role in protecting against negative effects of stress and mental illness, see e.g., [20]. Research suggests that physical health quality of life is associated with greater ability to participate in social activities, and consequentially enhancing social connectedness and its health benefits. For example, longitudinal data from the Veterans Health Study, Ren et al. [21] shows that physical health is associated with a person's ability to participate and maintain social relationships and stronger social support. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,69,914,337]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Additionally, Rippentrop et al. [22] found that physical health quality of life is positively related to mental health quality of life for individuals with chronic pain. Similarly, in a study of Vietnam veterans, Schnurr et al. [23] found that reported physical health quality of life is related to PTSD symptom severity. General population studies also indicate that greater pain intensity is associated with greater interference with social participation and physical and recreational activities [24-26]. In a study of veterans, Naylor et al. [15] found a positive correlation between pain intensity and functional factors including physical disability and social support. Overall, research supports that pain, physical health quality of life, and the ability to participate in social functions are all related and contribute to mental health quality of life. Likely, the relationship between pain intensity and mental health quality of life is influenced by physical health quality of life and participation in social roles and activities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,339,914,668]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Although existing studies have examined the relationship between pain, social relationships, and physical and mental health quality of life for Veterans, none have systematically examined these factors together to better understand their impact on mental health quality of life. Therefore, the purpose of this study was to examine the intermediary role of physical health quality of life and ability to participate in social roles and activities in the relationship between pain intensity and mental health quality of life in veterans with mental illnesses. We hypothesized that (a) increased pain intensity is associated with reduced physical and mental health quality of life, (b) decreased physical health quality of life is associated with lower levels of the ability to participate social roles and activities, and (c) reduced ability to participate social roles and activities negatively affect mental health quality of life in veterans with mental illnesses. Health care systems could use this valuable information to potentially improve value of services for Veterans with mental illnesses by addressing modifiable risk factors such as physical health QOL and ability to participate through treatment. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,716,593,730]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,749,680,764]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Design and procedure ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,779,914,905]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This cross-sectional study was reviewed and approved as an exempt study by the Institutional Review Board by the University of Texas at El Paso. We collected data from Amazon's MTurk, a crowdsourcing tool enabling MTurk Workers to access and complete Human Intelligence Tasks (HITs). MTurk has been considered as a valid, diverse, reliable, and cost-effective large data collection tool [27, 28]. Based on MTurk options, we restricted participants to be residents in ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[784,39,915,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Quality of Life Research ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[84,929,154,943]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,68,487,148]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the United States who have military experience. We shared a Qualtrics survey link with participants. All participants read an online consent form and agreed to be participant in this study. All participants received $4.00 upon completing the online survey. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,163,159,178]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Measures ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[80,194,179,211]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Pain intensity ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[78,226,487,322]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Pain intensity was assessed using the PROMIS® Numeric Rating Scale v.1.0—Pain Intensity 1a [29-31]. It is a one-item measure that asks respondents to rate their pain on average, ranging from 0 (no pain) to 10 (worst imaginable pain) over the past 7 days. Higher scores indicate higher levels of pain intensity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,337,280,353]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Physical health quality of life ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[78,368,487,512]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Physical health QOL was assessed using the PROMIS® Scale v1.2—Global Health Physical 2a [32]. It is a 2-item measure that asks respondents to rate their physical health (ranging from 1 [poor] to 5 [excellent]) and their ability to carry out daily physical activities (ranging from 1 [not at all] to 5 [completely]). Higher scores indicate higher physical health QOL. Total raw scores were converted into $T$ scores. The Cronbach's alpha coefficient for the PROMIS global physical health in the present study was computed to be 0.52. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,527,413,541]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Ability to participate in social roles and activities ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[78,558,487,717]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Ability to participate was assessed using the PROMIS® Item Bank v2.0—Ability to Participate in Social Roles and Activities-Short Form 4a [33]. It is a 4-item measure that asks respondents to rate their perceptions on their ability to perform their social functions, ranging from 1 (always) to 5 (never). Higher scores indicate higher levels of ability to participate. Total raw scores were converted into $T$ scores. The Cronbach's alpha coefficient for the PROMIS ability to participate in social roles and activities in the present study was computed to be 0.90. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,732,213,746]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mental health QOL ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[78,763,487,891]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mental health QOL was assessed using the PROMIS® Scale v1.2—Global Health Mental 2a [32]. It is a 2-item measure that asks respondents to rate their mental health and satisfaction with social connections, ranging from 1 (poor) to 5 (excellent). Higher scores indicate higher mental health QOL. Total raw scores were converted into $T$ scores. The Cronbach's alpha coefficient for the PROMIS global mental health in the present study was computed to be 0.77. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,69,616,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data analysis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,100,915,387]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"All analyses were performed using the Statistical Package for the Social Sciences (SPSS; version 25). Descriptive statistics were computed to provide information about the demographic characteristics and for the independent variable, mediators, and dependent variable. Correlation analysis was conducted to examine relationships among variables. Finally, a serial mediation analysis was conducted to examine physical health QOL and ability to participate as mediators between pain intensity and mental health QOL. The SPSS PROCESS 3.4.1 [34] was used to conduct mediation analysis. A bootstrapping approach was also used to test the significance of indirect effects of pain intensity on mental health QOL with 5000 bootstrap samples through (a) physical health QOL, (b) ability to participate in social roles and activities, and (c) both physical health QOL and ability to participate. Although there is not a consensus how many bootstrap samples should be generated, researchers recommended at least 5000 resamples for final reporting [35]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,416,579,432]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,448,608,464]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Participants ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,479,915,764]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The total number of participants were 156 veterans with self-reported mental illnesses. Participants ranged in age from 23 to 72, with an average of 37.85 years old $(SD = 10.74)$ . Most participants were males $(66.7\\%)$ . The majority of participants identified as Caucasians $(69.9\\%)$ and married $(52.6\\%)$ . Regarding educational level, $39\\%$ obtained a bachelor's degree, followed by some college credit without a degree $(23.1\\%)$ , an associate's degree $(13.5\\%)$ , a graduate degree $(12.2\\%)$ , a trade/technical/vocational training $(7.1\\%)$ , and a high school degree $(5.8\\%)$ . Many participants served in the Army $(55.8\\%)$ , followed by Air Force $(17.9\\%)$ , Navy $(12.2\\%)$ , Marine Corps $(10.3\\%)$ , and Coast Guard $(3.8\\%)$ . In terms of mental illnesses, participants reported at least one type of mental illnesses, including $64.7\\%$ reported depression, $57.1\\%$ reported anxiety, $35.3\\%$ reported PTSD, $10.3\\%$ reported substance use disorder, $4.5\\%$ reported bipolar disorder, $4.5\\%$ reported personality disorder, and $3.9\\%$ reported others. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,779,672,797]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Descriptive statistics ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,812,917,908]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Participants' pain intensity scores ranged from 0 to 10 with an average of 3.44 ( $SD = 2.41$ ). Physical health QOL $T$ scores ranged from 23.40 to 63.30 with an average of 45.10 ( $SD = 8.03$ ). Ability to participate in social roles and activities $T$ scores ranged from 31.80 to 64.20 with an average of 47.78 ( $SD = 8.40$ ). Mental health QOL $T$ scores ranged from ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,37,213,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Quality of Life Research ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[838,927,914,944]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[78,68,487,211]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"25.80 to 64.60 with an average of 40.83 ( $SD = 8.40$ ). After examining $T$ scores, we found that $14.7\\%$ and $60.3\\%$ of the participants had physical health quality of life $T$ scores of above and below the mean, respectively; $11.5\\%$ and $88.5\\%$ of the participants had mental health quality of life $T$ scores of above and below the mean, respectively; and $30.8\\%$ and $60.3\\%$ of the participants had ability to participate in social roles and activities $T$ scores of above and below the mean, respectively. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,232,238,250]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Correlation analysis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[78,265,487,408]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Pain intensity was negatively correlated with physical health QOL ( $r = -0.56$ , $p < 0.001$ ), ability to participate in social roles and activities ( $r = -0.54$ , $p < 0.001$ ), and mental health QOL ( $r = -0.33$ , $p < 0.001$ ). Physical health QOL ( $r = 0.44$ , $p < 0.001$ ) and ability to participate in social roles and activities ( $r = 0.55$ , $p < 0.001$ ) were positively associated with mental health QOL, respectively. Physical health QOL was positively correlated with an ability to participate in social roles and activities ( $r = 0.55$ , $p < 0.001$ ). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[80,431,231,448]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mediation analysis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[78,463,489,637]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The serial mediation model is presented in Fig. 1. Pain intensity was significantly associated with mental health QOL ( $c = -0.33$ , $p < 0.001$ ). Pain intensity was significantly associated with physical health QOL ( $a_1 = -0.56$ , $p < 0.001$ ) and was significantly associated with ability to participate in social roles and activities after controlling for physical health QOL ( $a_2 = -0.34$ , $p < 0.001$ ). Physical health QOL was significantly associated with ability to participate in social roles and activities after controlling for pain intensity ( $d_{21} = 0.35$ , $p < 0.001$ ). Additionally, physical health QOL was significantly associated with mental health ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,68,915,160]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"QOL after controlling for pain intensity and ability to participate in social roles and activities ( $b_{1} = 0.22$ , $p < 0.05$ ). Ability to participate in social roles and activities was significantly associated with mental health QOL after controlling for pain intensity and physical health QOL ( $b_{2} = 0.45$ , $p < 0.001$ ). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,164,915,511]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Importantly, pain intensity was no longer significantly associated with mental health QOL after controlling for physical health QOL and ability to participate in social roles and activities ( $c' = 0.04$ , $p = 0.65$ ). This suggests that physical health QOL and the ability to participate in social roles and activities mediated the relationship between pain intensity and mental health QOL. In addition, results using the PROCESS with 5000 bootstrap samples, demonstrated that the indirect paths were significant because the $95\\%$ confidence intervals did not contain zero, suggesting that the indirect effects were different from zero. The indirect effect of pain intensity through physical health QOL on mental QOL was significant ( $a_1b_1 = -0.12$ ; $95\\%$ CI $[-0.23, -0.02]$ ). The indirect effect of pain intensity through ability to participate on mental health QOL was significant ( $a_2b_2 = -0.15$ ; $95\\%$ CI $[-0.25, -0.07]$ ). The indirect effect of pain intensity through physical health QOL and ability to participate in social roles and activities on mental health QOL was significant ( $a_1d_{21}b_2 = -0.09$ ; $95\\%$ CI $[-0.16, -0.04]$ ). Overall, the mediation analysis indicated that the effect of pain intensity on mental health QOL can be explained by physical health QOL and ability to participate in social roles and activities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,526,596,541]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Discussion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,558,915,637]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Our analyses provide novel insights by clarifying the intermediary role of physical health quality of life and ability to participate in social roles and activities in the relationship between pain intensity and mental health quality of life in veterans with mental illnesses. Similar associations were ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[85,665,914,860]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 1 Standardized path coefficients for serial mediation analysis on the relationship between pain intensity and mental health QOL. Note: Dotted line denotes the total effect of pain intensity on mental health QOL when mediators are not included. $^{**}p < 0.001$ . $^* p < 0.05$ . $^+ p = .65$ \"]","image_footnote":"[]","img_path":"images/0777/9f4bf6c6de46e086f03975f12dc2874a3997cd8447b6b0ca78132af9cb013668.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[781,37,915,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Quality of Life Research ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[80,927,157,945]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[82,69,485,256]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"found between pain intensity and physical health QOL, ability to participate in social roles and activities, and mental health QOL, respectively. However, one key finding is that the initial association between pain intensity and mental health QOL was mediated by physical QOL and ability to participate in social roles and activities. This is valuable information because the negative effect of pain on mental health QOL could be mitigated by increasing physical health QOL and ability to participate in social roles and activities and potentially improve value of services for veterans with mental illnesses by addressing these modifiable risk factors through treatment. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,258,485,746]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Physical health QOL and ability to participate in social roles and activities directly contribute to veterans' level of pain and mental health independently. As such, reduced mental health symptoms in veterans who also have identified pain symptoms can be achieved through improving physical health and ability to participate in social roles and activities in veterans with mental illnesses. Strategies to improve physical health and ability to participate in social roles and activities are effective treatment supplements for rehabilitation and mental health professionals to integrate into their psychotherapeutic or psychoeducational interventions for veterans with mental illnesses who have low mental health QOL due to pain intensity. In addition, increasing evidence is accumulating for the effectiveness of multidisciplinary pain management strategies [36-40], including the VA's own stepped care pain management approach, to manage severe chronic pain [41]. Supplementing traditional psychotherapeutic or psychoeducational pain management interventions with self-directed client activities constitutes an empirically supported approach to treatment. This approach is supported by recent research that has highlighted the importance of self-managed (i.e., initiated and managed by the client) interventions [42]. In their study, Harding et al. [42] found that while veterans with chronic pain psychological comorbidities were more likely to seek provider managed interventions, they were more likely to use self-managed interventions overall. This suggests that veterans are more willing to initiate self-managed interventions for chronic pain in general. Self-managed interventions can also be implemented through more direct ways through integrated primary and behavioral health care, see e.g., [43]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,749,485,905]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The specific relationships between pain intensity, mental health, physical health, and ability to participate in social roles and activities are central data that inform integrated treatment practices. This study provides important evidence that supports the argument for both multidisciplinary assessment and treatment. While multidisciplinary and holistic models of treatment have long been advocated in the mental health profession [44], the direct relationship between physical health and ability to participate in social roles and activities with patient's experienced pain provided by this ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,68,914,240]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"study supports the benefit of physical health and ability to participate in social roles and activities as our study provides the promising approach to complement the existing services. These factors could also be used to better guide future studies and clinical trials from the newly developed Pain Management Collaboratory [45], which has the main goal of developing the capacity to implement cost-effective large-scale pragmatic clinical research in military and veteran health care delivery organizations focusing on nonpharmacological approaches to pain management and other comorbid conditions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,241,914,494]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The value of this study is highlighted by the overall lack of research directly exploring the relationships between pain intensity, mental health, physical health, and social engagement. Historically, medical and mental health treatment have been viewed by health care and policy makers as separate [46], which has created barriers for overall treatment and negatively impacts help seeking behaviors for persons with both medical and mental health concerns. This is specifically relevant for veteran populations who have experienced increased rates of mental health disorders [47] and high rates of comorbidity between pain and mental health diagnoses [13, 48]. The results of the current study not only support the importance of mental health professionals using holistic interventions but also supports previous research that cites the benefit of integrated behavioral and primary healthcare, see e.g., [49, 50]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,497,914,905]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Although there is a lack of research examining the intermediary role of physical health QOL and ability to participate in social roles and activities for the relationship between pain intensity and mental health QOL among veterans, it is also important to report that our findings are partially consistent with some studies with different populations. For example, participation restriction was found to be a mediator between pain intensity and depression symptoms and QOL in individuals with spinal cord injury, respectively [51]. Nguyen et al. [52] examined whether changes in mental health was associated with improvements in pain and function scores 1 year after total hip arthroplasty. Their findings revealed that greater improvements in pain and function were related to greater improvements in mental health. In a sample with chronic low back pain, authors [53] reported that higher somatic symptoms were related to lower health-related QOL independent of depression and other comorbid disorders [52]. Interestingly, in a sample with chronic pain, authors [54] found that pain intensity and duration were found to have a minor role for QOL and disability although psychological variables (e.g., depression) were found to have a strong association with QOL and disability. Overall, these findings revealed that pain-related, psychological, and social factors are important for QOL although the magnitude of impacts of these variables on QOL may change based on the population. As indicated above, it is important to have ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,37,213,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Quality of Life Research ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[840,927,914,944]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[78,68,487,116]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"holistic and multidisciplinary treatment options to achieve optimal rehabilitation and health outcomes, which could eventually improve QOL. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,117,485,556]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Additionally, as this manuscript is being written, the U.S. is facing a global pandemic from the COVID-19 virus. The physical and social restrictions brought on by this pandemic limit social participation and is negatively impacting the mental health quality of life for all persons and may have elevated effects for groups that are already experiencing physical and mental health issues. Besides, the current COVID-19 pandemic has led to changes in mental health care (e.g., transition to telehealth service delivery), disruptions in daily life, and greater psychological distress that are unique to veterans [55, 56]. Since many veterans may already experience social isolation and activity restrictions, it is especially important to facilitate discussions around maintaining and improving positive social connections while following social distance measures, encourage the use of adaptive coping strategies to manage difficulties, and provide psychoeducation on how the COVID-19 pandemic might trigger trauma-related memories [57]. Our study provides further implications for clinicians to consider when working with Veterans with mental illnesses in the COVID-19 crisis. For instance, clinicians may take Veterans with mental illnesses' physical health QOL and ability to participate into consideration as the pandemic may have led to dramatic shifts in Veteran's daily life, which can further influence their mental health quality of life. During a public health crisis as such, Veterans with mental illnesses may benefit from individualized treatment plans that are tailored to their personal and contextual factors. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[82,559,485,906]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Some limitations of this study will need to be addressed by future research. First, our design is incapable of evaluating the causal mechanisms that underlie the explored relationships. Future studies should utilize longitudinal designs to explore the temporal associations of these variables. Nevertheless, these findings provide important information that could ultimately improve the value of clinical services already available for Veterans with mental illnesses. Second, data for this study come primarily from veterans with heterogeneity of self-reported mental illness. Therefore, since different mental illnesses have different underlying pathophysiological mechanisms, associations could change by exploring mental illnesses separately. Third, in addition to pain intensity, future studies should explore pain interference, which is defined as the extent that pain negatively impacts engagement in social, cognitive, emotional, physical, and recreational activities. Fourth, female veterans seem to be slightly over-represented in our sample and the percentage of subjects with a bachelor's degree seems to be higher than the average in veterans (15.7–20.1%) [58]. Fifth, we measured pain intensity with a single item. Given the complexity of pain and its impact on QOL (e.g., pain ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,68,915,177]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and mental health and physical health relationships), future studies may consider measuring pain intensity with a scale that has a strong evidence of discriminant validity. Finally, it is important to take into consideration that there may be some conceptual overlap between the concepts examined in our study, which we suggest that future research should use more robust means of measurements. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,179,915,416]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In summary, these findings support continued efforts to provide multidisciplinary, holistic and integrated health care for the management of pain conditions for veterans with mental illnesses. Specific recommendations for practitioners include implementing treatment goals that simultaneously focus on physical health and ability to participate in social roles and activities for clients who present with both physical pain and low mental health QOL. While many practitioners may use patients' levels of physical health and social engagement as a measure to predict pain and mental health symptom reduction, identifying these two factors (physical health QOL and social activity) more directly in conceptualizing client's mental health symptoms with identified pain symptoms may help developing more targeted intervention, especially for veterans with mental illness. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,430,915,469]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgements We would like to thank Renee Viramontes and Cherylanne Hunter for their support in our lab, the Veteran VVell-Being Lab $(\\mathrm{V}^{3})$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,483,915,510]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Funding This study is funded by the College of Health Sciences of the UT-El Paso (PI: Dr. Emre Umucu). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,526,781,541]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Compliance with ethical standards ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,556,915,582]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conflict of interest The authors declare that they have no conflict of interest. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,594,915,632]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Ethical approval This study was reviewed and approved as exempt study by the Institutional Review Board by the University of Texas at El Paso (IRB ID: 1153068-2). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,645,915,670]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Informed consent Informed consent was obtained from all participants in this study. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,716,613,731]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,746,915,887]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1. Vogt, D., Fox, A. B., & Di Leone, B. A. L. (2014). Mental health beliefs and their relationship with treatment seeking among U.S. OEF/OIF Veterans. Journal of Traumatic Stress, 27(3), 307-313. https://doi.org/10.1002/jts.21919. \",\"2. U.S. Department of Veterans Affairs. (2020). VA mental health services. Retrieved August 8, 2020, from https://www.va.gov/health-care/health-needs-conditions/mental-health/. \",\"3. Riley, W. T., Rothrock, N., Bruce, B., Christodolou, C., Cook, K., Hahn, E. 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Patient-reported outcomes measurement information system (PROMIS) domain names and definitions revisions: further evaluation of content validity in IRT-derived item \"]","page_idx":"5","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[783,37,915,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Quality of Life Research ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[80,927,154,944]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[84,68,487,903]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"banks. Quality of Life Research, 19(9), 1311-1321. https://doi.org/10.1007/s11136-010-9694-5. \",\"4. Umucu, E., Villegas, D., Viramontes, R., Jung, H., & Lee, B. (2020). Measuring grit in veterans with mental illnesses: Examining the model structure of grit. *Psychiatric Rehabilitation Journal*. https://doi.org/10.1037/prj0000420. \",\"5. Umucu, E. (2020). Examining the structure of the PERMA theory of well-being in veterans with mental illnesses. Rehabilitation Counseling Bulletin. https://doi.org/10.1177/0034355220957093. \",\"6. Higgins, D. M., Kerns, R. D., Brandt, C. A., Haskell, S. G., Bathulapalli, H., Gilliam, W., et al. (2014). Persistent pain and comorbidity among operation enduring freedom/operation Iraqi Freedom/Operation New Dawn Veterans. *Pain Medicine*, 15(5), 782-790. https://doi.org/10.1111/pme.12388. \",\"7. Nahin, R. L. (2017). Severe pain in veterans: The effect of age and sex, and comparisons with the general population. The Journal of Pain, 18(3), 247-254. https://doi.org/10.1016/j.jpain.2016.10.021. \",\"8. Goulet, J. L., Kerns, R. D., Bair, M., Becker, W. C., Brennan, P., Burgess, D. J., et al. (2016). The musculoskeletal diagnosis cohort: Examining pain and pain care among veterans. Pain, 157(8), 1696-1703. https://doi.org/10.1097/j.pain.000000000000567. \",\"9. Kang, H. K., Mahan, C. M., Lee, K. Y., Magee, C. A., & Murphy, F. M. (2000). Illnesses among united states veterans of the gulf war: A population-based survey of 30,000 veterans. Journal of Occupational and Environmental Medicine, 42(5), 491-501. \",\"10. Frank, J. W., Carey, E., Nolan, C., Kerns, R. D., Sandbrink, F., Gallagher, R., et al. (2018). Increased nonopioid chronic pain treatment in the Veterans Health Administration, 2010-2016. Pain Medicine, 20(5), 869-877. https://doi.org/10.1093/pm/pny149. \",\"11. Morasco, B. J., Duckart, J. P., Carr, T. P., Deyo, R. A., & Dobscha, S. K. (2010). Clinical characteristics of veterans prescribed high doses of opioid medications for chronic non-cancer pain. *Pain*, 151(3), 625-632. https://doi.org/10.1016/j.pain.2010.08.002. \",\"12. Matthias, M. S., Kukla, M., McGuire, A. B., & Bair, M. J. (2016). How do patients with chronic pain benefit from a peer-supported pain self-management intervention? A qualitative investigation. Pain Medicine, 17(12), 2247-2255. https://doi.org/10.1093/pm/pnw138. \",\"13. Plagge, J. M., Lu, M. W., Lovejoy, T. I., Karl, A. I., & Dobscha, S. K. (2013). Treatment of comorbid pain and PTSD in returning Veterans: A collaborative approach utilizing behavioral activation. *Pain Medicine*, 14(8), 1164–1172. https://doi.org/10.1111/pme.12155. \",\"14. Von Korff, M., & Simon, G. (1996). The Relationship Between Pain and Depression. *British Journal of Psychiatry*, 168(S30), 101-108. https://doi.org/10.1192/S0007125000298474. \",\"15. Naylor, J. C., Wagner, H. R., Johnston, C., Elbogen, E. E., Brancu, M., Marx, C. E., et al. (2019). Pain intensity and pain interference in male and female Iraq/Afghanistan-era Veterans. Women's Health Issues, 29, S24-S31. https://doi.org/10.1016/j.whi.2019.04.015. \",\"16. Poundja, J., Fikretoglu, D., Guay, S., & Brunet, A. (2007). Validation of the French version of the brief pain inventory in Canadian veterans suffering from traumatic stress. Journal of Pain and Symptom Management, 33(6), 720-726. https://doi.org/10.1016/j.jpainsymman.2006.09.031. \",\"17. Boakye, M., Moore, R., Kong, M., Skirboll, S. L., & Arrigo, R. T. (2013). Health-related quality-of-life status in Veterans with spinal disorders. Quality of Life Research, 22(1), 45-52. https://doi.org/10.1007/s11136-012-0121-y. \",\"18. Kazis, L. E., Miller, D. R., Clark, J., Skinner, K., Lee, A., Rogers, W., et al. (1998). Health-Related quality of life in patients served by the Department of Veterans Affairs: Results from the Veterans Health Study. Archives of Internal Medicine, 158(6), 626-632. https://doi.org/10.1001/archinte.158.6.626. \"]","page_idx":"6","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[512,68,914,889]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"19. Cohen, S. (2004). Social relationships and health. American Psychologist, 59(8), 676-684. https://doi.org/10.1037/0003-066X.59.8.676. \",\"20. Kessler, R. C., & McLeod, J. D. (1985). Social support and mental health in community samples. In S. Cohen & S. L. Syme (Eds.), Social support and health (pp. 219-240). San Diego, CA: Academic Press. \",\"21. Ren, X. S., Skinner, K., Lee, A., & Kansas, L. (1999). Social support, social selection and self-assessed health status: results from the veterans health study in the United States. *Social Science & Medicine*, 48(12), 1721-1734. https://doi.org/10.1016/S0277-9536(99)00069-6. \",\"22. Elizabeth Rippentrop, A., Altmaier, E. M., Chen, J. J., Found, E. M., & Keffala, V. J. (2005). The relationship between religion/spirituality and physical health, mental health, and pain in a chronic pain population. Pain, 116(3), 311-321. https://doi.org/10.1016/j.pain.2005.05.008. \",\"23. Schnurr, P. P., Hayes, A. F., Lunney, C. A., McFall, M., & Uddo, M. (2006). Longitudinal analysis of the relationship between symptoms and quality of life in veterans treated for posttraumatic stress disorder. Journal of Consulting and Clinical Psychology, 74(4), 707-713. https://doi.org/10.1037/0022-006X.74.4.707. \",\"24. Avluk, O. C., Gurcay, E., Gurcay, A. G., Karaahmet, O. Z., Tamkan, U., & Cakci, A. (2014). Effects of chronic pain on function, depression, and sleep among patients with traumatic spinal cord injury. Annals of Saudi Medicine, 34(3), 211-216. https://doi.org/10.5144/0256-4947.2014.211. \",\"25. Cadogan, M. P., Edelen, M. O., Lorenz, K. A., Jones, M., Yosef, J., Hascall, T., et al. (2008). The relationship of reported pain severity to perceived effect on function of nursing home residents. The Journals of Gerontology: Series A, 63(9), 969-973. https://doi.org/10.1093/gerona/63.9.969. \",\"26. van Severenter, R., Serpell, M., Bach, F. W., Morlion, B., Zlateva, G., Bushmakin, A. G., et al. (2011). Relationships between changes in pain severity and other patient-reported outcomes: An analysis in patients with posttraumatic peripheral neuropathic pain. Health and Quality of Life Outcomes, 9, 17. https://doi.org/10.1186/1477-7525-9-17. \",\"27. Goodman, J. K., Cryder, C. E., & Cheema, A. (2013). Data collection in a flat world: The strengths and weaknesses of Mechanical Turk samples. Journal of Behavioral Decision Making, 26(3), 213-224. https://doi.org/10.1002/bdm.1753. \",\"28. Rand, D. G. (2012). The promise of Mechanical Turk: How online labor markets can help theorists run behavioral experiments. Journal of Theoretical Biology, 299, 172-179. https://doi.org/10.1016/j.jtbi.2011.03.004. \",\"29. Amtmann, D., Cook, K. F., Jensen, M. P., Chen, W.-H., Choi, S., Revicki, D., et al. (2010). Development of a PROMIS item bank to measure pain interference. Pain, 150(1), 173-182. https://doi.org/10.1016/j.pain.2010.04.025. \",\"30. Cleeland, C. S., & Ryan, K. M. (1994). Pain assessment: Global use of the Brief Pain Inventory. Annals, Academy of Medicine, Singapore, 23(2), 129-138. \",\"31. Jensen, M. P. (2010). Measurement of pain. In S. M. Fishman, J. C. Ballantyne, & J. P. Rathmell (Eds.), *Bonica's management of pain* (pp. 251-270). Philadelphia, PA: Williams & Wilkins. \",\"32. Hays, R. D., Schalet, B. D., Spritzer, K. L., & Cella, D. (2017). Two-item PROMIS® global physical and mental health scales. Journal of Patient-Reported Outcomes, 1(1), 2. https://doi.org/10.1186/s41687-017-0003-8. \",\"33. Hahn, E. A., DeWalt, D. A., Bode, R. K., Garcia, S. F., DeVellis, R. F., Correia, H., et al. (2014). New English and Spanish social health measures will facilitate evaluating health determinants. Health Psychology, 33(5), 490-499. https://doi.org/10.1037/hea0000055. \"]","page_idx":"6","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[82,37,215,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Quality of Life Research ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[840,927,915,944]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,68,487,841]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"34. Hayes, A. F. (2017). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach. New York: Guilford Press. \",\"35. Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40(3), 879-891. https://doi.org/10.3758/BRM.40.3.879. \",\"36. Flor, H., Fydrich, T., & Turk, D. C. (1992). Efficacy of multidisciplinary pain treatment centers: A meta-analytic review. Pain, 49(2), 221-230. https://doi.org/10.1016/0304-3959(92)90145-2. \",\"37. Gunreben-Stempfle, B., Grießinger, N., Lang, E., Muehlhans, B., Sittl, R., & Ulrich, K. (2009). Effectiveness of an intensive multidisciplinary headache treatment program. *Headache: The Journal of Head and Face Pain*, 49(7), 990–1000. https://doi.org/10.1111/j.1526-4610.2009.01448.x. \",\"38. Håland Haldorsen, E. M., Grasdal, A. L., Skouen, J. S., Risa, A. E., Kronholm, K., & Ursin, H. (2002). Is there a right treatment for a particular patient group? Comparison of ordinary treatment, light multidisciplinary treatment, and extensive multidisciplinary treatment for long-term sick-listed employees with musculoskeletal pain. Pain, 95(1), 49-63. https://doi.org/10.1016/S0304-3959(01)00374-8. \",\"39. Scascighini, L., Toma, V., Dober-Spielmann, S., & Sprott, H. (2008). Multidisciplinary treatment for chronic pain: A systematic review of interventions and outcomes. *Rheumatology*, 47(5), 670-678. https://doi.org/10.1093/rheumatology/ken021. \",\"40. Skouen, J. S., Grasdal, A. L., Haldorsen, E. M. H., & Ursin, H. (2002). Relative cost-effectiveness of extensive and light multidisciplinary treatment programs versus treatment as usual for patients with chronic low back pain on long-term sick leave: Randomized controlled study. Spine, 27(9), 901-909. \",\"41. Bair, M. J., Ang, D., Wu, J., Outcalt, S. D., Sargent, C., Kempf, C., et al. (2015). Evaluation of stepped care for chronic pain (ESCAPE) in veterans of the Iraq and Afghanistan conflicts: A randomized clinical trial. *JAMA Internal Medicine*, 175(5), 682-689. https://doi.org/10.1001/jamainternmed.2015.97. \",\"42. Harding, K., Day, M. A., Ehde, D. M., Wood, A. E., McCall, A., & Williams, R. (2018). Mental and physical health correlates of pain treatment utilization among Veterans with chronic pain: A cross-sectional study. Military Medicine, 184(3-4), e127-e134. https://doi.org/10.1093/milmed/usy235. \",\"43. Lenz, A. S., Dell'Aquila, J., & Balkin, R. S. (2018). Effectiveness of integrated primary and behavioral healthcare. Journal of Mental Health Counseling, 40(3), 249-265. https://doi.org/10.17744/mehc.40.3.06. \",\"44. Myers, J. E., Sweeney, T. J., & Witmer, J. M. (2000). The wheel of wellness counseling for wellness: A holistic model for treatment planning. Journal of Counseling & Development, 78(3), 251-266. https://doi.org/10.1002/j.1556-6676.2000.tb01906.x. \",\"45. Kerns, R. D., Brandt, C. A., & Peduzzi, P. (2019). NIH-DoD-VA pain management collaboration. *Pain Medicine*, 20(12), 2336–2345. https://doi.org/10.1093/pm/pnz186. \",\"46. Shim, R., & Rust, G. (2013). Primary care, behavioral health, and public health: Partners in reducing mental health stigma. American Journal of Public Health, 103(5), 774-776. https://doi.org/10.2105/ajph.2013.301214. \",\"47. Hunt, M. G., Cuddeback, G. S., Bromley, E., Bradford, D. W., & Hoff, R. A. (2019). Changing rates of mental health disorders among Veterans treated in the VHA during troop drawdown, 2007-2013. Community Mental Health Journal, 55(7), 1120-1124. https://doi.org/10.1007/s10597-019-00437-1. \"]","page_idx":"7","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[510,67,915,765]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"48. Outcalt, S., Kroenke, K., Krebs, E., Chumbler, N., Wu, J., Yu, Z., et al. (2015). Chronic pain and comorbid mental health conditions: independent associations of posttraumatic stress disorder and depression with pain, disability, and quality of life. Journal of Behavioral Medicine, 38(3), 535-543. https://doi.org/10.1007/s10865-015-9628-3. \",\"49. Yoon, J., Bruckner, T. A., & Brown, T. T. (2013). The association between client characteristics and recovery in California's Comprehensive Community Mental Health Programs. American Journal of Public Health, 103(10), e89-e95. https://doi.org/10.2105/ajph.2013.301233. \",\"50. Schmit, M. K., Watson, J. C., & Fernandez, M. A. (2018). Examining the effectiveness of integrated behavioral and primary health care treatment. Journal of Counseling & Development, 96(1), 3-14. https://doi.org/10.1002/jcad.12173. \",\"51. Müller, R., Landmann, G., Bechir, M., Hinrichs, T., Arnet, U., Jordan, X., et al. (2017). Chronic pain, depression and quality of life in individuals with spinal cord injury: Mediating role of participation. Journal of Rehabilitation Medicine, 49, 489-496. \",\"52. Nguyen, U.-S. D. T., Perneger, T., Franklin, P. D., Barea, C., Hoffmeyer, P., & Lübbeke, A. (2019). Improvement in mental health following total hip arthroplasty: the role of pain and function. BMC Musculoskeletal Disorders, 20(1), 307. https://doi.org/10.1186/s12891-019-2669-y. \",\"53. Fujii, T., Oka, H., Katsuhira, J., Tonosu, J., Kasahara, S., Tanaka, S., et al. (2018). Association between somatic symptom burden and health-related quality of life in people with chronic low back pain. PLoS ONE, 13(2), e0193208. https://doi.org/10.1371/journal.pone.0193208. \",\"54. Börsbo, B., Peolsson, M., & Gerdle, B. (2009). The complex interplay between pain intensity, depression, anxiety and catastrophising with respect to quality of life and disability. *Disability and Rehabilitation*, 31(19), 1605–1613. https://doi.org/10.1080/09638280903110079. \",\"55. Shelton, C. J., Kim, A., Hassan, A. M., Bhat, A., Barnello, J., & Castro, C. A. (2020). System-wide implementation of telehealth to support military Veterans and their families in response to COVID-19: A paradigm shift. Journal of Military, Veteran and Family Health., https://doi.org/10.3138/jmvfh.CO19-003. \",\"56. James Riegler, L., Raj, S. P., Moscato, E. L., Narad, M. E., Kincaid, A., & Wade, S. L. (2020). Pilot trial of a telepsychotherapy parenting skills intervention for veteran families: Implications for managing parenting stress during COVID-19. Journal of Psychotherapy Integration, 30(2), 290–303. https://doi.org/10.1037/int000220. \",\"57. Marini, C. M., Pless Kaiser, A., Smith, B. N., & Fiori, K. L. (2020). Aging veterans' mental health and well-being in the context of COVID-19: The importance of social ties during physical distancing. Psychological Trauma: Theory, Research, Practice, and Policy, 12(S1), S217-S219. https://doi.org/10.1037/tra0000736. \",\"58. U.S. Department of Veterans Affairs (2016). Profile of veterans: 2014 data from the American Community Survey. Retrieved August 8, 2020, from https://www.va.gov/vetdata/docs/SpecialReports/Profile_of_Veterans_2014.pdf. \"]","page_idx":"7","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[507,777,915,803]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[783,37,915,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Quality of Life Research ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[82,927,100,944]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"# ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[102,930,154,944]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Springer ","text_format":null,"text_level":null,"type":"footer"}],"string":"[\n {\n \"bbox\": \"[80,130,843,200]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Pain intensity and mental health quality of life in veterans with mental illnesses: the intermediary role of physical health and the ability to participate in activities \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,218,826,251]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Emre Umucu<sup>1</sup> $\\\\cdot$ Antonio Reyes<sup>2</sup> $\\\\cdot$ Paul Carrola<sup>3</sup> $\\\\cdot$ Thenral Mangadu<sup>4</sup> $\\\\cdot$ Beatrice Lee<sup>1</sup> $\\\\cdot$ Jessica M. Brooks<sup>5</sup> $\\\\cdot$ Karen L. Fortuna<sup>6</sup> $\\\\cdot$ Diana Villegas<sup>1</sup> $\\\\cdot$ Chung-Yi Chiu<sup>7</sup> $\\\\cdot$ Carolina Valencia<sup>1</sup> \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,273,252,284]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Accepted: 12 September 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,286,300,300]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\odot$ Springer Nature Switzerland AG 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,321,152,335]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,337,917,383]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Purpose The purpose of this study was to examine the intermediary role of physical health quality of life and ability to participate social roles and activities in the relationship between pain intensity and mental health quality of life in veterans with mental illnesses. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,384,917,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methods This is a cross-sectional correlational design study. Our participants are 156 veterans with self-reported mental illness $(M_{\\\\mathrm{age}} = 37.85; \\\\mathrm{SD}_{\\\\mathrm{age}} = 10.74)$ . Descriptive, correlation, and mediation analyses were conducted for the current study. Results Pain intensity was negatively correlated with physical health QOL, ability to participate in social roles and activities, and mental health QOL. Physical health QOL and ability to participate in social roles and activities were positively associated with mental health QOL, respectively. Physical health QOL was positively correlated with a ability to participate in social roles and activities. Study results indicate that the effect of pain intensity on mental health QOL can be explained by physical health QOL and ability to participate. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,496,915,541]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conclusions Specific recommendations for practitioners include implementing treatment goals that simultaneously focus on physical health and ability to participate in social roles and activities for clients who present with both physical pain and low mental health QOL. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,558,576,574]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords Quality of life $\\\\cdot$ Veterans $\\\\cdot$ Mental illness $\\\\cdot$ Participation $\\\\cdot$ Pain \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,606,915,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Due to the intense experiences associated with deployment and combat, Veterans are at high risk of developing a mental illness [1]. More than 1.7 million Veterans received treatment in a Department of Veterans Affairs (VA) mental health specialty program in fiscal year 2018 [2], and this number may not fully reflect the problem of mental illness among Veterans given that many do not seek treatment through the VA [1]. Mental illness is associated with poorer mental health quality of life, which is comprised of a combination of the perception of mental health and functional effects of mental illness [3]. Mental health quality of life provides a useful understanding of the burden of mental illness because it appreciates that the impact of mental illness may be variable among individuals. Additional research is needed to better understand predictors of mental health quality of life and well-being for Veterans with a mental illness [4, 5]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,859,915,906]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Veterans are also at high risk of developing chronic pain due to the extraordinary physical stress associated with military service [6]. Studies indicate that $66\\\\%$ of veterans \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,39,213,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Quality of Life Research \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[82,53,331,67]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1007/s11136-020-02642-y \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[862,81,915,120]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Check for updates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[82,615,188,627]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Emre Umucu \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[105,629,216,641]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"eumucu@utep.edu \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[82,651,426,691]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{1}$ Department of Rehabilitation Sciences, The University of Texas at El Paso, 500 W University Ave, El Paso, TX 79968, USA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[82,696,433,724]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 Division of Special Education and Counseling, CA State University - Los Angeles, Los Angeles, CA, USA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[82,727,460,755]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{3}$ Department of Educational Psychology and Special Services, The University of Texas at El Paso, El Paso, TX, USA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[82,759,421,786]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{4}$ Department of Public Health Sciences, The University of Texas at El Paso, El Paso, TX, USA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[82,789,440,829]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 Department of Psychiatry, School of Medicine and Public Health, University of Wisconsin - Madison, Madison, WI, USA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[82,835,436,863]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 The Geisel School of Medicine at Dartmouth, Dartmouth College, Concord, NH, USA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[82,865,440,906]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{7}$ Department of Kinesiology and Community Health, University of Illinois Urbana Champaign, Champaign, IL, USA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[80,929,302,944]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Published online: 24 September 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[840,927,915,945]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[82,69,485,305]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"report experiencing pain with $9\\\\%$ reporting severe pain [7]. Over $50\\\\%$ of Veterans who receive care at the VA are diagnosed with musculoskeletal pain [8] and a survey of Veterans found a high prevalence of headaches $(54\\\\%)$ , joint pain $(45\\\\%)$ , back pain, $(44\\\\%)$ , muscle pain $(33\\\\%)$ , and abdominal pain $(23\\\\%)$ [9]. Researchers argue that addressing and treating pain, including addressing opioid use disorder (OUD) risk, is an increasingly important challenge for the VA due to the aging population and growth in number of Veterans with chronic pain related to recent military service [10]. Prior studies also indicate that veterans with chronic pain and comorbid psychiatric disorders are more likely to receive opioids than pain patients without comorbid psychopathology, these diagnoses are also associated with prescription of high opioid doses [11]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,307,485,621]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For Veterans who experience pain, the effects can extend to every aspect of their life. Pain can interfere with participation in daily activities and is associated with higher levels of emotional distress [12]. Thus, it is not surprising that pain and mental illnesses are commonly comorbid for Veterans [13]. Research suggests that pain is strongly associated with symptoms of anxiety, depressive disorders, suicidal ideation, and PTSD [13-15]. Poundja et al. [16] found that both pain severity and pain interference are negatively correlated with mental health quality of life in Canadian veterans suffering from traumatic stress. Boakye et al. [17] examined health-related quality of life in veterans with spinal cord injury (SCI) and found that a visual analog pain score was the most important predictor of worsened mental health quality of life scores. Likewise, Kazis et al. [18] reported that chronic low back pain is negatively associated with mental health quality of life in patients served by the VA. These studies and others highlight the importance of better understanding the underlying mechanisms by which pain intensity impacts mental health quality of life for Veterans. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,622,485,889]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mental health quality of life and pain are also associated with physical health quality of life (i.e., ratings of physical health and the ability to carry out physical activities) and participation in social roles and activities. The ability to participate in social roles and activities improves mental health while decreasing mental health symptoms [19]. Social participation is also strongly associated with social support, which has long been known to play an important role in protecting against negative effects of stress and mental illness, see e.g., [20]. Research suggests that physical health quality of life is associated with greater ability to participate in social activities, and consequentially enhancing social connectedness and its health benefits. For example, longitudinal data from the Veterans Health Study, Ren et al. [21] shows that physical health is associated with a person's ability to participate and maintain social relationships and stronger social support. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,69,914,337]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Additionally, Rippentrop et al. [22] found that physical health quality of life is positively related to mental health quality of life for individuals with chronic pain. Similarly, in a study of Vietnam veterans, Schnurr et al. [23] found that reported physical health quality of life is related to PTSD symptom severity. General population studies also indicate that greater pain intensity is associated with greater interference with social participation and physical and recreational activities [24-26]. In a study of veterans, Naylor et al. [15] found a positive correlation between pain intensity and functional factors including physical disability and social support. Overall, research supports that pain, physical health quality of life, and the ability to participate in social functions are all related and contribute to mental health quality of life. Likely, the relationship between pain intensity and mental health quality of life is influenced by physical health quality of life and participation in social roles and activities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,339,914,668]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Although existing studies have examined the relationship between pain, social relationships, and physical and mental health quality of life for Veterans, none have systematically examined these factors together to better understand their impact on mental health quality of life. Therefore, the purpose of this study was to examine the intermediary role of physical health quality of life and ability to participate in social roles and activities in the relationship between pain intensity and mental health quality of life in veterans with mental illnesses. We hypothesized that (a) increased pain intensity is associated with reduced physical and mental health quality of life, (b) decreased physical health quality of life is associated with lower levels of the ability to participate social roles and activities, and (c) reduced ability to participate social roles and activities negatively affect mental health quality of life in veterans with mental illnesses. Health care systems could use this valuable information to potentially improve value of services for Veterans with mental illnesses by addressing modifiable risk factors such as physical health QOL and ability to participate through treatment. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,716,593,730]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,749,680,764]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Design and procedure \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,779,914,905]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This cross-sectional study was reviewed and approved as an exempt study by the Institutional Review Board by the University of Texas at El Paso. We collected data from Amazon's MTurk, a crowdsourcing tool enabling MTurk Workers to access and complete Human Intelligence Tasks (HITs). MTurk has been considered as a valid, diverse, reliable, and cost-effective large data collection tool [27, 28]. Based on MTurk options, we restricted participants to be residents in \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[784,39,915,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Quality of Life Research \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[84,929,154,943]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,68,487,148]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the United States who have military experience. We shared a Qualtrics survey link with participants. All participants read an online consent form and agreed to be participant in this study. All participants received $4.00 upon completing the online survey. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,163,159,178]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Measures \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,194,179,211]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Pain intensity \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,226,487,322]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Pain intensity was assessed using the PROMIS® Numeric Rating Scale v.1.0—Pain Intensity 1a [29-31]. It is a one-item measure that asks respondents to rate their pain on average, ranging from 0 (no pain) to 10 (worst imaginable pain) over the past 7 days. Higher scores indicate higher levels of pain intensity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,337,280,353]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Physical health quality of life \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,368,487,512]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Physical health QOL was assessed using the PROMIS® Scale v1.2—Global Health Physical 2a [32]. It is a 2-item measure that asks respondents to rate their physical health (ranging from 1 [poor] to 5 [excellent]) and their ability to carry out daily physical activities (ranging from 1 [not at all] to 5 [completely]). Higher scores indicate higher physical health QOL. Total raw scores were converted into $T$ scores. The Cronbach's alpha coefficient for the PROMIS global physical health in the present study was computed to be 0.52. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,527,413,541]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Ability to participate in social roles and activities \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,558,487,717]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Ability to participate was assessed using the PROMIS® Item Bank v2.0—Ability to Participate in Social Roles and Activities-Short Form 4a [33]. It is a 4-item measure that asks respondents to rate their perceptions on their ability to perform their social functions, ranging from 1 (always) to 5 (never). Higher scores indicate higher levels of ability to participate. Total raw scores were converted into $T$ scores. The Cronbach's alpha coefficient for the PROMIS ability to participate in social roles and activities in the present study was computed to be 0.90. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,732,213,746]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mental health QOL \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,763,487,891]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mental health QOL was assessed using the PROMIS® Scale v1.2—Global Health Mental 2a [32]. It is a 2-item measure that asks respondents to rate their mental health and satisfaction with social connections, ranging from 1 (poor) to 5 (excellent). Higher scores indicate higher mental health QOL. Total raw scores were converted into $T$ scores. The Cronbach's alpha coefficient for the PROMIS global mental health in the present study was computed to be 0.77. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,69,616,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data analysis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,100,915,387]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"All analyses were performed using the Statistical Package for the Social Sciences (SPSS; version 25). Descriptive statistics were computed to provide information about the demographic characteristics and for the independent variable, mediators, and dependent variable. Correlation analysis was conducted to examine relationships among variables. Finally, a serial mediation analysis was conducted to examine physical health QOL and ability to participate as mediators between pain intensity and mental health QOL. The SPSS PROCESS 3.4.1 [34] was used to conduct mediation analysis. A bootstrapping approach was also used to test the significance of indirect effects of pain intensity on mental health QOL with 5000 bootstrap samples through (a) physical health QOL, (b) ability to participate in social roles and activities, and (c) both physical health QOL and ability to participate. Although there is not a consensus how many bootstrap samples should be generated, researchers recommended at least 5000 resamples for final reporting [35]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,416,579,432]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,448,608,464]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Participants \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,479,915,764]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The total number of participants were 156 veterans with self-reported mental illnesses. Participants ranged in age from 23 to 72, with an average of 37.85 years old $(SD = 10.74)$ . Most participants were males $(66.7\\\\%)$ . The majority of participants identified as Caucasians $(69.9\\\\%)$ and married $(52.6\\\\%)$ . Regarding educational level, $39\\\\%$ obtained a bachelor's degree, followed by some college credit without a degree $(23.1\\\\%)$ , an associate's degree $(13.5\\\\%)$ , a graduate degree $(12.2\\\\%)$ , a trade/technical/vocational training $(7.1\\\\%)$ , and a high school degree $(5.8\\\\%)$ . Many participants served in the Army $(55.8\\\\%)$ , followed by Air Force $(17.9\\\\%)$ , Navy $(12.2\\\\%)$ , Marine Corps $(10.3\\\\%)$ , and Coast Guard $(3.8\\\\%)$ . In terms of mental illnesses, participants reported at least one type of mental illnesses, including $64.7\\\\%$ reported depression, $57.1\\\\%$ reported anxiety, $35.3\\\\%$ reported PTSD, $10.3\\\\%$ reported substance use disorder, $4.5\\\\%$ reported bipolar disorder, $4.5\\\\%$ reported personality disorder, and $3.9\\\\%$ reported others. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,779,672,797]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Descriptive statistics \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,812,917,908]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Participants' pain intensity scores ranged from 0 to 10 with an average of 3.44 ( $SD = 2.41$ ). Physical health QOL $T$ scores ranged from 23.40 to 63.30 with an average of 45.10 ( $SD = 8.03$ ). Ability to participate in social roles and activities $T$ scores ranged from 31.80 to 64.20 with an average of 47.78 ( $SD = 8.40$ ). Mental health QOL $T$ scores ranged from \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,37,213,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Quality of Life Research \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[838,927,914,944]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[78,68,487,211]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"25.80 to 64.60 with an average of 40.83 ( $SD = 8.40$ ). After examining $T$ scores, we found that $14.7\\\\%$ and $60.3\\\\%$ of the participants had physical health quality of life $T$ scores of above and below the mean, respectively; $11.5\\\\%$ and $88.5\\\\%$ of the participants had mental health quality of life $T$ scores of above and below the mean, respectively; and $30.8\\\\%$ and $60.3\\\\%$ of the participants had ability to participate in social roles and activities $T$ scores of above and below the mean, respectively. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,232,238,250]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Correlation analysis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,265,487,408]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Pain intensity was negatively correlated with physical health QOL ( $r = -0.56$ , $p < 0.001$ ), ability to participate in social roles and activities ( $r = -0.54$ , $p < 0.001$ ), and mental health QOL ( $r = -0.33$ , $p < 0.001$ ). Physical health QOL ( $r = 0.44$ , $p < 0.001$ ) and ability to participate in social roles and activities ( $r = 0.55$ , $p < 0.001$ ) were positively associated with mental health QOL, respectively. Physical health QOL was positively correlated with an ability to participate in social roles and activities ( $r = 0.55$ , $p < 0.001$ ). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[80,431,231,448]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mediation analysis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,463,489,637]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The serial mediation model is presented in Fig. 1. Pain intensity was significantly associated with mental health QOL ( $c = -0.33$ , $p < 0.001$ ). Pain intensity was significantly associated with physical health QOL ( $a_1 = -0.56$ , $p < 0.001$ ) and was significantly associated with ability to participate in social roles and activities after controlling for physical health QOL ( $a_2 = -0.34$ , $p < 0.001$ ). Physical health QOL was significantly associated with ability to participate in social roles and activities after controlling for pain intensity ( $d_{21} = 0.35$ , $p < 0.001$ ). Additionally, physical health QOL was significantly associated with mental health \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,68,915,160]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"QOL after controlling for pain intensity and ability to participate in social roles and activities ( $b_{1} = 0.22$ , $p < 0.05$ ). Ability to participate in social roles and activities was significantly associated with mental health QOL after controlling for pain intensity and physical health QOL ( $b_{2} = 0.45$ , $p < 0.001$ ). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,164,915,511]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Importantly, pain intensity was no longer significantly associated with mental health QOL after controlling for physical health QOL and ability to participate in social roles and activities ( $c' = 0.04$ , $p = 0.65$ ). This suggests that physical health QOL and the ability to participate in social roles and activities mediated the relationship between pain intensity and mental health QOL. In addition, results using the PROCESS with 5000 bootstrap samples, demonstrated that the indirect paths were significant because the $95\\\\%$ confidence intervals did not contain zero, suggesting that the indirect effects were different from zero. The indirect effect of pain intensity through physical health QOL on mental QOL was significant ( $a_1b_1 = -0.12$ ; $95\\\\%$ CI $[-0.23, -0.02]$ ). The indirect effect of pain intensity through ability to participate on mental health QOL was significant ( $a_2b_2 = -0.15$ ; $95\\\\%$ CI $[-0.25, -0.07]$ ). The indirect effect of pain intensity through physical health QOL and ability to participate in social roles and activities on mental health QOL was significant ( $a_1d_{21}b_2 = -0.09$ ; $95\\\\%$ CI $[-0.16, -0.04]$ ). Overall, the mediation analysis indicated that the effect of pain intensity on mental health QOL can be explained by physical health QOL and ability to participate in social roles and activities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,526,596,541]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,558,915,637]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Our analyses provide novel insights by clarifying the intermediary role of physical health quality of life and ability to participate in social roles and activities in the relationship between pain intensity and mental health quality of life in veterans with mental illnesses. Similar associations were \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[85,665,914,860]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 1 Standardized path coefficients for serial mediation analysis on the relationship between pain intensity and mental health QOL. Note: Dotted line denotes the total effect of pain intensity on mental health QOL when mediators are not included. $^{**}p < 0.001$ . $^* p < 0.05$ . $^+ p = .65$ \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0777/9f4bf6c6de46e086f03975f12dc2874a3997cd8447b6b0ca78132af9cb013668.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[781,37,915,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Quality of Life Research \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[80,927,157,945]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[82,69,485,256]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"found between pain intensity and physical health QOL, ability to participate in social roles and activities, and mental health QOL, respectively. However, one key finding is that the initial association between pain intensity and mental health QOL was mediated by physical QOL and ability to participate in social roles and activities. This is valuable information because the negative effect of pain on mental health QOL could be mitigated by increasing physical health QOL and ability to participate in social roles and activities and potentially improve value of services for veterans with mental illnesses by addressing these modifiable risk factors through treatment. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,258,485,746]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Physical health QOL and ability to participate in social roles and activities directly contribute to veterans' level of pain and mental health independently. As such, reduced mental health symptoms in veterans who also have identified pain symptoms can be achieved through improving physical health and ability to participate in social roles and activities in veterans with mental illnesses. Strategies to improve physical health and ability to participate in social roles and activities are effective treatment supplements for rehabilitation and mental health professionals to integrate into their psychotherapeutic or psychoeducational interventions for veterans with mental illnesses who have low mental health QOL due to pain intensity. In addition, increasing evidence is accumulating for the effectiveness of multidisciplinary pain management strategies [36-40], including the VA's own stepped care pain management approach, to manage severe chronic pain [41]. Supplementing traditional psychotherapeutic or psychoeducational pain management interventions with self-directed client activities constitutes an empirically supported approach to treatment. This approach is supported by recent research that has highlighted the importance of self-managed (i.e., initiated and managed by the client) interventions [42]. In their study, Harding et al. [42] found that while veterans with chronic pain psychological comorbidities were more likely to seek provider managed interventions, they were more likely to use self-managed interventions overall. This suggests that veterans are more willing to initiate self-managed interventions for chronic pain in general. Self-managed interventions can also be implemented through more direct ways through integrated primary and behavioral health care, see e.g., [43]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,749,485,905]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The specific relationships between pain intensity, mental health, physical health, and ability to participate in social roles and activities are central data that inform integrated treatment practices. This study provides important evidence that supports the argument for both multidisciplinary assessment and treatment. While multidisciplinary and holistic models of treatment have long been advocated in the mental health profession [44], the direct relationship between physical health and ability to participate in social roles and activities with patient's experienced pain provided by this \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,68,914,240]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"study supports the benefit of physical health and ability to participate in social roles and activities as our study provides the promising approach to complement the existing services. These factors could also be used to better guide future studies and clinical trials from the newly developed Pain Management Collaboratory [45], which has the main goal of developing the capacity to implement cost-effective large-scale pragmatic clinical research in military and veteran health care delivery organizations focusing on nonpharmacological approaches to pain management and other comorbid conditions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,241,914,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The value of this study is highlighted by the overall lack of research directly exploring the relationships between pain intensity, mental health, physical health, and social engagement. Historically, medical and mental health treatment have been viewed by health care and policy makers as separate [46], which has created barriers for overall treatment and negatively impacts help seeking behaviors for persons with both medical and mental health concerns. This is specifically relevant for veteran populations who have experienced increased rates of mental health disorders [47] and high rates of comorbidity between pain and mental health diagnoses [13, 48]. The results of the current study not only support the importance of mental health professionals using holistic interventions but also supports previous research that cites the benefit of integrated behavioral and primary healthcare, see e.g., [49, 50]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,497,914,905]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Although there is a lack of research examining the intermediary role of physical health QOL and ability to participate in social roles and activities for the relationship between pain intensity and mental health QOL among veterans, it is also important to report that our findings are partially consistent with some studies with different populations. For example, participation restriction was found to be a mediator between pain intensity and depression symptoms and QOL in individuals with spinal cord injury, respectively [51]. Nguyen et al. [52] examined whether changes in mental health was associated with improvements in pain and function scores 1 year after total hip arthroplasty. Their findings revealed that greater improvements in pain and function were related to greater improvements in mental health. In a sample with chronic low back pain, authors [53] reported that higher somatic symptoms were related to lower health-related QOL independent of depression and other comorbid disorders [52]. Interestingly, in a sample with chronic pain, authors [54] found that pain intensity and duration were found to have a minor role for QOL and disability although psychological variables (e.g., depression) were found to have a strong association with QOL and disability. Overall, these findings revealed that pain-related, psychological, and social factors are important for QOL although the magnitude of impacts of these variables on QOL may change based on the population. As indicated above, it is important to have \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,37,213,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Quality of Life Research \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[840,927,914,944]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[78,68,487,116]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"holistic and multidisciplinary treatment options to achieve optimal rehabilitation and health outcomes, which could eventually improve QOL. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,117,485,556]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Additionally, as this manuscript is being written, the U.S. is facing a global pandemic from the COVID-19 virus. The physical and social restrictions brought on by this pandemic limit social participation and is negatively impacting the mental health quality of life for all persons and may have elevated effects for groups that are already experiencing physical and mental health issues. Besides, the current COVID-19 pandemic has led to changes in mental health care (e.g., transition to telehealth service delivery), disruptions in daily life, and greater psychological distress that are unique to veterans [55, 56]. Since many veterans may already experience social isolation and activity restrictions, it is especially important to facilitate discussions around maintaining and improving positive social connections while following social distance measures, encourage the use of adaptive coping strategies to manage difficulties, and provide psychoeducation on how the COVID-19 pandemic might trigger trauma-related memories [57]. Our study provides further implications for clinicians to consider when working with Veterans with mental illnesses in the COVID-19 crisis. For instance, clinicians may take Veterans with mental illnesses' physical health QOL and ability to participate into consideration as the pandemic may have led to dramatic shifts in Veteran's daily life, which can further influence their mental health quality of life. During a public health crisis as such, Veterans with mental illnesses may benefit from individualized treatment plans that are tailored to their personal and contextual factors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,559,485,906]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Some limitations of this study will need to be addressed by future research. First, our design is incapable of evaluating the causal mechanisms that underlie the explored relationships. Future studies should utilize longitudinal designs to explore the temporal associations of these variables. Nevertheless, these findings provide important information that could ultimately improve the value of clinical services already available for Veterans with mental illnesses. Second, data for this study come primarily from veterans with heterogeneity of self-reported mental illness. Therefore, since different mental illnesses have different underlying pathophysiological mechanisms, associations could change by exploring mental illnesses separately. Third, in addition to pain intensity, future studies should explore pain interference, which is defined as the extent that pain negatively impacts engagement in social, cognitive, emotional, physical, and recreational activities. Fourth, female veterans seem to be slightly over-represented in our sample and the percentage of subjects with a bachelor's degree seems to be higher than the average in veterans (15.7–20.1%) [58]. Fifth, we measured pain intensity with a single item. Given the complexity of pain and its impact on QOL (e.g., pain \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,68,915,177]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and mental health and physical health relationships), future studies may consider measuring pain intensity with a scale that has a strong evidence of discriminant validity. Finally, it is important to take into consideration that there may be some conceptual overlap between the concepts examined in our study, which we suggest that future research should use more robust means of measurements. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,179,915,416]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In summary, these findings support continued efforts to provide multidisciplinary, holistic and integrated health care for the management of pain conditions for veterans with mental illnesses. Specific recommendations for practitioners include implementing treatment goals that simultaneously focus on physical health and ability to participate in social roles and activities for clients who present with both physical pain and low mental health QOL. While many practitioners may use patients' levels of physical health and social engagement as a measure to predict pain and mental health symptom reduction, identifying these two factors (physical health QOL and social activity) more directly in conceptualizing client's mental health symptoms with identified pain symptoms may help developing more targeted intervention, especially for veterans with mental illness. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,430,915,469]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgements We would like to thank Renee Viramontes and Cherylanne Hunter for their support in our lab, the Veteran VVell-Being Lab $(\\\\mathrm{V}^{3})$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,483,915,510]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Funding This study is funded by the College of Health Sciences of the UT-El Paso (PI: Dr. Emre Umucu). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,526,781,541]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Compliance with ethical standards \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,556,915,582]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conflict of interest The authors declare that they have no conflict of interest. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,594,915,632]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Ethical approval This study was reviewed and approved as exempt study by the Institutional Review Board by the University of Texas at El Paso (IRB ID: 1153068-2). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,645,915,670]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Informed consent Informed consent was obtained from all participants in this study. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,716,613,731]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,746,915,887]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1. 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Community Mental Health Journal, 55(7), 1120-1124. https://doi.org/10.1007/s10597-019-00437-1. \\\"]\",\n \"page_idx\": \"7\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[510,67,915,765]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"48. Outcalt, S., Kroenke, K., Krebs, E., Chumbler, N., Wu, J., Yu, Z., et al. (2015). Chronic pain and comorbid mental health conditions: independent associations of posttraumatic stress disorder and depression with pain, disability, and quality of life. Journal of Behavioral Medicine, 38(3), 535-543. https://doi.org/10.1007/s10865-015-9628-3. \\\",\\\"49. Yoon, J., Bruckner, T. A., & Brown, T. T. (2013). The association between client characteristics and recovery in California's Comprehensive Community Mental Health Programs. American Journal of Public Health, 103(10), e89-e95. https://doi.org/10.2105/ajph.2013.301233. \\\",\\\"50. Schmit, M. K., Watson, J. C., & Fernandez, M. A. (2018). Examining the effectiveness of integrated behavioral and primary health care treatment. Journal of Counseling & Development, 96(1), 3-14. https://doi.org/10.1002/jcad.12173. \\\",\\\"51. Müller, R., Landmann, G., Bechir, M., Hinrichs, T., Arnet, U., Jordan, X., et al. (2017). Chronic pain, depression and quality of life in individuals with spinal cord injury: Mediating role of participation. Journal of Rehabilitation Medicine, 49, 489-496. \\\",\\\"52. Nguyen, U.-S. D. T., Perneger, T., Franklin, P. D., Barea, C., Hoffmeyer, P., & Lübbeke, A. (2019). Improvement in mental health following total hip arthroplasty: the role of pain and function. BMC Musculoskeletal Disorders, 20(1), 307. https://doi.org/10.1186/s12891-019-2669-y. \\\",\\\"53. Fujii, T., Oka, H., Katsuhira, J., Tonosu, J., Kasahara, S., Tanaka, S., et al. (2018). Association between somatic symptom burden and health-related quality of life in people with chronic low back pain. PLoS ONE, 13(2), e0193208. https://doi.org/10.1371/journal.pone.0193208. \\\",\\\"54. Börsbo, B., Peolsson, M., & Gerdle, B. (2009). The complex interplay between pain intensity, depression, anxiety and catastrophising with respect to quality of life and disability. *Disability and Rehabilitation*, 31(19), 1605–1613. https://doi.org/10.1080/09638280903110079. \\\",\\\"55. Shelton, C. J., Kim, A., Hassan, A. M., Bhat, A., Barnello, J., & Castro, C. A. (2020). System-wide implementation of telehealth to support military Veterans and their families in response to COVID-19: A paradigm shift. Journal of Military, Veteran and Family Health., https://doi.org/10.3138/jmvfh.CO19-003. \\\",\\\"56. James Riegler, L., Raj, S. P., Moscato, E. L., Narad, M. E., Kincaid, A., & Wade, S. L. (2020). Pilot trial of a telepsychotherapy parenting skills intervention for veteran families: Implications for managing parenting stress during COVID-19. Journal of Psychotherapy Integration, 30(2), 290–303. https://doi.org/10.1037/int000220. \\\",\\\"57. Marini, C. M., Pless Kaiser, A., Smith, B. N., & Fiori, K. L. (2020). Aging veterans' mental health and well-being in the context of COVID-19: The importance of social ties during physical distancing. Psychological Trauma: Theory, Research, Practice, and Policy, 12(S1), S217-S219. https://doi.org/10.1037/tra0000736. \\\",\\\"58. U.S. Department of Veterans Affairs (2016). Profile of veterans: 2014 data from the American Community Survey. Retrieved August 8, 2020, from https://www.va.gov/vetdata/docs/SpecialReports/Profile_of_Veterans_2014.pdf. \\\"]\",\n \"page_idx\": \"7\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[507,777,915,803]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[783,37,915,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Quality of Life Research \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[82,927,100,944]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"# \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[102,930,154,944]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Springer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1007/s11136-020-02642-y"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Medicine and Health Sciences"},"sha256":{"kind":"string","value":"365b455183e32ca7e42bf41cdda7de78dc84b99e6544248fcc575e4a1d64ad7a"},"title":{"kind":"string","value":"Pain intensity and mental health quality of life in veterans with mental illnesses: the intermediary role of physical health and the ability to participate in activities"}}},{"rowIdx":258,"cells":{"abstract":{"kind":"string","value":"A combination of magnetic resonance imaging (MRI), computed tomography (CT), and radionuclide cisternography are typically used to locate a cerebrospinal fluid (CSF) leak. However, the site of leakage cannot be determined, making treatment more difficult. Therefore, more sensitive imaging tools are needed. A whole-body 18Ffluorodeoxyglucose (FDG) positron emission tomography (PET)/MRI was conducted on six patients with suspected CSF leak and the resulting images were reviewed in comparison with those from six healthy controls. Paraspinal regions of focally increased uptake of 18FFDG were quantified using maximum standardized uptake values (SUVmax) and compared to the SUVmax of corresponding regions in the healthy controls. All six patients with suspected CSF leak showed paraspinal regions of significantly greater 18FFDG uptake compared to the corresponding areas in controls (P < 0.05). Two patients treated with local injections (epidural blood patches and/or epidural fibrin patches) on the site of abnormal PET/MRI findings reported temporary but significant improvement in symptoms. Our results suggest 18FFDG PET/MRI is sensitive to abnormalities potentially due to suspected CSF leak, which are not necessarily visible on conventional MRI alone or by the standard-of-care imaging methods."},"author":{"kind":"string","value":"Peter William Cipriano|Ryan Penticuff|Ian Richard Carroll|Daehyun Yoon|Yingding Xu|Jessa Ballesteros Castillo|Sandip Biswal"},"content_list":{"kind":"list like","value":[{"bbox":"[154,166,238,189]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"OPEN ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,164,860,315]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abnormal [18F]FDG PET/MRI findings in paraspinal structures of patients with suspected cerebrospinal fluid leak ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,322,884,355]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Daehyun Yoon $^{1,5}$ , Peter William Cipriano $^{1,5}$ , Ryan Penticuff $^{2}$ , Jessa Ballesteros Castillo $^{1}$ , Yingding Xu $^{3}$ , Ian Richard Carroll $^{4\\boxtimes}$ & Sandip Biswal $^{1\\boxtimes}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[253,364,926,563]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A combination of magnetic resonance imaging (MRI), computed tomography (CT), and radionuclide cisternography are typically used to locate a cerebrospinal fluid (CSF) leak. However, the site of leakage cannot be determined, making treatment more difficult. Therefore, more sensitive imaging tools are needed. A whole-body [18F]fluorodeoxyglucose (FDG) positron emission tomography (PET)/ MRI was conducted on six patients with suspected CSF leak and the resulting images were reviewed in comparison with those from six healthy controls. Paraspinal regions of focally increased uptake of [18F]FDG were quantified using maximum standardized uptake values $(\\mathrm{SUV}_{\\max})$ and compared to the $\\mathrm{SUV}_{\\max}$ of corresponding regions in the healthy controls. All six patients with suspected CSF leak showed paraspinal regions of significantly greater [18F]FDG uptake compared to the corresponding areas in controls $(P < 0.05)$ . Two patients treated with local injections (epidural blood patches and/or epidural fibrin patches) on the site of abnormal PET/MRI findings reported temporary but significant improvement in symptoms. Our results suggest [18F]FDG PET/MRI is sensitive to abnormalities potentially due to suspected CSF leak, which are not necessarily visible on conventional MRI alone or by the standard-of-care imaging methods. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[253,586,931,805]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Cerebrospinal fluid (CSF) leak is a condition caused by drainage of CSF from the brain or the spinal cord through a hole in their surrounding structures, such as the skull and the dura. The prevalence rate of the CSF leak is estimated to be 1 in 50,000 individuals, but this relatively uncommon occurrence may be due to underdiagnosis<sup>1</sup>. The most characteristic symptom of a CSF leak is a persistent headache that worsens when upright and improves with recumbency (orthostatic headaches)<sup>2</sup>. When chronic, CSF leaks may present as \"second half of the day headache\" with patients consistently better in the morning after prolonged nocturnal recumbency followed by worsening symptoms as the day progresses with prolonged upright time<sup>3</sup>. Other symptoms include nausea, memory difficulties, cranial nerve dysfunction, neck and interscapular pain<sup>4,5</sup>. Hereditary disorders of connective tissue such as Marfan Syndrome, Ehlers-Danlos Syndrome, Neurofibromatosis type 1, and Polycystic kidney disease have been associated with spinal CSF leaks, suggesting these and other associated disorders of connective tissue may lead to abnormally vulnerable dura prone to CSF leak<sup>6</sup>. Among those who can identify a precipitating event, atraumatic activities such as stretching, or Valsalva maneuver are commonly involved<sup>7-9</sup>. Traumatic head/neck injury such as whiplash as well as iatrogenic dural tear during surgical interventions including lumbar puncture, duromy, and skull base surgery are also important causes<sup>10-12</sup>. However, two thirds of patients with a spontaneous CSF leak can identify no precipitating events. The most common site of leak is along the spinal cord<sup>13</sup>. If the site of CSF leak is located, it is treated most commonly with an epidural injection of autologous blood (epidural blood patch) or an epidural fibrin patch, or surgery, depending on the case<sup>14</sup>. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[253,805,931,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Unfortunately, no one diagnostic test can consistently exclude the diagnosis of CSF leak or identify the site(s) of leakage<sup>15</sup>. Misdiagnosis is common, preventing proper treatment as the symptoms are often mistaken for those of other diseases, such as postural orthostatic tachycardia syndrome or new daily persistent headache<sup>14,16</sup>. The underlying sensitivity of magnetic resonance imaging (MRI) and computed tomography (CT) myelography ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[253,878,931,943]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{1}$ Department of Radiology, Stanford University, 300 Pasteur Drive, Stanford, CA 94305, USA. $^{2}$ Department of Radiology, UC San Diego School of Medicine, La Jolla, CA, USA. $^{3}$ Newport Harbor Radiology Associates, Irvine, CA, USA. $^{4}$ Department of Anesthesia Perioperative and Pain Medicine, Stanford University, 300 Pasteur Drive, Stanford, CA 94305, USA. $^{5}$ These authors contributed equally: Daehyun Yoon and Peter William Cipriano. $^{\\text{串}}$ email: ic38@stanford.edu; biswal@stanford.edu ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[652,14,922,30]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[63,63,452,104]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"scientific reports ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[811,136,831,154]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"# ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[836,140,927,150]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Check for updates ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,285,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports| (2021) 11:15926 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[376,965,636,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"| https://doi.org/10.1038/s41598-021-95056-w ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[919,966,931,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[258,62,931,227]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0216/39b301178c9b37007b701a0bcbf1636ae92526e045364965df5782080673bd05.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":"<table><tr><td>Patient</td><td>Sites of increased [18F]FDG uptake</td><td>MRI abnormalities</td></tr><tr><td>Pt. 1</td><td>Interspinous ligaments from L4-5</td><td>T2 hyperintensity of paraspinal muscles and interspinous liga-ment at L4-5</td></tr><tr><td>Pt. 2</td><td>Interspinous ligaments from L1-5</td><td>None</td></tr><tr><td>Pt. 3</td><td>Intra/extrathecal space extending into neuroforamina at C2Paraspinal muscles at C6 (bilateral), T6-7 (right), T8 (right)</td><td>None</td></tr><tr><td>Pt. 4</td><td>Interspinous ligaments from L2-3Left neuroforamina from L3-4Right neuroforamina/facet joints from L4-5</td><td>None</td></tr><tr><td>Pt. 5</td><td>Interspinous ligaments, paraspinal muscles, and spinousprocesses from L2-3</td><td>Large focal T2 hyperintensity of the paraspinal soft tissues atL2-3</td></tr><tr><td>Pt. 6</td><td>Multiple fluid collections from T10-L1Spinous process and neuroforamen at T10</td><td>Multiple fluid collections from T10-L1Bilateral pars defects at L5</td></tr></table>","table_caption":"[\"Table 1. Summary of abnormal paraspinal findings from [18F]FDG PET/MRI of 6 patients with suspected CSF leak. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[258,301,768,393]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0929/31fc5bc177b5e4796272d2b63eefad83238fdf80806cf676b6e106b6bf40fe0e.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":"<table><tr><td>Tissue type</td><td>Patients</td><td>Controls</td><td>P-values</td></tr><tr><td>Paraspinal muscle</td><td>2.26 ± 0.78</td><td>1.00 ± 0.48</td><td>0.0017</td></tr><tr><td>Interspinous ligament</td><td>2.44 ± 0.73</td><td>1.07 ± 0.25</td><td>0.000024</td></tr><tr><td>Osseous tissue</td><td>3.53 ± 1.37</td><td>0.98 ± 0.19</td><td>0.0018</td></tr><tr><td>Neuroforamen</td><td>2.50 ± 1.37</td><td>1.20 ± 0.23</td><td>0.033</td></tr><tr><td>Fluid collection</td><td>5.30 ± 0.96</td><td>1.10 ± 0.32</td><td>0.000028</td></tr></table>","table_caption":"[\"Table 2. $\\\\mathrm{SUV}_{\\\\mathrm{max}}$ (mean ± standard deviation) from detected lesions of the patient group and corresponding regions of the control group for different tissue types. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[255,476,931,618]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"remains unknown. While these two imaging modalities often are consistent in retrospective comparison $^{17}$ , this may reflect the common clinical scenario of using invasive CT myelography much more frequently in patients with positive MRI than in patients with negative MRI—attempting to localize the source of leak suggested by findings seen on the subset of positive MRI. In contrast, prospective studies of patients with orthostatic headaches suggest a potentially much lower sensitivity. In one study of 100 patients with orthostatic headaches suspected of having CSF leaks from a consortium of 11 hospitals in Japan, 70 had axial T2 spine MRI, finding 14 leaks, while 86 had MR myelograms, where only 3 leaks were noted $^{18}$ . For CT myelography, cases with slow or intermittent CSF leakage are very difficult to identify due to the insufficient contrast and resolution between CSF and background $^{19}$ . Previous studies estimate that $46 - 55\\%$ of these cases present no detectable signs of CSF leak on CT myelogram $^{20,21}$ . Thus, better non-invasive imaging techniques for detecting and localizing spinal CSF leaks are needed. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,618,931,696]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this report, we introduce the use of simultaneous [18F]fluorodeoxyglucose (FDG) positron emission tomography (PET)/MRI to locate CSF leaks. We hypothesized that [18F]FDG PET, if coupled with the high spatial and contrast resolution of MRI, could accurately identify inflammation around the sites of CSF leak due to its pro-inflammatory nature[22]. We recently presented initial findings from our study[23], and here we describe in detail our early experience of [18F]FDG PET/MRI of patients with chronic symptoms of suspected CSF leaks in comparison with healthy controls. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,708,319,721]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,722,931,812]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abnormal [18F]FDG PET/MRI findings. In all six patients, we observed sites of abnormally increased focal uptake of [18F]FDG in paraspinal structures at various levels of the spine (cervical, thoracic, and lumbar) as summarized in Table 1. However, only three patients showed MRI abnormalities (abnormal signal increase on T2-weighted contrast), which were in the same corresponding region of the PET abnormalities (Table 1). Abnormal [18F]FDG uptake was found on paraspinal muscles in 3 patients, interspinous ligament in 2 patients, osseous tissue in 3 patients, and fluid collection in one patient. Except one patient case, all other cases presented abnormalities at multiple spine levels. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,812,931,888]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The [18F]FDG $\\mathrm{SUV}_{\\mathrm{max}}$ in lesions from the patient group showed a higher mean value than the corresponding areas from the control group in all tissue types (Table 2). The $\\mathrm{SUV}_{\\mathrm{max}}$ of the abnormal lesions in the patient group ranged from 1.148 to 6.565 while the $\\mathrm{SUV}_{\\mathrm{max}}$ of the corresponding tissues in the controls ranged from 0.416 to 2.893. $P$ -values from the Mann-Whitney U-test comparing the $\\mathrm{SUV}_{\\mathrm{max}}$ between the patient and control groups were less than 0.05 in all tissue types, indicating a significant difference of the [18F]FDG uptake between the two groups. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,888,931,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figures 1, 2, 3, and 4 present different cases of abnormally increased [18F]FDG uptake in patients: in cervical paraspinal muscles (Fig. 1), at the level of the interspinous ligament in the lumbar spine (Figs. 2 and 3a), and in areas corresponding to fluid, neuroforamina, and osseous tissue (Fig. 4). The controls did not show areas of focally increased [18F]FDG uptake in these paraspinal regions as shown in an example case of Fig. 3b. Note that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,16,337,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2021) 11:15926 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,636,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-021-95056-w ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[922,965,929,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[258,63,559,242]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0585/eb9245a296d83766f750e1b340832e89701888529a2117c3a4f8654cc0393c87.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[564,62,867,242]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0687/98fb927ba35806d263339329f245b1798e3d41aef8100874f6b63f702cf76ffb.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[258,244,559,425]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0185/9c316d45bf5d2bbf8b089de6f4aae969b72b06c669a5893ca26416fc05833b06.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[564,244,865,424]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0437/c742b00a15348ea9ec5ca8f7ca881bb570fbc2523d926385f305950e88b1222a.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[258,425,559,606]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0568/a0c0943b707672b84b7f52659d24a4be24bca894cc636bb6852006b7ea114682.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[564,425,865,606]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 1. Increased [18F]FDG uptake in cervical paraspinal muscles of patient with suspected cerebrospinal fluid leak. Axial MRI at C6 (a) appears normal, while the corresponding axial PET/MRI (d) shows increased [18F]FDG uptake in paraspinal muscles (arrows, mean $\\\\mathrm{SUV}_{\\\\mathrm{max}} = 2.24$ ) of a CSF-leak patient presenting with head pain. The same pattern is also shown in coronal MRI (b) and PET/MRI (e). The corresponding coronal MRI and PET/MRI images from a healthy control subject is displayed in (c) and (f), respectively. No abnormal focal uptake of [18F]FDG as high as those in the patient case is observed in the asymptomatic subject (mean $\\\\mathrm{SUV}_{\\\\mathrm{max}} = 1.38$ ). \"]","image_footnote":"[]","img_path":"images/0582/14d59995c706243169e13fef0ce818435f21654a9d7d698cc76069eb24c5d695.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[255,746,931,787]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the cases in Figs. 1 and 3 show no abnormal MRI signal change, whereas in Fig. 2, increased signal was observed on MSDE-CUBE MRI images in the vicinity of interspinous ligament and paraspinal muscles with high [18F] FDG uptake. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,801,931,867]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Blood-patch treatment outcome. Epidural blood-patching was performed on multiple levels of the spine for three patients. Two patients underwent epidural blood-patching on the sites covering abnormalities identified by our PET/MRI study and reported temporary improvement in symptoms significantly greater than previous blood-patches (Table 3). However, the other patient whose blood-patch sites marginally included the PET/MRI abnormalities reported no symptomatic improvement. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,879,344,892]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Discussion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,893,931,932]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this report, we introduce a novel [18F]FDG PET/MRI approach for detecting the sites of CSF leak. While other nuclear medicine approaches such as radioisotope cisternography have been used to identify CSF leaks $^{24}$ , to our knowledge neither [18F]FDG PET nor simultaneous PET/MRI has been used for this purpose until now. In this ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,16,337,30]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2021) 11:15926 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,636,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-021-95056-w ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[919,965,931,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[258,63,458,255]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0255/d0858c065eb7d21c5242ae1d9c0931c1910bce390e48439c4a629f748dd3ffa6.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[463,62,665,255]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0939/2927efd5ec310964008f3f915c3010a4c254b720f8ecd00c5beaac299e3e3c6c.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[667,62,867,255]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0911/c6ec662db69f035f452442d1b59a3f49601a31da4268a322bc6a9d70f572a750.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[258,257,460,450]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0865/d2fd9d851818477a7f3a8969473637a45773448050e04e3891989d23b9d1e40f.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[463,257,665,450]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0740/96136dec4c739b58944c1fd6d61b44d32f73b044a2f82852f7d5f736ceaeeca5.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[667,257,867,450]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 2. [18F]FDG PET/MRI abnormalities at L4-5 at level of interspinous ligament of patient with suspected cerebrospinal fluid leak, not observed on conventional MRI. High resolution axial MSDE-UBE MRI (a) shows increased signal in the vicinity of the interspinous ligament and paraspinal muscles, which was not observed in the original conventional lumbar spine MRI the patient had recently before this PET/MRI. Axial [18F]FDG PET (b) and PET/MRI (c) shows increased radiotracer uptake posterior to the spinal canal in the region of the interspinous ligament (red arrow, $\\\\mathrm{SUV}_{\\\\mathrm{max}}3.25$ ). Sagittal reformats of the MSDE-CUBE MRI, PET, and PET/ MRI are shown in (d), (e), and (f), respectively to help appreciating the abnormally increased uptake in this level compared to those in other levels. \"]","image_footnote":"[]","img_path":"images/0604/1eb7df7295d5e8e381dcbaa586912580ca10bef4319772909e1f85c97a9d1a8c.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[255,604,931,668]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"study, all 6 patients presented significantly higher uptake values of [18F]FDG at various paraspinal structures than those of healthy controls $(P < 0.05)$ . On the other hand, abnormalities on MRI that might be related to CSF leak were identified in only half of the patients. In a limited number of patients followed for the treatment outcome, the patients whose blood-patch treatment sites covered the abnormalities identified by our method achieved better symptomatic relief than the patient whose treatment marginally included the identified abnormalities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,668,931,820]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The proposed approach for the improved detection of CSF leak is based on the observation that extradural CSF may irritate and inflame tissues outside of the nervous system[22]. This CSF-induced irritation is reflected clinically in studies of patients with chronic CSF leaks following accidental dural puncture, who report much higher rates of spinal pain at the site of CSF leak than controls without dural puncture[10,25]. Lesions with active inflammatory responses can have increased metabolism and energy requirements, becoming more glucose-avid than normal tissues[26]. [18F]FDG PET is a highly sensitive imaging modality of glucose metabolism, and has demonstrated its effectiveness in detection of such hypermetabolic inflammation[27-29]. Our results show abnormally increased uptake of [18F]FDG in the paraspinal region of all patients, supporting the feasibility of our approach for the detection of CSF leak. More abnormalities were found with [18F]FDG PET than 3T MRI, which suggests [18F]FDG PET might be better suited than MRI for the detection of early inflammatory changes due to CSF leak. However, our approach may not be feasible for detecting other etiologies without extradural CSF inflammation, such as CSF-venous fistular where CSF escapes the thecal sac directly into adjacent epidural veins. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,820,931,938]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Unlike the conventional imaging methods for CSF leak diagnosis, our [18F]FDG PET approach is to find the paraspinal tissues potentially affected by CSF leak rather than the tear or puncture through which the CSF leaks. Therefore, using [18F]FDG PET in conjunction with an imaging modality that enables the investigation of the anatomic cause of the leak can create a synergistic effect in accurately specifying the site(s) of CSF leak. MRI is more advantageous than CT for accompanying [18F]FDG PET in that it can provide detailed anatomic examination with no further deposition of ionizing radiation to sensitive areas. The simultaneous acquisition of PET and MRI employed in this study also offers improved image co-registration compared to the conventional PET/CT that sequentially acquires PET and CT, rendering it susceptible to mis-registration due to patient motion between the two scans. Our PET/MRI approach has the additional benefit of potentially discriminating a benign ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,16,337,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2021) 11:15926 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,636,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-021-95056-w ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[922,966,929,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[258,61,544,277]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0960/703f6684222443ebd0c1d88883bcfc3cbdc4b9528a6ff8658a1a804c7566b01d.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[546,61,833,277]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 3. Increased spinal uptake of [18]F-FDG in patient with suspected cerebrospinal fluid leak. Sagittal PET of patient with suspected CSF leak (a) shows areas of increased tracer uptake in the region of the interspinous ligament between L1 and L2 (red arrow, $\\\\mathrm{SUV}_{\\\\mathrm{max}} = 2.90$ ), in the region of the interspinous ligament between L2 and L3 (yellow arrow, $\\\\mathrm{SUV}_{\\\\mathrm{max}} = 2.14$ ), and in the area between the spinal cord and vertebral arch of the lower lumbar vertebrae (white arrows, $\\\\mathrm{SUV}_{\\\\mathrm{max}}$ at $L3 = 2.02$ , $\\\\mathrm{SUV}_{\\\\mathrm{max}}$ at $L4 = 2.22$ ). By comparison, sagittal PET of a healthy control (b) at the same level does not show increased uptake in these regions (Mean $\\\\mathrm{SUV}_{\\\\mathrm{max}}$ between L1 and $L2 = 1.23$ , between L2 and $L3 = 1.23$ , at $L3 = 0.98$ , at $L4 = 0.98$ for controls). This patient underwent paramedian interlaminar blood patching at L1-2 and L2-3, left transforaminal blood patching at L1-2 and L2-3, and right paramedian caudal fibrin blood patching following the PET/MRI study. The patient reported these patches made him feel better for a week, unlike previous patches that had provided no relief at all. \"]","image_footnote":"[]","img_path":"images/0000/db649d77e5feee6d6aca79be50e285dee767c1861a15c6bae5fc9d4964782012.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[258,462,546,667]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0702/76b3c430d2cad73d46443f237e5014c981fd0c5618138f58cbe69acc27fc3db9.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[546,462,833,667]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 4. PET/MRI showing abnormalities at the level T10, especially at the site of a right-sided laminotomy, in patient with suspected cerebrospinal fluid leak. Axial DESS MRI (a) at T10 level of Patient 6 shows right-sided laminotomy (white arrow) with fluid collection (red arrow). Increased [18F]FDG uptake (white arrow, $\\\\mathrm{SUV}_{\\\\mathrm{max}} = 4.6$ ) is visible on PET/MRI (b) in areas corresponding to osseous tissue and neuroforamina. In addition, focal fluid collection is observed around the spinous process, which also has increased [18F]FDG uptake (red arrow, $\\\\mathrm{SUV}_{\\\\mathrm{max}} = 2.6$ ). \"]","image_footnote":"[]","img_path":"images/0316/cd40b1feeb63352b3f3534fd3fbdfc57fe0c0a0b76a677435764cc50b62ee8c3.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[65,797,931,879]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/1003/516e3bf2649621352ea6cc52e3bf332ce921a9216be74fdcb6a338bcc694c87d.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":"<table><tr><td>Patient</td><td>Imaging/Treatment date (mm.dd.yy)</td><td>Treatment sites</td><td>PET/MRI findings and treatment sites incongruous?</td><td>Symptomatic relief after treatments</td></tr><tr><td>Pt.2</td><td>02.28.18/05.14.18</td><td>Left paramedian L1-3, Right paramedian caudal</td><td>Yes</td><td>Substantial for 1 week</td></tr><tr><td>Pt.4</td><td>03.28.18/06.04.18</td><td>Right T9-10, L2-3, Caudal</td><td>Yes</td><td>Substantial for 8-plus weeks</td></tr><tr><td>Pt.6</td><td>05.29.18/08.24.18</td><td>Bilateral L5-S1, Right paramedian L1-2</td><td>No</td><td>None</td></tr></table>","table_caption":"[\"Table 3. Blood patch treatment information and the treatment outcome. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[65,16,337,30]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2021) 11:15926 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,636,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-021-95056-w ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[921,966,929,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[260,61,931,138]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"post-operative seroma from an extraspinal collection of CSF. On MRI, they are difficult to differentiate because they are likely to appear isointense to each other. However, on [18F]FDG PET, the benign seroma is expected to have minimal or no [18F]FDG uptake, while the extraspinal CSF collection is significantly [18F]FDG avid, such as the one seen in Patient 6 (Fig. 4). Indeed, a study by Amini et al. $^{30}$ has demonstrated that seromas typically present a thin rim of mildly increased [18F]FDG uptake surrounding a central area of no [18F]FDG uptake in contrast to 'solid' or 'thick-walled' [18F]FDG avidity of more aggressive lesions such as soft tissue sarcomas. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,139,931,254]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Our study has a few limitations. More study subjects are needed to determine whether this [18F]FDG PET/ MRI approach is overall more sensitive and specific to CSF leaks than other imaging modalities. Uptake of [18F] FDG is relatively non-specific and can be seen in other paraspinal inflammatory processes such as myositis and in musculoskeletal degenerative changes such as Baastrup's disease[31,32]. Therefore, careful consideration of other etiologies should be considered when abnormal uptake of [18F]FDG is observed in the paraspinal regions. Our early results suggest it could be effective as an additional tool for locating the sites of CSF leak and target sites for epidural patching. Optimizing MRI sequences that can better complement [18F]FDG PET is also necessary to pinpoint the site of CSF leaks. Additionally, post-treatment scans in these same patients will be useful in determining whether a decrease in symptoms correlates with a decrease in [18F]FDG tracer uptake. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,267,347,280]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conclusion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[260,281,931,320]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Increased [18F]FDG uptake can be observed on PET in the paraspinal tissues of patients with suspected CSF leak. Our results suggest [18F]FDG PET/MRI is sensitive to abnormalities potentially due to suspected CSF leak, which are not necessarily visible on the standard-of-care diagnostic imaging modalities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,333,332,347]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[260,347,931,386]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Ethics statement. All experimental protocols in our prospective observational research were approved by the institutional review board (IRB) of the Research Compliance Office, Stanford University, U.S.A. (protocol number IRB-24972). All methods were conducted in accordance with relevant guidelines and regulations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,401,931,554]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Study participants. For the patient group, 4 male and 2 female patients suspected of suffering from CSF leaks were recruited (mean age $\\pm$ standard deviation: $36.2\\pm 8.9\\mathrm{y}$ ; age range: $25 - 54\\mathrm{y})$ . All patients presented with orthostatic headache and previously received standard-of-care imaging methods (including CT myelogram), which did not identify sources of CSF leak. The events identified by the patients as a precipitating event were epidural steroid injection (Patient 1 and 3), traumatic injury (Patient 4 and 5), lumbar puncture (Patient 6), and none (Patient 2). Six healthy controls (mean age $\\pm$ standard deviation: $28.5\\pm 3.3$ ; age range: $22 - 31\\mathrm{y})$ were also imaged with the same [18F]FDG PET/MRI protocol used for patients to compare the [18F]FDG uptake between the patient and control groups. Prior to imaging, all participants signed an informed consent form regarding study participation and publishing acquired data and images. All data were acquired in compliance with the Health Insurance Portability and Accountability Act. The clinical trial registration number of our study is NCT03195270 (registration date: 07/22/2017), and the name of the associated clinical trial registry is ClinicalTrials.gov. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,570,931,658]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Image acquisition. All subjects were requested to fast for 4 hours before our imaging study to avoid nonspecific elevation of the blood glucose level. One hour after a single 10-mCi injection of [18F]FDG, subjects were admitted to a SIGNA PET/MRI scanner (GE Healthcare, Waukesha, WI, U.S.) for imaging. We performed a whole-body PET/MRI scan of subjects, which consisted of 8 to 10 consecutive imaging stations. In each station, 4-8-min simultaneous PET/MRI scan was performed, making the total scan time to be 1 to $1.5\\mathrm{h}$ depending on the patient's height. Acquired PET and MRI raw data were reconstructed using the algorithms equipped in the scanner[33,34]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,659,931,787]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In each station, we conducted following two MRI sequences: 3D axial T1-weighted spoiled gradient-recalled echo sequence with two-point Dixon fat-water separation (TR: 4.6 ms, TE: 1.8 ms, resolution: $1.3 \\times 1.3 \\times 3.4 \\mathrm{~mm}$ , flip angle: $15^{\\circ}$ ) and 2D axial T2-weighted fast-spin-echo sequence with two-point Dixon fat-water separation (TR: 7.6 s TE: 93.3 ms, resolution: $1.5 \\times 1.5 \\times 4 \\mathrm{~mm}$ , echo train length: 15). For one or two imaging stations where we suspected CSF leaks might occur based on the patient's history, we additionally ran the following two sequences for high-resolution imaging: 3D axial double-echo-in-steady-state (DESS) with water-only excitation (TR: 18.7 ms, TE: 8.1 ms, resolution: $0.8 \\times 0.8 \\times 2 \\mathrm{~mm}$ , flip angle: $30^{\\circ}$ ) and 3D coronal motion-sensitized-driven-equilibrium (MSDE) fast-spin-echo sequence (CUBE) with triple-echo Dixon fat-water separation (TR: 2.5 s, TE: 71.8 ms, resolution: $1.4 \\times 1.4 \\times 1.4 \\mathrm{~mm}$ echo train length: 80). For MRI signal acquisition, a 16-channel head-neck coil, an integrated spine coil, and two 32-channel anterior body array coils were employed. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,801,931,918]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data analysis. Two radiologists reviewed patient PET and MRI images concurrently to find abnormalities that are likely to be related with patients' symptoms. Abnormal [18F]FDG hotspots were identified as potential lesions and the maximum standardized uptake value $(\\mathrm{SUV}_{\\mathrm{max}})$ of [18F]FDG was measured. We used image analysis software (Horos v.3.3.5, 64 bit) for measuring $\\mathrm{SUV}_{\\mathrm{max}}$ . The lesions on the PET images were categorized into 5 types: paraspinal muscle, interspinous ligament, osseous tissue, neuroforamina, and fluid collection. The $\\mathrm{SUV}_{\\mathrm{max}}$ measurements in each lesion type were compared with the $\\mathrm{SUV}_{\\mathrm{max}}$ of corresponding areas in the healthy controls using a two-sided Mann-Whitney U-test. We employed this nonparametric test because we could not assume the normality in the measurements from patients and the sample size was small. $P$ -value of 0.05 was adopted as a significance level. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[0,0,1000,33]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2021) 11:15926 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,636,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-021-95056-w ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[921,965,931,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[255,62,934,180]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Patient follow-up. After our imaging study, three patients received epidural blood-patch treatments based on the information from the standard-of-care diagnostic methods, without using our imaging findings. Patient 2 had targeted fibrin epidural patches while Patients 4 and 6 had targeted epidural blood patches. When a leak site has been identified, fibrin patches may resolve the symptoms of some patients with CSF leak refractory to epidural patching with blood<sup>35</sup>. The intervals between the imaging and the treatment of these patients were about 2.5 months, 2 months, and 3 months, respectively. We recorded the patient's qualitative evaluation on the symptomatic improvements (Yes/No) following the treatments in comparison with previous treatments, if possible. We compared the sites of the blood patches with the sites of PET/MRI abnormalities from our study to assess the relevance of detected abnormalities to the symptom based on the patient's post-treatment evaluation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,187,394,204]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data availability ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,204,932,255]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The datasets generated during and/or analyzed during the current study are not publicly available due to the fact we are (1) describing the off-label use of [18F]fluorodeoxyglucose and (2) the data is currently being utilized/analyzed for development of intellectual property, but are available from the corresponding author on reasonable request. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,267,574,281]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received: 29 September 2020; Accepted: 14 July 2021 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,281,455,292]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Published online: 05 August 2021 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[258,306,349,320]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[265,322,929,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1. 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Abnormal [18F]FDG PET/MRI findings in paraspinal structures of patients with suspected cerebrospinal fluid leak. Proc. Int., Soc. Mag. Res. Med. 60, 1148 (2020). \",\"24. Monteith, T. S., Kralik, S. F., Dillon, W. P., Hawkins, R. A. & Goadsby, P. J. The utility of radioisotope cisternography in low CSF/volume syndromes compared to myelography. Cephalalgia 36, 1291-1295. https://doi.org/10.1177/0333102416628467 (2016). \",\"25. Ranganathan, P. et al. Chronic headache and backache are long-term sequelae of unintentional dural puncture in the obstetric population. J. Clin. Anesth. 27, 201-206. https://doi.org/10.1016/j.jclinane.2014.07.008 (2015). \",\"26. Gaber, T., Strehl, C. & Buttgereit, F. Metabolic regulation of inflammation. Nat. Rev. Rheumatol. 13, 267-279. https://doi.org/10.1038/nrrrheum.2017.37 (2017). \"]","page_idx":"6","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[65,15,341,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2021) 11:15926 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,636,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-021-95056-w ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[922,965,929,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[260,61,931,269]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"27. Behera, D., Jacobs, K. E., Behera, S., Rosenberg, J. & Biswal, S. (18)F-FDG PET/MRI can be used to identify injured peripheral nerves in a model of neuropathic pain. J. Nucl. Med. 52, 1308-1312. https://doi.org/10.2967/jnumed.110.084731 (2011). \",\"28. Catalano, O. A. et al. An overview of PET/MR, focused on clinical applications. *Abdom. Radiol.* (NY) 42, 631-644. https://doi.org/10.1007/s00261-016-0894-5 (2017). \",\"29. Cipriano, P. W. et al. (18)F-FDG PET/MRI in chronic sciatica: Early results revealing spinal and nonspinal abnormalities. J. Nucl. Med. 59, 967-972. https://doi.org/10.2967/jnumed.117.198259 (2018). \",\"30. Amini, B. et al. Differentiation of benign fluid collections from soft-tissue sarcomas on FDG-PET/CT. J. Cancer 5, 328-335. https://doi.org/10.7150/jca.8310 (2014). \",\"31. Tateyama, M. et al. Clinical values of FDG PET in polymyositis and dermatomyositis syndromes: Imaging of skeletal muscle inflammation. BMJ Open 5, e006763. https://doi.org/10.1136/bmjopen-2014-006763 (2015). \",\"32. Subramanyam, P. & Palaniswamy, S. S. Role of FDG PET/CT in Baastrup's disease. Indian J. Nucl. Med. 31, 235-237. https://doi.org/10.4103/0972-3919.183604 (2016). \",\"33. Sekine, T. et al. Evaluation of atlas-based attenuation correction for integrated PET/MR in human brain: Application of a head atlas and comparison to true CT-based attenuation correction. J. Nucl. Med. 57, 215-220. https://doi.org/10.2967/jnumed.115.159228 (2016). \",\"34. Ahn, S. et al. Quantitative comparison of OSEM and penalized likelihood image reconstruction using relative difference penalties for clinical PET. Phys. Med. Biol. 60, 5733-5751. https://doi.org/10.1088/0031-9155/60/15/5733 (2015). \",\"35. Pagani-Estevez, G. L. et al. Procedural predictors of epidural blood patch efficacy in spontaneous intracranial hypotension. Reg. Anesth. Pain Med. https://doi.org/10.1136/rapm-2018-000021 (2019). \"]","page_idx":"7","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[258,278,421,294]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgements ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,294,931,320]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We would like to thank Dawn Holley and Harsh Gandhi, PET/MRI technologists, for their assistance in acquiring the images. We also thank General Electric Healthcare for the funding support. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,331,430,343]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Author contributions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,345,931,384]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conceptualization and Study design: I.R.C., S.B. Data Acquisitions: P.W.C., J.B.C., D.Y. Formal analysis and investigation: All authors. Initial drafting of the manuscript: P.W.C., D.Y. Reviewing/Editing: All authors. Funding acquisition: I.R.C., S.B. Supervision: I.R.C., S.B. All authors read and approved the manuscript. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,396,425,411]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Competing interests ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,411,931,437]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PWC, DY, and SB's work has been in part funded by research grant from GE Healthcare. IRC's work has been in part funded by the Considine CSF Leak fund. RP, JBC, and YX declare no potential conflict of interest. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,447,445,460]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Additional information ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,461,746,475]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Correspondence and requests for materials should be addressed to I.R.C. or S.B. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,480,747,494]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Reprints and permissions information is available at www.nature.com/reprints. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,500,931,525]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,531,332,554]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0280/d4e05ff53f5765e5911c06c605236a91b4107154795c25bb24ede393a58e48a8.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[334,531,931,554]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,557,931,635]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,647,391,659]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"© The Author(s) 2021 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,16,341,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2021) 11:15926 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,636,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-021-95056-w ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[921,965,929,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[154,166,238,189]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"OPEN \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,164,860,315]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abnormal [18F]FDG PET/MRI findings in paraspinal structures of patients with suspected cerebrospinal fluid leak \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,322,884,355]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Daehyun Yoon $^{1,5}$ , Peter William Cipriano $^{1,5}$ , Ryan Penticuff $^{2}$ , Jessa Ballesteros Castillo $^{1}$ , Yingding Xu $^{3}$ , Ian Richard Carroll $^{4\\\\boxtimes}$ & Sandip Biswal $^{1\\\\boxtimes}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,364,926,563]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A combination of magnetic resonance imaging (MRI), computed tomography (CT), and radionuclide cisternography are typically used to locate a cerebrospinal fluid (CSF) leak. However, the site of leakage cannot be determined, making treatment more difficult. Therefore, more sensitive imaging tools are needed. A whole-body [18F]fluorodeoxyglucose (FDG) positron emission tomography (PET)/ MRI was conducted on six patients with suspected CSF leak and the resulting images were reviewed in comparison with those from six healthy controls. Paraspinal regions of focally increased uptake of [18F]FDG were quantified using maximum standardized uptake values $(\\\\mathrm{SUV}_{\\\\max})$ and compared to the $\\\\mathrm{SUV}_{\\\\max}$ of corresponding regions in the healthy controls. All six patients with suspected CSF leak showed paraspinal regions of significantly greater [18F]FDG uptake compared to the corresponding areas in controls $(P < 0.05)$ . Two patients treated with local injections (epidural blood patches and/or epidural fibrin patches) on the site of abnormal PET/MRI findings reported temporary but significant improvement in symptoms. Our results suggest [18F]FDG PET/MRI is sensitive to abnormalities potentially due to suspected CSF leak, which are not necessarily visible on conventional MRI alone or by the standard-of-care imaging methods. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,586,931,805]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Cerebrospinal fluid (CSF) leak is a condition caused by drainage of CSF from the brain or the spinal cord through a hole in their surrounding structures, such as the skull and the dura. The prevalence rate of the CSF leak is estimated to be 1 in 50,000 individuals, but this relatively uncommon occurrence may be due to underdiagnosis<sup>1</sup>. The most characteristic symptom of a CSF leak is a persistent headache that worsens when upright and improves with recumbency (orthostatic headaches)<sup>2</sup>. When chronic, CSF leaks may present as \\\"second half of the day headache\\\" with patients consistently better in the morning after prolonged nocturnal recumbency followed by worsening symptoms as the day progresses with prolonged upright time<sup>3</sup>. Other symptoms include nausea, memory difficulties, cranial nerve dysfunction, neck and interscapular pain<sup>4,5</sup>. Hereditary disorders of connective tissue such as Marfan Syndrome, Ehlers-Danlos Syndrome, Neurofibromatosis type 1, and Polycystic kidney disease have been associated with spinal CSF leaks, suggesting these and other associated disorders of connective tissue may lead to abnormally vulnerable dura prone to CSF leak<sup>6</sup>. Among those who can identify a precipitating event, atraumatic activities such as stretching, or Valsalva maneuver are commonly involved<sup>7-9</sup>. Traumatic head/neck injury such as whiplash as well as iatrogenic dural tear during surgical interventions including lumbar puncture, duromy, and skull base surgery are also important causes<sup>10-12</sup>. However, two thirds of patients with a spontaneous CSF leak can identify no precipitating events. The most common site of leak is along the spinal cord<sup>13</sup>. If the site of CSF leak is located, it is treated most commonly with an epidural injection of autologous blood (epidural blood patch) or an epidural fibrin patch, or surgery, depending on the case<sup>14</sup>. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,805,931,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Unfortunately, no one diagnostic test can consistently exclude the diagnosis of CSF leak or identify the site(s) of leakage<sup>15</sup>. Misdiagnosis is common, preventing proper treatment as the symptoms are often mistaken for those of other diseases, such as postural orthostatic tachycardia syndrome or new daily persistent headache<sup>14,16</sup>. The underlying sensitivity of magnetic resonance imaging (MRI) and computed tomography (CT) myelography \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,878,931,943]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{1}$ Department of Radiology, Stanford University, 300 Pasteur Drive, Stanford, CA 94305, USA. $^{2}$ Department of Radiology, UC San Diego School of Medicine, La Jolla, CA, USA. $^{3}$ Newport Harbor Radiology Associates, Irvine, CA, USA. $^{4}$ Department of Anesthesia Perioperative and Pain Medicine, Stanford University, 300 Pasteur Drive, Stanford, CA 94305, USA. $^{5}$ These authors contributed equally: Daehyun Yoon and Peter William Cipriano. $^{\\\\text{串}}$ email: ic38@stanford.edu; biswal@stanford.edu \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[652,14,922,30]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[63,63,452,104]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"scientific reports \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[811,136,831,154]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"# \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[836,140,927,150]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Check for updates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,285,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports| (2021) 11:15926 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[376,965,636,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"| https://doi.org/10.1038/s41598-021-95056-w \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[919,966,931,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[258,62,931,227]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0216/39b301178c9b37007b701a0bcbf1636ae92526e045364965df5782080673bd05.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Patient</td><td>Sites of increased [18F]FDG uptake</td><td>MRI abnormalities</td></tr><tr><td>Pt. 1</td><td>Interspinous ligaments from L4-5</td><td>T2 hyperintensity of paraspinal muscles and interspinous liga-ment at L4-5</td></tr><tr><td>Pt. 2</td><td>Interspinous ligaments from L1-5</td><td>None</td></tr><tr><td>Pt. 3</td><td>Intra/extrathecal space extending into neuroforamina at C2Paraspinal muscles at C6 (bilateral), T6-7 (right), T8 (right)</td><td>None</td></tr><tr><td>Pt. 4</td><td>Interspinous ligaments from L2-3Left neuroforamina from L3-4Right neuroforamina/facet joints from L4-5</td><td>None</td></tr><tr><td>Pt. 5</td><td>Interspinous ligaments, paraspinal muscles, and spinousprocesses from L2-3</td><td>Large focal T2 hyperintensity of the paraspinal soft tissues atL2-3</td></tr><tr><td>Pt. 6</td><td>Multiple fluid collections from T10-L1Spinous process and neuroforamen at T10</td><td>Multiple fluid collections from T10-L1Bilateral pars defects at L5</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. Summary of abnormal paraspinal findings from [18F]FDG PET/MRI of 6 patients with suspected CSF leak. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[258,301,768,393]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0929/31fc5bc177b5e4796272d2b63eefad83238fdf80806cf676b6e106b6bf40fe0e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Tissue type</td><td>Patients</td><td>Controls</td><td>P-values</td></tr><tr><td>Paraspinal muscle</td><td>2.26 ± 0.78</td><td>1.00 ± 0.48</td><td>0.0017</td></tr><tr><td>Interspinous ligament</td><td>2.44 ± 0.73</td><td>1.07 ± 0.25</td><td>0.000024</td></tr><tr><td>Osseous tissue</td><td>3.53 ± 1.37</td><td>0.98 ± 0.19</td><td>0.0018</td></tr><tr><td>Neuroforamen</td><td>2.50 ± 1.37</td><td>1.20 ± 0.23</td><td>0.033</td></tr><tr><td>Fluid collection</td><td>5.30 ± 0.96</td><td>1.10 ± 0.32</td><td>0.000028</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2. $\\\\\\\\mathrm{SUV}_{\\\\\\\\mathrm{max}}$ (mean ± standard deviation) from detected lesions of the patient group and corresponding regions of the control group for different tissue types. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[255,476,931,618]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"remains unknown. While these two imaging modalities often are consistent in retrospective comparison $^{17}$ , this may reflect the common clinical scenario of using invasive CT myelography much more frequently in patients with positive MRI than in patients with negative MRI—attempting to localize the source of leak suggested by findings seen on the subset of positive MRI. In contrast, prospective studies of patients with orthostatic headaches suggest a potentially much lower sensitivity. In one study of 100 patients with orthostatic headaches suspected of having CSF leaks from a consortium of 11 hospitals in Japan, 70 had axial T2 spine MRI, finding 14 leaks, while 86 had MR myelograms, where only 3 leaks were noted $^{18}$ . For CT myelography, cases with slow or intermittent CSF leakage are very difficult to identify due to the insufficient contrast and resolution between CSF and background $^{19}$ . Previous studies estimate that $46 - 55\\\\%$ of these cases present no detectable signs of CSF leak on CT myelogram $^{20,21}$ . Thus, better non-invasive imaging techniques for detecting and localizing spinal CSF leaks are needed. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,618,931,696]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this report, we introduce the use of simultaneous [18F]fluorodeoxyglucose (FDG) positron emission tomography (PET)/MRI to locate CSF leaks. We hypothesized that [18F]FDG PET, if coupled with the high spatial and contrast resolution of MRI, could accurately identify inflammation around the sites of CSF leak due to its pro-inflammatory nature[22]. We recently presented initial findings from our study[23], and here we describe in detail our early experience of [18F]FDG PET/MRI of patients with chronic symptoms of suspected CSF leaks in comparison with healthy controls. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,708,319,721]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,722,931,812]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abnormal [18F]FDG PET/MRI findings. In all six patients, we observed sites of abnormally increased focal uptake of [18F]FDG in paraspinal structures at various levels of the spine (cervical, thoracic, and lumbar) as summarized in Table 1. However, only three patients showed MRI abnormalities (abnormal signal increase on T2-weighted contrast), which were in the same corresponding region of the PET abnormalities (Table 1). Abnormal [18F]FDG uptake was found on paraspinal muscles in 3 patients, interspinous ligament in 2 patients, osseous tissue in 3 patients, and fluid collection in one patient. Except one patient case, all other cases presented abnormalities at multiple spine levels. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,812,931,888]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The [18F]FDG $\\\\mathrm{SUV}_{\\\\mathrm{max}}$ in lesions from the patient group showed a higher mean value than the corresponding areas from the control group in all tissue types (Table 2). The $\\\\mathrm{SUV}_{\\\\mathrm{max}}$ of the abnormal lesions in the patient group ranged from 1.148 to 6.565 while the $\\\\mathrm{SUV}_{\\\\mathrm{max}}$ of the corresponding tissues in the controls ranged from 0.416 to 2.893. $P$ -values from the Mann-Whitney U-test comparing the $\\\\mathrm{SUV}_{\\\\mathrm{max}}$ between the patient and control groups were less than 0.05 in all tissue types, indicating a significant difference of the [18F]FDG uptake between the two groups. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,888,931,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figures 1, 2, 3, and 4 present different cases of abnormally increased [18F]FDG uptake in patients: in cervical paraspinal muscles (Fig. 1), at the level of the interspinous ligament in the lumbar spine (Figs. 2 and 3a), and in areas corresponding to fluid, neuroforamina, and osseous tissue (Fig. 4). The controls did not show areas of focally increased [18F]FDG uptake in these paraspinal regions as shown in an example case of Fig. 3b. Note that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,16,337,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2021) 11:15926 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,636,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-021-95056-w \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[922,965,929,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[258,63,559,242]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0585/eb9245a296d83766f750e1b340832e89701888529a2117c3a4f8654cc0393c87.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[564,62,867,242]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0687/98fb927ba35806d263339329f245b1798e3d41aef8100874f6b63f702cf76ffb.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[258,244,559,425]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0185/9c316d45bf5d2bbf8b089de6f4aae969b72b06c669a5893ca26416fc05833b06.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[564,244,865,424]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0437/c742b00a15348ea9ec5ca8f7ca881bb570fbc2523d926385f305950e88b1222a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[258,425,559,606]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0568/a0c0943b707672b84b7f52659d24a4be24bca894cc636bb6852006b7ea114682.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[564,425,865,606]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 1. Increased [18F]FDG uptake in cervical paraspinal muscles of patient with suspected cerebrospinal fluid leak. Axial MRI at C6 (a) appears normal, while the corresponding axial PET/MRI (d) shows increased [18F]FDG uptake in paraspinal muscles (arrows, mean $\\\\\\\\mathrm{SUV}_{\\\\\\\\mathrm{max}} = 2.24$ ) of a CSF-leak patient presenting with head pain. The same pattern is also shown in coronal MRI (b) and PET/MRI (e). The corresponding coronal MRI and PET/MRI images from a healthy control subject is displayed in (c) and (f), respectively. No abnormal focal uptake of [18F]FDG as high as those in the patient case is observed in the asymptomatic subject (mean $\\\\\\\\mathrm{SUV}_{\\\\\\\\mathrm{max}} = 1.38$ ). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0582/14d59995c706243169e13fef0ce818435f21654a9d7d698cc76069eb24c5d695.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[255,746,931,787]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the cases in Figs. 1 and 3 show no abnormal MRI signal change, whereas in Fig. 2, increased signal was observed on MSDE-CUBE MRI images in the vicinity of interspinous ligament and paraspinal muscles with high [18F] FDG uptake. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,801,931,867]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Blood-patch treatment outcome. Epidural blood-patching was performed on multiple levels of the spine for three patients. Two patients underwent epidural blood-patching on the sites covering abnormalities identified by our PET/MRI study and reported temporary improvement in symptoms significantly greater than previous blood-patches (Table 3). However, the other patient whose blood-patch sites marginally included the PET/MRI abnormalities reported no symptomatic improvement. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,879,344,892]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,893,931,932]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this report, we introduce a novel [18F]FDG PET/MRI approach for detecting the sites of CSF leak. While other nuclear medicine approaches such as radioisotope cisternography have been used to identify CSF leaks $^{24}$ , to our knowledge neither [18F]FDG PET nor simultaneous PET/MRI has been used for this purpose until now. In this \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,16,337,30]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2021) 11:15926 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,636,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-021-95056-w \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[919,965,931,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[258,63,458,255]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0255/d0858c065eb7d21c5242ae1d9c0931c1910bce390e48439c4a629f748dd3ffa6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[463,62,665,255]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0939/2927efd5ec310964008f3f915c3010a4c254b720f8ecd00c5beaac299e3e3c6c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[667,62,867,255]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0911/c6ec662db69f035f452442d1b59a3f49601a31da4268a322bc6a9d70f572a750.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[258,257,460,450]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0865/d2fd9d851818477a7f3a8969473637a45773448050e04e3891989d23b9d1e40f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[463,257,665,450]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0740/96136dec4c739b58944c1fd6d61b44d32f73b044a2f82852f7d5f736ceaeeca5.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[667,257,867,450]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 2. [18F]FDG PET/MRI abnormalities at L4-5 at level of interspinous ligament of patient with suspected cerebrospinal fluid leak, not observed on conventional MRI. High resolution axial MSDE-UBE MRI (a) shows increased signal in the vicinity of the interspinous ligament and paraspinal muscles, which was not observed in the original conventional lumbar spine MRI the patient had recently before this PET/MRI. Axial [18F]FDG PET (b) and PET/MRI (c) shows increased radiotracer uptake posterior to the spinal canal in the region of the interspinous ligament (red arrow, $\\\\\\\\mathrm{SUV}_{\\\\\\\\mathrm{max}}3.25$ ). Sagittal reformats of the MSDE-CUBE MRI, PET, and PET/ MRI are shown in (d), (e), and (f), respectively to help appreciating the abnormally increased uptake in this level compared to those in other levels. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0604/1eb7df7295d5e8e381dcbaa586912580ca10bef4319772909e1f85c97a9d1a8c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[255,604,931,668]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"study, all 6 patients presented significantly higher uptake values of [18F]FDG at various paraspinal structures than those of healthy controls $(P < 0.05)$ . On the other hand, abnormalities on MRI that might be related to CSF leak were identified in only half of the patients. In a limited number of patients followed for the treatment outcome, the patients whose blood-patch treatment sites covered the abnormalities identified by our method achieved better symptomatic relief than the patient whose treatment marginally included the identified abnormalities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,668,931,820]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The proposed approach for the improved detection of CSF leak is based on the observation that extradural CSF may irritate and inflame tissues outside of the nervous system[22]. This CSF-induced irritation is reflected clinically in studies of patients with chronic CSF leaks following accidental dural puncture, who report much higher rates of spinal pain at the site of CSF leak than controls without dural puncture[10,25]. Lesions with active inflammatory responses can have increased metabolism and energy requirements, becoming more glucose-avid than normal tissues[26]. [18F]FDG PET is a highly sensitive imaging modality of glucose metabolism, and has demonstrated its effectiveness in detection of such hypermetabolic inflammation[27-29]. Our results show abnormally increased uptake of [18F]FDG in the paraspinal region of all patients, supporting the feasibility of our approach for the detection of CSF leak. More abnormalities were found with [18F]FDG PET than 3T MRI, which suggests [18F]FDG PET might be better suited than MRI for the detection of early inflammatory changes due to CSF leak. However, our approach may not be feasible for detecting other etiologies without extradural CSF inflammation, such as CSF-venous fistular where CSF escapes the thecal sac directly into adjacent epidural veins. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,820,931,938]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Unlike the conventional imaging methods for CSF leak diagnosis, our [18F]FDG PET approach is to find the paraspinal tissues potentially affected by CSF leak rather than the tear or puncture through which the CSF leaks. Therefore, using [18F]FDG PET in conjunction with an imaging modality that enables the investigation of the anatomic cause of the leak can create a synergistic effect in accurately specifying the site(s) of CSF leak. MRI is more advantageous than CT for accompanying [18F]FDG PET in that it can provide detailed anatomic examination with no further deposition of ionizing radiation to sensitive areas. The simultaneous acquisition of PET and MRI employed in this study also offers improved image co-registration compared to the conventional PET/CT that sequentially acquires PET and CT, rendering it susceptible to mis-registration due to patient motion between the two scans. Our PET/MRI approach has the additional benefit of potentially discriminating a benign \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,16,337,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2021) 11:15926 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,636,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-021-95056-w \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[922,966,929,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[258,61,544,277]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0960/703f6684222443ebd0c1d88883bcfc3cbdc4b9528a6ff8658a1a804c7566b01d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[546,61,833,277]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 3. Increased spinal uptake of [18]F-FDG in patient with suspected cerebrospinal fluid leak. Sagittal PET of patient with suspected CSF leak (a) shows areas of increased tracer uptake in the region of the interspinous ligament between L1 and L2 (red arrow, $\\\\\\\\mathrm{SUV}_{\\\\\\\\mathrm{max}} = 2.90$ ), in the region of the interspinous ligament between L2 and L3 (yellow arrow, $\\\\\\\\mathrm{SUV}_{\\\\\\\\mathrm{max}} = 2.14$ ), and in the area between the spinal cord and vertebral arch of the lower lumbar vertebrae (white arrows, $\\\\\\\\mathrm{SUV}_{\\\\\\\\mathrm{max}}$ at $L3 = 2.02$ , $\\\\\\\\mathrm{SUV}_{\\\\\\\\mathrm{max}}$ at $L4 = 2.22$ ). By comparison, sagittal PET of a healthy control (b) at the same level does not show increased uptake in these regions (Mean $\\\\\\\\mathrm{SUV}_{\\\\\\\\mathrm{max}}$ between L1 and $L2 = 1.23$ , between L2 and $L3 = 1.23$ , at $L3 = 0.98$ , at $L4 = 0.98$ for controls). This patient underwent paramedian interlaminar blood patching at L1-2 and L2-3, left transforaminal blood patching at L1-2 and L2-3, and right paramedian caudal fibrin blood patching following the PET/MRI study. The patient reported these patches made him feel better for a week, unlike previous patches that had provided no relief at all. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0000/db649d77e5feee6d6aca79be50e285dee767c1861a15c6bae5fc9d4964782012.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[258,462,546,667]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0702/76b3c430d2cad73d46443f237e5014c981fd0c5618138f58cbe69acc27fc3db9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[546,462,833,667]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 4. PET/MRI showing abnormalities at the level T10, especially at the site of a right-sided laminotomy, in patient with suspected cerebrospinal fluid leak. Axial DESS MRI (a) at T10 level of Patient 6 shows right-sided laminotomy (white arrow) with fluid collection (red arrow). Increased [18F]FDG uptake (white arrow, $\\\\\\\\mathrm{SUV}_{\\\\\\\\mathrm{max}} = 4.6$ ) is visible on PET/MRI (b) in areas corresponding to osseous tissue and neuroforamina. In addition, focal fluid collection is observed around the spinous process, which also has increased [18F]FDG uptake (red arrow, $\\\\\\\\mathrm{SUV}_{\\\\\\\\mathrm{max}} = 2.6$ ). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0316/cd40b1feeb63352b3f3534fd3fbdfc57fe0c0a0b76a677435764cc50b62ee8c3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[65,797,931,879]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/1003/516e3bf2649621352ea6cc52e3bf332ce921a9216be74fdcb6a338bcc694c87d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Patient</td><td>Imaging/Treatment date (mm.dd.yy)</td><td>Treatment sites</td><td>PET/MRI findings and treatment sites incongruous?</td><td>Symptomatic relief after treatments</td></tr><tr><td>Pt.2</td><td>02.28.18/05.14.18</td><td>Left paramedian L1-3, Right paramedian caudal</td><td>Yes</td><td>Substantial for 1 week</td></tr><tr><td>Pt.4</td><td>03.28.18/06.04.18</td><td>Right T9-10, L2-3, Caudal</td><td>Yes</td><td>Substantial for 8-plus weeks</td></tr><tr><td>Pt.6</td><td>05.29.18/08.24.18</td><td>Bilateral L5-S1, Right paramedian L1-2</td><td>No</td><td>None</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 3. Blood patch treatment information and the treatment outcome. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[65,16,337,30]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2021) 11:15926 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,636,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-021-95056-w \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[921,966,929,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[260,61,931,138]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"post-operative seroma from an extraspinal collection of CSF. On MRI, they are difficult to differentiate because they are likely to appear isointense to each other. However, on [18F]FDG PET, the benign seroma is expected to have minimal or no [18F]FDG uptake, while the extraspinal CSF collection is significantly [18F]FDG avid, such as the one seen in Patient 6 (Fig. 4). Indeed, a study by Amini et al. $^{30}$ has demonstrated that seromas typically present a thin rim of mildly increased [18F]FDG uptake surrounding a central area of no [18F]FDG uptake in contrast to 'solid' or 'thick-walled' [18F]FDG avidity of more aggressive lesions such as soft tissue sarcomas. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,139,931,254]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Our study has a few limitations. More study subjects are needed to determine whether this [18F]FDG PET/ MRI approach is overall more sensitive and specific to CSF leaks than other imaging modalities. Uptake of [18F] FDG is relatively non-specific and can be seen in other paraspinal inflammatory processes such as myositis and in musculoskeletal degenerative changes such as Baastrup's disease[31,32]. Therefore, careful consideration of other etiologies should be considered when abnormal uptake of [18F]FDG is observed in the paraspinal regions. Our early results suggest it could be effective as an additional tool for locating the sites of CSF leak and target sites for epidural patching. Optimizing MRI sequences that can better complement [18F]FDG PET is also necessary to pinpoint the site of CSF leaks. Additionally, post-treatment scans in these same patients will be useful in determining whether a decrease in symptoms correlates with a decrease in [18F]FDG tracer uptake. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,267,347,280]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conclusion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,281,931,320]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Increased [18F]FDG uptake can be observed on PET in the paraspinal tissues of patients with suspected CSF leak. Our results suggest [18F]FDG PET/MRI is sensitive to abnormalities potentially due to suspected CSF leak, which are not necessarily visible on the standard-of-care diagnostic imaging modalities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,333,332,347]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,347,931,386]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Ethics statement. All experimental protocols in our prospective observational research were approved by the institutional review board (IRB) of the Research Compliance Office, Stanford University, U.S.A. (protocol number IRB-24972). All methods were conducted in accordance with relevant guidelines and regulations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,401,931,554]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Study participants. For the patient group, 4 male and 2 female patients suspected of suffering from CSF leaks were recruited (mean age $\\\\pm$ standard deviation: $36.2\\\\pm 8.9\\\\mathrm{y}$ ; age range: $25 - 54\\\\mathrm{y})$ . All patients presented with orthostatic headache and previously received standard-of-care imaging methods (including CT myelogram), which did not identify sources of CSF leak. The events identified by the patients as a precipitating event were epidural steroid injection (Patient 1 and 3), traumatic injury (Patient 4 and 5), lumbar puncture (Patient 6), and none (Patient 2). Six healthy controls (mean age $\\\\pm$ standard deviation: $28.5\\\\pm 3.3$ ; age range: $22 - 31\\\\mathrm{y})$ were also imaged with the same [18F]FDG PET/MRI protocol used for patients to compare the [18F]FDG uptake between the patient and control groups. Prior to imaging, all participants signed an informed consent form regarding study participation and publishing acquired data and images. All data were acquired in compliance with the Health Insurance Portability and Accountability Act. The clinical trial registration number of our study is NCT03195270 (registration date: 07/22/2017), and the name of the associated clinical trial registry is ClinicalTrials.gov. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,570,931,658]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Image acquisition. All subjects were requested to fast for 4 hours before our imaging study to avoid nonspecific elevation of the blood glucose level. One hour after a single 10-mCi injection of [18F]FDG, subjects were admitted to a SIGNA PET/MRI scanner (GE Healthcare, Waukesha, WI, U.S.) for imaging. We performed a whole-body PET/MRI scan of subjects, which consisted of 8 to 10 consecutive imaging stations. In each station, 4-8-min simultaneous PET/MRI scan was performed, making the total scan time to be 1 to $1.5\\\\mathrm{h}$ depending on the patient's height. Acquired PET and MRI raw data were reconstructed using the algorithms equipped in the scanner[33,34]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,659,931,787]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In each station, we conducted following two MRI sequences: 3D axial T1-weighted spoiled gradient-recalled echo sequence with two-point Dixon fat-water separation (TR: 4.6 ms, TE: 1.8 ms, resolution: $1.3 \\\\times 1.3 \\\\times 3.4 \\\\mathrm{~mm}$ , flip angle: $15^{\\\\circ}$ ) and 2D axial T2-weighted fast-spin-echo sequence with two-point Dixon fat-water separation (TR: 7.6 s TE: 93.3 ms, resolution: $1.5 \\\\times 1.5 \\\\times 4 \\\\mathrm{~mm}$ , echo train length: 15). For one or two imaging stations where we suspected CSF leaks might occur based on the patient's history, we additionally ran the following two sequences for high-resolution imaging: 3D axial double-echo-in-steady-state (DESS) with water-only excitation (TR: 18.7 ms, TE: 8.1 ms, resolution: $0.8 \\\\times 0.8 \\\\times 2 \\\\mathrm{~mm}$ , flip angle: $30^{\\\\circ}$ ) and 3D coronal motion-sensitized-driven-equilibrium (MSDE) fast-spin-echo sequence (CUBE) with triple-echo Dixon fat-water separation (TR: 2.5 s, TE: 71.8 ms, resolution: $1.4 \\\\times 1.4 \\\\times 1.4 \\\\mathrm{~mm}$ echo train length: 80). For MRI signal acquisition, a 16-channel head-neck coil, an integrated spine coil, and two 32-channel anterior body array coils were employed. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,801,931,918]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data analysis. Two radiologists reviewed patient PET and MRI images concurrently to find abnormalities that are likely to be related with patients' symptoms. Abnormal [18F]FDG hotspots were identified as potential lesions and the maximum standardized uptake value $(\\\\mathrm{SUV}_{\\\\mathrm{max}})$ of [18F]FDG was measured. We used image analysis software (Horos v.3.3.5, 64 bit) for measuring $\\\\mathrm{SUV}_{\\\\mathrm{max}}$ . The lesions on the PET images were categorized into 5 types: paraspinal muscle, interspinous ligament, osseous tissue, neuroforamina, and fluid collection. The $\\\\mathrm{SUV}_{\\\\mathrm{max}}$ measurements in each lesion type were compared with the $\\\\mathrm{SUV}_{\\\\mathrm{max}}$ of corresponding areas in the healthy controls using a two-sided Mann-Whitney U-test. We employed this nonparametric test because we could not assume the normality in the measurements from patients and the sample size was small. $P$ -value of 0.05 was adopted as a significance level. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[0,0,1000,33]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2021) 11:15926 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,636,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-021-95056-w \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[921,965,931,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[255,62,934,180]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Patient follow-up. After our imaging study, three patients received epidural blood-patch treatments based on the information from the standard-of-care diagnostic methods, without using our imaging findings. Patient 2 had targeted fibrin epidural patches while Patients 4 and 6 had targeted epidural blood patches. When a leak site has been identified, fibrin patches may resolve the symptoms of some patients with CSF leak refractory to epidural patching with blood<sup>35</sup>. The intervals between the imaging and the treatment of these patients were about 2.5 months, 2 months, and 3 months, respectively. We recorded the patient's qualitative evaluation on the symptomatic improvements (Yes/No) following the treatments in comparison with previous treatments, if possible. We compared the sites of the blood patches with the sites of PET/MRI abnormalities from our study to assess the relevance of detected abnormalities to the symptom based on the patient's post-treatment evaluation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,187,394,204]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data availability \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,204,932,255]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The datasets generated during and/or analyzed during the current study are not publicly available due to the fact we are (1) describing the off-label use of [18F]fluorodeoxyglucose and (2) the data is currently being utilized/analyzed for development of intellectual property, but are available from the corresponding author on reasonable request. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,267,574,281]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received: 29 September 2020; Accepted: 14 July 2021 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,281,455,292]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Published online: 05 August 2021 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[258,306,349,320]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[265,322,929,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1. Schievink, W. I., Maya, M. M., Moser, F., Tourje, J. & Torbati, S. Frequency of spontaneous intracranial hypotension in the emergency department. J. Headache Pain 8, 325-328. https://doi.org/10.1007/s10194-007-0421-8 (2007). \\\",\\\"2. Schievink, W. I. Spontaneous spinal cerebrospinal fluid leaks and intracranial hypotension. JAMA 295, 2286-2296. https://doi.org/10.1001/jama.295.19.2286 (2006). \\\",\\\"3. Hunderfund, A. N. L. & Mokri, B. Second-half-of-the-day headache as a manifestation of spontaneous CSF leak. J. Neurol. 259, 306-310. https://doi.org/10.1007/s00415-011-6181-z (2012). \\\",\\\"4. Schievink, W. I. Spontaneous spinal cerebrospinal fluid leaks: A review. Neurosurg. Focus 9, e8. https://doi.org/10.3171/foc.2000.9.1.8 (2000). \\\",\\\"5. Mokri, B. Spontaneous intracranial hypotension. Contin. (Minneap. Minn.) 21, 1086-1108. https://doi.org/10.1212/CON.00000 00000000193 (2015). \\\",\\\"6. Schievink, W. I., Gordon, O. K. & Tourje, J. Connective tissue disorders with spontaneous spinal cerebrospinal fluid leaks and intracranial hypotension: a prospective study. Neurosurgery 54, 65-70; discussion 70-61. https://doi.org/10.1227/01.neu.0000097200.18478.7b (2004). \\\",\\\"7. Schievink, W. I. & Louy, C. Precipitating factors of spontaneous spinal CSF leaks and intracranial hypotension. *Neurology* 69, 700-702. https://doi.org/10.1212/01.wnl.0000267324.68013.8e (2007). \\\",\\\"8. Hashizume, K., Watanabe, K., Kawaguchi, M., Fujiwara, A. & Furuya, H. Comparison between computed tomography-myelography and radioisotope-cisternography findings in whiplash-associated disorders suspected to be caused by traumatic cerebrospinal fluid leak. Spine (Phila Pa 1976) 37, E721-E726. https://doi.org/10.1097/BRS.0b013e31824ae5d1 (2012). \\\",\\\"9. Ishikawa, S. et al. Epidural blood patch therapy for chronic whiplash-associated disorder. Anesth. Analg. 105, 809-814. https://doi.org/10.1213/01.ane.0000271922.04981.33 (2007). \\\",\\\"0. Webb, C. A. et al. Unintentional dural puncture with a Tuohy needle increases risk of chronic headache. Anesth. Analg. 115, 124-132. https://doi.org/10.1213/ANE.0b013e3182501c06 (2012). \\\",\\\"1. Floccari, L. V., Larson, A. N., Stans, A. A., Fogelson, J. & Helenius, I. Delayed dural leak following posterior spinal fusion for idiopathic scoliosis using all posterior pedicle screw technique. J. Pediatr. Orthop. 37, e415-e420. https://doi.org/10.1097/BPO.0000000000001008 (2017). \\\",\\\"2. Jeskins, G. D., Moore, P. A., Cooper, G. M. & Lewis, M. Long-term morbidity following dural puncture in an obstetric population. Int. J. Obstet. Anesth. 10, 17-24. https://doi.org/10.1054/jjoa.2000.0812 (2001). \\\",\\\"3. Cohen-Gadol, A. A., Mokri, B., Piepgras, D. G., Meyer, F. B. & Atkinson, J. L. Surgical anatomy of dural defects in spontaneous spinal cerebrospinal fluid leaks. Neurosurgery 58, ONS-238-245; discussion ONS-245. https://doi.org/10.1227/01.NEU.0000204712.16099.FB (2006). \\\",\\\"4. Mokri, B. Spontaneous low pressure, low CSF volume headaches: Spontaneous CSF leaks. Headache 53, 1034-1053. https://doi.org/10.1111/head.12149 (2013). \\\",\\\"5. Kranz, P. G., Malinzak, M. D., Amrhein, T. J. & Gray, L. Update on the diagnosis and treatment of spontaneous intracranial hypotension. Curr. Pain Headache Rep. 21, 37. https://doi.org/10.1007/s11916-017-0639-3 (2017). \\\",\\\"6. Schievink, W. I. Misdiagnosis of spontaneous intracranial hypotension. Arch. Neurol. 60, 1713-1718. https://doi.org/10.1001/archneur.60.12.1713 (2003). \\\",\\\"7. Starling, A. et al. Sensitivity of MRI of the spine compared with CT myelography in orthostatic headache with CSF leak. Neurology 81, 1789-1792. https://doi.org/10.1212/01.wnl.0000435555.13695.22 (2013). \\\",\\\"8. Hosoya, T. et al. Floating dural sac sign is a sensitive magnetic resonance imaging finding of spinal cerebrospinal fluid leakage. Neurol. Med. Chir. (Tokyo) 53, 207-212. https://doi.org/10.2176/nmc.53.207 (2013). \\\",\\\"9. Kranz, P. G. et al. Myelographic techniques for the detection of spinal CSF leaks in spontaneous intracranial hypotension. AJR Am. J. Roentgenol. 206, 8-19. https://doi.org/10.2214/AJR.15.14884 (2016). \\\",\\\"20. Sencakova, D., Mokri, B. & McClelland, R. L. The efficacy of epidural blood patch in spontaneous CSF leaks. *Neurology* 57, 1921-1923. https://doi.org/10.1212/wnl.57.10.1921 (2001). \\\",\\\"21. Luetmer, P. H. et al. When should I do dynamic CT myelography? Predicting fast spinal CSF leaks in patients with spontaneous intracranial hypotension. AJNR Am. J. Neuroradiol. 33, 690-694. https://doi.org/10.3174/ajnr.A2849 (2012). \\\",\\\"22. Schneider, U. C., Schiffler, J., Hakiy, N., Horn, P. & Vajkoczy, P. Functional analysis of pro-inflammatory properties within the cerebrospinal fluid after subarachnoid hemorrhage in vivo and in vitro. J. Neuroinflamm. 9, 28. https://doi.org/10.1186/1742-2094-9-28 (2012). \\\",\\\"23. Cipriano, P. W. et al. Abnormal [18F]FDG PET/MRI findings in paraspinal structures of patients with suspected cerebrospinal fluid leak. Proc. Int., Soc. Mag. Res. Med. 60, 1148 (2020). \\\",\\\"24. Monteith, T. S., Kralik, S. F., Dillon, W. P., Hawkins, R. A. & Goadsby, P. J. The utility of radioisotope cisternography in low CSF/volume syndromes compared to myelography. Cephalalgia 36, 1291-1295. https://doi.org/10.1177/0333102416628467 (2016). \\\",\\\"25. Ranganathan, P. et al. Chronic headache and backache are long-term sequelae of unintentional dural puncture in the obstetric population. J. Clin. Anesth. 27, 201-206. https://doi.org/10.1016/j.jclinane.2014.07.008 (2015). \\\",\\\"26. Gaber, T., Strehl, C. & Buttgereit, F. Metabolic regulation of inflammation. Nat. Rev. Rheumatol. 13, 267-279. https://doi.org/10.1038/nrrrheum.2017.37 (2017). \\\"]\",\n \"page_idx\": \"6\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[65,15,341,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2021) 11:15926 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,636,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-021-95056-w \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[922,965,929,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[260,61,931,269]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"27. Behera, D., Jacobs, K. E., Behera, S., Rosenberg, J. & Biswal, S. (18)F-FDG PET/MRI can be used to identify injured peripheral nerves in a model of neuropathic pain. J. Nucl. Med. 52, 1308-1312. https://doi.org/10.2967/jnumed.110.084731 (2011). \\\",\\\"28. Catalano, O. A. et al. An overview of PET/MR, focused on clinical applications. *Abdom. Radiol.* (NY) 42, 631-644. https://doi.org/10.1007/s00261-016-0894-5 (2017). \\\",\\\"29. Cipriano, P. W. et al. (18)F-FDG PET/MRI in chronic sciatica: Early results revealing spinal and nonspinal abnormalities. J. Nucl. Med. 59, 967-972. https://doi.org/10.2967/jnumed.117.198259 (2018). \\\",\\\"30. Amini, B. et al. Differentiation of benign fluid collections from soft-tissue sarcomas on FDG-PET/CT. J. Cancer 5, 328-335. https://doi.org/10.7150/jca.8310 (2014). \\\",\\\"31. Tateyama, M. et al. Clinical values of FDG PET in polymyositis and dermatomyositis syndromes: Imaging of skeletal muscle inflammation. BMJ Open 5, e006763. https://doi.org/10.1136/bmjopen-2014-006763 (2015). \\\",\\\"32. Subramanyam, P. & Palaniswamy, S. S. Role of FDG PET/CT in Baastrup's disease. Indian J. Nucl. Med. 31, 235-237. https://doi.org/10.4103/0972-3919.183604 (2016). \\\",\\\"33. Sekine, T. et al. Evaluation of atlas-based attenuation correction for integrated PET/MR in human brain: Application of a head atlas and comparison to true CT-based attenuation correction. J. Nucl. Med. 57, 215-220. https://doi.org/10.2967/jnumed.115.159228 (2016). \\\",\\\"34. Ahn, S. et al. Quantitative comparison of OSEM and penalized likelihood image reconstruction using relative difference penalties for clinical PET. Phys. Med. Biol. 60, 5733-5751. https://doi.org/10.1088/0031-9155/60/15/5733 (2015). \\\",\\\"35. Pagani-Estevez, G. L. et al. Procedural predictors of epidural blood patch efficacy in spontaneous intracranial hypotension. Reg. Anesth. Pain Med. https://doi.org/10.1136/rapm-2018-000021 (2019). \\\"]\",\n \"page_idx\": \"7\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[258,278,421,294]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgements \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,294,931,320]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We would like to thank Dawn Holley and Harsh Gandhi, PET/MRI technologists, for their assistance in acquiring the images. We also thank General Electric Healthcare for the funding support. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,331,430,343]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Author contributions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,345,931,384]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conceptualization and Study design: I.R.C., S.B. Data Acquisitions: P.W.C., J.B.C., D.Y. Formal analysis and investigation: All authors. Initial drafting of the manuscript: P.W.C., D.Y. Reviewing/Editing: All authors. Funding acquisition: I.R.C., S.B. Supervision: I.R.C., S.B. All authors read and approved the manuscript. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,396,425,411]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Competing interests \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,411,931,437]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PWC, DY, and SB's work has been in part funded by research grant from GE Healthcare. IRC's work has been in part funded by the Considine CSF Leak fund. RP, JBC, and YX declare no potential conflict of interest. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,447,445,460]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Additional information \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,461,746,475]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Correspondence and requests for materials should be addressed to I.R.C. or S.B. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,480,747,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Reprints and permissions information is available at www.nature.com/reprints. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,500,931,525]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,531,332,554]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0280/d4e05ff53f5765e5911c06c605236a91b4107154795c25bb24ede393a58e48a8.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[334,531,931,554]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,557,931,635]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,647,391,659]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"© The Author(s) 2021 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,16,341,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": 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}\n]","isConversational":false},"doi":{"kind":"string","value":"10.1038/s41598-021-95056-w"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Medicine and Health Sciences"},"sha256":{"kind":"string","value":"e3b6ac1c018fb26cc050e36316a8103fa1158c5e7c0802cb334f17002f9059b2"},"title":{"kind":"string","value":"Abnormal [18F]FDG PET/MRI findings in paraspinal structures of patients with suspected cerebrospinal fluid leak"}}},{"rowIdx":259,"cells":{"abstract":{"kind":"string","value":""},"author":{"kind":"string","value":"Keisuke WATANABE|Masatoshi SHIMPO"},"content_list":{"kind":"list like","value":[{"bbox":"[114,85,890,111]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"カタマラン型USV開発のための実海域実験システムの構築","text_format":null,"text_level":"1","type":"text"},{"bbox":"[243,200,752,254]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Examination of Sea Experimental System for Catamaran Type USV Development ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[423,292,905,311]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keisuke WATANABE and Masatoshi SHIMPO ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[462,344,537,359]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,364,907,521]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Catamaran type Unmanned Surface Vehicle (USV) has many applications as an autonomous platform in the field of marine engineering, such as collection of marine waste in harbors, support vessels for offshore work, ocean observation platforms, maintenance vessels for offshore wind power generation and so on. The authors have been constructing a tank experiment system and conducting a basic study of control algorithms by simulation with the aim of developing a system necessary for autonomy. As the next step, experiments in the actual sea area are essential for developing a system that autonomously navigates in unknown disturbances. In this paper, we discuss the optimal control algorithm that we designed based on the results of simulations of trajectory tracking control and the outline of the USV system from the viewpoint of constructing experimental system at sea. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,524,736,539]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords : ocean engineers, crew transfer vessel, ocean monitoring, USV, sea experiment +一7一 $\\boldsymbol { \\mathsf { \\Sigma } } ^ { \\bullet }$ ：海洋工学、CTV、海洋觀測、USV、美海域美 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,542,541,558]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,587,278,605]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1.研究の背景と目的","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,609,485,849]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"海洋プラスティックごみの問題、海洋環境の広域観測ネットワークの構築、洋上風力発電プラットフォームのメンテナンス等、近年の海洋工学分野における技術開発や運用において、カタ ラン型 USV が共通のプラットフォームとして有用であり、筆者らはその開発を進めている。USV は他船や洋上の障害物を回避しながら、風、潮流等の未知外乱中で、与えられた軌道に追従してミッションを遂行する能力が求められる。与えられたミッションに応じて、実際の個々のオペレーションに違いはあるものの、プラットフォームに必要不可欠な機能として、与軌道の追従、目標地点 $\\frown O$ 到達、障害物回避等の自律航行アルゴリズムの開発は非常に重要である。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[110,852,484,868]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"これまでに、水槽実験システムを構築し、2 基の水槽実験用模型船を製作して、障害物回避アルゴリズムの検証(1)(2)等を行ってきた。これらの水槽実験による検討は、初期検討の手法としては有用であったものの、水槽では未知外乱を模擬することが難しく、USV が航行可能な範囲も限定されてしまうことや、USV と陸上の通信環境等の模擬が難しい等の課題が手法上の限界として認識されてきた。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,589,905,717]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,720,905,849]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"そこで次のステップとして、波、風、潮流のような未知外乱中で、複数 $\\mathcal { O }$ USV が通信しながら協調的に航行する実験を実施することを目標に、実海域実験システムを構築することとした。一つの USV は、大人二人で運搬でき、岸から 2km 程度の距離までを数時間航行させられることとし、複数台での運用が可能なシステム構成にすることを目標としている。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[526,852,905,868]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"実海域実験システムの構築においては、軌道追従制御性能が重要であり、数多 $< \\phi$ 研究論文が発表されている。特に、メインスラスターと舵の 2個のアクチュエーターによって、緯度経度と方位角の 3 変数を制御する、いわゆる劣駆動制御アルゴリズムに関する研究が活発である(3)(4)。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[90,889,855,932]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 正会員 東海大学海洋学部航海工学科（〒424-8610 静岡市清水区折戸 3-20-1）keisuke@tsc.u-tokai.ac.jp2 正会員 東海大学海洋学部航海工学科（〒424-8610 静岡市清水区折戸 3-20-1）shimpo-masatoshi@tsc.u-tokai.ac.jp","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[294,35,705,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"日本航海学会論文集 第146巻 第145回講演会にて講演","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[489,950,509,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"30 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[628,147,905,168]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"渡邉 啓介1 ・新保 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を導入した適応的な制御アルゴリズムに関する実海域実験を展開していきたいと考えているが、本稿では、AI に学習させる軌道追従実験データの取得も念頭に、最も基礎的な軌道追従制御系を実装することを目的として、制御ステップ毎にシステム行列を変更し、リカッチ方程式を解いて最適ゲインを計算する1形サーボ形最適制御アルゴリズムについて、シミュレーションにより検討を行った。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,876,484,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"本稿で検討した1形サーボ系最適制御アルゴリズムを用いた軌道追従制御手法は、上記の非線形制御アルゴリズムと比較して、計算時間が早く計算機負荷も小さく、ボードコンピューターを用いた実装も容易である。また、最適制御のフィードバックゲインを算定するためのシステム行列を各制御ステップの姿勢角に応じて変更し、制御ステップ毎に最適ゲインを計算し直す方法は、適応制御的手法でありながら簡易な計算で安定したゲインを決定でき、ロバスト性の観点からも優位であると考えられる。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,85,905,213]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,233,776,250]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. 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\"]","image_footnote":"[]","img_path":"images/0930/e69168850d9f7bcdf1887adb986cfdc2ed75a07daf7d3d473462a8aaa6dfb98e.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[514,724,905,834]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,837,905,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"船体に作用する環境外力としては、潮流力、波力、風力が挙げられるが、ここでは、潮流力で代表させて検討することとした。潮流の向きは X 軸から時計回 $\\varnothing \\mathcal { O }$ 角θとして算定することとした。ヒーブ、ロール、ピッチの影響は無視できるものとし、2 次元","text_format":null,"text_level":null,"type":"text"},{"bbox":"[294,35,705,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"日本航海学会論文集 第146巻 第145回講演会にて講演","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[489,948,509,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"32 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[89,70,485,869]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"平面内で $\\mathcal { O }$ 運動についてのみ考察する。船体固定座標系方向 $\\mathcal { O }$ 対地速度成分を $( u , v )$ 、潮流 $\\mathcal { O }$ 船体固定座標系方向 $\\mathcal { O }$ 速度成分を $( u _ { C } , v _ { C } )$ とする。流体力について並進方向については、速度に関する流体力はモリソン式で評価することとし、一つのハルの没水部分のx軸に垂直な代表面積を $\\cdot A _ { x }$ 、y軸に垂直な没水部分$\\mathcal { O }$ 代表面積を $A _ { y }$ とする。上から見て右側のスラスター力を $T _ { R }$ 、左側 $\\mathcal { O }$ スラスター力を $T _ { L }$ 、サイドスラスター力を $T _ { S }$ とする。回転方向については、角速度 $r =$ $\\dot { \\psi } \\xi L$ 、速度に関する流体力は船体長 L として、長さ $\\mathrm { L } / 2$ 部分にかかる流体力は船体中央か $\\it { \\Omega } _ { 3 } \\pm \\mathrm { L } / 4 \\mathrm { ~ } \\mathcal { O } \\mathcal { O }$ 位置 $\\frown O D$ 集中荷重として近似する。加速度に関する流体力は付加慣性モーメントで評価することとする。船体 $\\mathcal { O }$ 運動方程式は、船体中央線 $\\mathrm { \\langle { x } }$ 軸)からサージ方向スラスターまでの距離を 、サイドスラスター $\\mathcal { O }$ 重心から $\\mathcal { O }$ 距離を $l _ { S }$ として、 \n$\\begin{array} { r } { ( m + m _ { x } ) ( \\dot { u } - v r ) + 2 \\times \\frac { 1 } { 2 } \\rho C _ { d x } A _ { x } | u - u _ { C } | ( u - u _ { C } ) = } \\end{array}$ $T _ { R } + T _ { L }$ ． ．．．(1) \n$\\begin{array} { r } { \\big ( m + m _ { y } \\big ) ( \\dot { v } + u r ) + 2 \\times \\frac { 1 } { 2 } \\rho C _ { d y } A _ { y } | v - v _ { C } | ( v - v _ { C } ) = } \\end{array}$ $T _ { S }$ ．． ．(2) \n$\\begin{array} { r } { ( J + J _ { z } ) \\dot { r } + \\frac 1 2 \\rho C _ { d r } \\frac { A _ { y } } 2 \\Big \\lvert r \\frac { L } { 4 } \\Big \\rvert \\left( r \\frac { L } { 4 } \\right) \\cdot \\frac { L } { 4 } \\times 4 = - l \\cdot T _ { R } + l \\cdot } \\end{array}$ $T _ { L } + l _ { S } \\cdot T _ { S }$ ．． ．(3)と表すことができる。ここに、 $m + m _ { x }$ 、 $m + m _ { y }$ は質量およびそれぞれ $\\mathcal { O }$ 方向 $\\mathcal { O }$ 付加質量、 $J + J _ { z }$ は $\\mathbf { Z }$ 軸周$\\boldsymbol { \\nabla }$ 慣性モーメント及び付加慣性モーメント、 $\\rho$ は海水密度、 $C _ { d x }$ などは潮流に対する抵抗係数を表す。このとき、方位角、XY 座標系での位置は、 \n$\\begin{array} { r } { \\psi = \\psi _ { 0 } + \\int _ { 0 } ^ { t } \\omega d t \\ \\underbrace { \\phantom { \\psi = \\gamma \\psi } \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\ \\cdot \\ \\cdot \\ \\cdot \\ \\ \\cdot \\ \\cdot \\ \\ \\cdot \\ \\ \\cdot \\ \\ \\cdot \\ \\ \\cdot \\ \\ \\cdot \\ \\ \\cdot \\ } } _ { \\mathrm { ~ } } \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\ \\cdot \\ \\cdot \\ \\ \\cdot \\ \\ \\cdot \\ \\ \\cdot \\ , \\end{array}$ (4)$\\begin{array} { r } { X = X _ { 0 } + \\int _ { 0 } ^ { t } ( u \\cos \\psi - v \\sin \\psi ) d t \\ \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot } \\end{array} .$ (5)$\\begin{array} { r } { Y = Y _ { 0 } + \\int _ { 0 } ^ { t } ( u \\sin \\psi + v \\cos \\psi ) d t \\ \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot } \\end{array} .$ (6)また、潮流 $\\mathcal { O }$ 船体固定座標系成分は、 \n$u _ { C } = U \\cos ( \\theta - \\psi )$ ．．(7)$v _ { C } = U \\sin ( \\theta - \\psi )$ ．(8)と表すことができる。 \n最適制御系を設計するため、未知外乱である潮流を無視し、速度 $\\mathcal { O } \\mathcal { 2 }$ 乗に比例する抵抗は代表速度（通","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,838,485,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"常 $\\mathcal { O }$ 巡航速度）を用いて線形近似し、さらに慣性力$\\mathcal { O }$ 角速度依存成分は微小であると仮定して線形近似した運動方程式を最適ゲイン算出のためのノミナル","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,85,710,99]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"モデルとする。すなわち、","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,106,761,155]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0792/d614297e3630fbbf4dd16a26c257e3cb64802c15b5f9e396a8036e2a19bc4485.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array} { r } { \\left[ \\begin{array} { c c c } { m + m _ { x } } & { 0 } & { 0 } \\\\ { 0 } & { m + m _ { y } } & { 0 } \\\\ { 0 } & { 0 } & { J + J _ { z } } \\end{array} \\right] \\left[ \\begin{array} { c c c } { \\dot { u } } \\\\ { \\dot { v } } \\\\ { \\dot { r } } \\end{array} \\right] + } \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,159,826,214]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0538/2b39d9c9b5051284171f34b2a9e0a69e212e3c2b29ed06414597d3f44a812e50.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array} { r l r } & \\left[ { \\rho { C _ { d x } } A _ { x } \\bar { u } } & { 0 } & { 0 } \\\\ { 0 } & { \\rho { C _ { d y } } A _ { y } \\bar { v } } & { 0 } \\\\ { 0 } & { 0 } & { \\frac { 1 } { 6 4 } \\rho { C _ { d I } } A _ { y } L ^ { 3 } \\bar { r } \\right] \\left[ { \\begin{array} { c } { u } \\\\ { v } \\\\ { r } \\end{array} } \\right] = } \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,220,882,266]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0067/d730a241e0bea59509db9e9317fb6405b5af0155a6f79dfa7a86ccef04824774.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left[ { \\begin{array} { c c c } { 1 } & { 1 } & { 0 } \\\\ { - l } & { l } & { l _ { S } } \\\\ { 0 } & { 0 } & { 1 } \\end{array} } \\right] \\left[ { \\begin{array} { c } { T _ { R } } \\\\ { T _ { L } } \\\\ { T _ { S } } \\end{array} } \\right] \\ldots \\ldots \\ldots \\ldots \\ldots \\ldots \\ldots \\ldots \\ldots \\ldots \\ldots \\ldots \\ldots .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[515,274,710,288]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"これを以下 $\\mathcal { O }$ ように書く。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,292,873,308]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"1004/141e82aef48591d45ec3e352213c3ba8457ac74465f3daf1315662f38d1f293f.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nM \\ddot { \\xi } + C \\dot { \\xi } = L f \\ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[514,311,904,344]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"空間固定座標系で見た速度と物体固定座標系で見た速度には、","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,353,870,397]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0057/252a401297cb2655ad172b5dd52685789b75a5c9129add1b470525034333910c.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left[ \\begin{array} { l } { u } \\\\ { v } \\\\ { r } \\end{array} \\right] = \\left[ \\begin{array} { c c c } { \\cos \\psi } & { \\sin \\psi } & { 0 } \\\\ { - \\sin \\psi } & { \\cos \\psi } & { 0 } \\\\ { 0 } & { 0 } & { 1 } \\end{array} \\right] \\left[ \\begin{array} { l } { \\dot { X } } \\\\ { \\dot { Y } } \\\\ { \\dot { r } } \\end{array} \\right] \\enspace \\enspace \\cdot \\enspace \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot \\cdot .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[512,403,907,515]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\mathcal { O }$ 関係があ $\\boldsymbol { \\nabla }$ 、これを \n$\\dot { \\boldsymbol { \\xi } } = \\pmb { R } \\dot { \\pmb { X } }$ ．．．(12)と書 $\\bigtriangleup$ 。 \n$\\ddot { \\xi } = \\dot { R } \\dot { X } + R \\ddot { X } \\ \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots .$ (13)であるから、 \n$M R { \\ddot { X } } + ( M { \\dot { R } } + C R ) { \\dot { X } } = L f$ ．．．．．(14)","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,519,904,552]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"これを制御系設計のために線形近似したノミナルモデルとする。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,573,825,590]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.2 最適制御アルゴリズ $\\bigtriangleup \\textcircled { \\oslash }$ 定式化","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,591,907,681]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"船舶における軌道 $\\mathcal { O }$ 最適トラッキング問題は、例えば文献(6)(7)他、これまでにも国内外で多 $< \\phi$ 研究がなされている。ここでは本 USV に実装することを目的として設計した最適制御アルゴリズムについて述べる。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,685,909,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"目標位置や軌道は、平面固定座標系で与えることとし、軌道上 $\\mathcal { O }$ 到達目標位置(Waypoint)を $\\mathbf { { \\boldsymbol { X } } } _ { t }$ 、目標速度を $\\dot { \\boldsymbol X } _ { t }$ として、以下 $\\mathcal { O }$ 誤差ベクトルを導入し、誤差フ $1 - \\mathrm { K } \\times \\mathrm { i }$ ック系を設計する。$e = [ X \\quad \\dot { X } ] ^ { T } - [ X _ { t } \\quad \\dot { X } _ { t } ] ^ { T } \\enspace \\dotsc \\enspace \\dotsc \\enspace \\dotsc \\enspace \\dotsc \\enspace \\dotsc \\enspace \\dotsc \\enspace \\dotsc \\enspace \\dotsc \\enspace .$ ．(15)シミュレーション結果 $\\mathcal { O }$ 節において後述するが、単純に位置と速度をフィードバックするのみでは、PD制御であるため、潮流が速 $\\bigtriangledown$ なると定常偏差が大きくな $\\boldsymbol { \\nabla }$ 、定点保持性能、軌道追従性能が劣化する。そこで、位置に関する誤差 $\\mathcal { O }$ 積分器を導入して、1 形 $\\mathcal { O }$ サーボ系を構成することとした。すなわち、$\\dot { \\boldsymbol { z } } = \\boldsymbol { X } - \\boldsymbol { X } _ { t }$ ．． ．．．．．(16)とし、状態変数を $\\pmb { x } = [ \\pmb { z } \\quad \\pmb { e } ] ^ { T }$ とすると、位置と速度$\\mathcal { O }$ 誤差に関する状態方程式は、","text_format":null,"text_level":null,"type":"text"},{"bbox":"[294,35,705,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"日本航海学会論文集 第146巻 第145回講演会にて講演","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[489,948,509,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"33 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[92,85,322,99]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[90,106,465,153]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"0599/19a9231bdff77644fbe71748da58f1c68c4452c3d9009f20ec5548a3f25ecf19.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\dot { x } = \\left[ \\begin{array} { c c c } { { 0 } } & { { I } } & { { o } } \\\\ { { 0 } } & { { O } } & { { I } } \\\\ { { O } } & { { O } } & { { - M R ^ { - 1 } \\big ( M \\dot { R } + C R \\big ) } } \\end{array} \\right] x + \\left[ \\begin{array} { c } { { 0 } } \\\\ { { 0 } } \\\\ { { M R ^ { - 1 } L } } \\end{array} \\right] f ( 1 )\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[87,160,485,364]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"と表すことができる。ここに、 、 は3行3列のゼロ行列、単位行列である。これらを \n${ \\dot { \\pmb { x } } } = \\pmb { A } \\pmb { x } + \\pmb { B } \\pmb { f }$ ．．．．(19)${ \\boldsymbol { y } } = { \\pmb { C } } { \\boldsymbol { x } }$ ．．． ．．．．．(20)として、以下 $\\mathcal { O }$ 評価関数 \n$\\begin{array} { r } { J = \\int _ { 0 } ^ { \\infty } ( x ^ { T } Q x f ^ { T } R f ) d t \\ \\underbrace { \\phantom { \\frac { J } { \\varepsilon } } \\cdots \\cdots \\cdots \\cdots \\cdots \\cdots \\cdots \\cdots \\cdots \\cdots } _ { } . } \\end{array}$ ．(21)を最小化するゲインを求めると、制御力は、 \n$\\pmb { f } = - \\pmb { G } \\pmb { x } = - \\pmb { G _ { 1 } } \\pmb { z } - \\pmb { G _ { 2 } } \\pmb { e } \\enspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .$ ．(22)$\\mathcal { O }$ ように計算できる。ゲインは、座標変換行列 に依存するため、各制御ステップでリカッチ方程式を解き更新しながら制御することになる。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,385,366,401]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.3 シミュレーション結果 $\\pmb { \\oslash }$ 例","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,403,484,494]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"上記 $\\mathcal { O }$ 式(22)で求められる制御力を用い、式(1)$\\sim ( 3 )$ で示した潮流との相対速度の 2 乗に比例する流体力を考慮し、ニューマーク $\\beta$ 法による数値積分を行って、シミュレーションによる検討を実施した。実際のカタ ランの質量 $\\mathrm { m } { = } 2 0$ [kg]として計算した。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,496,485,757]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"抵抗係数、付加質量係数は船体の形状に依存するため厳密には水槽実験にて検証する必要がある。けれども、4.3.3 で述べるようにこれらの数値の違いによる影響で軌道追従性能が大幅に悪化する可能性は低いことが推定されたため、ここではノミナルモデルの初期値として、例えば付加質量については元良 $\\mathcal { O }$ 論文(8)(9) 等を参考にして、サージ方向は$m _ { - x } = 2 [ \\mathrm { k g } ] ( - \\infty , \\infty , \\infty , \\infty )$ き付加質量係数 0.1 相当)、スウェー方向は $m _ { - y } = 2 0$ [kg]（一つのハルにつき付加質量係数 1.0 相当）等としてシミュレーションを実施した。没水面積は、波の影響を無視し、静水中喫水で算定している。ノミナルモデルと実船のモデル誤差に関する制御系のロバスト性については、今後実海域実験を通じて検証する。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,761,484,832]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"以下に軌道追従制御 $\\yen 123,456$ 結果の例を示す。軌道追従においては、進行方向と船体の方位角が異なる場合、すなわち船体が進行方向を向いていない場合に、","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,836,485,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(a)目標地点に向かいながら方位角を修正する方法(b)まず方位角を進行方向に合わせてから目標地点に向かう方法$\\scriptscriptstyle \\mathcal { O } ) 2$ 種類の方法が考えられる。後に示すように、(a)$\\mathcal { O }$ 方法では角度の修正のために軌道が歪むため、原則として(b) $\\mathcal { O }$ 方法で軌道追従させることとする。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,102,905,267]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0430/11d5865f87d81e2fda578723abe370cce255f38913949cd57b4fed02ee2061b9.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":"<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Mode</td><td rowspan=1 colspan=1>StartPoint</td><td rowspan=1 colspan=1>InitialAzimuth[deg]</td><td rowspan=1 colspan=1>TargetAzimuth[deg]</td><td rowspan=1 colspan=1>TargetWaypoint</td></tr><tr><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>Cruise</td><td rowspan=1 colspan=1>[0,0]</td><td rowspan=1 colspan=1>90</td><td rowspan=1 colspan=1>90</td><td rowspan=1 colspan=1>[0,20]</td></tr><tr><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>TurningAround</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>From 90</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>[0,20]</td></tr><tr><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>Cruise</td><td rowspan=1 colspan=1>From[0,20]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>[20,20]</td></tr><tr><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>TurningAround</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>From 0</td><td rowspan=1 colspan=1>-90</td><td rowspan=1 colspan=1>[20,20]</td></tr><tr><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>Cruise</td><td rowspan=1 colspan=1>From[20,20]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>-90</td><td rowspan=1 colspan=1>[20,0]</td></tr></table>","table_caption":"[\"Table 1 Simulation condition for trajectory tracking \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[514,286,887,301]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,324,714,340]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.3.1 潮流無しの場合","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,344,905,566]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"シミュレーションプログラムが機能しているかを確認するため、潮流無しの場合について、シミュレーションを実施した結果の一例を図 4 から図 6 に示す。今回のシミュレーションの軌道は表 1 に示すように、点[0,0]を始点とし、途中の通過点を[0,20],[20,20]の2点とし、終点を[20,0]となるように設定した。表 1 に示すように、各点を結ぶ直線状を追従するモードを Cruise モードとする。方位角については、ターゲット通過点において、次のターゲット目標点を目指した目標角となるように回頭してから次の目標地点に進むように設定し、これをTurning Around モードとして制御した。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,568,904,604]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"図 6 に示すように、表1で設定した軌道を追従することが確認できた。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,624,830,641]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.3.2 PD フィードバックのみの場合","text_format":null,"text_level":"1","type":"text"},{"bbox":"[514,643,907,922]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1形サーボ系の性能を確認するため、ここではサーボ系ではなく、位置と速度のフィードバックのみで最適制御系を構成した場合の軌道のシミュレーション結果の例を図 7 に示す。潮流は $0 . 2 \\left[ \\mathrm { m } / \\mathrm { s } \\right] \\mathcal { O }$ 南から来る流れの場合を示す。図 7 からわかるように、潮流が $0 . 2 [ \\mathrm { m } / \\mathrm { s } ]$ と弱いにも関わらず、 $\\mathrm { P D } \\supset _ { 1 } - \\kappa , \\bar { \\bf { \\sigma } } $ ックのみでは、軌道のゆがみが生じている。表 1 に示すモー $\\mathrm { F } \\mathcal { O }$ 遷移は、位置の許容誤差 $3 [ \\mathrm { m } ]$ 、角度 $\\mathcal { O }$ 許容誤差 5[deg]に達した時点で次 $\\mathcal { O }$ モードに移る設定としている。実海域実験で使用するスラスター$\\mathcal { O }$ 推力は最大 40[N]であることを考慮して評価関数の重みを調整し,ゲインを設定しているが、さらに潮流を早くすると、許容誤差内に制御目標が達成せず、Mode 遷移が行われないという欠点が観測された。従って、サーボ系を組む必要がある。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[294,35,705,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"日本航海学会論文集 第146巻 第145回講演会にて講演","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[489,950,509,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"34 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[90,83,463,290]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.4 Azimuth and surge, sway, yaw velocities (without \"]","image_footnote":"[]","img_path":"images/0914/91aa03cfaafd00cf7bc64581feecd93f2b794e8d416c68081759e72e54bd787c.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[109,338,442,532]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.5 Control force (without \"]","image_footnote":"[]","img_path":"images/0488/666af0f673a11d8b27b8b4e7d27f402d9814de2e5d37fbf47535257ba8a89401.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[109,584,442,776]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.6 Trajectory (without current, $m _ { - x } { = } 2 [ \\\\mathrm { k g } ]$ , $m _ { - y } { = } 2 0 [ \\\\mathrm { k g } ]$ ) \"]","image_footnote":"[]","img_path":"images/0670/48465219dc8dfffe7e0fecb4833411e9adf70cac15fe6840c37d6585b13c00b6.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[92,837,405,853]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.3.3 1形サーボ系による結果 $\\pmb { \\oslash }$ 例","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,857,485,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"図 $8 \\sim$ 図 $1 0 \\ \\ell \\geq 4 . 3 . 2$ と同じ潮流条件で、1形サーボ系による制御を実施した結果を示す。図 7と図 10を比較すればわかるように、サーボ系を組むことで、軌道追従性能が向上している。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[531,95,862,287]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.7 Trajectory (PD feedback only, current $= 0 . 2 [ \\\\mathrm { m } / \\\\mathrm { s } ]$ , \"]","image_footnote":"[]","img_path":"images/0135/a7370f516c414b46c0344dd8d771234a7ed2417da4ca7d602ad27f9e1e4ce03b.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[512,313,885,535]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.8 Azimuth and surge, sway, yaw velocities (Servo feedback, current $= 0 . 2 [ \\\\mathrm { m } / \\\\mathrm { s } ]$ , from South) \"]","image_footnote":"[]","img_path":"images/0022/a659235d4e6bfa743d3ed60d0b64a99f74eb3d58f3ce214f1b671299a8fdc021.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[532,584,863,776]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.9 Control force (Servo feedback, current $\\\\mathrm { \\\\varepsilon = 0 . 2 [ m / s ] }$ , from South) \"]","image_footnote":"[]","img_path":"images/0352/6ce1c0cf1f1e0ca48bbbd74287502c33e7c57ee207bca1c3ce3710d9197a6834.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[514,819,905,890]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"また、図 8 の左上図はヨー角を示しているが、この図から、表 1 の Mode2（0度 $=$ 北向き）, Mode4（-90度 $=$ 西向き）における回頭が指定通りに遂行されたことがわかる。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[515,894,904,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"次に、図 $1 1 { \\sim } 1 3$ にさらに潮流を $0 . 5 [ \\mathrm { m } / \\mathrm { s } ]$ と早くし、北西方向から流れているとした場合の例を示す。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[294,35,705,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"日本航海学会論文集 第146巻 第145回講演会にて講演","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[489,948,509,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"35 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[109,96,442,287]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.10 Trajectory (Servo feedback, current $= 0 . 2 [ \\\\mathrm { m } / \\\\mathrm { s } ]$ , \"]","image_footnote":"[]","img_path":"images/0425/49ee38536928541bfea11489118afea57a13d1f25a5d0bf4127932de4adf2bb1.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[90,313,463,535]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.11 Azimuth and surge, sway, yaw velocities (Servo feedback, current $\\\\mathrm { \\\\Sigma = 0 . 5 [ m / s ] }$ , from North \"]","image_footnote":"[]","img_path":"images/0361/d61e28bb7601c7d52ca2442b73b642515a745f3b8085456c58a60af9fe82bd09.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[109,602,442,795]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.12 Control force (Servo feedback, current= $\\\\mathrm { \\\\Delta \\\\ z 0 . 5 [ m / s ] }$ , from North West, $m _ { - x } = 2 [ \\\\mathrm { k g } ] , m _ { - y } = 2 0 [ \\\\mathrm { k g } ] )$ \"]","image_footnote":"[]","img_path":"images/0516/df2d606509324a505da066c541342b32c607ef84b4cd2a08c410999ff99f84ff.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[92,856,485,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"潮流を強くした場合には、表 1 に示すモー $\\mathrm { F } \\mathcal { O }$ 遷移は、位置 $\\mathcal { O }$ 許容誤差 $3 [ \\mathrm { m } ]$ 、角度 $\\mathcal { O }$ 許容誤差 5[deg]ではモード遷移できなかったため、位置 $\\mathcal { O }$ 許容誤差4[m]、角度 $\\mathcal { O }$ 許容誤差 8[deg]に達した時点で次のモードに移る設定とした。この例からわかるように、潮流が $1 \\ \\nearrow \\ \\gg \\ \\vdash$ 程度までは、本スラスターで対応可能であることが確認できた。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[531,95,863,287]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.13 Trajectory (Servo feedback, current= $\\\\mathrm { \\\\Delta } [ 0 . 5 [ \\\\mathrm { m } / \\\\mathrm { s } ]$ \"]","image_footnote":"[]","img_path":"images/0802/4174f3e84a5bce74f052da279d6fca0a4fb5648575bac3105b19c33860af8544.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[512,313,884,535]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.14 Azimuth and surge, sway, yaw velocities (Servo feedback, current $\\\\mathrm { \\\\Sigma = 0 . 5 [ m / s ] }$ , from North \"]","image_footnote":"[]","img_path":"images/0029/00b85ea661a2c6840159bafbace947204447eae02dda6120ba294735c5457307.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[532,602,863,795]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.15 Control force (Servo feedback, current= $\\\\mathrm { \\\\cdot 0 . 5 [ m / s ] }$ , from North West, $m _ { - x } = 1 0 [ \\\\mathrm { k g } ] , m _ { - y } = 1 0 [ \\\\mathrm { k g } ] )$ \"]","image_footnote":"[]","img_path":"images/0575/4e79855944a72406cf5b6d74ea9e4931a99788be817d21fc100f470acf3d785c.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[514,857,905,909]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[527,913,905,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ここで、付加質量 $\\mathcal { O }$ 違いが計算結果に与える影響について検討するため、図 13 と同じ潮流の場合に、例えば、付加質量を $m _ { - x } { = } 1 0$ [kg]、 $m _ { - y } = 1 0$ [kg] として計算した結果を図 14から図 16 に示す。これらの結果からわかるように、付加質量 $\\mathcal { O }$ 違いによって、図 11 と図 14 にみられるような速度 $\\mathcal { O }$ 違いや、図 12と図 15 にみられるように制御力の最大値や時系列に違いが生じ、図 13 と図 16 からわかるように到達地点での誤差にも多少の差が生じる。しかしながら、付加質量の推定に誤差があったとしても、表1で設定した目標軌道について、許容誤差の範囲で追従できることは確認できた。付加質量、抵抗係数も含めて、他の値に変更して計算した結果も許容誤差の範囲で軌道追従できたことから、潮流ありのシミュレーションにおいては、先に述べたノミナルモデルの設定値で計算を実施することとした。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[294,35,705,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"日本航海学会論文集 第146巻 第145回講演会にて講演","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[489,948,509,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"36 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[107,95,442,287]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.16 Trajectory (Servo feedback, current= $\\\\mathrm { \\\\bar { \\\\varepsilon } 0 . 5 [ m / s ] } ,$ , from North West, $m _ { - x } = 1 0 [ \\\\mathrm { k g } ] , m _ { - y } = 1 0 [ \\\\mathrm { k g } ] )$ \"]","image_footnote":"[]","img_path":"images/0201/b33e405908e0c4befa0037f22e14b6a4ccb63d09798c711de38e51072ec35223.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[92,346,485,628]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,648,442,666]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.3.4 船首方向が進行方向と異なる場合","text_format":null,"text_level":"1","type":"text"},{"bbox":"[94,669,485,741]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"船首方向が進行方向と異なる場合に、定点で回頭して船首方向を進行方向に向けるのではなく、(a)目標地点に向かいながら同時に方位角を修正する方法、での軌道追従結果の例を図 $1 7 \\sim$ 図 19 に示す。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,744,485,815]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"これらの結果から、現在の制御系では、目標地点に向かって進行しながら船首方向を進行方向にセットする場合には、自身が進行することと、潮流の影響により、軌道が歪むことがわかる。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,837,423,853]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.3.5 定点保持性能及び制御系の課題","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,857,485,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"図 20 に定点保持性能に関する結果の一例を示す。現時点での目標範囲には収まっているものの、構造物インスペクション等のミッションにおいては、さらに定点保持精度を上げる必要がある。ゲインを調整すれば、さらに誤差は小さくなるものの、外乱が2 次非線形のため 1 形サーボ系では完全に定常偏差を除去することができない。この点については、定常的な外乱を学習して定常偏差を補償する制御系の設計が今後の課題である。また、ゲインを決定する評価関数内の重み行列を外乱に応じて適応的に調整する適応ゲイン調整も今後の検討課題である。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,83,885,289]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.17 Azimuth and surge, sway, yaw velocities (Servo feedback, current= $\\\\mathrm { \\\\Delta } [ 0 . 5 [ \\\\mathrm { m } / \\\\mathrm { s } ]$ , from North West) \"]","image_footnote":"[]","img_path":"images/0636/8aed5287aeab8331ebe54e0386eae920dc0cdbc128d177302552464404e35698.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[527,339,865,532]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.18 Control force (Servo feedback, current $\\\\mathrm { \\\\Sigma = 0 . 5 [ m / s ] }$ , from North West) \"]","image_footnote":"[]","img_path":"images/0537/1c37777623b7f5e09ee5ca2f8ab19cc5a2b149894b97dc93888a68d49c5cf3b1.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[531,583,862,776]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.19 Trajectory (Servo feedback, current $\\\\mathrm { \\\\Sigma = 0 . 5 [ m / s ] }$ , from North West) \"]","image_footnote":"[]","img_path":"images/0998/f242b9cf1543c2c3e331de9c67fe717de26f8b46d1fd9221e5dac3c3dd782798.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[514,837,907,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[294,35,705,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"日本航海学会論文集 第146巻 第145回講演会にて講演","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[489,948,509,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"37 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[99,93,442,287]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.20 Trajectory (Servo feedback, current $\\\\mathrm { \\\\Sigma = 0 . 5 [ m / s ] }$ , from North West) \"]","image_footnote":"[]","img_path":"images/0006/5ce703da71a6010fb7863d8e44508dcc3351a9b331522599cff57c66d57772c7.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[92,347,485,382]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,402,462,420]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5. 実海域における USV 基本性能の確認","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,422,485,625]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.で述べたシミュレーションにより、本カタマランにおける最も基本的な制御アルゴリズムの機能が確認された。そこで、アクチュエーター、及び GNSSセンサ、スラスター、PCとの無線シリアル通信等各プログラムモジュールの基本的な性能確認を実施するため、本学の桟橋において、基本性能の確認実験を実施した。図 21 に構築した USV 全体の外観、図22 に基本性能確認実験の様子を示す。図 23 中のスタートポイントからの白い線は、USV の航跡について GNSS の緯度経度の結果を Google Map 上に表示したものである。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,629,485,775]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"この実験では、USV は図のスタートポイントから270 度方向に航行し、途中から 250 度方向に変針している。図 24 はこの航跡に対応した方位角の時系列データを示している。図 $2 4 ~ \\mathcal { O }$ 方位角が図 $2 3 ~ \\mathcal { O } )$ 地図における方向とおおむね一致している様子が見て取れる。このように、本実験を通じて構築した全てのモジュールが動作し、軌道追従実験に必要な位置や方位角の検出が可能であることを確認できた。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,796,178,813]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6. 結論","text_format":null,"text_level":"1","type":"text"},{"bbox":"[94,814,485,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"本稿では、USV 実海域実験システムの構築を目的として、姿勢角に応じて各制御サンプリング時間内で最適フィードバックゲインを変更する1形サーボ系最適制御アルゴリズムを提案し、潮流を外乱として条件を変化させたシミュレーションを実施して、性能の有効性と限界を確認した。また、実海域実験を実施するためのテストベッドを構築し、基本機能$\\mathcal { O }$ 実装を終了した。本稿で提案したアルゴリズムは、今後開発を進めるより高度な制御手法の基礎となるデータを取得するためのもので、今後、本アルゴリズムを用いて実海域実験による軌道追従データを蓄積し、AIを用いた適応制御系の設計を実施する予定である。","text_format":null,"text_level":null,"type":"text"},{"bbox":"[519,84,899,287]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.21 USV experiment system \"]","image_footnote":"[]","img_path":"images/0924/e2d7cf5b81e0ab2240251c3d654ba3a98f919bf51850925f16edac2a5827147e.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[522,309,895,459]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.22 Experiment field \"]","image_footnote":"[]","img_path":"images/0231/231e53aa9521acba03c8fbda40ab1062ea5148efe940098ed6a3f62029f41135.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[526,482,890,700]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.23 Trajectory mapping example \"]","image_footnote":"[]","img_path":"images/0362/847610c1f031efe23cf208249569e148fbcadfdf583e3f484421071312454481.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[531,729,889,884]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.24 Azimuth from GNSS record \"]","image_footnote":"[]","img_path":"images/0827/12e5e83fdfa5a5fa46900c27251bec5e47b7c880b8cef54de2fa34f87102321b.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[294,35,705,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"日本航海学会論文集 第146巻 第145回講演会にて講演","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[489,950,509,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"38 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[92,85,485,213]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,233,176,250]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"参考文献","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,252,485,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(1) 原田和柾、渡邉啓介、新保雅俊、宇都宮洪志、“無人調査船群制御のための水槽実験システムの構築”、日本航海学会論文集、140 巻 pp.77-87、2019. \n(2) 渡邉啓介、新保雅俊、“カタマラン型 USV の位置制御に関する基礎検討”、日本航海学会第 143回講演会講演予稿集、pp. 35-37、2020.11. \n(3) Z. Dong, L. Wan, Y. Li, T. Liu, G. Zhang,“Trajectory Tracking Control of Underactuated USVBased on Modified Backstepping Approach”, Int. J.Nav. Archit. Ocean Eng., pp.817-832, 2015 \n(4) T.I.Fossen,”Marine Control Systems”, ISBN82-92356-00-2, 2002 \n(5) Keisuke Watanabe, Koshi Utsunomiya, KazumasaHarada, “Development of a Floating LBL Systemand a Lightweight ROV for Sky to Water System”,IEEEXplore,doi.org/10.23919/OCEANS40490.2019.8962848,2019 \n(6) 三好晋太郎、原洋輔、大津皓平、“カルマンフィルタを用いた最適トラッキング制御に関する研究”、日本航海学会論文集 118 号,pp.47-53, 2008 \n(7) 三好晋太郎、原洋輔、大津皓平、“線形化モデル用いた最適トラッキング制御に関する研究”、日本航海学会論文集、日本航海学会論文集 117 号, pp.183-189, 2007 \n(8) 元良誠三、“船体運動に対する附加質量及び附加慣性モーメントについてー其の2. 前後動に対する附加質量ー”、造船協会論文集第105 号,pp.59-62, 1959. \n(9) 元良誠三、“船体運動に対する附加質量及び附加慣性モーメントについてー其の3. 左右動に対する附加質量ー”、造船協会論文集第106 号,pp.63-68, 1959.","text_format":null,"text_level":null,"type":"text"},{"bbox":"[294,35,705,51]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"日本航海学会論文集 第146巻 第145回講演会にて講演","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[489,950,509,961]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"39 ","text_format":null,"text_level":null,"type":"discarded"},{"bbox":"[257,912,477,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"（原稿投稿2022年1月31日）","text_format":null,"text_level":null,"type":"discarded"}],"string":"[\n {\n \"bbox\": \"[114,85,890,111]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"カタマラン型USV開発のための実海域実験システムの構築\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[243,200,752,254]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Examination of Sea Experimental System for Catamaran Type USV Development \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[423,292,905,311]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keisuke WATANABE and Masatoshi SHIMPO \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[462,344,537,359]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,364,907,521]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Catamaran type Unmanned Surface Vehicle (USV) has many applications as an autonomous platform in the field of marine engineering, such as collection of marine waste in harbors, support vessels for offshore work, ocean observation platforms, maintenance vessels for offshore wind power generation and so on. The authors have been constructing a tank experiment system and conducting a basic study of control algorithms by simulation with the aim of developing a system necessary for autonomy. As the next step, experiments in the actual sea area are essential for developing a system that autonomously navigates in unknown disturbances. In this paper, we discuss the optimal control algorithm that we designed based on the results of simulations of trajectory tracking control and the outline of the USV system from the viewpoint of constructing experimental system at sea. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,524,736,539]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords : ocean engineers, crew transfer vessel, ocean monitoring, USV, sea experiment +一7一 $\\\\boldsymbol { \\\\mathsf { \\\\Sigma } } ^ { \\\\bullet }$ ：海洋工学、CTV、海洋觀測、USV、美海域美 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,542,541,558]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,587,278,605]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1.研究の背景と目的\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,609,485,849]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"海洋プラスティックごみの問題、海洋環境の広域観測ネットワークの構築、洋上風力発電プラットフォームのメンテナンス等、近年の海洋工学分野における技術開発や運用において、カタ ラン型 USV が共通のプラットフォームとして有用であり、筆者らはその開発を進めている。USV は他船や洋上の障害物を回避しながら、風、潮流等の未知外乱中で、与えられた軌道に追従してミッションを遂行する能力が求められる。与えられたミッションに応じて、実際の個々のオペレーションに違いはあるものの、プラットフォームに必要不可欠な機能として、与軌道の追従、目標地点 $\\\\frown O$ 到達、障害物回避等の自律航行アルゴリズムの開発は非常に重要である。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,852,484,868]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"これまでに、水槽実験システムを構築し、2 基の水槽実験用模型船を製作して、障害物回避アルゴリズムの検証(1)(2)等を行ってきた。これらの水槽実験による検討は、初期検討の手法としては有用であったものの、水槽では未知外乱を模擬することが難しく、USV が航行可能な範囲も限定されてしまうことや、USV と陸上の通信環境等の模擬が難しい等の課題が手法上の限界として認識されてきた。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,589,905,717]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,720,905,849]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"そこで次のステップとして、波、風、潮流のような未知外乱中で、複数 $\\\\mathcal { O }$ USV が通信しながら協調的に航行する実験を実施することを目標に、実海域実験システムを構築することとした。一つの USV は、大人二人で運搬でき、岸から 2km 程度の距離までを数時間航行させられることとし、複数台での運用が可能なシステム構成にすることを目標としている。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,852,905,868]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"実海域実験システムの構築においては、軌道追従制御性能が重要であり、数多 $< \\\\phi$ 研究論文が発表されている。特に、メインスラスターと舵の 2個のアクチュエーターによって、緯度経度と方位角の 3 変数を制御する、いわゆる劣駆動制御アルゴリズムに関する研究が活発である(3)(4)。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[90,889,855,932]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 正会員 東海大学海洋学部航海工学科（〒424-8610 静岡市清水区折戸 3-20-1）keisuke@tsc.u-tokai.ac.jp2 正会員 東海大学海洋学部航海工学科（〒424-8610 静岡市清水区折戸 3-20-1）shimpo-masatoshi@tsc.u-tokai.ac.jp\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[294,35,705,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"日本航海学会論文集 第146巻 第145回講演会にて講演\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[489,950,509,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"30 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[628,147,905,168]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"渡邉 啓介1 ・新保 雅俊2\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[92,85,484,175]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,179,485,477]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"これらの研究に共通した特徴は、船体の流体力微係数を水槽実験によって正確に推定した上で、比較的厳密な非線形運動方程式を導出し、この非線形運動方程式に基づいてリアプノフ関数を作成して、スライディングモード制御やバックステッピング制御といった非線形制御系を構成することと言える。これらの制御アルゴリズムは、水槽実験を通じた正確な非線形モデリングが必要であり、実装も複雑で船体の変更等 $\\\\frown O D$ 対応は比較的敷居が高い。また、航行軌道は比較的直線的な軌道に追従させる設定の場合が多く、軌道からのずれに対し、自身の進行方向ベクトルと設定軌道との交点を目標地点として追いかける Line of Sight (LOS)による軌道追従を前提として制御系が設計される場合が多い。この手法は、一般的な船舶の航行軌道である比較的直線的な軌道を追従させる際には有効である。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,480,484,665]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"しかしながら、現在筆者らが検討している USV は、ミッションに応じて周囲に付加物を取り付ける可能性もあり、コストをかけた水槽実験による非線形モデリングが難しいことや、例えば、海洋観測のための定点保持機能、海洋構造物コラムインスペクションのために舳先をコラム中心に向けた状態で周回する機能など、LOS による手法では対応できない軌道追従性能を持たせることを想定しており、上記のLOS を想定した非線形制御アルゴリズムとは異なる軌道追従制御系を導入する必要がある。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,668,484,871]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"そこで、劣駆動ではなく、平面内の3自由度に対し、スラスター3基による制御システムを実装することとした。将来的には、AI を導入した適応的な制御アルゴリズムに関する実海域実験を展開していきたいと考えているが、本稿では、AI に学習させる軌道追従実験データの取得も念頭に、最も基礎的な軌道追従制御系を実装することを目的として、制御ステップ毎にシステム行列を変更し、リカッチ方程式を解いて最適ゲインを計算する1形サーボ形最適制御アルゴリズムについて、シミュレーションにより検討を行った。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,876,484,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"本稿で検討した1形サーボ系最適制御アルゴリズムを用いた軌道追従制御手法は、上記の非線形制御アルゴリズムと比較して、計算時間が早く計算機負荷も小さく、ボードコンピューターを用いた実装も容易である。また、最適制御のフィードバックゲインを算定するためのシステム行列を各制御ステップの姿勢角に応じて変更し、制御ステップ毎に最適ゲインを計算し直す方法は、適応制御的手法でありながら簡易な計算で安定したゲインを決定でき、ロバスト性の観点からも優位であると考えられる。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,85,905,213]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,233,776,250]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. 想定しているミッション\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,252,907,399]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"本カタマラン USV は、実海域実験を通じて自律航行システムの開発を進めることが主目的であるが、自律航行のレベルは、船舶のミッションに大きく依存する。筆者らが想定している最終的なミッションは、自律船(Autonomous Surface Vehicle)である。以下に制御性能の検討上、プラットフォームとして応用を想定しているいくつかのミッションの例について簡単に述べる。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,420,843,437]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.1 洋上風力発電の無人メンテナンス\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,438,905,699]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Crew Transfer Vessel (CTV)を用いた専門要員によるメンテナンスを補完し、プロジェクトコストを低減させるために、将来的には無人メンテナンスシステムが導入されることが望ましいと思われる。自律船と水中ロボットと空中ドローンを一体とし、カタマランから海底ケーブルを検査する水中ロボットを繰り出すと同時に、カタマランデッキに搭載した空中ドローンを発進させて風車の検査等を行わせるシステムの開発を目指し、水中ロボット、空中ドローンの運搬と検査中の無人サポート基地としてのミッションを想定している。このミッションでは、例えば、コラムの周囲を撮影するために、舳先をコラム中心に向けたままスライドしながら円軌道を描くといった航行制御システムが必要である。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,719,863,735]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2 港湾内浮遊プラスティックごみ回収\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,738,905,884]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"海洋プラスティックごみは、外洋に流れ出る前に港内で除去することが望ましい。プラスティックごみをカメラで発見し、カタマランの双胴部分に取り込んだごみを回収する装置を搭載し、港内を定期的に無人で巡回するミッションを想定している。このミッションでは、港内にはプレジャーボート等の他船が不定期に航行しているため、軌道追従に加え、衝突回避システムの開発が重要である。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,904,786,922]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.3 海洋観測プラットフォーム\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[294,35,705,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"日本航海学会論文集 第146巻 第145回講演会にて講演\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[489,950,507,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[92,85,485,251]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"海洋環境の保全のためには、全世界的な多点同時データの蓄積とネットワーク化が重要である(5)。筆者らは特に沿岸域において、空中―洋上―水中の鉛直方向の観測データを同時に記録できる観測装置の開発を進めてきており、これらを多数展開し、観測機器を搭載した USV が群として行動するミッションを想定している。このミッションでは、複数 USV 間の協調制御が不可欠であり、お互いの位置を通信しながらの軌道追従制御システムが必要である。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,271,273,288]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.4 養殖自動給餌船\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,289,485,399]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"現在世界中で開発が進められているスマート養殖システムにおいて、低コスト化された自動給餌船等の導入が望まれている。このミッションでは、複数の養殖いけすを巡回する機能に加え、いけす内での給餌ポイントを一定に保つために定点保持機能が重要である。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,419,401,437]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. 実験船の形状とシステム構成\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,439,487,566]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"カタマランの形状とスラスター配置を図 1に示す。デッキ上に、浮力調整用の重りと、ボードコンピューター、センサ、バッテリー等を水密パッケージした制御装置を搭載する。デッキカバー上部からポールを立て、GNSS アンテナ及び無線通信モジュールを取り付ける。スラスターは、前後進用に左右 2 基、サイドスラスター1 基を搭載する。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,568,485,850]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"内部システムは、図 2 に示すように、2 枚のボードコンピューターを用い、1 枚は USB カメラをつないで画像処理を行う。もう 1 枚は姿勢センサ、GNSSモジュール、モータードライバーを用いた軌道制御を主として行う。ボードコンピューター同士の通信は有線LAN、近距離での陸上PCとの通信は、WirelessLAN を用いる。岸から離れると Wireless LAN が届かなくなるため、データ容量は限られるものの、公称$\\\\mathcal { O }$ 見通し距離で 2km 通信可能な特定小電力無線シリアル通信装置を搭載する。これにより、緯度経度など簡単な内部状態を陸上の PC からモニタリングできるようにし、さらに、緊急時には陸上 PCからの操作で USVをコントロールできるように構成した。また、複数台の USVによる協調制御実験においても、この無線通信システムが各 USV の通信リンクとなる。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,869,420,902]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. 軌道追従制御シミュレーション4.1 モデリング\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,904,467,920]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"制御系設計のためにカタマランのノミナルモデルを運動方程式に基づき定式化する。座標系は図 3のように設定した。GNSS 測位に基づき、スタート地点を原点とし、平面固定座標系として北方向に X軸、東方向に Y 軸を取る。船体固定座標系は、船体のsurge 方向を x 軸、sway 方向を y 軸とする。X 軸と$\\\\mathrm { X }$ 軸のなす角を $\\\\phi$ とし、時計回りを正とする。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,86,897,249]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.1 Catamaran USV size and thrusters arrangement \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0123/5953d3959ac066f53822f4a72507fd527cf5a30a37883f8a70300ec96ac2ab30.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[519,275,895,438]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.2 Schematic diagram of the inner modules \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0963/d28aee38e3a8fda414caf0cf1e447be4f75b87b3b362bd7fa290f93b493eabe1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[541,470,873,676]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.3 Coordinate system \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0930/e69168850d9f7bcdf1887adb986cfdc2ed75a07daf7d3d473462a8aaa6dfb98e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[514,724,905,834]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,837,905,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"船体に作用する環境外力としては、潮流力、波力、風力が挙げられるが、ここでは、潮流力で代表させて検討することとした。潮流の向きは X 軸から時計回 $\\\\varnothing \\\\mathcal { O }$ 角θとして算定することとした。ヒーブ、ロール、ピッチの影響は無視できるものとし、2 次元\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[294,35,705,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"日本航海学会論文集 第146巻 第145回講演会にて講演\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[489,948,509,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"32 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[89,70,485,869]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"平面内で $\\\\mathcal { O }$ 運動についてのみ考察する。船体固定座標系方向 $\\\\mathcal { O }$ 対地速度成分を $( u , v )$ 、潮流 $\\\\mathcal { O }$ 船体固定座標系方向 $\\\\mathcal { O }$ 速度成分を $( u _ { C } , v _ { C } )$ とする。流体力について並進方向については、速度に関する流体力はモリソン式で評価することとし、一つのハルの没水部分のx軸に垂直な代表面積を $\\\\cdot A _ { x }$ 、y軸に垂直な没水部分$\\\\mathcal { O }$ 代表面積を $A _ { y }$ とする。上から見て右側のスラスター力を $T _ { R }$ 、左側 $\\\\mathcal { O }$ スラスター力を $T _ { L }$ 、サイドスラスター力を $T _ { S }$ とする。回転方向については、角速度 $r =$ $\\\\dot { \\\\psi } \\\\xi L$ 、速度に関する流体力は船体長 L として、長さ $\\\\mathrm { L } / 2$ 部分にかかる流体力は船体中央か $\\\\it { \\\\Omega } _ { 3 } \\\\pm \\\\mathrm { L } / 4 \\\\mathrm { ~ } \\\\mathcal { O } \\\\mathcal { O }$ 位置 $\\\\frown O D$ 集中荷重として近似する。加速度に関する流体力は付加慣性モーメントで評価することとする。船体 $\\\\mathcal { O }$ 運動方程式は、船体中央線 $\\\\mathrm { \\\\langle { x } }$ 軸)からサージ方向スラスターまでの距離を 、サイドスラスター $\\\\mathcal { O }$ 重心から $\\\\mathcal { O }$ 距離を $l _ { S }$ として、 \\n$\\\\begin{array} { r } { ( m + m _ { x } ) ( \\\\dot { u } - v r ) + 2 \\\\times \\\\frac { 1 } { 2 } \\\\rho C _ { d x } A _ { x } | u - u _ { C } | ( u - u _ { C } ) = } \\\\end{array}$ $T _ { R } + T _ { L }$ ． ．．．(1) \\n$\\\\begin{array} { r } { \\\\big ( m + m _ { y } \\\\big ) ( \\\\dot { v } + u r ) + 2 \\\\times \\\\frac { 1 } { 2 } \\\\rho C _ { d y } A _ { y } | v - v _ { C } | ( v - v _ { C } ) = } \\\\end{array}$ $T _ { S }$ ．． ．(2) \\n$\\\\begin{array} { r } { ( J + J _ { z } ) \\\\dot { r } + \\\\frac 1 2 \\\\rho C _ { d r } \\\\frac { A _ { y } } 2 \\\\Big \\\\lvert r \\\\frac { L } { 4 } \\\\Big \\\\rvert \\\\left( r \\\\frac { L } { 4 } \\\\right) \\\\cdot \\\\frac { L } { 4 } \\\\times 4 = - l \\\\cdot T _ { R } + l \\\\cdot } \\\\end{array}$ $T _ { L } + l _ { S } \\\\cdot T _ { S }$ ．． ．(3)と表すことができる。ここに、 $m + m _ { x }$ 、 $m + m _ { y }$ は質量およびそれぞれ $\\\\mathcal { O }$ 方向 $\\\\mathcal { O }$ 付加質量、 $J + J _ { z }$ は $\\\\mathbf { Z }$ 軸周$\\\\boldsymbol { \\\\nabla }$ 慣性モーメント及び付加慣性モーメント、 $\\\\rho$ は海水密度、 $C _ { d x }$ などは潮流に対する抵抗係数を表す。このとき、方位角、XY 座標系での位置は、 \\n$\\\\begin{array} { r } { \\\\psi = \\\\psi _ { 0 } + \\\\int _ { 0 } ^ { t } \\\\omega d t \\\\ \\\\underbrace { \\\\phantom { \\\\psi = \\\\gamma \\\\psi } \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\ \\\\cdot \\\\ \\\\cdot \\\\ \\\\cdot \\\\ \\\\ \\\\cdot \\\\ \\\\cdot \\\\ \\\\ \\\\cdot \\\\ \\\\ \\\\cdot \\\\ \\\\ \\\\cdot \\\\ \\\\ \\\\cdot \\\\ \\\\ \\\\cdot \\\\ \\\\ \\\\cdot \\\\ } } _ { \\\\mathrm { ~ } } \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\ \\\\cdot \\\\ \\\\cdot \\\\ \\\\ \\\\cdot \\\\ \\\\ \\\\cdot \\\\ \\\\ \\\\cdot \\\\ , \\\\end{array}$ (4)$\\\\begin{array} { r } { X = X _ { 0 } + \\\\int _ { 0 } ^ { t } ( u \\\\cos \\\\psi - v \\\\sin \\\\psi ) d t \\\\ \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot } \\\\end{array} .$ (5)$\\\\begin{array} { r } { Y = Y _ { 0 } + \\\\int _ { 0 } ^ { t } ( u \\\\sin \\\\psi + v \\\\cos \\\\psi ) d t \\\\ \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot } \\\\end{array} .$ (6)また、潮流 $\\\\mathcal { O }$ 船体固定座標系成分は、 \\n$u _ { C } = U \\\\cos ( \\\\theta - \\\\psi )$ ．．(7)$v _ { C } = U \\\\sin ( \\\\theta - \\\\psi )$ ．(8)と表すことができる。 \\n最適制御系を設計するため、未知外乱である潮流を無視し、速度 $\\\\mathcal { O } \\\\mathcal { 2 }$ 乗に比例する抵抗は代表速度（通\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,838,485,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"常 $\\\\mathcal { O }$ 巡航速度）を用いて線形近似し、さらに慣性力$\\\\mathcal { O }$ 角速度依存成分は微小であると仮定して線形近似した運動方程式を最適ゲイン算出のためのノミナル\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,85,710,99]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"モデルとする。すなわち、\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,106,761,155]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0792/d614297e3630fbbf4dd16a26c257e3cb64802c15b5f9e396a8036e2a19bc4485.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array} { r } { \\\\left[ \\\\begin{array} { c c c } { m + m _ { x } } & { 0 } & { 0 } \\\\\\\\ { 0 } & { m + m _ { y } } & { 0 } \\\\\\\\ { 0 } & { 0 } & { J + J _ { z } } \\\\end{array} \\\\right] \\\\left[ \\\\begin{array} { c c c } { \\\\dot { u } } \\\\\\\\ { \\\\dot { v } } \\\\\\\\ { \\\\dot { r } } \\\\end{array} \\\\right] + } \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,159,826,214]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0538/2b39d9c9b5051284171f34b2a9e0a69e212e3c2b29ed06414597d3f44a812e50.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array} { r l r } & \\\\left[ { \\\\rho { C _ { d x } } A _ { x } \\\\bar { u } } & { 0 } & { 0 } \\\\\\\\ { 0 } & { \\\\rho { C _ { d y } } A _ { y } \\\\bar { v } } & { 0 } \\\\\\\\ { 0 } & { 0 } & { \\\\frac { 1 } { 6 4 } \\\\rho { C _ { d I } } A _ { y } L ^ { 3 } \\\\bar { r } \\\\right] \\\\left[ { \\\\begin{array} { c } { u } \\\\\\\\ { v } \\\\\\\\ { r } \\\\end{array} } \\\\right] = } \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,220,882,266]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0067/d730a241e0bea59509db9e9317fb6405b5af0155a6f79dfa7a86ccef04824774.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left[ { \\\\begin{array} { c c c } { 1 } & { 1 } & { 0 } \\\\\\\\ { - l } & { l } & { l _ { S } } \\\\\\\\ { 0 } & { 0 } & { 1 } \\\\end{array} } \\\\right] \\\\left[ { \\\\begin{array} { c } { T _ { R } } \\\\\\\\ { T _ { L } } \\\\\\\\ { T _ { S } } \\\\end{array} } \\\\right] \\\\ldots \\\\ldots \\\\ldots \\\\ldots \\\\ldots \\\\ldots \\\\ldots \\\\ldots \\\\ldots \\\\ldots \\\\ldots \\\\ldots \\\\ldots .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[515,274,710,288]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"これを以下 $\\\\mathcal { O }$ ように書く。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,292,873,308]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"1004/141e82aef48591d45ec3e352213c3ba8457ac74465f3daf1315662f38d1f293f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nM \\\\ddot { \\\\xi } + C \\\\dot { \\\\xi } = L f \\\\ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[514,311,904,344]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"空間固定座標系で見た速度と物体固定座標系で見た速度には、\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,353,870,397]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0057/252a401297cb2655ad172b5dd52685789b75a5c9129add1b470525034333910c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left[ \\\\begin{array} { l } { u } \\\\\\\\ { v } \\\\\\\\ { r } \\\\end{array} \\\\right] = \\\\left[ \\\\begin{array} { c c c } { \\\\cos \\\\psi } & { \\\\sin \\\\psi } & { 0 } \\\\\\\\ { - \\\\sin \\\\psi } & { \\\\cos \\\\psi } & { 0 } \\\\\\\\ { 0 } & { 0 } & { 1 } \\\\end{array} \\\\right] \\\\left[ \\\\begin{array} { l } { \\\\dot { X } } \\\\\\\\ { \\\\dot { Y } } \\\\\\\\ { \\\\dot { r } } \\\\end{array} \\\\right] \\\\enspace \\\\enspace \\\\cdot \\\\enspace \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot \\\\cdot .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[512,403,907,515]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\mathcal { O }$ 関係があ $\\\\boldsymbol { \\\\nabla }$ 、これを \\n$\\\\dot { \\\\boldsymbol { \\\\xi } } = \\\\pmb { R } \\\\dot { \\\\pmb { X } }$ ．．．(12)と書 $\\\\bigtriangleup$ 。 \\n$\\\\ddot { \\\\xi } = \\\\dot { R } \\\\dot { X } + R \\\\ddot { X } \\\\ \\\\dots \\\\dots \\\\dots \\\\dots \\\\dots \\\\dots \\\\dots \\\\dots \\\\dots \\\\dots \\\\dots \\\\dots \\\\dots \\\\dots \\\\dots .$ (13)であるから、 \\n$M R { \\\\ddot { X } } + ( M { \\\\dot { R } } + C R ) { \\\\dot { X } } = L f$ ．．．．．(14)\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,519,904,552]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"これを制御系設計のために線形近似したノミナルモデルとする。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,573,825,590]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.2 最適制御アルゴリズ $\\\\bigtriangleup \\\\textcircled { \\\\oslash }$ 定式化\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,591,907,681]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"船舶における軌道 $\\\\mathcal { O }$ 最適トラッキング問題は、例えば文献(6)(7)他、これまでにも国内外で多 $< \\\\phi$ 研究がなされている。ここでは本 USV に実装することを目的として設計した最適制御アルゴリズムについて述べる。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,685,909,927]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"目標位置や軌道は、平面固定座標系で与えることとし、軌道上 $\\\\mathcal { O }$ 到達目標位置(Waypoint)を $\\\\mathbf { { \\\\boldsymbol { X } } } _ { t }$ 、目標速度を $\\\\dot { \\\\boldsymbol X } _ { t }$ として、以下 $\\\\mathcal { O }$ 誤差ベクトルを導入し、誤差フ $1 - \\\\mathrm { K } \\\\times \\\\mathrm { i }$ ック系を設計する。$e = [ X \\\\quad \\\\dot { X } ] ^ { T } - [ X _ { t } \\\\quad \\\\dot { X } _ { t } ] ^ { T } \\\\enspace \\\\dotsc \\\\enspace \\\\dotsc \\\\enspace \\\\dotsc \\\\enspace \\\\dotsc \\\\enspace \\\\dotsc \\\\enspace \\\\dotsc \\\\enspace \\\\dotsc \\\\enspace \\\\dotsc \\\\enspace .$ ．(15)シミュレーション結果 $\\\\mathcal { O }$ 節において後述するが、単純に位置と速度をフィードバックするのみでは、PD制御であるため、潮流が速 $\\\\bigtriangledown$ なると定常偏差が大きくな $\\\\boldsymbol { \\\\nabla }$ 、定点保持性能、軌道追従性能が劣化する。そこで、位置に関する誤差 $\\\\mathcal { O }$ 積分器を導入して、1 形 $\\\\mathcal { O }$ サーボ系を構成することとした。すなわち、$\\\\dot { \\\\boldsymbol { z } } = \\\\boldsymbol { X } - \\\\boldsymbol { X } _ { t }$ ．． ．．．．．(16)とし、状態変数を $\\\\pmb { x } = [ \\\\pmb { z } \\\\quad \\\\pmb { e } ] ^ { T }$ とすると、位置と速度$\\\\mathcal { O }$ 誤差に関する状態方程式は、\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[294,35,705,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"日本航海学会論文集 第146巻 第145回講演会にて講演\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[489,948,509,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"33 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[92,85,322,99]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[90,106,465,153]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"0599/19a9231bdff77644fbe71748da58f1c68c4452c3d9009f20ec5548a3f25ecf19.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\dot { x } = \\\\left[ \\\\begin{array} { c c c } { { 0 } } & { { I } } & { { o } } \\\\\\\\ { { 0 } } & { { O } } & { { I } } \\\\\\\\ { { O } } & { { O } } & { { - M R ^ { - 1 } \\\\big ( M \\\\dot { R } + C R \\\\big ) } } \\\\end{array} \\\\right] x + \\\\left[ \\\\begin{array} { c } { { 0 } } \\\\\\\\ { { 0 } } \\\\\\\\ { { M R ^ { - 1 } L } } \\\\end{array} \\\\right] f ( 1 )\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[87,160,485,364]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"と表すことができる。ここに、 、 は3行3列のゼロ行列、単位行列である。これらを \\n${ \\\\dot { \\\\pmb { x } } } = \\\\pmb { A } \\\\pmb { x } + \\\\pmb { B } \\\\pmb { f }$ ．．．．(19)${ \\\\boldsymbol { y } } = { \\\\pmb { C } } { \\\\boldsymbol { x } }$ ．．． ．．．．．(20)として、以下 $\\\\mathcal { O }$ 評価関数 \\n$\\\\begin{array} { r } { J = \\\\int _ { 0 } ^ { \\\\infty } ( x ^ { T } Q x f ^ { T } R f ) d t \\\\ \\\\underbrace { \\\\phantom { \\\\frac { J } { \\\\varepsilon } } \\\\cdots \\\\cdots \\\\cdots \\\\cdots \\\\cdots \\\\cdots \\\\cdots \\\\cdots \\\\cdots \\\\cdots } _ { } . } \\\\end{array}$ ．(21)を最小化するゲインを求めると、制御力は、 \\n$\\\\pmb { f } = - \\\\pmb { G } \\\\pmb { x } = - \\\\pmb { G _ { 1 } } \\\\pmb { z } - \\\\pmb { G _ { 2 } } \\\\pmb { e } \\\\enspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .$ ．(22)$\\\\mathcal { O }$ ように計算できる。ゲインは、座標変換行列 に依存するため、各制御ステップでリカッチ方程式を解き更新しながら制御することになる。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,385,366,401]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.3 シミュレーション結果 $\\\\pmb { \\\\oslash }$ 例\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,403,484,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"上記 $\\\\mathcal { O }$ 式(22)で求められる制御力を用い、式(1)$\\\\sim ( 3 )$ で示した潮流との相対速度の 2 乗に比例する流体力を考慮し、ニューマーク $\\\\beta$ 法による数値積分を行って、シミュレーションによる検討を実施した。実際のカタ ランの質量 $\\\\mathrm { m } { = } 2 0$ [kg]として計算した。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,496,485,757]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"抵抗係数、付加質量係数は船体の形状に依存するため厳密には水槽実験にて検証する必要がある。けれども、4.3.3 で述べるようにこれらの数値の違いによる影響で軌道追従性能が大幅に悪化する可能性は低いことが推定されたため、ここではノミナルモデルの初期値として、例えば付加質量については元良 $\\\\mathcal { O }$ 論文(8)(9) 等を参考にして、サージ方向は$m _ { - x } = 2 [ \\\\mathrm { k g } ] ( - \\\\infty , \\\\infty , \\\\infty , \\\\infty )$ き付加質量係数 0.1 相当)、スウェー方向は $m _ { - y } = 2 0$ [kg]（一つのハルにつき付加質量係数 1.0 相当）等としてシミュレーションを実施した。没水面積は、波の影響を無視し、静水中喫水で算定している。ノミナルモデルと実船のモデル誤差に関する制御系のロバスト性については、今後実海域実験を通じて検証する。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,761,484,832]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"以下に軌道追従制御 $\\\\yen 123,456$ 結果の例を示す。軌道追従においては、進行方向と船体の方位角が異なる場合、すなわち船体が進行方向を向いていない場合に、\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,836,485,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(a)目標地点に向かいながら方位角を修正する方法(b)まず方位角を進行方向に合わせてから目標地点に向かう方法$\\\\scriptscriptstyle \\\\mathcal { O } ) 2$ 種類の方法が考えられる。後に示すように、(a)$\\\\mathcal { O }$ 方法では角度の修正のために軌道が歪むため、原則として(b) $\\\\mathcal { O }$ 方法で軌道追従させることとする。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,102,905,267]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0430/11d5865f87d81e2fda578723abe370cce255f38913949cd57b4fed02ee2061b9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Mode</td><td rowspan=1 colspan=1>StartPoint</td><td rowspan=1 colspan=1>InitialAzimuth[deg]</td><td rowspan=1 colspan=1>TargetAzimuth[deg]</td><td rowspan=1 colspan=1>TargetWaypoint</td></tr><tr><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>Cruise</td><td rowspan=1 colspan=1>[0,0]</td><td rowspan=1 colspan=1>90</td><td rowspan=1 colspan=1>90</td><td rowspan=1 colspan=1>[0,20]</td></tr><tr><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>TurningAround</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>From 90</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>[0,20]</td></tr><tr><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>Cruise</td><td rowspan=1 colspan=1>From[0,20]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>[20,20]</td></tr><tr><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>TurningAround</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>From 0</td><td rowspan=1 colspan=1>-90</td><td rowspan=1 colspan=1>[20,20]</td></tr><tr><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>Cruise</td><td rowspan=1 colspan=1>From[20,20]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>-90</td><td rowspan=1 colspan=1>[20,0]</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1 Simulation condition for trajectory tracking \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[514,286,887,301]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,324,714,340]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.3.1 潮流無しの場合\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,344,905,566]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"シミュレーションプログラムが機能しているかを確認するため、潮流無しの場合について、シミュレーションを実施した結果の一例を図 4 から図 6 に示す。今回のシミュレーションの軌道は表 1 に示すように、点[0,0]を始点とし、途中の通過点を[0,20],[20,20]の2点とし、終点を[20,0]となるように設定した。表 1 に示すように、各点を結ぶ直線状を追従するモードを Cruise モードとする。方位角については、ターゲット通過点において、次のターゲット目標点を目指した目標角となるように回頭してから次の目標地点に進むように設定し、これをTurning Around モードとして制御した。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,568,904,604]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"図 6 に示すように、表1で設定した軌道を追従することが確認できた。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,624,830,641]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.3.2 PD フィードバックのみの場合\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,643,907,922]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1形サーボ系の性能を確認するため、ここではサーボ系ではなく、位置と速度のフィードバックのみで最適制御系を構成した場合の軌道のシミュレーション結果の例を図 7 に示す。潮流は $0 . 2 \\\\left[ \\\\mathrm { m } / \\\\mathrm { s } \\\\right] \\\\mathcal { O }$ 南から来る流れの場合を示す。図 7 からわかるように、潮流が $0 . 2 [ \\\\mathrm { m } / \\\\mathrm { s } ]$ と弱いにも関わらず、 $\\\\mathrm { P D } \\\\supset _ { 1 } - \\\\kappa , \\\\bar { \\\\bf { \\\\sigma } } $ ックのみでは、軌道のゆがみが生じている。表 1 に示すモー $\\\\mathrm { F } \\\\mathcal { O }$ 遷移は、位置の許容誤差 $3 [ \\\\mathrm { m } ]$ 、角度 $\\\\mathcal { O }$ 許容誤差 5[deg]に達した時点で次 $\\\\mathcal { O }$ モードに移る設定としている。実海域実験で使用するスラスター$\\\\mathcal { O }$ 推力は最大 40[N]であることを考慮して評価関数の重みを調整し,ゲインを設定しているが、さらに潮流を早くすると、許容誤差内に制御目標が達成せず、Mode 遷移が行われないという欠点が観測された。従って、サーボ系を組む必要がある。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[294,35,705,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"日本航海学会論文集 第146巻 第145回講演会にて講演\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[489,950,509,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"34 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[90,83,463,290]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.4 Azimuth and surge, sway, yaw velocities (without \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0914/91aa03cfaafd00cf7bc64581feecd93f2b794e8d416c68081759e72e54bd787c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[109,338,442,532]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.5 Control force (without \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0488/666af0f673a11d8b27b8b4e7d27f402d9814de2e5d37fbf47535257ba8a89401.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[109,584,442,776]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.6 Trajectory (without current, $m _ { - x } { = } 2 [ \\\\\\\\mathrm { k g } ]$ , $m _ { - y } { = } 2 0 [ \\\\\\\\mathrm { k g } ]$ ) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0670/48465219dc8dfffe7e0fecb4833411e9adf70cac15fe6840c37d6585b13c00b6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[92,837,405,853]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.3.3 1形サーボ系による結果 $\\\\pmb { \\\\oslash }$ 例\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,857,485,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"図 $8 \\\\sim$ 図 $1 0 \\\\ \\\\ell \\\\geq 4 . 3 . 2$ と同じ潮流条件で、1形サーボ系による制御を実施した結果を示す。図 7と図 10を比較すればわかるように、サーボ系を組むことで、軌道追従性能が向上している。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[531,95,862,287]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.7 Trajectory (PD feedback only, current $= 0 . 2 [ \\\\\\\\mathrm { m } / \\\\\\\\mathrm { s } ]$ , \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0135/a7370f516c414b46c0344dd8d771234a7ed2417da4ca7d602ad27f9e1e4ce03b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[512,313,885,535]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.8 Azimuth and surge, sway, yaw velocities (Servo feedback, current $= 0 . 2 [ \\\\\\\\mathrm { m } / \\\\\\\\mathrm { s } ]$ , from South) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0022/a659235d4e6bfa743d3ed60d0b64a99f74eb3d58f3ce214f1b671299a8fdc021.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[532,584,863,776]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.9 Control force (Servo feedback, current $\\\\\\\\mathrm { \\\\\\\\varepsilon = 0 . 2 [ m / s ] }$ , from South) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0352/6ce1c0cf1f1e0ca48bbbd74287502c33e7c57ee207bca1c3ce3710d9197a6834.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[514,819,905,890]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"また、図 8 の左上図はヨー角を示しているが、この図から、表 1 の Mode2（0度 $=$ 北向き）, Mode4（-90度 $=$ 西向き）における回頭が指定通りに遂行されたことがわかる。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[515,894,904,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"次に、図 $1 1 { \\\\sim } 1 3$ にさらに潮流を $0 . 5 [ \\\\mathrm { m } / \\\\mathrm { s } ]$ と早くし、北西方向から流れているとした場合の例を示す。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[294,35,705,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"日本航海学会論文集 第146巻 第145回講演会にて講演\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[489,948,509,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"35 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[109,96,442,287]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.10 Trajectory (Servo feedback, current $= 0 . 2 [ \\\\\\\\mathrm { m } / \\\\\\\\mathrm { s } ]$ , \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0425/49ee38536928541bfea11489118afea57a13d1f25a5d0bf4127932de4adf2bb1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[90,313,463,535]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.11 Azimuth and surge, sway, yaw velocities (Servo feedback, current $\\\\\\\\mathrm { \\\\\\\\Sigma = 0 . 5 [ m / s ] }$ , from North \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0361/d61e28bb7601c7d52ca2442b73b642515a745f3b8085456c58a60af9fe82bd09.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[109,602,442,795]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.12 Control force (Servo feedback, current= $\\\\\\\\mathrm { \\\\\\\\Delta \\\\\\\\ z 0 . 5 [ m / s ] }$ , from North West, $m _ { - x } = 2 [ \\\\\\\\mathrm { k g } ] , m _ { - y } = 2 0 [ \\\\\\\\mathrm { k g } ] )$ \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0516/df2d606509324a505da066c541342b32c607ef84b4cd2a08c410999ff99f84ff.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[92,856,485,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"潮流を強くした場合には、表 1 に示すモー $\\\\mathrm { F } \\\\mathcal { O }$ 遷移は、位置 $\\\\mathcal { O }$ 許容誤差 $3 [ \\\\mathrm { m } ]$ 、角度 $\\\\mathcal { O }$ 許容誤差 5[deg]ではモード遷移できなかったため、位置 $\\\\mathcal { O }$ 許容誤差4[m]、角度 $\\\\mathcal { O }$ 許容誤差 8[deg]に達した時点で次のモードに移る設定とした。この例からわかるように、潮流が $1 \\\\ \\\\nearrow \\\\ \\\\gg \\\\ \\\\vdash$ 程度までは、本スラスターで対応可能であることが確認できた。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[531,95,863,287]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.13 Trajectory (Servo feedback, current= $\\\\\\\\mathrm { \\\\\\\\Delta } [ 0 . 5 [ \\\\\\\\mathrm { m } / \\\\\\\\mathrm { s } ]$ \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0802/4174f3e84a5bce74f052da279d6fca0a4fb5648575bac3105b19c33860af8544.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[512,313,884,535]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.14 Azimuth and surge, sway, yaw velocities (Servo feedback, current $\\\\\\\\mathrm { \\\\\\\\Sigma = 0 . 5 [ m / s ] }$ , from North \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0029/00b85ea661a2c6840159bafbace947204447eae02dda6120ba294735c5457307.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[532,602,863,795]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.15 Control force (Servo feedback, current= $\\\\\\\\mathrm { \\\\\\\\cdot 0 . 5 [ m / s ] }$ , from North West, $m _ { - x } = 1 0 [ \\\\\\\\mathrm { k g } ] , m _ { - y } = 1 0 [ \\\\\\\\mathrm { k g } ] )$ \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0575/4e79855944a72406cf5b6d74ea9e4931a99788be817d21fc100f470acf3d785c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[514,857,905,909]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,913,905,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ここで、付加質量 $\\\\mathcal { O }$ 違いが計算結果に与える影響について検討するため、図 13 と同じ潮流の場合に、例えば、付加質量を $m _ { - x } { = } 1 0$ [kg]、 $m _ { - y } = 1 0$ [kg] として計算した結果を図 14から図 16 に示す。これらの結果からわかるように、付加質量 $\\\\mathcal { O }$ 違いによって、図 11 と図 14 にみられるような速度 $\\\\mathcal { O }$ 違いや、図 12と図 15 にみられるように制御力の最大値や時系列に違いが生じ、図 13 と図 16 からわかるように到達地点での誤差にも多少の差が生じる。しかしながら、付加質量の推定に誤差があったとしても、表1で設定した目標軌道について、許容誤差の範囲で追従できることは確認できた。付加質量、抵抗係数も含めて、他の値に変更して計算した結果も許容誤差の範囲で軌道追従できたことから、潮流ありのシミュレーションにおいては、先に述べたノミナルモデルの設定値で計算を実施することとした。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[294,35,705,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"日本航海学会論文集 第146巻 第145回講演会にて講演\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[489,948,509,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"36 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[107,95,442,287]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.16 Trajectory (Servo feedback, current= $\\\\\\\\mathrm { \\\\\\\\bar { \\\\\\\\varepsilon } 0 . 5 [ m / s ] } ,$ , from North West, $m _ { - x } = 1 0 [ \\\\\\\\mathrm { k g } ] , m _ { - y } = 1 0 [ \\\\\\\\mathrm { k g } ] )$ \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0201/b33e405908e0c4befa0037f22e14b6a4ccb63d09798c711de38e51072ec35223.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[92,346,485,628]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,648,442,666]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.3.4 船首方向が進行方向と異なる場合\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,669,485,741]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"船首方向が進行方向と異なる場合に、定点で回頭して船首方向を進行方向に向けるのではなく、(a)目標地点に向かいながら同時に方位角を修正する方法、での軌道追従結果の例を図 $1 7 \\\\sim$ 図 19 に示す。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,744,485,815]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"これらの結果から、現在の制御系では、目標地点に向かって進行しながら船首方向を進行方向にセットする場合には、自身が進行することと、潮流の影響により、軌道が歪むことがわかる。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,837,423,853]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.3.5 定点保持性能及び制御系の課題\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,857,485,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"図 20 に定点保持性能に関する結果の一例を示す。現時点での目標範囲には収まっているものの、構造物インスペクション等のミッションにおいては、さらに定点保持精度を上げる必要がある。ゲインを調整すれば、さらに誤差は小さくなるものの、外乱が2 次非線形のため 1 形サーボ系では完全に定常偏差を除去することができない。この点については、定常的な外乱を学習して定常偏差を補償する制御系の設計が今後の課題である。また、ゲインを決定する評価関数内の重み行列を外乱に応じて適応的に調整する適応ゲイン調整も今後の検討課題である。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,83,885,289]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.17 Azimuth and surge, sway, yaw velocities (Servo feedback, current= $\\\\\\\\mathrm { \\\\\\\\Delta } [ 0 . 5 [ \\\\\\\\mathrm { m } / \\\\\\\\mathrm { s } ]$ , from North West) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0636/8aed5287aeab8331ebe54e0386eae920dc0cdbc128d177302552464404e35698.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[527,339,865,532]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.18 Control force (Servo feedback, current $\\\\\\\\mathrm { \\\\\\\\Sigma = 0 . 5 [ m / s ] }$ , from North West) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0537/1c37777623b7f5e09ee5ca2f8ab19cc5a2b149894b97dc93888a68d49c5cf3b1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[531,583,862,776]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.19 Trajectory (Servo feedback, current $\\\\\\\\mathrm { \\\\\\\\Sigma = 0 . 5 [ m / s ] }$ , from North West) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0998/f242b9cf1543c2c3e331de9c67fe717de26f8b46d1fd9221e5dac3c3dd782798.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[514,837,907,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[294,35,705,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"日本航海学会論文集 第146巻 第145回講演会にて講演\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[489,948,509,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"37 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[99,93,442,287]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.20 Trajectory (Servo feedback, current $\\\\\\\\mathrm { \\\\\\\\Sigma = 0 . 5 [ m / s ] }$ , from North West) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0006/5ce703da71a6010fb7863d8e44508dcc3351a9b331522599cff57c66d57772c7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[92,347,485,382]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,402,462,420]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5. 実海域における USV 基本性能の確認\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,422,485,625]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.で述べたシミュレーションにより、本カタマランにおける最も基本的な制御アルゴリズムの機能が確認された。そこで、アクチュエーター、及び GNSSセンサ、スラスター、PCとの無線シリアル通信等各プログラムモジュールの基本的な性能確認を実施するため、本学の桟橋において、基本性能の確認実験を実施した。図 21 に構築した USV 全体の外観、図22 に基本性能確認実験の様子を示す。図 23 中のスタートポイントからの白い線は、USV の航跡について GNSS の緯度経度の結果を Google Map 上に表示したものである。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,629,485,775]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"この実験では、USV は図のスタートポイントから270 度方向に航行し、途中から 250 度方向に変針している。図 24 はこの航跡に対応した方位角の時系列データを示している。図 $2 4 ~ \\\\mathcal { O }$ 方位角が図 $2 3 ~ \\\\mathcal { O } )$ 地図における方向とおおむね一致している様子が見て取れる。このように、本実験を通じて構築した全てのモジュールが動作し、軌道追従実験に必要な位置や方位角の検出が可能であることを確認できた。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,796,178,813]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6. 結論\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,814,485,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"本稿では、USV 実海域実験システムの構築を目的として、姿勢角に応じて各制御サンプリング時間内で最適フィードバックゲインを変更する1形サーボ系最適制御アルゴリズムを提案し、潮流を外乱として条件を変化させたシミュレーションを実施して、性能の有効性と限界を確認した。また、実海域実験を実施するためのテストベッドを構築し、基本機能$\\\\mathcal { O }$ 実装を終了した。本稿で提案したアルゴリズムは、今後開発を進めるより高度な制御手法の基礎となるデータを取得するためのもので、今後、本アルゴリズムを用いて実海域実験による軌道追従データを蓄積し、AIを用いた適応制御系の設計を実施する予定である。\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,84,899,287]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.21 USV experiment system \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0924/e2d7cf5b81e0ab2240251c3d654ba3a98f919bf51850925f16edac2a5827147e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[522,309,895,459]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.22 Experiment field \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0231/231e53aa9521acba03c8fbda40ab1062ea5148efe940098ed6a3f62029f41135.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[526,482,890,700]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.23 Trajectory mapping example \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0362/847610c1f031efe23cf208249569e148fbcadfdf583e3f484421071312454481.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[531,729,889,884]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.24 Azimuth from GNSS record \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0827/12e5e83fdfa5a5fa46900c27251bec5e47b7c880b8cef54de2fa34f87102321b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[294,35,705,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"日本航海学会論文集 第146巻 第145回講演会にて講演\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[489,950,509,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"38 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[92,85,485,213]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,233,176,250]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"参考文献\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,252,485,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(1) 原田和柾、渡邉啓介、新保雅俊、宇都宮洪志、“無人調査船群制御のための水槽実験システムの構築”、日本航海学会論文集、140 巻 pp.77-87、2019. \\n(2) 渡邉啓介、新保雅俊、“カタマラン型 USV の位置制御に関する基礎検討”、日本航海学会第 143回講演会講演予稿集、pp. 35-37、2020.11. \\n(3) Z. Dong, L. Wan, Y. Li, T. Liu, G. Zhang,“Trajectory Tracking Control of Underactuated USVBased on Modified Backstepping Approach”, Int. J.Nav. Archit. Ocean Eng., pp.817-832, 2015 \\n(4) T.I.Fossen,”Marine Control Systems”, ISBN82-92356-00-2, 2002 \\n(5) Keisuke Watanabe, Koshi Utsunomiya, KazumasaHarada, “Development of a Floating LBL Systemand a Lightweight ROV for Sky to Water System”,IEEEXplore,doi.org/10.23919/OCEANS40490.2019.8962848,2019 \\n(6) 三好晋太郎、原洋輔、大津皓平、“カルマンフィルタを用いた最適トラッキング制御に関する研究”、日本航海学会論文集 118 号,pp.47-53, 2008 \\n(7) 三好晋太郎、原洋輔、大津皓平、“線形化モデル用いた最適トラッキング制御に関する研究”、日本航海学会論文集、日本航海学会論文集 117 号, pp.183-189, 2007 \\n(8) 元良誠三、“船体運動に対する附加質量及び附加慣性モーメントについてー其の2. 前後動に対する附加質量ー”、造船協会論文集第105 号,pp.59-62, 1959. \\n(9) 元良誠三、“船体運動に対する附加質量及び附加慣性モーメントについてー其の3. 左右動に対する附加質量ー”、造船協会論文集第106 号,pp.63-68, 1959.\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[294,35,705,51]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"日本航海学会論文集 第146巻 第145回講演会にて講演\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[489,950,509,961]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"39 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n },\n {\n \"bbox\": \"[257,912,477,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"（原稿投稿2022年1月31日）\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"discarded\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.9749/jin.146.30"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Engineering and Manufacturing Science/Earth and Atmospheric Sciences"},"sha256":{"kind":"string","value":"9dd2c312bd2a9960be177645150224f272c841120d5c0467b00570b323e8866b"},"title":{"kind":"string","value":"Examination of Sea Experimental System for Catamaran Type USV Development"}}},{"rowIdx":260,"cells":{"abstract":{"kind":"string","value":"\n \nWe introduce an approach for augmenting text-to-video generation models with customized motions, extending their capabilities beyond the motions depicted in the original training data. By leveraging a few video samples demonstrating specific movements as input, our method learns and generalizes the input motion patterns for diverse, text-specified scenarios. Our contributions are threefold. First, to achieve our results, we finetune an existing text-to-video model to learn a novel mapping between the depicted motion in the input examples to a new unique token. To avoid overfitting to the new custom motion, we introduce an approach for regularization over videos. Second, by leveraging the motion priors in a pretrained model, our method can produce novel videos featuring multiple people doing the custom motion, and can invoke the motion in combination with other motions. Furthermore, our approach extends to the multimodal customization of motion and appearance of individualized subjects, enabling the generation of videos featuring unique characters and distinct motions. Third, to validate our method, we introduce an approach for quantitatively evaluating the learned custom motion and perform a systematic ablation study. We show that our method significantly outperforms prior appearance-based customization approaches when extended to the motion customization task.\n "},"author":{"kind":"string","value":"Antonio Torralba|Richard Zhang|Bryan Russell|Josef Sivic|Eli Shechtman|Joanna Materzynska"},"content_list":{"kind":"list like","value":[{"bbox":"[207,130,764,152]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Customizing Motion in Text-to-Video Diffusion Models ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[233,179,413,215]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Joanna Materzynska $^{1*}$ Antonio Torralba $^{1}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[433,179,563,217]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Josef Sivic $^{2,3}$ Richard Zhang $^{2}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[598,180,733,217]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Eli Shechtman $^{2}$ Bryan Russell $^{2}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[184,224,784,262]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"<sup>1</sup>Massachusetts Institute of Technology <sup>2</sup>Adobe Research <sup>3</sup>CIIRC CTU joanna.github.io/customizing_motion/ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,282,274,537]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0496/2c0b71cc88f54c9ecdc7e168eda8611669a4d624db3da004e00723d92d272ace.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[305,282,782,364]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0530/1e595349249ca2c6126783adb56fc1a1eb21bfa3280fb4f8e8535dec0b2c1f07.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[305,369,782,452]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0391/fdd43dbcbd1b34657ca09362e07e2825456dd881fec817534d9c555826334bbe.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[305,455,782,539]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 1. (Left) Given a few examples (\\\"Carlton dance\\\"), our customization method incorporates the depicted motion into a pretrained text-to-video diffusion model using a new motion identifier (\\\"V* dance\\\"). (Right) We generate the depicted motion across a variety of novel contexts, including with a non-humanoid subject (robot), multiple motions (lady), and multiple subjects (group of nurses). To best view the results, please view the our website. \"]","image_footnote":"[]","img_path":"images/0791/369177308c58072f15cb736be003a9862f60bfe370877e242a9e8c0771b66e5b.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[802,301,880,506]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nonhumanoid Multiple motions Multiple subjects ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[233,619,313,636]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[75,652,472,849]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We introduce an approach for augmenting text-to-video generation models with customized motions, extending their capabilities beyond the motions depicted in the original training data. By leveraging a few video samples demonstrating specific movements as input, our method learns and generalizes the input motion patterns for diverse, text-specified scenarios. Our contributions are threefold. First, to achieve our results, we finetune an existing text-to-video model to learn a novel mapping between the depicted motion in the input examples to a new unique token. To avoid overfitting to the new custom motion, we introduce an approach for regularization over videos. Second, by leveraging the motion priors in a pretrained model, our method can ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[500,622,893,801]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"produce novel videos featuring multiple people doing the custom motion, and can invoke the motion in combination with other motions. Furthermore, our approach extends to the multimodal customization of motion and appearance of individualized subjects, enabling the generation of videos featuring unique characters and distinct motions. Third, to validate our method, we introduce an approach for quantitatively evaluating the learned custom motion and perform a systematic ablation study. We show that our method significantly outperforms prior appearance-based customization approaches when extended to the motion customization task. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[500,829,632,845]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[500,854,893,902]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Recent advancements in text-to-video synthesis have yielded remarkable outcomes [2, 18, 28, 40, 42, 43, 50], marking progress in a traditionally challenging area of ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[22,267,58,700]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"arXiv:2312.04966v1 [cs.CV] 7 Dec 2023 ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[99,862,387,875]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"*Work done in part as an intern with Adobe Research. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[76,875,468,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{3}$ Czech Institute of Informatics, Robotics and Cybernetics at the Czech Technical University in Prague. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[75,90,472,330]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"video generation. However, the capabilities of these models remain confined to their training data. Conveying specific motions not covered in the training set is challenging. For example, consider the examples of the depicted 'Carlton' dance shown in Figure 1 (left). To describe the 'Carlton' dance in a text prompt, it is difficult to describe with natural language the nuances of the swinging arms and the timings of the poses in the dance. The ability to generate a new motion unknown to the model for one or more desired characters with the flexibility of using text to control the subjects' appearance, as shown in Figure 1 (right), can be particularly useful for animation or content creation applications. This ability leads us to a question: How can we harness an existing text-to-video model's knowledge about motion and appearance while augmenting them with new, custom motions? ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,334,472,546]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"While appearance-based customization techniques in text-to-image synthesis have enabled tailored image generation [9, 22, 32], their scope is confined to still images. This setting introduces a limitation where only object customization is feasible. Recent works have extended a pretrained text-to-image synthesis model with trainable temporal layers and applied one-shot tuning over a single video [7, 45]. While these approaches enable text-based stylization of the single video, the generated videos have motions that adhere closely to the timing and spatial layout of the input video and cannot generalize to any other motions. As a result, for an input video's depicted motion, these methods cannot combine it with other motions, apply it to multiple people in a scene, or vary its viewpoint/timing. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,547,472,671]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this work, we present a new approach for customizing text-to-video diffusion models to a novel motion regardless of the appearance of the motion's subject. Given a few videos depicting a new motion, e.g., dance or gesture, our goal is to map the novel motion to a unique text token (\"V*\"). Given the unique text token, we can generate videos with varied subjects undertaking the novel motion (cf., Figure 1 right). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,671,472,808]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As our first contribution, our approach goes beyond prior work by leveraging the rich motion and appearance prior information contained in a pretrained text-to-video generation model. We augment this model with new custom motions by fine tuning the temporal layers and spatial cross-attention keys/values, which we show are crucial for modeling the novel motion. To maintain the model's motion prior and avoid overfitting to the new motion, we introduce a new approach for regularization tailored to videos. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,810,472,902]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As our second contribution, we show that our approach learns to generalize and hence we can invoke the custom motion in novel applications. For example, we first show how to apply a custom motion to multiple people in a scene. Second, we show how to invoke the newly learned custom motion in combination with other motions. Finally, we ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,90,890,121]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"show how to perform multimodal customization over motion and appearance. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,121,893,257]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As our third contribution, to validate our method, we introduce a new approach for quantitatively evaluating the fidelity of the generated custom motions along with the model's ability to respect the subject's desired appearance as described in a text prompt. We use this evaluation protocol to perform a systematic ablation of our method and find that we significantly outperform baseline appearance-based customization approaches when extended to the motion customization task. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[498,270,640,286]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. Related Work ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[496,297,893,688]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Text-to-image customization. Previous approaches to customization in text-to-image generation models are focused on introducing a novel subject or object [5, 6, 9, 10, 16, 22, 24, 26, 32-34, 37, 44, 46, 47, 51]. One strategy fine-tunes a subset of the parameters of the generation network given a few images of a subject and its descriptions [22, 32]. Through this optimization, a new text-image mapping is created between the subject depicted in the images and the textual description. At test time, the subject is invoked via the description but can be now used in a free-form context. Similarly, Gal et al. [9] showed that this mapping can be created purely by optimizing a text embedding of the textual description without modifying the generation network, at a price of image quality. More recent approaches investigate efficient formulations for modifying an approximation of the parameters responsible for the text-image mapping in the generation network [16, 37]. Other methods, alternatively to adjusting the model's parameters, introduce an image encoder that can be directly plugged into the pretrained network [10, 44, 51]. Alternatively to customizing individual concepts, Huang et al. [20] propose to learn relations between two subjects from a set of images via a similar technique to Gal et al. [9]. The text-to-image customization is limited to static objects due to the static nature of still images. In contrast, we focus on customization with respect to a given motion depicted in a small set of videos. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,688,893,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Controllable video generation. The study of controllable video generation is widely researched; we summarize briefly here works that are closest to ours. Han et al. [15] use multi-modal input like sketches or semantic layout to control the synthesized content. Previous works learn GAN representations that disentangle motion and structure [39] or decompose foreground and background to manipulate the foreground only [19]. Chan et al. [4] use a single source video of a dancing person to generate a novel video depicting the motion transferred to a new subject. Geyer et al. [13] propose a method for semantic video editing of real-world videos, using a text-to-image model. Our approach differs from these prior works in that we learn a generalized motion from a few video examples. Then, the motion ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,88,893,224]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 2. Overview. Given a small set of exemplar videos, our approach fine-tunes the U-Net of a text-to-video model using a reconstruction objective. The motion is identified with a unique motion identifier and can be used at test time to synthesize novel subjects performing the motion. To represent the added motion but preserve information from the pretrained model, we tune a subset of weights – the temporal convolution and attention layers, in addition to the key & value layers in the spatial attention layer. A set of related videos is used to regularize the tuning process. \"]","image_footnote":"[]","img_path":"images/0000/beb7c631ea59ff025b7c0f2eb2c80e9477affb30a8951f594279d0a5c0b8deb3.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[75,321,470,429]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"can be used in new contexts with text conditioning, and the motion can be used in an array of new applications where text controls for the number of subjects performing the motion, their appearance, and the background. While previous works focus primarily on transferring motion between humans, our approach generalizes the motion pattern such that it can be applied also to non-human subjects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,460,468,672]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Video synthesis with image generation models. Prior work has used text-to-image generation models for video generation. Guo et al. [14] learn a motion prior network with text-video data and leverage the prior in personalized text-image models. Similarly, prior work has shown video generation with text-to-image models [21, 35, 48]. Ge et al. [12] demonstrates an approach for zero-shot text-to-video generation by designing a video noise prior. Our work differs in that we use a video generation model directly to learn new motions. Wu et al. [45] inverts an existing video frame-by-frame using a pre-trained text-to-image model then, using the inverted noise maps and text guidance, synthesizes a novel video. This method edits an existing video, while our focus is on generating completely new videos from scratch. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,703,470,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Text-to-video models. Recently, several methods have demonstrated text-to-video generation [2, 18, 28, 40, 42, 43, 50]. An important line of research involves studying architectures and optimization for training video generation models. A high-quality model is a prerequisite for our method. In this work, we use the model from Wang et al. [42]. Molad et al. [28] show qualitative results of adding a custom subject to the base video model. They, however, do not explore customization beyond static objects [28]. The idea of multi-modal customization, however, facilitates user-controllability and creative applications, since no matter how powerful the model, there are always novel subjects and motions that cannot be all contained in the training set. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[498,321,609,339]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. Approach ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[496,345,890,438]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We aim to customize text-to-video models with respect to a novel motion. That is, we wish to introduce novel dynamic concepts in the model's knowledge base and associate them with unique text tokens. In this section, we first give a preliminary description of text-to-video diffusion models, followed by our approach for motion customization. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[498,445,877,460]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1. Text-to-Video Diffusion Model Preliminaries ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[496,468,890,648]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Diffusion models are probabilistic models that can approximate distributions through a gradual denoising process [17, 36]. Given a Gaussian noise sample, the model learns to iteratively remove a portion of noise until a sample is within the approximated distribution. The objective function of this process minimizes the $L_{2}$ distance of the predicted noise and the sampled noise. Latent Diffusion Models (LDMs) [31] are diffusion models operating in the latent space instead of pixel space. Instead of learning the denoising process in a complex high-dimensional space, the videos are first encoded into a lower-dimensional vector through a learned encoder-decoder model. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,650,890,816]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Specifically, a video $x$ is represented with a latent vector, and a text condition $c$ is encoded through a text-embedding from a pre-trained text encoder. The initial noise map $\\epsilon$ is sampled from a Gaussian distribution $\\epsilon \\sim \\mathcal{N}(0,1)$ . For the diffusion timestep $t$ sampled from a probability density $t \\sim f(t)$ , the noisy latent sample can be computed from the noise prediction by $x_{t} = \\sqrt{\\alpha_{t}} x_{0} + \\sqrt{1 - \\alpha_{t}}\\epsilon$ , where $x_0$ is the original video and $\\alpha_{t}$ controls the amount of noise added at each diffusion timestep according to a noise scheduler [17, 36]. The model $\\epsilon_{\\theta}$ with parameters $\\theta$ is trained with the following weighted denoising loss, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[547,824,890,861]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {L} _ {\\theta} (x, c) = \\underset { \\begin{array}{c} \\epsilon \\sim \\mathcal {N} (0, 1) \\\\ t \\sim f (t) \\end{array} } {\\mathbb {E}} \\left[ w _ {t} \\| \\epsilon_ {\\theta} (x, \\epsilon , c, t) - \\epsilon \\| _ {2} ^ {2} \\right], \\tag {1}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[496,869,890,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $w_{t}$ is a user-defined variable that controls the sample quality. At inference time, a new video can be generated ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,90,468,121]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"by sampling a Gaussian noise sample $\\epsilon$ and a text prompt, denoising them with the learned model. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[76,133,392,148]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2. Approach for Motion Customization ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[75,157,470,338]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We illustrate our overall approach for motion customization in Figure 2. Let the motion be represented through a small exemplar set of videos and corresponding text prompts $D^{m} = \\{(x^{m},c^{m})\\}$ . The motion can be performed by different subjects across different backgrounds, and the commonality within the videos is purely the dynamic movement. We choose a generic textual description across the videos, such as \"a person doing the V*\". In practice, we select unique tokens like \"pll\" as \"V*\". To customize a text-to-video model's parameters $\\theta$ , we fine-tune the model's parameters by minimizing the diffusion objective $\\mathcal{L}_{\\theta}$ summed over the exemplar set $D^{m}$ , ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[192,351,468,386]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\min _ {\\theta} \\sum_ {(x, c) \\sim D ^ {m}} \\mathcal {L} _ {\\theta} (x, c). \\tag {2}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[75,398,468,444]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"At test time we can generate novel videos of the target with variations controlled by text. Next, we describe the important components of our motion customization approach. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,445,468,565]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Choice of customization parameters. The quality and generalization ability of the novel motion depends on the choice of the model parameters updated during customization. A text-to-video diffusion model $\\epsilon_{\\theta}$ has parameters $\\theta$ that can be categorized to those operating on the temporal dimensions $\\theta_t \\subset \\theta$ and those operating on the spatial dimensions (per-frame) $\\theta_s \\subset \\theta$ . Let $\\theta_s^{k,v} \\subset \\theta_s$ be the keys and values parameters of the spatial cross-attention modules. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,566,468,686]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The temporal layers $\\theta_{t}$ are transformers and temporal convolutions, and are responsible for modelling temporal patterns across frames. In Section 4, we empirically show that the temporal layers alone do not effectively model a new motion pattern due to time-varying appearance changes. For example, consider an object rotating in 3D, which requires the model to generate the appearance of disoccluded surfaces. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,688,468,838]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To faithfully learn a motion pattern, we also modify a subset of parameters in the spatial layers of the model. As illustrated in Figure 2, our approach fine tunes the spatial keys/values $\\theta_s^{k,v}$ and temporal $\\theta_t$ parameters. Note that in image customization [22, 38] and model editing [11], it has been shown that the spatial keys and values of the cross-attention modules in text-to-image models are sufficiently powerful to represent the appearance of new concepts. Our experiments also show the effectiveness of adjusting those parameters for the motion customization task. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,839,468,901]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Video regularization. Prior work has shown that directly optimizing Equation (2) leads to forgetting related concepts or the concept category [23, 25, 32]. For example, if the concept is a specific person, all people start resembling that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,90,890,167]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"person. To mitigate this issue, prior work has utilized a regularization set that ensures that this knowledge is preserved. For example, Ruiz et al. [32] proposed collecting a regularization set via generation from the original model. Kumari et al. [22] proposed using pairs of real images and text. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,167,890,316]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In contrast to prior work, we seek to mitigate forgetting of related motions that the model has already learned. To address this goal, we consider a video-based regularization. Let $D^{r}$ be a regularization set of paired videos with text descriptions that have similar but not identical motion to the target custom motion videos $D_{m}$ . For example, when learning the 'Carlton' dance, we chose a regularization set of real videos containing people dancing. For customization, we optimize the diffusion objective $\\mathcal{L}_{\\theta}$ over the target custom videos $D^{m}$ and regularization set $D^{r}$ : ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[602,327,890,362]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\min _ {\\theta} \\sum_ {(x, c) \\sim D ^ {m} \\cup D ^ {r}} \\mathcal {L} _ {\\theta} (x, c). \\tag {3}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[496,372,890,431]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Empirically, we show in Section 4 that using real videos for the regularization set is superior to using generated videos from the model. We find that using generated videos degrades the quality of the customized model substantially. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,433,890,824]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Learning the motion patterns. To facilitate learning the common motion in $D^{m}$ , during the training process, we aim to put emphasis on the motion pattern of the videos, rather than the appearance or subject presenting the motion. For example, in the case of the 'Carlton' dance in Figure 1 we wish to capture the motion pattern of the dance rather than the appearance of the background or the individual performers. The denoising process in diffusion models samples a Gaussian noise and then gradually removes the noise. The initial noise as well as early denoising steps have large influence on the output overall dynamic structure of the video, whereas the later stages correspond to finer details [41]. To focus on the dynamic structure of the videos and de-emphasize the appearance of the subjects performing the motion, we define a timestep sampling strategy. In particular, we build on [20] who develop a non-uniform sampling strategy for generating still images. Here we adopt it for generating dynamic video content. In detail, instead of uniformly sampling the denoising steps in Equation (1), we define a probability distribution $f_{\\alpha}(t) = \\frac{1}{T} (1 - \\alpha \\cos(\\frac{\\pi t}{T}))$ over the timesteps that focuses more on the earlier denoising steps and hence emphasizes learning the overall dynamic motion pattern rather than the fine appearance details of the background or the individual subjects. The $\\alpha$ parameter increases the skewness of the function. We use $\\alpha = 0.5$ for all of our experiments. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,825,890,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Customizing appearance and motion. Our method can be easily extended to customizing both appearance and motion. The appearance of a new subject is represented through an exemplar dataset $D^{s}$ of pairs of still images and captions describing the images. To learn the appearance of ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[101,88,446,176]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0901/7e049dc2bbf9dbd237e18e2dd9bfc54504a1412389e7427f02ce0c199b6ef6d1.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":"<table><tr><td></td><td>Motion accuracy ↑</td><td>Text Alignment ↑</td></tr><tr><td>Textual Inversion [9]</td><td>0.3</td><td>0.2733</td></tr><tr><td>Custom Diffusion [22]</td><td>10.5</td><td>0.2788</td></tr><tr><td>Dreambooth [32]</td><td>28.4</td><td>0.2796</td></tr><tr><td>Ours</td><td>70.6</td><td>0.2818</td></tr></table>","table_caption":"[\"Table 1. Quantitative comparison with image customization methods applied to the motion customization task. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[75,229,470,335]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"a person we follow [22] and update the spatial layers of the model, and optimize the text embedding associated with our subject. We customize the model first with the motion, then train both the appearance and the subject jointly, choosing an example of either dataset in the mini-batch. When learning the subject we treat the images as a one-frame video and only update the selected spatial layers. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[76,352,209,369]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. Experiments ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[75,378,468,422]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this section, we quantitatively evaluate our approach (Section 4.1), perform an ablation study (Section 4.2), and show qualitative results (Section 4.3). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,425,468,546]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Implementation details. In all our experiments we use the ZeroScope text-to-video diffusion model [3] as the pretrained network. Our implementation is building on the public repository [8]. In our concept exemplar dataset $D^{m}$ , we apply spatial and color augmentation on the video examples. We train the model with a mini-batch size 1 on a single A100 Nvidia GPU. We train the models up to 3000 training steps with learning rate $5 \\times 10^{-6}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[76,558,299,574]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.1. Quantitative Evaluation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[75,582,468,643]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We quantitatively evaluate our approach by computing metrics corresponding to the quality of the generated motion and the overall fidelity of the generated video with respect to the input text prompt. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,643,470,901]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dataset. We quantitatively evaluate our approach on the Jester Dataset [27]. The dataset contains 148,092 crowdsourced videos of 27 human gestures by diverse actors performing a gesture in front of a static camera. We select 5 gesture classes as our target motions - $\\{\\text{Swiping Down, Drumming Fingers, Rolling Hand Forward, Shaking Hand, Sliding Two Fingers Up}\\}$ . From each class, we choose at random 10 videos from the validation set as our training set. To learn the motion, we caption the videos with a generic text description \"a person doing a V* sign\". As a regularization set for the motion learning, we also choose 50 videos from each of the dataset classes $\\{\\text{Doing Other Things, No gesture}\\}$ and assign them text captions \"a person doing other things\" and \"a person in front of a computer\". We design a test set containing 100 text prompts that detail a person's appearance, for example \"A female firefighter doing the V* gesture\" or \"A Japanese toddler doing the V ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,92,885,354]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 3. Visual comparison with image customization methods. Examples of learning a customized motion Sliding Two Fingers Up from the Jester dataset with prompt \\\"A female firefighter doing the $V^{*}$ sign\\\". Image personalization methods (top three rows) fail to capture the motion and produce a temporally coherent video. Please see supplemental video. \"]","image_footnote":"[]","img_path":"images/0626/110e7cf684fbbe4ceeaf62e5d233ad2d4f29f554c8523b5a5c85bf22914d7daa.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[498,462,890,491]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"gesture\". We fix 3 random seeds per text prompt to evaluate our experiments. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,492,892,643]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Motion accuracy metric. The Jester dataset has been widely adopted for the task of action recognition. We leverage this for our motion accuracy metric, measuring gesture recognition accuracy with a video classifier, pre-trained on the Jester training set [49]. The classifier achieves $94.78\\%$ accuracy across all gesture classes, making it suitable for our evaluation. Note that the simple test set prompts typically result in generated videos that adhere to the spatial layout of the gesture recognition classifier's training videos with a single person, making them in-distribution. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,643,892,853]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Text alignment metrics. To regulate overfitting, we measure how faithfully the model adheres to the appearance described in the text prompt with an appearance score defined as the mean CLIP score between the generated frames and the part of the text prompt describing the person's appearance (e.g., \"A female firefighter\"). We empirically find that the appearance score is a good proxy to determine when the model starts to overfit. For a fair comparison across all models, we fine-tune each model until this appearance score reaches a chosen value (here 0.265), determined empirically based on the visual quality of the results. Please refer to the Supplemental Material for an additional discussion on the tradeoff between motion accuracy and appearance alignment. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[498,854,893,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To assess how well the generated video corresponds to the overall text prompt (both motion and appearance), we measure the text alignment score as a mean CLIP score be ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[116,88,349,138]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0246/94e2c98339769a05314e18c8a5a8a6e706e33512a4a132665548dfa7e28121fe.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td>Spatial layers</td><td>Accuracy ↑</td><td>Copy ↓</td></tr><tr><td>None</td><td>62.3</td><td>5.9</td></tr><tr><td>All</td><td>68.7</td><td>17.0</td></tr><tr><td>K,V (Ours)</td><td>70.6</td><td>8.7</td></tr></table>","table_caption":"[\"(a) Spatial layers \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[385,93,614,133]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0054/52d2b6e70d93b88f15b30ed84a7560f3c5a26120626e82f50db2cc86664c3e9e.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td>Trans. layers</td><td>Accuracy ↑</td><td>Copy ↓</td></tr><tr><td>None</td><td>22.7</td><td>1.4</td></tr><tr><td>All (Ours)</td><td>70.6</td><td>8.7</td></tr></table>","table_caption":"[\"(b) Temporal layers \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[656,93,877,133]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0114/9f6c73b97e2bbcabda337ebc2ef09cc1eb8077cf89923299c900a16516d6f0be.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td>Text Token</td><td>Accuracy ↑</td><td>Copy ↓</td></tr><tr><td>✓</td><td>75.5</td><td>22.7</td></tr><tr><td>X (Ours)</td><td>70.6</td><td>8.7</td></tr></table>","table_caption":"[\"(c) Text Token \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[217,157,485,199]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0612/93dbf0367cbcd484a1e9d546e570300d3997d1eb92b7a521caeb3fc420b8c143.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td>Sampling</td><td>Accuracy ↑</td><td>Copy ↓</td></tr><tr><td>Uniform</td><td>66.9</td><td>15.4</td></tr><tr><td>Coarse-noise (Ours)</td><td>70.6</td><td>8.7</td></tr></table>","table_caption":"[\"(d) Sampling Strategy \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[550,152,776,204]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0715/674b99ddc9ffda9e24487e0702b31371fa8a04c3d45a4a7335d9a69be5ca1126.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td>Prior</td><td>Accuracy ↑</td><td>Copy ↓</td></tr><tr><td>None</td><td>43.9</td><td>1.2</td></tr><tr><td>Synthetic</td><td>48.3</td><td>3.7</td></tr><tr><td>Real (Ours)</td><td>70.6</td><td>8.7</td></tr></table>","table_caption":"[\"(e) Regularization \",\"Table 2. Quantitative results of the ablation study. Each table examines the design choices of our method. We report the motion recognition accuracy (\\\"Accuracy\\\") obtained with a pre-trained classifier for gesture recognition. The copying score (\\\"Copy\\\") is the percentage of generated videos with an image copy detection score higher than a specified threshold. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[75,273,468,363]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tween the video frames and a full caption written in natural language. For example, for the class Swiping Down and a text prompt \"A female firefighter doing the V* gesture\", a full caption would be \"A female firefighter swiping hand down.\" We use this score as another criterion to compare different methods. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,366,470,805]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Comparison with image customization methods. We select three well-established image customization approaches: Textual Inversion [9], Dreambooth [32] and Custom Diffusion [22], and adapt them to the motion customization task. Textual Inversion [9] optimizes a text token embedding to learn a novel subject. For Dreambooth [32], we optimize all spatial layers of the model and use a synthetic video regularization set following their prior preservation loss. Custom Diffusion trains the key and value projection matrices in the cross-attention layers of text-to-image diffusion models, optimizes a text token embedding, and uses a regularization set containing real videos. We report the motion accuracy and text alignment metrics in Table 1 and show qualitative comparison in Figure 3. We observe that Textual Inversion completely fails to learn the motion. We hypothesize that this failure is because the text encoder has been trained only on image-text pairs, and the embedding fails to generalize to the video domain. Additionally, the text embedding is injected only into spatial layers in the cross-attention layers, and not the temporal ones. Alternatively, because we are learning an unseen motion pattern, which is more complex than a static object, the embedding does not have enough parameters to learn it. On the other hand, Dreambooth and Custom Diffusion learn to adhere to the spatial structure of the training videos and some hand manipulation. However they fail to accurately reproduce the motion and produce a temporally smooth video. In contrast, our approach yields over a $2 \\times$ improvement in motion accuracy and more faithfully adheres to the text prompt. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[76,816,225,832]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.2. Ablation study ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[75,839,468,901]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We perform an ablation study of our method's components and report the motion accuracy metric in Table 2. In addition, we report a copying score (\"Copy\") that measures how much of the training data appearance leaks into the gener ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,273,890,426]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ated data. We use the SSCD description score [29] to detect image copying between the training videos and the generated videos. We compute our copying score as the maximum SSCD description score between the generated frames of the video and first frames of the training examples, and report the percentage of samples that are above a specified threshold. For our experiments, we manually determine a threshold of 0.25, which corresponds to significant copying of the appearance of the person or the background (please see examples in the Supp. Mat.). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,426,892,593]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"First, we study the choice of the optimized parameters. As in the case of the image customization methods, it is clear that optimizing the spatial layers of the model is not enough to learn a novel motion pattern, as shown in Table 2b. We can further observe that training the key and value projections in the cross-attention layers of the spatial layers achieves a good balance in terms of accuracy and copying score, as shown Table 2a. We observe a two-fold reduction in the copying score when training only those parameters and an $8\\%$ improvement in motion accuracy compared to not training any spatial parameters. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,595,890,744]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Next, in Table 2c, we consider the role of optimizing the text token embedding. We notice that when jointly training the text token embedding with the model's parameters, the motion accuracy is higher than when training only the model parameters. However, it also leads to nearly three times as much memorization of the training video appearance, as evidenced by the significantly increased Copy score. We hypothesize that this indicates that the text token embedding is learning something related to the appearance of the training videos. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,748,890,883]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Consequently, we test our sampling strategy. We compare a model trained with our motion pattern sampling strategy (\"Coarse-noise\") to a model that simply samples diffusion time steps uniformly (\"Uniform\"). As shown in Table 2d, our sampling strategy improves the motion accuracy and reduces the appearance copying. Following our intuition regarding learning motion patterns rather than fine-grained details, our model is less prone to replicating elements from the training examples. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,885,890,901]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lastly, we study the effect of the regularization prior ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[91,92,869,679]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 4. Qualitative results of our method. We demonstrate two custom motions: Dab and Air quotes, trained using collected internet examples as well as a 3D camera rotation trained with examples from the CO3D dataset [30]. Our method can generalize to unseen subjects and multiple people performing the action. Please refer to our supplemental video to view these results. \"]","image_footnote":"[]","img_path":"images/0666/9029b8457e92b7b2226fabb7ac704970eeeedf3c6b8f0d4ef15bcd0f736fabd4.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[75,741,472,893]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"in Table 2e. We train three models with the same design choice as our method, yet we choose the regularization set to be either: (i) empty, (ii) a synthetic set of videos generated from the original text-to-video model, or (iii) containing real videos. We observe a significant drop in performance both without using a prior as well as using a synthetic prior. Interestingly, despite all settings using the same finetuning set, a high-quality regularization set containing real videos improves the overall training. Overall, our method achieves a good balance between high motion accuracy and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[500,742,627,757]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"low copying score. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[500,770,720,787]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.3. Qualitative experiments ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[496,794,890,902]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To further demonstrate the effectiveness of our approach, we choose the motions: Dab, Airquotes, and 3D rotation, which the original model does not know or cannot reliably perform. For the first two motions, we curate videos from the internet searching for the description of the motion. We use between 5 and 6 videos for each motion and caption the videos with a generic text description such as \"A person do ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[86,106,472,161]","code_body":null,"code_caption":null,"image_caption":"[\"Tune-A-Video \",\"\\\"A clown doing the V* gesture while eating a burger with his other hand\\\" \"]","image_footnote":"[]","img_path":"images/0058/1c599c130d8869c07df10ac4169fca0797cc940ceb373565493948d22d1b8d2b.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[86,176,472,232]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0858/2f7364896cee9ec38b94b882aa3ac1f4aa11e069cd169409167b30ff0205f321.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[86,244,472,299]","code_body":null,"code_caption":null,"image_caption":"[\"\\\"An elder woman doing the V* gesture very slowly and precisely\\\" \",\"\\\"Children doing the V* gesture in the classroom in front of a blackboard\\\" \"]","image_footnote":"[]","img_path":"images/0457/e88581279d2ec859a2d5b9d4faaf3e7a38ec03d8d464f152ba20768015d9b6a2.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[498,107,885,162]","code_body":null,"code_caption":null,"image_caption":"[\"Ours \",\"\\\"A clown doing the V* gesture while eating a burger with his other hand\\\" \"]","image_footnote":"[]","img_path":"images/0506/4e083cb5d22d15feab7f0319ecedef356785431ef0df92de968dd130b11f236b.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[500,176,885,232]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0204/f608afaa248c5a3ba3741100aa6bd8919a8b6f4905a47a571db20f9730955f28.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[500,244,885,299]","code_body":null,"code_caption":null,"image_caption":"[\"\\\"An elder woman doing the V* gesture very slowly and precisely\\\" \",\"\\\"Children doing the V* gesture in the classroom in front of a blackboard\\\" \",\"Figure 5. Tune-A-Video versus our method trained on few examples of a custom motion \\\"Shaking Hand\\\". Our method seamlessly renders a custom motion in novel scenarios. Despite the videos in the training set only showing a single actor doing one single motion in the same way, our method can generate the custom motion in conjunction with a different motion (\\\"doing the gesture while eating a burger with other hand\\\"). Our method can also vary the timing of the motion (\\\"doing the gesture very slowly and precisely\\\") and involve multiple people (\\\"children\\\"). On the contrary, Tune-A-Video fails to generalize to these novel scenarios or produce a temporally coherent video. \"]","image_footnote":"[]","img_path":"images/0938/58e8e98ec68713d47fcd62ec0e9f50b7dda1c10250d3f3506f90e3691bbdc4c6.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[96,410,274,521]","code_body":null,"code_caption":null,"image_caption":"[\"Appearance \",\"\\\"A photo of a $X^{*}$ man\\\" \"]","image_footnote":"[]","img_path":"images/0510/a5828cc253329ccdac8595b6be9bc0a7613e50727e3596d075754ca8f6842420.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[303,410,454,446]","code_body":null,"code_caption":null,"image_caption":"[\"Motion \"]","image_footnote":"[]","img_path":"images/0104/738ecb91e2a2f3fc8cc63b6b454469d5b88c4d4d80e6bacbfd5e3fb720fba1f1.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[305,446,454,484]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0533/2ee6420d77beaa5581126c801dbf0a1bd34adbc16b7adb0e25591076ce75fe33.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[305,484,454,522]","code_body":null,"code_caption":null,"image_caption":"[\"\\\"A person doing the V* sign\\\" \"]","image_footnote":"[]","img_path":"images/0675/565b41c4db5de3d4d11fd94a800c0e6ddb9a869849bafb954979c58118a3c1f1.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[86,539,452,593]","code_body":null,"code_caption":null,"image_caption":"[\"\\\"A $X^{*}$ man doing the $V^{*}$ sign\\\" \",\"Figure 6. Appearance and motion customization. Given few images of a person and few videos of a custom motion (top), our method can generate a novel video depicting that person doing the novel motion (bottom). \"]","image_footnote":"[]","img_path":"images/0295/7ae94062064ed03262c83bdaf95563d1d2f26029cde4d607f39302e7f03a75ed.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[75,684,467,835]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ing the V* sign\" or \"A person V*\". To learn 3D rotation, we select 10 sequences of distinct objects from the CO3D Dataset [30] and caption the videos with the text prompt \"A camera V* around an [object]\", where [object] is an object class. The results are shown in Figure 4. For visualization, we query for objects not present in the training videos. For the regularization set, we select 100 video and text pairs from the WebVid-10M Dataset [1]. We fine-tune the models for 2000 steps. Please see our companion webpage for additional results and comparison with the pre-trained model. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,839,467,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Motion and appearance customization. We combine the appearance of a specific person with a gesture motion Drumming Fingers from the Jester Dataset. We use the publicly available images of a particular person from the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,396,890,486]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CustomConcept101 Dataset [22], and annotate them with generic text captions {\"A X* man\", \"A close-up of a X* man\", \"A X* man smiling.}. For the motion dataset, we choose the same 10 videos as in Section 4.1 and a generic text description \"a person doing a V* sign\". Our qualitative results are shown in Fig. 6. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[496,488,890,789]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Comparison with a reference-based method. We compare our method with Tune-A-Video [45], a video editing method that, given a source video, inflates a text-to-image model to learn a motion pattern from a single video. This method allows generation of novel videos with the same pattern but varying appearance. We adapt Tune-A-Video to fine-tune from multiple videos using the same training set as our setup. In Figure 5 we compare the two methods. We test the generalization abilities of the two methods, firstly combining the novel motion with a different motion: \"doing the V* gesture while eating a burger with other hand\". We can see that our method can generate the two motions. Next, we test the motion variation. We show that we can manipulate the execution of the motion with a natural language description; here we specify \"doing the V* gesture very slowly and precisely\". Lastly, we show that our method can generalize to multiple people doing the motion while preserving the temporal consistency of the video. The Tune-A-Video baseline produces qualitatively worse results, as can be seen in Figure 5 and the supplementary video. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[500,805,617,820]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5. Conclusion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[496,830,890,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We present an approach for motion customization in text-to-video diffusion models. Our method can learn a new motion from a set of few exemplar videos of different subjects performing the same gesture. We conduct a thorough ablation study that identifies the key components ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,90,472,203]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"of the method and evaluate them with respect to motion accuracy. We demonstrate qualitative results of our method, specifically in scenarios where our method generalizes the motion to unseen actors, multiple people performing the motion, and different viewpoints. Additionally, we show how our method can be extended to multimodal motion and appearance customization to generate videos with custom subjects performing custom motions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[78,229,173,244]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[78,253,470,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[1] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. 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Enhancing detail preservation for customized text-to-image generation: A regularization-free approach. arXiv preprint arXiv:2305.13579, 2023. 2 \"]","page_idx":"9","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[207,85,764,138]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Customizing Motion in Text-to-Video Diffusion Models Supplementary Material ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[94,157,434,172]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This supplemental contains the following material: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[76,176,468,357]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- Accompanying webpage of qualitative results of our method, the videos shown in the main paper and comparison with the pre-trained text-to-video generations. \",\"- (Section A) We provide additional implementation details regarding our quantitative experiments. \",\"- (Section B) We discuss the tradeoff between the motion accuracy, appearance alignment and copying score across training iterations. \",\"- (Section C) We show qualitative examples along with their copying score. \",\"- (Section D) We show the original model's (i.e. before customization) performance on the Jester dataset. \"]","page_idx":"10","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[76,386,303,402]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A. Implementation Details ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[76,416,468,477]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As described in Section 4.1 we design a test set of 100 prompts detailing a person's appearance and fix three random seeds per prompt. We show the list of the prompts in Figure 9. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[76,505,468,540]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"B. Tradeoff between motion accuracy, appearance alignment, and copying score ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[76,553,472,902]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"When customizing a model with a new motion, we observe a natural bias-variance tradeoff. The longer we train the model, the better motion accuracy becomes, we memorize elements of the training examples, and the model becomes less diverse. We illustrate this in Figure 7. With more training iterations, the network memorizes the gesture as well as visual elements of the training examples. These findings are indicated by both the motion accuracy and copying score increasing. On the other hand, the CLIP appearance score, decreases. The CLIP appearance is defined as an average CLIP score between the part of the text prompt that describes a person's appearance and the video frames (i.e. in a prompt \"A female firefighter doing the V* sign\", the CLIP appearance score accounts for \"A female firefighter\"). This score is a proxy for visual diversity, since our test set contains visual description of a person, it measures how accurate the description is. As we increase the number of iterations, the videos become less diverse, hence the score decreases. This trend is persistent across the models from our ablation study. To find a balance between those factors, we perform early stopping for all models when the CLIP appearance score reaches 0.265 (i.e. when the image still reasonably well corresponds to the text description). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[540,157,851,349]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0065/303d7b2acba7ae36fe166a5b7a896b5d1b23d0475557e40a2956c15fb467cacf.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[540,353,851,544]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0148/2470e6b9b862501d989f1bfaa63cc67abfa5e170e4a1079ff034763d06ff1ff8.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[563,547,849,750]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 7. Our model's performance in terms of motion accuracy (top), CLIP appearance score (middle), and copying score (bottom) across training steps (x-axis). \"]","image_footnote":"[]","img_path":"images/0946/c63650c4ee69939141b059a6da714024427e02a01d2e7a40dadf555ce3cab41c.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[500,839,648,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"C. Copying score ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[500,869,890,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Copying score, as defined in 4.2 measures how much of the training data appearance leaks into the generated data. The ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[76,90,472,272]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"score corresponds to the percentage of examples in the test set that are above a specified threshold of the SSCD score with any of the training examples. We find that the SSCD copy detection score [29] is a good proxy for determining the memorization of the training examples' appearance. We measure the SSCD detection as a maximum score between any frame of the training videos and any video frame from the test set. We empirically determine that pairs of videos with a score greater than 0.25 share significant visual similarities. As seen in Figure 8, the similarities can be either the background or the appearance of the person performing the gesture. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[83,285,176,357]","code_body":null,"code_caption":null,"image_caption":"[\"A blond girl doing the V\\\\* sign. \"]","image_footnote":"[]","img_path":"images/0516/1f0f759364c6d0d15504487d12f956dcedd61bf7cbafeffd49808ccd7fe1b3ea.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[176,285,267,357]","code_body":null,"code_caption":null,"image_caption":"[\"Training Video \",\"\"]","image_footnote":"[]","img_path":"images/0536/f1d46f37ff0aaaf899f84c3ac1815253a9975374edd2986d02f8e291a25a0a9b.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[282,285,377,357]","code_body":null,"code_caption":null,"image_caption":"[\"A man wearing glasses doing the V* sign. \"]","image_footnote":"[]","img_path":"images/0782/c1307f4a8d1e2e07769e75acd1c5b5cff20d8b7121c6d47909a5f005a8008e8a.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[377,285,468,357]","code_body":null,"code_caption":null,"image_caption":"[\"Training Video \"]","image_footnote":"[]","img_path":"images/0762/689b370f1c1bef17aac835f8ab01fbc2fcdb69b74c94b15f9fe915fda6ae4e1e.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[83,385,176,457]","code_body":null,"code_caption":null,"image_caption":"[\"A ginger girl doing the V* sign. \"]","image_footnote":"[]","img_path":"images/0452/03c603ebb1b8408dd00b899fe13df85a4a660849b5186a1f224d6ba9f8db17ce.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[176,385,267,457]","code_body":null,"code_caption":null,"image_caption":"[\"Training Video \"]","image_footnote":"[]","img_path":"images/0668/6cd885d057b8c8d61f03f673d9a13cdb98a4766f44613bb80935b23bc503b2a7.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[282,385,377,457]","code_body":null,"code_caption":null,"image_caption":"[\"A person in a summer dress doing the V* sign \"]","image_footnote":"[]","img_path":"images/0353/269da3585ce7d0eaa512ad5fc2e41d2a22c11110b986775fcd513538c48e152c.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[377,385,468,457]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 9. Test set prompts for the quantitative evaluation of learning the Jester motions \"]","image_footnote":"[]","img_path":"images/0274/613115e71f642058ef2d5cf8be3b46a080057851f5474aa769c1c2367e02c654.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[401,459,455,469]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Training Video ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[76,492,468,547]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 8. Examples of pairs of generated frames and training frames with SSCD score 0.25. Notice the similarity in the background (top-left and bottom-left) and foreground (t-shirt logo in the top-right, person's face in the bottom-right). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[76,578,468,612]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"D. Pre-trained model's performance on motions from the Jester dataset. ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[76,621,472,832]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To test whether the gestures from the Jester dataset, are well-represented in the pre-trained text-to-video model, we evaluate the model with a similar experiment as our ablation experiment (4.2). We query the pre-trained text-to-video model with the prompts from the test set (Section A), replacing the \"doing the sks gesture\" with a natural language description of the class, e.g., for the class \"Drumming Fingers\" - \"drumming finger\". We then classify the videos with the pre-trained network trained on the Jester dataset. No videos were correctly classified because (i) the gestures are not well represented in the model and (ii) the generated videos do not adhere to the spatial assumption of the Jester dataset (where a single person is performing a gesture in front of a camera). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[500,95,756,852]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"A woman doing the sks sign. \",\"A tribe man doing the sks sign \",\"A young woman doing the sks sign. \",\"A Korean girl doing the sks sign \",\"A Korean boy doing the sks sign A korean man doing the sks sign \",\"A korean man doing the sks sign. A korean woman doing the sks sig \",\"A korean toddler doing the sks sign. \",\"A japanese woman doing the sks sign. \",\"A japanese boy doing the sks sign \",\"A japanese girl doing the sks sign \",\"A japanese toddler doing the sks sign. \",\"A japanese man doing the sks sign \",\"A firefighter doing the sks sign \",\"A female firefighter doing the sks sign \",\"A clown doing the sks sign \",\"Mickey Mouse doing the sks sign. And we did being the stars. \",\"A housemaid doing the sky sign A female press doing the job \",\"A female nurse doing the sks sign . \",\"A male nurse doing the sks sign .A toddler doing the also sign \",\"An african woman doing the sks sign. \",\"An african man doing the sks sign. \",\"An african boy doing the sks sign \",\"An african toddler doing the sks sign \",\"An elderly woman doing the sks sign. \",\"An elderly man doing the sks sign \",\"A mexican man doing the sks sign \",\"A mexican woman doing the sks sign. \",\"A mexican boy doing the sks sign \",\"A mexican girl doing the sks sign \",\"A mexican toddler doing the sks sign \",\"A slavic man doing the sks sign. \",\"A slavic woman doing the sks sign \",\"A slavic boy doing the sks sign. A clastic girl doing the oks sign. \",\"A slavic girl doing the sky sign. A clavigic child doing the sky sign. \",\"A slavie child doing the sks sign. A blond woman doing the asks sign. \",\"A blond woman doing the sks sign. A blond man doing the sks sign. \",\"A blond boy doing the sks sign. \",\"A blond girl doing the sks sign. \",\"A ginger woman doing the sks sign. \",\"A ginger man doing the sks sign. \",\"A ginger boy doing the sks sign. \",\"A ginger girl doing the sks sign \",\"A woman with glasses doing the sks sign. \",\"A man with glasses doing the sks sign. \",\"A girl with glasses doing the sks \",\"A boy with glasses doing the sks sign \",\"A child with glasses doing the sks sign \",\"A man with a beard doing the sks sign \",\"A teacher doing the sks sign \",\"A musician doing the sks sign. \",\"A chef doing the sks sign \",\"A construction worker doing the sks sign \",\"A police officer doing the sks sign. \",\"A student doing the sks sign \",\"A doctor doing the sks sign \",\"A scientist doing the sks sign. \",\"A farmer doing the sks sign \",\"A dancer doing the sks sign. \",\"A pilot doing the sks sign \",\"A yoga instructor doing the sks sign \",\"A surfer doing the sks sign \",\"A skateboarder doing the sks sign. \",\"A hiker doing the sks \",\"A painter doing the sks sign \",\"A photographer doing the sks sign. \",\"A writer doing the sks sign. \",\"A woman with long hair doing the sks sign. \",\"A man with a mustache doing the sks sign \",\"A woman with a ponytail doing the sks sign \",\"A man with a bald head doing the sks sign \",\"A teenager doing the sks sign \",\"A senior citizen doing the sks sign. \",\"A person in a wheelchair doing the sks sign. \",\"A person with a backpack doing the sks sign. \",\"A person wearing a hat doing the sks sign \",\"A person in traditional clothing doing the sks sign. \",\"A person in casual attire doing the sks sign \",\"A person in formal attire doing the sks sign \",\"A person with tattoos doing the sks sign. \",\"A person with piercings doing the sks sign \",\"A person with a camera doing the sks sign. \",\"A person holding a book doing the sks sign \",\"A person using a smartphone doing the sks sign. \",\"A person with a pet doing the sks sign \",\"A person with a bicycle doing the sks sign. \",\"A person in workout clothes doing the sks sign. \",\"A person in a swimsuit doing the sks sign. \",\"A person wearing a backpack doing the sks \",\"A person wearing a business suit doing the sks sign. \",\"A person wearing a lab coat doing the sks sign. \",\"A person wearing a uniform doing the sks sign. \",\"A person in a winter coat doing the sks sign \",\"A person in a summer dress doing the sks sign \",\"A person in a cowboy hat doing the sks sign \",\"A person in a graduation gown doing the sks \",\"A person in a superhero costume doing the sks sign. \",\"A person in a traditional robe doing the sks sign \"]","page_idx":"11","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"}],"string":"[\n {\n \"bbox\": \"[207,130,764,152]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Customizing Motion in Text-to-Video Diffusion Models \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[233,179,413,215]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Joanna Materzynska $^{1*}$ Antonio Torralba $^{1}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[433,179,563,217]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Josef Sivic $^{2,3}$ Richard Zhang $^{2}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[598,180,733,217]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Eli Shechtman $^{2}$ Bryan Russell $^{2}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[184,224,784,262]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"<sup>1</sup>Massachusetts Institute of Technology <sup>2</sup>Adobe Research <sup>3</sup>CIIRC CTU joanna.github.io/customizing_motion/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,282,274,537]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0496/2c0b71cc88f54c9ecdc7e168eda8611669a4d624db3da004e00723d92d272ace.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[305,282,782,364]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0530/1e595349249ca2c6126783adb56fc1a1eb21bfa3280fb4f8e8535dec0b2c1f07.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[305,369,782,452]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0391/fdd43dbcbd1b34657ca09362e07e2825456dd881fec817534d9c555826334bbe.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[305,455,782,539]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 1. (Left) Given a few examples (\\\\\\\"Carlton dance\\\\\\\"), our customization method incorporates the depicted motion into a pretrained text-to-video diffusion model using a new motion identifier (\\\\\\\"V* dance\\\\\\\"). (Right) We generate the depicted motion across a variety of novel contexts, including with a non-humanoid subject (robot), multiple motions (lady), and multiple subjects (group of nurses). To best view the results, please view the our website. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0791/369177308c58072f15cb736be003a9862f60bfe370877e242a9e8c0771b66e5b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[802,301,880,506]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nonhumanoid Multiple motions Multiple subjects \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[233,619,313,636]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,652,472,849]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We introduce an approach for augmenting text-to-video generation models with customized motions, extending their capabilities beyond the motions depicted in the original training data. By leveraging a few video samples demonstrating specific movements as input, our method learns and generalizes the input motion patterns for diverse, text-specified scenarios. Our contributions are threefold. First, to achieve our results, we finetune an existing text-to-video model to learn a novel mapping between the depicted motion in the input examples to a new unique token. To avoid overfitting to the new custom motion, we introduce an approach for regularization over videos. Second, by leveraging the motion priors in a pretrained model, our method can \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,622,893,801]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"produce novel videos featuring multiple people doing the custom motion, and can invoke the motion in combination with other motions. Furthermore, our approach extends to the multimodal customization of motion and appearance of individualized subjects, enabling the generation of videos featuring unique characters and distinct motions. Third, to validate our method, we introduce an approach for quantitatively evaluating the learned custom motion and perform a systematic ablation study. We show that our method significantly outperforms prior appearance-based customization approaches when extended to the motion customization task. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,829,632,845]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,854,893,902]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Recent advancements in text-to-video synthesis have yielded remarkable outcomes [2, 18, 28, 40, 42, 43, 50], marking progress in a traditionally challenging area of \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[22,267,58,700]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"arXiv:2312.04966v1 [cs.CV] 7 Dec 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[99,862,387,875]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"*Work done in part as an intern with Adobe Research. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[76,875,468,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{3}$ Czech Institute of Informatics, Robotics and Cybernetics at the Czech Technical University in Prague. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[75,90,472,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"video generation. However, the capabilities of these models remain confined to their training data. Conveying specific motions not covered in the training set is challenging. For example, consider the examples of the depicted 'Carlton' dance shown in Figure 1 (left). To describe the 'Carlton' dance in a text prompt, it is difficult to describe with natural language the nuances of the swinging arms and the timings of the poses in the dance. The ability to generate a new motion unknown to the model for one or more desired characters with the flexibility of using text to control the subjects' appearance, as shown in Figure 1 (right), can be particularly useful for animation or content creation applications. This ability leads us to a question: How can we harness an existing text-to-video model's knowledge about motion and appearance while augmenting them with new, custom motions? \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,334,472,546]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"While appearance-based customization techniques in text-to-image synthesis have enabled tailored image generation [9, 22, 32], their scope is confined to still images. This setting introduces a limitation where only object customization is feasible. Recent works have extended a pretrained text-to-image synthesis model with trainable temporal layers and applied one-shot tuning over a single video [7, 45]. While these approaches enable text-based stylization of the single video, the generated videos have motions that adhere closely to the timing and spatial layout of the input video and cannot generalize to any other motions. As a result, for an input video's depicted motion, these methods cannot combine it with other motions, apply it to multiple people in a scene, or vary its viewpoint/timing. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,547,472,671]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this work, we present a new approach for customizing text-to-video diffusion models to a novel motion regardless of the appearance of the motion's subject. Given a few videos depicting a new motion, e.g., dance or gesture, our goal is to map the novel motion to a unique text token (\\\"V*\\\"). Given the unique text token, we can generate videos with varied subjects undertaking the novel motion (cf., Figure 1 right). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,671,472,808]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As our first contribution, our approach goes beyond prior work by leveraging the rich motion and appearance prior information contained in a pretrained text-to-video generation model. We augment this model with new custom motions by fine tuning the temporal layers and spatial cross-attention keys/values, which we show are crucial for modeling the novel motion. To maintain the model's motion prior and avoid overfitting to the new motion, we introduce a new approach for regularization tailored to videos. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,810,472,902]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As our second contribution, we show that our approach learns to generalize and hence we can invoke the custom motion in novel applications. For example, we first show how to apply a custom motion to multiple people in a scene. Second, we show how to invoke the newly learned custom motion in combination with other motions. Finally, we \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,90,890,121]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"show how to perform multimodal customization over motion and appearance. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,121,893,257]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As our third contribution, to validate our method, we introduce a new approach for quantitatively evaluating the fidelity of the generated custom motions along with the model's ability to respect the subject's desired appearance as described in a text prompt. We use this evaluation protocol to perform a systematic ablation of our method and find that we significantly outperform baseline appearance-based customization approaches when extended to the motion customization task. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[498,270,640,286]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. Related Work \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,297,893,688]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Text-to-image customization. Previous approaches to customization in text-to-image generation models are focused on introducing a novel subject or object [5, 6, 9, 10, 16, 22, 24, 26, 32-34, 37, 44, 46, 47, 51]. One strategy fine-tunes a subset of the parameters of the generation network given a few images of a subject and its descriptions [22, 32]. Through this optimization, a new text-image mapping is created between the subject depicted in the images and the textual description. At test time, the subject is invoked via the description but can be now used in a free-form context. Similarly, Gal et al. [9] showed that this mapping can be created purely by optimizing a text embedding of the textual description without modifying the generation network, at a price of image quality. More recent approaches investigate efficient formulations for modifying an approximation of the parameters responsible for the text-image mapping in the generation network [16, 37]. Other methods, alternatively to adjusting the model's parameters, introduce an image encoder that can be directly plugged into the pretrained network [10, 44, 51]. Alternatively to customizing individual concepts, Huang et al. [20] propose to learn relations between two subjects from a set of images via a similar technique to Gal et al. [9]. The text-to-image customization is limited to static objects due to the static nature of still images. In contrast, we focus on customization with respect to a given motion depicted in a small set of videos. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,688,893,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Controllable video generation. The study of controllable video generation is widely researched; we summarize briefly here works that are closest to ours. Han et al. [15] use multi-modal input like sketches or semantic layout to control the synthesized content. Previous works learn GAN representations that disentangle motion and structure [39] or decompose foreground and background to manipulate the foreground only [19]. Chan et al. [4] use a single source video of a dancing person to generate a novel video depicting the motion transferred to a new subject. Geyer et al. [13] propose a method for semantic video editing of real-world videos, using a text-to-image model. Our approach differs from these prior works in that we learn a generalized motion from a few video examples. Then, the motion \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,88,893,224]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 2. Overview. Given a small set of exemplar videos, our approach fine-tunes the U-Net of a text-to-video model using a reconstruction objective. The motion is identified with a unique motion identifier and can be used at test time to synthesize novel subjects performing the motion. To represent the added motion but preserve information from the pretrained model, we tune a subset of weights – the temporal convolution and attention layers, in addition to the key & value layers in the spatial attention layer. A set of related videos is used to regularize the tuning process. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0000/beb7c631ea59ff025b7c0f2eb2c80e9477affb30a8951f594279d0a5c0b8deb3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[75,321,470,429]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"can be used in new contexts with text conditioning, and the motion can be used in an array of new applications where text controls for the number of subjects performing the motion, their appearance, and the background. While previous works focus primarily on transferring motion between humans, our approach generalizes the motion pattern such that it can be applied also to non-human subjects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,460,468,672]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Video synthesis with image generation models. Prior work has used text-to-image generation models for video generation. Guo et al. [14] learn a motion prior network with text-video data and leverage the prior in personalized text-image models. Similarly, prior work has shown video generation with text-to-image models [21, 35, 48]. Ge et al. [12] demonstrates an approach for zero-shot text-to-video generation by designing a video noise prior. Our work differs in that we use a video generation model directly to learn new motions. Wu et al. [45] inverts an existing video frame-by-frame using a pre-trained text-to-image model then, using the inverted noise maps and text guidance, synthesizes a novel video. This method edits an existing video, while our focus is on generating completely new videos from scratch. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,703,470,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Text-to-video models. Recently, several methods have demonstrated text-to-video generation [2, 18, 28, 40, 42, 43, 50]. An important line of research involves studying architectures and optimization for training video generation models. A high-quality model is a prerequisite for our method. In this work, we use the model from Wang et al. [42]. Molad et al. [28] show qualitative results of adding a custom subject to the base video model. They, however, do not explore customization beyond static objects [28]. The idea of multi-modal customization, however, facilitates user-controllability and creative applications, since no matter how powerful the model, there are always novel subjects and motions that cannot be all contained in the training set. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[498,321,609,339]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. Approach \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,345,890,438]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We aim to customize text-to-video models with respect to a novel motion. That is, we wish to introduce novel dynamic concepts in the model's knowledge base and associate them with unique text tokens. In this section, we first give a preliminary description of text-to-video diffusion models, followed by our approach for motion customization. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[498,445,877,460]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1. Text-to-Video Diffusion Model Preliminaries \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,468,890,648]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Diffusion models are probabilistic models that can approximate distributions through a gradual denoising process [17, 36]. Given a Gaussian noise sample, the model learns to iteratively remove a portion of noise until a sample is within the approximated distribution. The objective function of this process minimizes the $L_{2}$ distance of the predicted noise and the sampled noise. Latent Diffusion Models (LDMs) [31] are diffusion models operating in the latent space instead of pixel space. Instead of learning the denoising process in a complex high-dimensional space, the videos are first encoded into a lower-dimensional vector through a learned encoder-decoder model. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,650,890,816]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Specifically, a video $x$ is represented with a latent vector, and a text condition $c$ is encoded through a text-embedding from a pre-trained text encoder. The initial noise map $\\\\epsilon$ is sampled from a Gaussian distribution $\\\\epsilon \\\\sim \\\\mathcal{N}(0,1)$ . For the diffusion timestep $t$ sampled from a probability density $t \\\\sim f(t)$ , the noisy latent sample can be computed from the noise prediction by $x_{t} = \\\\sqrt{\\\\alpha_{t}} x_{0} + \\\\sqrt{1 - \\\\alpha_{t}}\\\\epsilon$ , where $x_0$ is the original video and $\\\\alpha_{t}$ controls the amount of noise added at each diffusion timestep according to a noise scheduler [17, 36]. The model $\\\\epsilon_{\\\\theta}$ with parameters $\\\\theta$ is trained with the following weighted denoising loss, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[547,824,890,861]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {L} _ {\\\\theta} (x, c) = \\\\underset { \\\\begin{array}{c} \\\\epsilon \\\\sim \\\\mathcal {N} (0, 1) \\\\\\\\ t \\\\sim f (t) \\\\end{array} } {\\\\mathbb {E}} \\\\left[ w _ {t} \\\\| \\\\epsilon_ {\\\\theta} (x, \\\\epsilon , c, t) - \\\\epsilon \\\\| _ {2} ^ {2} \\\\right], \\\\tag {1}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[496,869,890,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $w_{t}$ is a user-defined variable that controls the sample quality. At inference time, a new video can be generated \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,90,468,121]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"by sampling a Gaussian noise sample $\\\\epsilon$ and a text prompt, denoising them with the learned model. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[76,133,392,148]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2. Approach for Motion Customization \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,157,470,338]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We illustrate our overall approach for motion customization in Figure 2. Let the motion be represented through a small exemplar set of videos and corresponding text prompts $D^{m} = \\\\{(x^{m},c^{m})\\\\}$ . The motion can be performed by different subjects across different backgrounds, and the commonality within the videos is purely the dynamic movement. We choose a generic textual description across the videos, such as \\\"a person doing the V*\\\". In practice, we select unique tokens like \\\"pll\\\" as \\\"V*\\\". To customize a text-to-video model's parameters $\\\\theta$ , we fine-tune the model's parameters by minimizing the diffusion objective $\\\\mathcal{L}_{\\\\theta}$ summed over the exemplar set $D^{m}$ , \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[192,351,468,386]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\min _ {\\\\theta} \\\\sum_ {(x, c) \\\\sim D ^ {m}} \\\\mathcal {L} _ {\\\\theta} (x, c). \\\\tag {2}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[75,398,468,444]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"At test time we can generate novel videos of the target with variations controlled by text. Next, we describe the important components of our motion customization approach. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,445,468,565]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Choice of customization parameters. The quality and generalization ability of the novel motion depends on the choice of the model parameters updated during customization. A text-to-video diffusion model $\\\\epsilon_{\\\\theta}$ has parameters $\\\\theta$ that can be categorized to those operating on the temporal dimensions $\\\\theta_t \\\\subset \\\\theta$ and those operating on the spatial dimensions (per-frame) $\\\\theta_s \\\\subset \\\\theta$ . Let $\\\\theta_s^{k,v} \\\\subset \\\\theta_s$ be the keys and values parameters of the spatial cross-attention modules. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,566,468,686]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The temporal layers $\\\\theta_{t}$ are transformers and temporal convolutions, and are responsible for modelling temporal patterns across frames. In Section 4, we empirically show that the temporal layers alone do not effectively model a new motion pattern due to time-varying appearance changes. For example, consider an object rotating in 3D, which requires the model to generate the appearance of disoccluded surfaces. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,688,468,838]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To faithfully learn a motion pattern, we also modify a subset of parameters in the spatial layers of the model. As illustrated in Figure 2, our approach fine tunes the spatial keys/values $\\\\theta_s^{k,v}$ and temporal $\\\\theta_t$ parameters. Note that in image customization [22, 38] and model editing [11], it has been shown that the spatial keys and values of the cross-attention modules in text-to-image models are sufficiently powerful to represent the appearance of new concepts. Our experiments also show the effectiveness of adjusting those parameters for the motion customization task. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,839,468,901]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Video regularization. Prior work has shown that directly optimizing Equation (2) leads to forgetting related concepts or the concept category [23, 25, 32]. For example, if the concept is a specific person, all people start resembling that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,90,890,167]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"person. To mitigate this issue, prior work has utilized a regularization set that ensures that this knowledge is preserved. For example, Ruiz et al. [32] proposed collecting a regularization set via generation from the original model. Kumari et al. [22] proposed using pairs of real images and text. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,167,890,316]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In contrast to prior work, we seek to mitigate forgetting of related motions that the model has already learned. To address this goal, we consider a video-based regularization. Let $D^{r}$ be a regularization set of paired videos with text descriptions that have similar but not identical motion to the target custom motion videos $D_{m}$ . For example, when learning the 'Carlton' dance, we chose a regularization set of real videos containing people dancing. For customization, we optimize the diffusion objective $\\\\mathcal{L}_{\\\\theta}$ over the target custom videos $D^{m}$ and regularization set $D^{r}$ : \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[602,327,890,362]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\min _ {\\\\theta} \\\\sum_ {(x, c) \\\\sim D ^ {m} \\\\cup D ^ {r}} \\\\mathcal {L} _ {\\\\theta} (x, c). \\\\tag {3}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[496,372,890,431]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Empirically, we show in Section 4 that using real videos for the regularization set is superior to using generated videos from the model. We find that using generated videos degrades the quality of the customized model substantially. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,433,890,824]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Learning the motion patterns. To facilitate learning the common motion in $D^{m}$ , during the training process, we aim to put emphasis on the motion pattern of the videos, rather than the appearance or subject presenting the motion. For example, in the case of the 'Carlton' dance in Figure 1 we wish to capture the motion pattern of the dance rather than the appearance of the background or the individual performers. The denoising process in diffusion models samples a Gaussian noise and then gradually removes the noise. The initial noise as well as early denoising steps have large influence on the output overall dynamic structure of the video, whereas the later stages correspond to finer details [41]. To focus on the dynamic structure of the videos and de-emphasize the appearance of the subjects performing the motion, we define a timestep sampling strategy. In particular, we build on [20] who develop a non-uniform sampling strategy for generating still images. Here we adopt it for generating dynamic video content. In detail, instead of uniformly sampling the denoising steps in Equation (1), we define a probability distribution $f_{\\\\alpha}(t) = \\\\frac{1}{T} (1 - \\\\alpha \\\\cos(\\\\frac{\\\\pi t}{T}))$ over the timesteps that focuses more on the earlier denoising steps and hence emphasizes learning the overall dynamic motion pattern rather than the fine appearance details of the background or the individual subjects. The $\\\\alpha$ parameter increases the skewness of the function. We use $\\\\alpha = 0.5$ for all of our experiments. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,825,890,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Customizing appearance and motion. Our method can be easily extended to customizing both appearance and motion. The appearance of a new subject is represented through an exemplar dataset $D^{s}$ of pairs of still images and captions describing the images. To learn the appearance of \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[101,88,446,176]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0901/7e049dc2bbf9dbd237e18e2dd9bfc54504a1412389e7427f02ce0c199b6ef6d1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td></td><td>Motion accuracy ↑</td><td>Text Alignment ↑</td></tr><tr><td>Textual Inversion [9]</td><td>0.3</td><td>0.2733</td></tr><tr><td>Custom Diffusion [22]</td><td>10.5</td><td>0.2788</td></tr><tr><td>Dreambooth [32]</td><td>28.4</td><td>0.2796</td></tr><tr><td>Ours</td><td>70.6</td><td>0.2818</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. Quantitative comparison with image customization methods applied to the motion customization task. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[75,229,470,335]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"a person we follow [22] and update the spatial layers of the model, and optimize the text embedding associated with our subject. We customize the model first with the motion, then train both the appearance and the subject jointly, choosing an example of either dataset in the mini-batch. When learning the subject we treat the images as a one-frame video and only update the selected spatial layers. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[76,352,209,369]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. Experiments \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,378,468,422]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this section, we quantitatively evaluate our approach (Section 4.1), perform an ablation study (Section 4.2), and show qualitative results (Section 4.3). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,425,468,546]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Implementation details. In all our experiments we use the ZeroScope text-to-video diffusion model [3] as the pretrained network. Our implementation is building on the public repository [8]. In our concept exemplar dataset $D^{m}$ , we apply spatial and color augmentation on the video examples. We train the model with a mini-batch size 1 on a single A100 Nvidia GPU. We train the models up to 3000 training steps with learning rate $5 \\\\times 10^{-6}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[76,558,299,574]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.1. Quantitative Evaluation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,582,468,643]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We quantitatively evaluate our approach by computing metrics corresponding to the quality of the generated motion and the overall fidelity of the generated video with respect to the input text prompt. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,643,470,901]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dataset. We quantitatively evaluate our approach on the Jester Dataset [27]. The dataset contains 148,092 crowdsourced videos of 27 human gestures by diverse actors performing a gesture in front of a static camera. We select 5 gesture classes as our target motions - $\\\\{\\\\text{Swiping Down, Drumming Fingers, Rolling Hand Forward, Shaking Hand, Sliding Two Fingers Up}\\\\}$ . From each class, we choose at random 10 videos from the validation set as our training set. To learn the motion, we caption the videos with a generic text description \\\"a person doing a V* sign\\\". As a regularization set for the motion learning, we also choose 50 videos from each of the dataset classes $\\\\{\\\\text{Doing Other Things, No gesture}\\\\}$ and assign them text captions \\\"a person doing other things\\\" and \\\"a person in front of a computer\\\". We design a test set containing 100 text prompts that detail a person's appearance, for example \\\"A female firefighter doing the V* gesture\\\" or \\\"A Japanese toddler doing the V \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,92,885,354]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 3. Visual comparison with image customization methods. Examples of learning a customized motion Sliding Two Fingers Up from the Jester dataset with prompt \\\\\\\"A female firefighter doing the $V^{*}$ sign\\\\\\\". Image personalization methods (top three rows) fail to capture the motion and produce a temporally coherent video. Please see supplemental video. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0626/110e7cf684fbbe4ceeaf62e5d233ad2d4f29f554c8523b5a5c85bf22914d7daa.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[498,462,890,491]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"gesture\\\". We fix 3 random seeds per text prompt to evaluate our experiments. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,492,892,643]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Motion accuracy metric. The Jester dataset has been widely adopted for the task of action recognition. We leverage this for our motion accuracy metric, measuring gesture recognition accuracy with a video classifier, pre-trained on the Jester training set [49]. The classifier achieves $94.78\\\\%$ accuracy across all gesture classes, making it suitable for our evaluation. Note that the simple test set prompts typically result in generated videos that adhere to the spatial layout of the gesture recognition classifier's training videos with a single person, making them in-distribution. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,643,892,853]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Text alignment metrics. To regulate overfitting, we measure how faithfully the model adheres to the appearance described in the text prompt with an appearance score defined as the mean CLIP score between the generated frames and the part of the text prompt describing the person's appearance (e.g., \\\"A female firefighter\\\"). We empirically find that the appearance score is a good proxy to determine when the model starts to overfit. For a fair comparison across all models, we fine-tune each model until this appearance score reaches a chosen value (here 0.265), determined empirically based on the visual quality of the results. Please refer to the Supplemental Material for an additional discussion on the tradeoff between motion accuracy and appearance alignment. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[498,854,893,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To assess how well the generated video corresponds to the overall text prompt (both motion and appearance), we measure the text alignment score as a mean CLIP score be \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[116,88,349,138]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0246/94e2c98339769a05314e18c8a5a8a6e706e33512a4a132665548dfa7e28121fe.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Spatial layers</td><td>Accuracy ↑</td><td>Copy ↓</td></tr><tr><td>None</td><td>62.3</td><td>5.9</td></tr><tr><td>All</td><td>68.7</td><td>17.0</td></tr><tr><td>K,V (Ours)</td><td>70.6</td><td>8.7</td></tr></table>\",\n \"table_caption\": \"[\\\"(a) Spatial layers \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[385,93,614,133]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0054/52d2b6e70d93b88f15b30ed84a7560f3c5a26120626e82f50db2cc86664c3e9e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Trans. layers</td><td>Accuracy ↑</td><td>Copy ↓</td></tr><tr><td>None</td><td>22.7</td><td>1.4</td></tr><tr><td>All (Ours)</td><td>70.6</td><td>8.7</td></tr></table>\",\n \"table_caption\": \"[\\\"(b) Temporal layers \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[656,93,877,133]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0114/9f6c73b97e2bbcabda337ebc2ef09cc1eb8077cf89923299c900a16516d6f0be.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Text Token</td><td>Accuracy ↑</td><td>Copy ↓</td></tr><tr><td>✓</td><td>75.5</td><td>22.7</td></tr><tr><td>X (Ours)</td><td>70.6</td><td>8.7</td></tr></table>\",\n \"table_caption\": \"[\\\"(c) Text Token \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[217,157,485,199]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0612/93dbf0367cbcd484a1e9d546e570300d3997d1eb92b7a521caeb3fc420b8c143.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Sampling</td><td>Accuracy ↑</td><td>Copy ↓</td></tr><tr><td>Uniform</td><td>66.9</td><td>15.4</td></tr><tr><td>Coarse-noise (Ours)</td><td>70.6</td><td>8.7</td></tr></table>\",\n \"table_caption\": \"[\\\"(d) Sampling Strategy \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[550,152,776,204]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0715/674b99ddc9ffda9e24487e0702b31371fa8a04c3d45a4a7335d9a69be5ca1126.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Prior</td><td>Accuracy ↑</td><td>Copy ↓</td></tr><tr><td>None</td><td>43.9</td><td>1.2</td></tr><tr><td>Synthetic</td><td>48.3</td><td>3.7</td></tr><tr><td>Real (Ours)</td><td>70.6</td><td>8.7</td></tr></table>\",\n \"table_caption\": \"[\\\"(e) Regularization \\\",\\\"Table 2. Quantitative results of the ablation study. Each table examines the design choices of our method. We report the motion recognition accuracy (\\\\\\\"Accuracy\\\\\\\") obtained with a pre-trained classifier for gesture recognition. The copying score (\\\\\\\"Copy\\\\\\\") is the percentage of generated videos with an image copy detection score higher than a specified threshold. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[75,273,468,363]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tween the video frames and a full caption written in natural language. For example, for the class Swiping Down and a text prompt \\\"A female firefighter doing the V* gesture\\\", a full caption would be \\\"A female firefighter swiping hand down.\\\" We use this score as another criterion to compare different methods. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,366,470,805]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Comparison with image customization methods. We select three well-established image customization approaches: Textual Inversion [9], Dreambooth [32] and Custom Diffusion [22], and adapt them to the motion customization task. Textual Inversion [9] optimizes a text token embedding to learn a novel subject. For Dreambooth [32], we optimize all spatial layers of the model and use a synthetic video regularization set following their prior preservation loss. Custom Diffusion trains the key and value projection matrices in the cross-attention layers of text-to-image diffusion models, optimizes a text token embedding, and uses a regularization set containing real videos. We report the motion accuracy and text alignment metrics in Table 1 and show qualitative comparison in Figure 3. We observe that Textual Inversion completely fails to learn the motion. We hypothesize that this failure is because the text encoder has been trained only on image-text pairs, and the embedding fails to generalize to the video domain. Additionally, the text embedding is injected only into spatial layers in the cross-attention layers, and not the temporal ones. Alternatively, because we are learning an unseen motion pattern, which is more complex than a static object, the embedding does not have enough parameters to learn it. On the other hand, Dreambooth and Custom Diffusion learn to adhere to the spatial structure of the training videos and some hand manipulation. However they fail to accurately reproduce the motion and produce a temporally smooth video. In contrast, our approach yields over a $2 \\\\times$ improvement in motion accuracy and more faithfully adheres to the text prompt. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[76,816,225,832]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.2. Ablation study \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,839,468,901]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We perform an ablation study of our method's components and report the motion accuracy metric in Table 2. In addition, we report a copying score (\\\"Copy\\\") that measures how much of the training data appearance leaks into the gener \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,273,890,426]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ated data. We use the SSCD description score [29] to detect image copying between the training videos and the generated videos. We compute our copying score as the maximum SSCD description score between the generated frames of the video and first frames of the training examples, and report the percentage of samples that are above a specified threshold. For our experiments, we manually determine a threshold of 0.25, which corresponds to significant copying of the appearance of the person or the background (please see examples in the Supp. Mat.). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,426,892,593]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"First, we study the choice of the optimized parameters. As in the case of the image customization methods, it is clear that optimizing the spatial layers of the model is not enough to learn a novel motion pattern, as shown in Table 2b. We can further observe that training the key and value projections in the cross-attention layers of the spatial layers achieves a good balance in terms of accuracy and copying score, as shown Table 2a. We observe a two-fold reduction in the copying score when training only those parameters and an $8\\\\%$ improvement in motion accuracy compared to not training any spatial parameters. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,595,890,744]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Next, in Table 2c, we consider the role of optimizing the text token embedding. We notice that when jointly training the text token embedding with the model's parameters, the motion accuracy is higher than when training only the model parameters. However, it also leads to nearly three times as much memorization of the training video appearance, as evidenced by the significantly increased Copy score. We hypothesize that this indicates that the text token embedding is learning something related to the appearance of the training videos. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,748,890,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Consequently, we test our sampling strategy. We compare a model trained with our motion pattern sampling strategy (\\\"Coarse-noise\\\") to a model that simply samples diffusion time steps uniformly (\\\"Uniform\\\"). As shown in Table 2d, our sampling strategy improves the motion accuracy and reduces the appearance copying. Following our intuition regarding learning motion patterns rather than fine-grained details, our model is less prone to replicating elements from the training examples. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,885,890,901]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lastly, we study the effect of the regularization prior \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[91,92,869,679]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 4. Qualitative results of our method. We demonstrate two custom motions: Dab and Air quotes, trained using collected internet examples as well as a 3D camera rotation trained with examples from the CO3D dataset [30]. Our method can generalize to unseen subjects and multiple people performing the action. Please refer to our supplemental video to view these results. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0666/9029b8457e92b7b2226fabb7ac704970eeeedf3c6b8f0d4ef15bcd0f736fabd4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[75,741,472,893]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"in Table 2e. We train three models with the same design choice as our method, yet we choose the regularization set to be either: (i) empty, (ii) a synthetic set of videos generated from the original text-to-video model, or (iii) containing real videos. We observe a significant drop in performance both without using a prior as well as using a synthetic prior. Interestingly, despite all settings using the same finetuning set, a high-quality regularization set containing real videos improves the overall training. Overall, our method achieves a good balance between high motion accuracy and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,742,627,757]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"low copying score. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,770,720,787]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.3. Qualitative experiments \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,794,890,902]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To further demonstrate the effectiveness of our approach, we choose the motions: Dab, Airquotes, and 3D rotation, which the original model does not know or cannot reliably perform. For the first two motions, we curate videos from the internet searching for the description of the motion. We use between 5 and 6 videos for each motion and caption the videos with a generic text description such as \\\"A person do \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[86,106,472,161]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Tune-A-Video \\\",\\\"\\\\\\\"A clown doing the V* gesture while eating a burger with his other hand\\\\\\\" \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0058/1c599c130d8869c07df10ac4169fca0797cc940ceb373565493948d22d1b8d2b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[86,176,472,232]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0858/2f7364896cee9ec38b94b882aa3ac1f4aa11e069cd169409167b30ff0205f321.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[86,244,472,299]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"\\\\\\\"An elder woman doing the V* gesture very slowly and precisely\\\\\\\" \\\",\\\"\\\\\\\"Children doing the V* gesture in the classroom in front of a blackboard\\\\\\\" \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0457/e88581279d2ec859a2d5b9d4faaf3e7a38ec03d8d464f152ba20768015d9b6a2.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[498,107,885,162]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Ours \\\",\\\"\\\\\\\"A clown doing the V* gesture while eating a burger with his other hand\\\\\\\" \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0506/4e083cb5d22d15feab7f0319ecedef356785431ef0df92de968dd130b11f236b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[500,176,885,232]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0204/f608afaa248c5a3ba3741100aa6bd8919a8b6f4905a47a571db20f9730955f28.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[500,244,885,299]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"\\\\\\\"An elder woman doing the V* gesture very slowly and precisely\\\\\\\" \\\",\\\"\\\\\\\"Children doing the V* gesture in the classroom in front of a blackboard\\\\\\\" \\\",\\\"Figure 5. Tune-A-Video versus our method trained on few examples of a custom motion \\\\\\\"Shaking Hand\\\\\\\". Our method seamlessly renders a custom motion in novel scenarios. Despite the videos in the training set only showing a single actor doing one single motion in the same way, our method can generate the custom motion in conjunction with a different motion (\\\\\\\"doing the gesture while eating a burger with other hand\\\\\\\"). Our method can also vary the timing of the motion (\\\\\\\"doing the gesture very slowly and precisely\\\\\\\") and involve multiple people (\\\\\\\"children\\\\\\\"). On the contrary, Tune-A-Video fails to generalize to these novel scenarios or produce a temporally coherent video. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0938/58e8e98ec68713d47fcd62ec0e9f50b7dda1c10250d3f3506f90e3691bbdc4c6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[96,410,274,521]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Appearance \\\",\\\"\\\\\\\"A photo of a $X^{*}$ man\\\\\\\" \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0510/a5828cc253329ccdac8595b6be9bc0a7613e50727e3596d075754ca8f6842420.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[303,410,454,446]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Motion \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0104/738ecb91e2a2f3fc8cc63b6b454469d5b88c4d4d80e6bacbfd5e3fb720fba1f1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[305,446,454,484]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0533/2ee6420d77beaa5581126c801dbf0a1bd34adbc16b7adb0e25591076ce75fe33.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[305,484,454,522]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"\\\\\\\"A person doing the V* sign\\\\\\\" \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0675/565b41c4db5de3d4d11fd94a800c0e6ddb9a869849bafb954979c58118a3c1f1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[86,539,452,593]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"\\\\\\\"A $X^{*}$ man doing the $V^{*}$ sign\\\\\\\" \\\",\\\"Figure 6. Appearance and motion customization. Given few images of a person and few videos of a custom motion (top), our method can generate a novel video depicting that person doing the novel motion (bottom). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0295/7ae94062064ed03262c83bdaf95563d1d2f26029cde4d607f39302e7f03a75ed.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[75,684,467,835]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ing the V* sign\\\" or \\\"A person V*\\\". To learn 3D rotation, we select 10 sequences of distinct objects from the CO3D Dataset [30] and caption the videos with the text prompt \\\"A camera V* around an [object]\\\", where [object] is an object class. The results are shown in Figure 4. For visualization, we query for objects not present in the training videos. For the regularization set, we select 100 video and text pairs from the WebVid-10M Dataset [1]. We fine-tune the models for 2000 steps. Please see our companion webpage for additional results and comparison with the pre-trained model. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,839,467,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Motion and appearance customization. We combine the appearance of a specific person with a gesture motion Drumming Fingers from the Jester Dataset. We use the publicly available images of a particular person from the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,396,890,486]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CustomConcept101 Dataset [22], and annotate them with generic text captions {\\\"A X* man\\\", \\\"A close-up of a X* man\\\", \\\"A X* man smiling.}. For the motion dataset, we choose the same 10 videos as in Section 4.1 and a generic text description \\\"a person doing a V* sign\\\". Our qualitative results are shown in Fig. 6. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,488,890,789]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Comparison with a reference-based method. We compare our method with Tune-A-Video [45], a video editing method that, given a source video, inflates a text-to-image model to learn a motion pattern from a single video. This method allows generation of novel videos with the same pattern but varying appearance. We adapt Tune-A-Video to fine-tune from multiple videos using the same training set as our setup. In Figure 5 we compare the two methods. We test the generalization abilities of the two methods, firstly combining the novel motion with a different motion: \\\"doing the V* gesture while eating a burger with other hand\\\". We can see that our method can generate the two motions. Next, we test the motion variation. We show that we can manipulate the execution of the motion with a natural language description; here we specify \\\"doing the V* gesture very slowly and precisely\\\". Lastly, we show that our method can generalize to multiple people doing the motion while preserving the temporal consistency of the video. The Tune-A-Video baseline produces qualitatively worse results, as can be seen in Figure 5 and the supplementary video. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,805,617,820]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5. Conclusion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[496,830,890,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We present an approach for motion customization in text-to-video diffusion models. Our method can learn a new motion from a set of few exemplar videos of different subjects performing the same gesture. We conduct a thorough ablation study that identifies the key components \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,90,472,203]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"of the method and evaluate them with respect to motion accuracy. We demonstrate qualitative results of our method, specifically in scenarios where our method generalizes the motion to unseen actors, multiple people performing the motion, and different viewpoints. Additionally, we show how our method can be extended to multimodal motion and appearance customization to generate videos with custom subjects performing custom motions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,229,173,244]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,253,470,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[1] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. 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Disenbooth: Identity-preserving disentangled tuning for subject-driven text-to-image generation. arXiv preprint arXiv:2305.03374, 2023. 2 \\\",\\\"[6] Wenhu Chen, Hexiang Hu, Yandong Li, Nataniel Rui, Xuhui Jia, Ming-Wei Chang, and William W Cohen. Subject-driven text-to-image generation via apprenticeship learning. arXiv preprint arXiv:2304.00186, 2023. 2 \\\",\\\"[7] Weifeng Chen, Jie Wu, Pan Xie, Hefeng Wu, Jiashi Li, Xin Xia, Xuefeng Xiao, and Liang Lin. Control-a-video: Controllable text-to-video generation with diffusion models. arXiv preprint arXiv:2305.13840, 2023. 2 \\\",\\\"[8] ExponentialML. Text-to-video-finetuning, 2023. Text-To-Video-Finetuning. 5 \\\",\\\"[9] Rinon Gal, Yuval Alaluf, Yuval Atzmon, Or Patashnik, Amit H Bermano, Gal Chechik, and Daniel Cohen-Or. 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High-resolution image synthesis with latent diffusion models. 2022 IEEE. In CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 10674-10685, 2021. 3 \\\",\\\"[32] Nataniel Ruiz, Yuanzhen Li, Varun Jampani, Yael Pritch, Michael Rubinstein, and Kfir Aberman. Dreambooth: Fine tuning text-to-image diffusion models for subject-driven generation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22500-22510, 2023. 2, 4, 5, 6 \\\",\\\"[33] Nataniel Ruiz, Yuanzhen Li, Varun Jampani, Wei Wei, Tingbo Hou, Yael Pritch, Neal Wadhwa, Michael Rubinstein, and Kfir Aberman. Hyperdreambooth: Hypernetworks for fast personalization of text-to-image models. arXiv preprint arXiv:2307.06949, 2023. \\\",\\\"[34] Jing Shi, Wei Xiong, Zhe Lin, and Hyun Joon Jung. Instantbooth: Personalized text-to-image generation without test-time finetuning. arXiv preprint arXiv:2304.03411, 2023. 2 \\\",\\\"[35] Uriel Singer, Adam Polyak, Thomas Hayes, Xi Yin, Jie An, Songyang Zhang, Qiyuan Hu, Harry Yang, Oron Ashual, Oran Gafni, et al. Make-a-video: Text-to-video generation without text-video data. arXiv preprint arXiv:2209.14792, 2022.3 \\\",\\\"[36] Jiaming Song, Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502, 2020. 3 \\\",\\\"[37] Yoad Tewel, Rinon Gal, Gal Chechik, and Yuval Atzmon. Key-locked rank one editing for text-to-image personalization. In ACM SIGGRAPH 2023 Conference Proceedings, pages 1–11, 2023. 2 \\\",\\\"[38] Yoad Tewel, Rinon Gal, Gal Chechik, and Yuval Atzmon. Key-locked rank one editing for text-to-image personalization. In ACM SIGGRAPH 2023 Conference Proceedings, 2023. 4 \\\"]\",\n \"page_idx\": \"9\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[501,90,892,853]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[39] Sergey Tulyakov, Ming-Yu Liu, Xiaodong Yang, and Jan Kautz. Mocogan: Decomposing motion and content for video generation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1526-1535, 2018. 2 \\\",\\\"[40] Ruben Villegas, Mohammad Babaeizadeh, Pieter-Jan Kindermans, Hernan Moraldo, Han Zhang, Mohammad Taghi Saffar, Santiago Castro, Julius Kunze, and Dumitru Erhan. Phenaki: Variable length video generation from open domain textual description. arXiv preprint arXiv:2210.02399, 2022. 1, 3 \\\",\\\"[41] Binxu Wang and John J Vastola. Diffusion models generate images like painters: an analytical theory of outline first, details later. arXiv preprint arXiv:2303.02490, 2023. 4 \\\",\\\"[42] Jiuniu Wang, Hangjie Yuan, Dayou Chen, Yingya Zhang, Xiang Wang, and Shiwei Zhang. Modelscope text-to-video technical report. arXiv preprint arXiv:2308.06571, 2023. 1, 3 \\\",\\\"[43] Wenjing Wang, Huan Yang, Zixi Tuo, Huiguo He, Junchen Zhu, Jianlong Fu, and Jiaying Liu. Videofactory: Swap attention in spatiotemporal diffusions for text-to-video generation. arXiv preprint arXiv:2305.10874, 2023. 1, 3 \\\",\\\"[44] Yuxiang Wei, Yabo Zhang, Zhilong Ji, Jinfeng Bai, Lei Zhang, and Wangmeng Zuo. Elite: Encoding visual concepts into textual embeddings for customized text-to-image generation. arXiv preprint arXiv:2302.13848, 2023. 2 \\\",\\\"[45] Jay Zhangjie Wu, Yixiao Ge, Xintao Wang, Weixian Lei, Yuchao Gu, Wynne Hsu, Ying Shan, Xiaohu Qie, and Mike Zheng Shou. Tune-a-video: One-shot tuning of image diffusion models for text-to-video generation. arXiv preprint arXiv:2212.11565, 2022. 2, 3, 8 \\\",\\\"[46] Guangxuan Xiao, Tianwei Yin, William T Freeman, Frédo Durand, and Song Han. Fastcomposer: Tuning-free multi-subject image generation with localized attention. arXiv preprint arXiv:2305.10431, 2023. 2 \\\",\\\"[47] Jianan Yang, Haobo Wang, Ruixuan Xiao, Sai Wu, Gang Chen, and Junbo Zhao. Controllable textual inversion for personalized text-to-image generation. arXiv preprint arXiv:2304.05265, 2023. 2 \\\",\\\"[48] Yabo Zhang, Yuxiang Wei, Dongsheng Jiang, Xiaopeng Zhang, Wangmeng Zuo, and Qi Tian. Controlvideo: Training-free controllable text-to-video generation. arXiv preprint arXiv:2305.13077, 2023. 3 \\\",\\\"[49] Bolei Zhou, Alex Andonian, Aude Oliva, and Antonio Torralba. Temporal relational reasoning in videos. European Conference on Computer Vision, 2018. 5 \\\",\\\"[50] Daquan Zhou, Weimin Wang, Hanshu Yan, Weiwei Lv, Yizhe Zhu, and Jiashi Feng. Magicvideo: Efficient video generation with latent diffusion models. arXiv preprint arXiv:2211.11018, 2022. 1, 3 \\\",\\\"[51] Yufan Zhou, Ruiyi Zhang, Tong Sun, and Jinhui Xu. Enhancing detail preservation for customized text-to-image generation: A regularization-free approach. arXiv preprint arXiv:2305.13579, 2023. 2 \\\"]\",\n \"page_idx\": \"9\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[207,85,764,138]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Customizing Motion in Text-to-Video Diffusion Models Supplementary Material \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,157,434,172]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This supplemental contains the following material: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[76,176,468,357]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- Accompanying webpage of qualitative results of our method, the videos shown in the main paper and comparison with the pre-trained text-to-video generations. \\\",\\\"- (Section A) We provide additional implementation details regarding our quantitative experiments. \\\",\\\"- (Section B) We discuss the tradeoff between the motion accuracy, appearance alignment and copying score across training iterations. \\\",\\\"- (Section C) We show qualitative examples along with their copying score. \\\",\\\"- (Section D) We show the original model's (i.e. before customization) performance on the Jester dataset. \\\"]\",\n \"page_idx\": \"10\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[76,386,303,402]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A. Implementation Details \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[76,416,468,477]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As described in Section 4.1 we design a test set of 100 prompts detailing a person's appearance and fix three random seeds per prompt. We show the list of the prompts in Figure 9. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[76,505,468,540]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"B. Tradeoff between motion accuracy, appearance alignment, and copying score \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[76,553,472,902]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"When customizing a model with a new motion, we observe a natural bias-variance tradeoff. The longer we train the model, the better motion accuracy becomes, we memorize elements of the training examples, and the model becomes less diverse. We illustrate this in Figure 7. With more training iterations, the network memorizes the gesture as well as visual elements of the training examples. These findings are indicated by both the motion accuracy and copying score increasing. On the other hand, the CLIP appearance score, decreases. The CLIP appearance is defined as an average CLIP score between the part of the text prompt that describes a person's appearance and the video frames (i.e. in a prompt \\\"A female firefighter doing the V* sign\\\", the CLIP appearance score accounts for \\\"A female firefighter\\\"). This score is a proxy for visual diversity, since our test set contains visual description of a person, it measures how accurate the description is. As we increase the number of iterations, the videos become less diverse, hence the score decreases. This trend is persistent across the models from our ablation study. To find a balance between those factors, we perform early stopping for all models when the CLIP appearance score reaches 0.265 (i.e. when the image still reasonably well corresponds to the text description). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[540,157,851,349]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0065/303d7b2acba7ae36fe166a5b7a896b5d1b23d0475557e40a2956c15fb467cacf.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[540,353,851,544]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0148/2470e6b9b862501d989f1bfaa63cc67abfa5e170e4a1079ff034763d06ff1ff8.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[563,547,849,750]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 7. Our model's performance in terms of motion accuracy (top), CLIP appearance score (middle), and copying score (bottom) across training steps (x-axis). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0946/c63650c4ee69939141b059a6da714024427e02a01d2e7a40dadf555ce3cab41c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[500,839,648,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"C. Copying score \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,869,890,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Copying score, as defined in 4.2 measures how much of the training data appearance leaks into the generated data. The \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[76,90,472,272]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"score corresponds to the percentage of examples in the test set that are above a specified threshold of the SSCD score with any of the training examples. We find that the SSCD copy detection score [29] is a good proxy for determining the memorization of the training examples' appearance. We measure the SSCD detection as a maximum score between any frame of the training videos and any video frame from the test set. We empirically determine that pairs of videos with a score greater than 0.25 share significant visual similarities. As seen in Figure 8, the similarities can be either the background or the appearance of the person performing the gesture. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[83,285,176,357]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"A blond girl doing the V\\\\\\\\* sign. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0516/1f0f759364c6d0d15504487d12f956dcedd61bf7cbafeffd49808ccd7fe1b3ea.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[176,285,267,357]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Training Video \\\",\\\"\\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0536/f1d46f37ff0aaaf899f84c3ac1815253a9975374edd2986d02f8e291a25a0a9b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[282,285,377,357]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"A man wearing glasses doing the V* sign. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0782/c1307f4a8d1e2e07769e75acd1c5b5cff20d8b7121c6d47909a5f005a8008e8a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[377,285,468,357]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Training Video \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0762/689b370f1c1bef17aac835f8ab01fbc2fcdb69b74c94b15f9fe915fda6ae4e1e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[83,385,176,457]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"A ginger girl doing the V* sign. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0452/03c603ebb1b8408dd00b899fe13df85a4a660849b5186a1f224d6ba9f8db17ce.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[176,385,267,457]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Training Video \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0668/6cd885d057b8c8d61f03f673d9a13cdb98a4766f44613bb80935b23bc503b2a7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[282,385,377,457]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"A person in a summer dress doing the V* sign \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0353/269da3585ce7d0eaa512ad5fc2e41d2a22c11110b986775fcd513538c48e152c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[377,385,468,457]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 9. Test set prompts for the quantitative evaluation of learning the Jester motions \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0274/613115e71f642058ef2d5cf8be3b46a080057851f5474aa769c1c2367e02c654.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[401,459,455,469]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Training Video \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[76,492,468,547]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 8. Examples of pairs of generated frames and training frames with SSCD score 0.25. Notice the similarity in the background (top-left and bottom-left) and foreground (t-shirt logo in the top-right, person's face in the bottom-right). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[76,578,468,612]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"D. Pre-trained model's performance on motions from the Jester dataset. \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[76,621,472,832]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To test whether the gestures from the Jester dataset, are well-represented in the pre-trained text-to-video model, we evaluate the model with a similar experiment as our ablation experiment (4.2). We query the pre-trained text-to-video model with the prompts from the test set (Section A), replacing the \\\"doing the sks gesture\\\" with a natural language description of the class, e.g., for the class \\\"Drumming Fingers\\\" - \\\"drumming finger\\\". We then classify the videos with the pre-trained network trained on the Jester dataset. No videos were correctly classified because (i) the gestures are not well represented in the model and (ii) the generated videos do not adhere to the spatial assumption of the Jester dataset (where a single person is performing a gesture in front of a camera). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,95,756,852]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"A woman doing the sks sign. \\\",\\\"A tribe man doing the sks sign \\\",\\\"A young woman doing the sks sign. \\\",\\\"A Korean girl doing the sks sign \\\",\\\"A Korean boy doing the sks sign A korean man doing the sks sign \\\",\\\"A korean man doing the sks sign. A korean woman doing the sks sig \\\",\\\"A korean toddler doing the sks sign. \\\",\\\"A japanese woman doing the sks sign. \\\",\\\"A japanese boy doing the sks sign \\\",\\\"A japanese girl doing the sks sign \\\",\\\"A japanese toddler doing the sks sign. \\\",\\\"A japanese man doing the sks sign \\\",\\\"A firefighter doing the sks sign \\\",\\\"A female firefighter doing the sks sign \\\",\\\"A clown doing the sks sign \\\",\\\"Mickey Mouse doing the sks sign. And we did being the stars. \\\",\\\"A housemaid doing the sky sign A female press doing the job \\\",\\\"A female nurse doing the sks sign . \\\",\\\"A male nurse doing the sks sign .A toddler doing the also sign \\\",\\\"An african woman doing the sks sign. \\\",\\\"An african man doing the sks sign. \\\",\\\"An african boy doing the sks sign \\\",\\\"An african toddler doing the sks sign \\\",\\\"An elderly woman doing the sks sign. \\\",\\\"An elderly man doing the sks sign \\\",\\\"A mexican man doing the sks sign \\\",\\\"A mexican woman doing the sks sign. \\\",\\\"A mexican boy doing the sks sign \\\",\\\"A mexican girl doing the sks sign \\\",\\\"A mexican toddler doing the sks sign \\\",\\\"A slavic man doing the sks sign. \\\",\\\"A slavic woman doing the sks sign \\\",\\\"A slavic boy doing the sks sign. A clastic girl doing the oks sign. \\\",\\\"A slavic girl doing the sky sign. A clavigic child doing the sky sign. \\\",\\\"A slavie child doing the sks sign. A blond woman doing the asks sign. \\\",\\\"A blond woman doing the sks sign. A blond man doing the sks sign. \\\",\\\"A blond boy doing the sks sign. \\\",\\\"A blond girl doing the sks sign. \\\",\\\"A ginger woman doing the sks sign. \\\",\\\"A ginger man doing the sks sign. \\\",\\\"A ginger boy doing the sks sign. \\\",\\\"A ginger girl doing the sks sign \\\",\\\"A woman with glasses doing the sks sign. \\\",\\\"A man with glasses doing the sks sign. \\\",\\\"A girl with glasses doing the sks \\\",\\\"A boy with glasses doing the sks sign \\\",\\\"A child with glasses doing the sks sign \\\",\\\"A man with a beard doing the sks sign \\\",\\\"A teacher doing the sks sign \\\",\\\"A musician doing the sks sign. \\\",\\\"A chef doing the sks sign \\\",\\\"A construction worker doing the sks sign \\\",\\\"A police officer doing the sks sign. \\\",\\\"A student doing the sks sign \\\",\\\"A doctor doing the sks sign \\\",\\\"A scientist doing the sks sign. \\\",\\\"A farmer doing the sks sign \\\",\\\"A dancer doing the sks sign. \\\",\\\"A pilot doing the sks sign \\\",\\\"A yoga instructor doing the sks sign \\\",\\\"A surfer doing the sks sign \\\",\\\"A skateboarder doing the sks sign. \\\",\\\"A hiker doing the sks \\\",\\\"A painter doing the sks sign \\\",\\\"A photographer doing the sks sign. \\\",\\\"A writer doing the sks sign. \\\",\\\"A woman with long hair doing the sks sign. \\\",\\\"A man with a mustache doing the sks sign \\\",\\\"A woman with a ponytail doing the sks sign \\\",\\\"A man with a bald head doing the sks sign \\\",\\\"A teenager doing the sks sign \\\",\\\"A senior citizen doing the sks sign. \\\",\\\"A person in a wheelchair doing the sks sign. \\\",\\\"A person with a backpack doing the sks sign. \\\",\\\"A person wearing a hat doing the sks sign \\\",\\\"A person in traditional clothing doing the sks sign. \\\",\\\"A person in casual attire doing the sks sign \\\",\\\"A person in formal attire doing the sks sign \\\",\\\"A person with tattoos doing the sks sign. \\\",\\\"A person with piercings doing the sks sign \\\",\\\"A person with a camera doing the sks sign. \\\",\\\"A person holding a book doing the sks sign \\\",\\\"A person using a smartphone doing the sks sign. \\\",\\\"A person with a pet doing the sks sign \\\",\\\"A person with a bicycle doing the sks sign. \\\",\\\"A person in workout clothes doing the sks sign. \\\",\\\"A person in a swimsuit doing the sks sign. \\\",\\\"A person wearing a backpack doing the sks \\\",\\\"A person wearing a business suit doing the sks sign. \\\",\\\"A person wearing a lab coat doing the sks sign. \\\",\\\"A person wearing a uniform doing the sks sign. \\\",\\\"A person in a winter coat doing the sks sign \\\",\\\"A person in a summer dress doing the sks sign \\\",\\\"A person in a cowboy hat doing the sks sign \\\",\\\"A person in a graduation gown doing the sks \\\",\\\"A person in a superhero costume doing the sks sign. \\\",\\\"A person in a traditional robe doing the sks sign \\\"]\",\n \"page_idx\": \"11\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.48550/arxiv.2312.04966"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Engineering and Manufacturing Science"},"sha256":{"kind":"string","value":"7e34a2ad2fe49694b17f3856bfdd295659d58a4df70aacd7f3de1860fac3b369"},"title":{"kind":"string","value":"NewMove: Customizing text-to-video models with novel motions"}}},{"rowIdx":261,"cells":{"abstract":{"kind":"string","value":""},"author":{"kind":"string","value":"Wiesław Kubiś|Saeed Ghasemi"},"content_list":{"kind":"list like","value":[{"bbox":"[92,263,404,289]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Universal AF-algebras ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,307,468,327]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Saeed Ghasemi a, Wiesław Kubiś a,b,* ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[790,267,852,311]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0149/9e456a09c85532a8fcb2c942e64b6f38c0a4436a4c51336963d5631572c0132f.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[89,336,717,375]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"a Institute of Mathematics, Czech Academy of Sciences, Czechia \",\"$^{\\\\mathrm{b}}$ Institute of Mathematics, Cardinal Stefan Wyszynski University in Warsaw, Poland \"]","page_idx":"0","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[92,408,316,422]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ARTICLE INFO ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,442,216,455]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article history: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,455,314,467]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received 26 September 2019 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,467,267,480]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Accepted 9 April 2020 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,480,327,492]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Available online 18 April 2020 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,494,340,505]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Communicated by Stefaan Vaes ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,517,141,529]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MSC: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,530,143,542]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"46L05 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,542,143,555]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"46L85 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,555,147,567]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"46M15 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,582,179,595]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,595,182,608]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"AF-algebra ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,608,222,620]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Cantor property ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,622,295,633]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Left-invertible embedding ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,635,190,645]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Fraissé limit ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[426,408,578,422]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABSTRACT ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[423,442,916,611]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We study the approximately finite-dimensional (AF) $C^*$ -algebras that appear as inductive limits of sequences of finite-dimensional $C^*$ -algebras and left-invertible embeddings. We show that there is such a separable AF-algebra $\\mathcal{A}_{\\mathfrak{F}}$ which is a split-extension of any finite-dimensional $C^*$ -algebra and has the property that any separable AF-algebra is isomorphic to a quotient of $\\mathcal{A}_{\\mathfrak{F}}$ . Equivalently, by Elliott's classification of separable AF-algebras, there are surjectively universal countable scaled (or with order-unit) dimension groups. This universality is a consequence of our result stating that $\\mathcal{A}_{\\mathfrak{F}}$ is the Fraissé limit of the category of all finite-dimensional $C^*$ -algebras and left-invertible embeddings. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[423,611,916,725]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"With the help of Fraïssé theory we describe the Bratteli diagram of $\\mathcal{A}_{\\mathfrak{F}}$ and provide conditions characterizing it up to isomorphisms. $\\mathcal{A}_{\\mathfrak{F}}$ belongs to a class of separable AF-algebras which are all Fraïssé limits of suitable categories of finite-dimensional $C^*$ -algebras, and resemble $C(2^{\\mathbb{N}})$ in many senses. For instance, they have no minimal projections, tensorially absorb $C(2^{\\mathbb{N}})$ (i.e. they are $C(2^{\\mathbb{N}})$ -stable) and satisfy similar homogeneity and universality properties as the Cantor set. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[593,725,914,738]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"© 2020 Elsevier Inc. All rights reserved. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[310,63,698,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[94,105,224,186]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"","text_format":null,"text_level":null,"type":"header"},{"bbox":"[96,189,222,205]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ELSEVIER ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[353,107,661,120]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Contents lists available at ScienceDirect ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[304,142,708,164]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Journal of Functional Analysis ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[396,189,616,205]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.elsevier.com/locate/jfa ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[790,97,916,204]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"JOURNAL OF FUNCTIONAL ANALYSIS ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[92,823,914,852]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{\\text{念}}$ Research of the first author was supported by the GACR project 19-05271Y and RVO: 67985840. Research of the second author was supported by the GACR project 20-31529X and RVO: 67985840. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[102,852,293,866]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"* Corresponding author. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[119,867,492,880]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"E-mail address: kubis@math.cas.cz (W. Kubis). ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[92,895,415,908]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1016/j.jfa.2020.108590 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[92,908,488,920]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"0022-1236/© 2020 Elsevier Inc. All rights reserved. ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[79,107,235,122]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[79,142,905,475]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Operator algebraists often refer to (for good reasons, of course) the UHF-algebras such as CAR-algebra as the noncommutative analogues of the Cantor set $2^{\\mathbb{N}}$ , or more precisely the commutative $C^*$ -algebra $C(2^{\\mathbb{N}})$ . We introduce a different class of separable AF-algebras, we call them \"AF-algebras with Cantor property\" (Definition 4.1), which in some contexts are more suitable noncommutative analogues of $C(2^{\\mathbb{N}})$ . One of the main features of AF-algebras with Cantor property is that they are direct limits of sequences of finite-dimensional $C^*$ -algebras where the connecting maps are left-invertible homomorphisms. This property, for example, guarantees that if the algebra is infinite-dimensional, it has plenty of nontrivial ideals and quotients, while UHF-algebras are simple. The Cantor set is a \"special and unique\" space in the category of all compact (zero-dimensional) metrizable spaces in the sense that it bears some universality and homogeneity properties; it maps onto any compact (zero-dimensional) metrizable space and it has the homogeneity property that any homeomorphism between finite quotients lifts to a homeomorphism of the Cantor set (see [10]). Moreover, Cantor set is the unique compact zero-dimensional metrizable space with the property that (stated algebraically): for every $m, n \\in \\mathbb{N}$ and unital embeddings $\\phi: \\mathbb{C}^n \\to \\mathbb{C}^m$ and $\\alpha: \\mathbb{C}^n \\to C(2^{\\mathbb{N}})$ there is an embedding $\\beta: \\mathbb{C}^m \\to C(2^{\\mathbb{N}})$ such that the diagram ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[411,494,576,564]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{c} C (2 ^ {\\mathbb {N}}) \\\\ \\mathbb {C} ^ {n} \\xrightarrow {\\phi} \\mathbb {C} ^ {m} \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[79,579,905,852]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"commutes. Note that the map $\\phi$ in the above must be left-invertible and if $\\alpha$ is left-invertible then $\\beta$ can be chosen to be left-invertible. Recall that a homomorphism $\\phi : \\mathcal{B} \\to \\mathcal{A}$ is left-invertible if there is a homomorphism $\\pi : \\mathcal{A} \\to \\mathcal{B}$ such that $\\pi \\circ \\phi = \\mathrm{id}_{\\mathcal{B}}$ . The AF-algebras with Cantor property satisfy similar universality and homogeneity properties in their corresponding categories of finite-dimensional $C^*$ -algebras and left-invertible homomorphisms. Although, in general AF-algebras with Cantor property are not assumed to be unital, when restricted to the categories with unital maps, one can obtain the unital AF-algebras with same properties subject to the condition that maps are unital. For instance, the \"truly\" noncommutative AF-algebra with Cantor property $\\mathcal{A}_{\\mathfrak{F}}$ , that was mentioned in the abstract, is the unique (nonunital) AF-algebra which is the limit of a sequence of finite-dimensional $C^*$ -algebras and left-invertible homomorphisms (necessarily embeddings), with the property that for every finite-dimensional $C^*$ -algebras $\\mathcal{D}, \\mathcal{E}$ and (not necessarily unital) left-invertible embeddings $\\phi : \\mathcal{D} \\to \\mathcal{E}$ and $\\alpha : \\mathcal{D} \\to \\mathcal{A}_{\\mathfrak{F}}$ there is a left-invertible embedding $\\beta : \\mathcal{E} \\to \\mathcal{A}_{\\mathfrak{F}}$ such that the diagram ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[430,870,552,938]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{c} \\mathcal {A} _ {\\mathfrak {F}} \\\\ \\mathcal {D} \\xrightarrow {\\stackrel {\\alpha} {\\phi}} \\mathcal {E} \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,64,96,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,63,796,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,105,916,164]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"commutes (Theorem 8.5). One of our main results (Theorem 8.1) states that $\\mathcal{A}_{\\mathfrak{F}}$ maps surjectively onto any separable AF-algebra. However, this universality property is not unique to $\\mathcal{A}_{\\mathfrak{F}}$ (Remark 8.2). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,167,918,558]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The properties of the Cantor set that are mentioned above can be viewed as consequences of the fact that it is the \"Fraïssé limit\" of the class of all nonempty finite spaces and surjective maps (as well as the class of all nonempty compact metric spaces and continuous surjections); see [11]. The theory of Fraïssé limits was introduced by R. Fraïssé [7] in 1954 as a model-theoretic approach to the back-and-forth argument. Roughly speaking, Fraïssé theory establishes a correspondence between classes of finite (or finitely generated) models of a first-order language with certain properties (the joint-embedding property, the amalgamation property and having countably many isomorphism types), known as Fraïssé classes, and the unique (ultra-)homogeneous and universal countable structure, known as the Fraïssé limit, which can be represented as the union of a chain of models from the class. Fraïssé theory has been recently extended way beyond the countable first-order structures, in particular, covering some topological spaces, Banach spaces and, even more recently, some $C^*$ -algebras. Usually in these extensions the classical Fraïssé theory is replaced by its \"approximate\" version. Approximate Fraïssé theory was developed by Ben Yaacov [1] in continuous model theory (an earlier approach was developed in [17]) and independently, in the framework of metric-enriched categories, by the second author [11]. The Urysohn metric space, the separable infinite-dimensional Hilbert space [1], and the Gurarié space [12] are some of the other well-known examples of Fraïssé limits of metric structures (see also [13] for more on Fraïssé limits in functional analysis). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,561,920,797]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Fraïssé limits of $C^*$ -algebras are studied in [5] and [14], where it has been shown that the Jiang-Su algebra, all UHF algebras, and the hyperfinite $\\Pi_1$ -factor are Fraïssé limits of suitable classes of finitely generated $C^*$ -algebras with distinguished traces. Here we investigate the separable AF-algebras that arise as limits of Fraïssé classes of finite-dimensional $C^*$ -algebras. Apart from $C(2^{\\mathbb{N}})$ , which is the Fraïssé limit of the class of all commutative finite-dimensional $C^*$ -algebras and unital (automatically left-invertible) embeddings, all UHF-algebras [5, Theorem 3.4] and a class of simple monotracial AF-algebras described in [5, Theorem 3.9], are Fraïssé limits of classes of finite-dimensional $C^*$ -algebras. It is also worth noticing that the $C^*$ -algebra $\\mathcal{K}(H)$ of all compact operators on a separable Hilbert space $H$ and the universal UHF-algebra $\\mathcal{Q}$ (see Section 8.1) are both Fraïssé limits of, respectively, the category of all matrix algebras and (not necessarily unital) embeddings and the category of all matrix algebras and unital embeddings. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[87,798,918,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In general, however, obstacles arising from the existence of traces prevent many classes of finite-dimensional $C^*$ -algebras from having the amalgamation property ([5, Proposition 3.3]), therefore making it difficult to realize AF-algebras as Fraïssé limits of such classes. The AF-algebra $C(2^{\\mathbb{N}})$ is neither a UHF-algebra nor it is among AF-algebras considered in [5, Theorem 3.9]. Therefore, it is natural to ask whether $C(2^{\\mathbb{N}})$ belongs to any larger nontrivial class of AF-algebras whose elements are Fraïssé limits of some class of finite-dimensional $C^*$ -algebras. This was our initial motivation behind introducing the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[903,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[81,105,903,144]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"class of separable AF-algebras with Cantor property (Definition 4.1). This class properly contains the AF-algebras of the form $M_{n} \\otimes C(2^{\\mathbb{N}})$ , for any matrix algebra $M_{n}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,145,903,183]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If $\\mathcal{A}$ and $\\mathcal{B}$ are $C^*$ -algebras, $\\phi : \\mathcal{B} \\hookrightarrow \\mathcal{A}$ is a left-invertible embedding and $\\pi : \\mathcal{A} \\twoheadrightarrow \\mathcal{B}$ is a left inverse of $\\phi$ , then we have the short exact sequence ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[289,204,691,236]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n0 \\xrightarrow {} \\ker (\\pi) \\xrightarrow {\\iota} \\mathcal {A} \\xrightarrow [ \\phi ]{\\frac {\\pi}{\\iota}} \\mathcal {B} \\xrightarrow {} 0.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,255,903,333]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Therefore $\\mathcal{A}$ is a \"split-extension\" of $\\mathcal{B}$ . In this case we say $\\mathcal{B}$ is a \"retract\" of $\\mathcal{A}$ . It would be more convenient for us to say \" $\\mathcal{B}$ is a retract of $\\mathcal{A}$ \" rather than the more familiar phrase (for $C^*$ -algebraists) \" $\\mathcal{A}$ is a split-extension of $\\mathcal{B}$ \". In Section 3 we consider direct sequences of finite-dimensional $C^*$ -algebras ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[370,352,614,380]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {A} _ {1} \\xrightarrow {\\phi_ {1} ^ {2}} \\mathcal {A} _ {2} \\xrightarrow {\\phi_ {2} ^ {3}} \\mathcal {A} _ {3} \\xrightarrow {\\phi_ {3} ^ {4}} \\dots\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,398,903,577]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where each $\\phi_n^{n+1}$ is a left-invertible embedding. The AF-algebra $\\mathcal{A}$ that arises as the limit of this sequence has the property that every matrix algebra $M_k$ appearing as a direct-sum component (an ideal) of some $\\mathcal{A}_n$ is a retract of $\\mathcal{A}$ (equivalently, $\\mathcal{A}$ is a split-extension of each $\\mathcal{A}_n$ and such $M_k$ ). Moreover, every retract of $\\mathcal{A}$ which is a matrix algebra, appears as a direct-sum component of some $\\mathcal{A}_n$ (Lemma 3.5). The AF-algebras with Cantor property are defined and studied in Section 4. They are characterized by the set of their matrix algebra retracts. That is, two AF-algebras with Cantor property are isomorphic if and only if they have exactly the same matrix algebras as their retracts (Corollary 7.8), i.e., they are split-extensions of the same class of matrix algebras. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,579,903,776]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We will use the Fraïssé-theoretic framework of (metric-enriched) categories described in [11], rather than the (metric) model-theoretic approach to the Fraïssé theory. A brief introduction to Fraïssé categories is provided in Section 5. We show that (Theorem 7.2) any category of finite-dimensional $C^*$ -algebras and (not necessarily unital) left-invertible embeddings, which is closed under taking direct sums and ideals of its objects (we call these categories $\\oplus$ -stable) is a Fraïssé category. Moreover, Fraïssé limits of these categories have the Cantor property (Lemma 7.4) and in fact any AF-algebra $\\mathcal{A}$ with Cantor property can be realized as Fraïssé limit of such a category, where the objects of this category are precisely the finite-dimensional retracts of $\\mathcal{A}$ (see Definition 3.1 and Theorem 7.6). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,777,903,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In particular, the category $\\mathfrak{F}$ of all finite-dimensional $C^*$ -algebras and left-invertible embeddings is a Fraïssé category (Section 8). A priori, the Fraïssé limit $\\mathcal{A}_{\\mathfrak{F}}$ of this category is a separable AF-algebra with the universality property that any separable AF-algebra $\\mathcal{A}$ which is the limit of a sequence of finite-dimensional $C^*$ -algebras with left-invertible embeddings as connecting maps, can be embedded into $\\mathcal{A}_{\\mathfrak{F}}$ via a left-invertible embedding, i.e., $\\mathcal{A}_{\\mathfrak{F}}$ is a split-extension of $\\mathcal{A}$ . In particular, there is a surjective homomorphism $\\theta : \\mathcal{A}_{\\mathfrak{F}} \\twoheadrightarrow \\mathcal{A}$ . Also any separable AF-algebra is isomorphic to a quotient (by an essential ideal) of an AF-algebra which is the limit of a sequence of finite-dimensional $C^*$ - ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,64,96,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,63,796,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,105,916,144]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"algebras with left-invertible embeddings (Proposition 3.8). Combining the two quotient maps, we have the following result, which is later restated as Theorem 8.1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,164,916,204]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 1.1. The category of all finite-dimensional $C^*$ -algebras and left-invertible embeddings is a Fraïssé category. Its Fraïssé limit $\\mathcal{A}_{\\mathfrak{F}}$ is a separable $AF$ -algebra such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[102,225,912,280]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- $\\\\mathcal{A}_{\\\\mathfrak{F}}$ is a split-extension of any $AF$ -algebra which is the limit of a sequence of finite-dimensional $C^*$ -algebras and left-invertible connecting maps. \",\"- there is a surjective homomorphism from $\\\\mathcal{A}_{\\\\mathfrak{F}}$ onto any separable $AF$ -algebra. \"]","page_idx":"4","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[89,302,916,420]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Bratteli diagram of $\\mathcal{A}_{\\mathfrak{F}}$ is described in Proposition 8.4, using the fact that it has the Cantor property. It is the unique AF-algebra with Cantor property which is a split-extension of every finite-dimensional $C^*$ -algebra. The unital versions of these results are given in Section 9 (with a bit of extra work, since unlike $\\mathfrak{F}$ , the category of all finite-dimensional $C^*$ -algebras and unital left-invertible maps is not a Fraïssé category, namely, it lacks the joint embedding property). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,422,916,480]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Separable AF-algebras are famously characterized [6] by their $K_{0}$ -invariants which are scaled countable dimension groups (with order-unit, in the unital case). By applying the $K_{0}$ -functor to Theorem 1.1 we have the following result. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,500,916,539]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Corollary 1.2. There is a scaled countable dimension group (with order-unit) which maps onto any scaled countable dimension group (with order-unit). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,558,914,594]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The corresponding characterizations of these dimension groups are mentioned in Section 10. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,598,916,675]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, this paper could have been written entirely in the language of partially ordered abelian groups, where the categories of \"simplicial groups\" and left-invertible positive embeddings replace our categories. However, we do not see any clear advantage in doing so. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,698,250,714]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. Preliminaries ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,738,918,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Recall that an approximately finite-dimensional (AF) algebra is a $C^*$ -algebra which is an inductive limit of a sequence of finite-dimensional $C^*$ -algebras. We review a few basic facts about separable AF-algebras. The background needed regarding AF-algebras is quite elementary and [4] is more than sufficient. The AF-algebras that are considered here are always separable and therefore by \"AF-algebra\" we always mean \"separable AF-algebra\". AF-algebras can be characterized up to isomorphisms by their Bratteli diagrams [3]. However, there is no efficient way (at least visually) to decide whether two Bratteli diagrams are isomorphic, i.e., they correspond to isomorphic AF-algebras. A much better characterization of AF-algebras uses $K$ -theory. To each $C^*$ -algebra the $K_0$ -functor assigns a partially ordered abelian group (its $K_0$ -group) which turns out to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[903,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[79,105,905,183]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"be a complete invariant for AF-algebras [6]. Moreover, there is a complete description of all possible $K_{0}$ -groups of AF-algebras. Namely, a partially ordered abelian group is isomorphic to the $K_{0}$ -group of an AF-algebra if and only if it is a countable dimension group. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,185,905,342]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We mostly use the notation from [4] with minor adjustments. Let $M_{k}$ denote the $C^*$ -algebra of all $k \\times k$ matrices over $\\mathbb{C}$ . Suppose $\\mathcal{A} = \\varinjlim (\\mathcal{A}_n, \\phi_n^m)$ is an AF-algebra with Bratteli diagram $\\mathfrak{D}$ such that each $\\mathcal{A}_n \\cong \\mathcal{A}_{n,1} \\oplus \\dots \\oplus \\mathcal{A}_{n,\\ell}$ , is a finite-dimensional $C^*$ -algebra and each $\\mathcal{A}_{n,s}$ is a full matrix algebra. The node of $\\mathfrak{D}$ corresponding to $\\mathcal{A}_{n,s}$ is \"officially\" denoted by $(n,s)$ , while intrinsically it carries over a natural number $\\dim(n,s)$ , which represents the dimension of the matrix algebra $\\mathcal{A}_{n,s}$ , i.e. $\\mathcal{A}_{n,s} \\cong M_{\\dim(n,s)}$ . For $(n,s), (m,t) \\in \\mathfrak{D}$ we write $(n,s) \\to (m,t)$ if $(n,t)$ is connected $(m,t)$ by at least one path in $\\mathfrak{D}$ , i.e. if $\\phi_n^m$ sends $\\mathcal{A}_{n,s}$ faithfully into $\\mathcal{A}_{m,t}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,344,905,482]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The ideals of AF-algebras are also AF-algebras and they can be recognized from the Bratteli diagram of the algebra. Namely, the Bratteli diagrams of ideals correspond to directed and hereditary subsets of the Bratteli diagram of the algebra (see [4, Theorem III.4.2]). Recall that an essential ideal $\\mathcal{I}$ of $\\mathcal{A}$ is an ideal which has nonzero intersections with every nonzero ideal of $\\mathcal{A}$ . Suppose $\\mathfrak{D}$ is the Bratteli diagram for an AF-algebra $\\mathcal{A}$ and $\\mathcal{I}$ is an ideal of $\\mathcal{A}$ whose Bratteli diagram corresponds to $\\mathfrak{J} \\subseteq \\mathfrak{D}$ . Then $\\mathcal{I}$ is essential if and only if for every $(n,s) \\in \\mathfrak{D}$ there is $(m,t) \\in \\mathfrak{J}$ such that $(n,s) \\to (m,t)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,483,905,560]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If $\\mathcal{D} = \\mathcal{D}_1 \\oplus \\dots \\oplus \\mathcal{D}_l$ and $\\mathcal{E} = \\mathcal{E}_1 \\oplus \\dots \\oplus \\mathcal{E}_k$ are finite-dimensional $C^*$ -algebras where $\\mathcal{D}_i$ and $\\mathcal{E}_j$ are matrix algebras and $\\phi : \\mathcal{D} \\to \\mathcal{E}$ is a homomorphism, we denote the \"multiplicity of $\\mathcal{D}_i$ in $\\mathcal{E}_j$ along $\\phi$ \" by $\\mathrm{Mult}_{\\phi}(\\mathcal{D}_i, \\mathcal{E}_j)$ . Also let $\\mathrm{Mult}_{\\phi}(\\mathcal{D}, \\mathcal{E}_j)$ denote the tuple ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[301,580,680,602]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left(\\operatorname {M u l t} _ {\\phi} \\left(\\mathcal {D} _ {1}, \\mathcal {E} _ {j}\\right), \\dots , \\operatorname {M u l t} _ {\\phi} \\left(\\mathcal {D} _ {l}, \\mathcal {E} _ {j}\\right)\\right) \\in \\mathbb {N} ^ {l}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,620,905,700]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Suppose $\\pi_j: \\mathcal{E} \\to \\mathcal{E}_j$ is the canonical projection. If $\\mathrm{Mult}_{\\phi}(\\mathcal{D}, \\mathcal{E}_j) = (x_1, \\ldots, x_l)$ then the group homomorphism $K_0(\\pi_j \\circ \\phi): \\mathbb{Z}^l \\to \\mathbb{Z}$ sends $(y_1, \\ldots, y_l)$ to $\\sum_{i \\leq l} x_i y_i$ . Therefore if $\\phi, \\psi: \\mathcal{D} \\to \\mathcal{E}$ are homomorphisms, we have $K_0(\\phi) = K_0(\\psi)$ if and only if $\\mathrm{Mult}_{\\phi}(\\mathcal{D}, \\mathcal{E}_j) = \\mathrm{Mult}_{\\psi}(\\mathcal{D}, \\mathcal{E}_j)$ for every $j \\leq k$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,700,903,758]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The following well known facts about AF-algebras will be used several times throughout the article. We denote the unitization of $\\mathcal{A}$ by $\\widetilde{\\mathcal{A}}$ and if $u$ is a unitary in $\\widetilde{\\mathcal{A}}$ , then $\\mathrm{Ad}_u$ denotes the inner automorphisms of $\\mathcal{A}$ given by $a \\to u^*au$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,777,905,857]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 2.1. [4, Lemma III.3.2] Suppose $\\epsilon > 0$ and $\\{\\mathcal{A}_n\\}$ is an increasing sequence of finite-dimensional $C^*$ -algebras such that $\\mathcal{A} = \\overline{\\bigcup \\mathcal{A}_n}$ . If $\\mathcal{F}$ is a finite-dimensional subalgebra of $\\mathcal{A}$ , then there are $m \\in \\mathbb{N}$ and a unitary $u$ in $\\widetilde{\\mathcal{A}}$ such that $u^* \\mathcal{F} u \\subseteq \\mathcal{A}_m$ and $\\|1 - u\\| < \\epsilon$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,876,905,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 2.2. Suppose $\\mathcal{D}$ is a finite-dimensional $C^*$ -algebra, $\\mathcal{A}$ is a separable $AF$ -algebra and $\\phi, \\psi : \\mathcal{D} \\to \\mathcal{A}$ are homomorphisms such that $\\| \\phi - \\psi \\| < 1$ . Then there is a unitary $u \\in \\widetilde{\\mathcal{A}}$ such that $\\mathrm{Ad}_u \\circ \\psi = \\phi$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,64,96,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,63,798,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,105,918,164]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. We have $K_{0}(\\phi) = K_{0}(\\psi)$ , since otherwise for some nonzero projection $p$ in $\\mathcal{D}$ the dimensions of the projections $\\phi(p)$ and $\\psi(p)$ differ and hence $\\| \\psi - \\phi \\| \\geq 1$ . Therefore there is a unitary $u$ in $\\widetilde{\\mathcal{A}}$ such that $\\mathrm{Ad}_u \\circ \\psi = \\phi$ , by [15, Lemma 7.3.2]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,186,918,245]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 2.3. Suppose $\\mathcal{D} = \\mathcal{D}_1 \\oplus \\dots \\oplus \\mathcal{D}_l$ is a finite-dimensional $C^*$ -algebra, where each $\\mathcal{D}_i$ is a matrix algebra. Assume $\\gamma : \\mathcal{D} \\hookrightarrow M_k$ and $\\phi : \\mathcal{D} \\hookrightarrow M_\\ell$ are embeddings. The following are equivalent. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,264,916,345]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(1) There is an embedding $\\\\delta : M_k \\\\hookrightarrow M_\\\\ell$ such that $\\\\delta \\\\circ \\\\gamma = \\\\phi$ . \",\"(2) There is an embedding $\\\\delta : M_k \\\\hookrightarrow M_\\\\ell$ such that $\\\\| \\\\delta \\\\circ \\\\gamma - \\\\phi \\\\| < 1$ . \",\"(3) There is a natural number $c \\\\geq 1$ such that $\\\\ell \\\\geq ck$ and $\\\\mathrm{Mult}_{\\\\phi}(\\\\mathcal{D}, M_{\\\\ell}) = c \\\\mathrm{Mult}_{\\\\gamma}(\\\\mathcal{D}, M_{k})$ . \"]","page_idx":"6","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[89,364,719,385]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. (1) trivially implies (2). To see $(2)\\Rightarrow (3)$ , note that we have ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,408,732,429]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\operatorname {M u l t} _ {\\phi} \\left(\\mathcal {D} _ {i}, M _ {\\ell}\\right) = \\operatorname {M u l t} _ {\\delta} \\left(M _ {k}, M _ {\\ell}\\right) \\operatorname {M u l t} _ {\\gamma} \\left(\\mathcal {D} _ {i}, M _ {k}\\right),\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,450,918,529]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"for every $i \\leq l$ , since otherwise $\\| \\delta \\circ \\gamma - \\phi \\| \\geq 1$ . Let $c = \\mathrm{Mult}_{\\delta}(M_k, M_\\ell)$ . To see $(3) \\Rightarrow (1)$ , let $\\delta': M_k \\to M_l$ be the embedding which sends an element of $M_k$ to $c$ many identical copies of it along the diagonal of $M_\\ell$ . Then we have $K_0(\\phi) = K_0(\\delta' \\circ \\gamma)$ , by the assumption of (3). Therefore there is a unitary $u$ in $M_\\ell$ such that $\\mathrm{Ad}_u \\circ \\delta' \\circ \\gamma = \\phi$ . Let $\\delta = \\mathrm{Ad}_u \\circ \\delta'$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,552,584,572]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. AF-algebras with left-invertible connecting maps ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,595,918,655]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Suppose $\\mathcal{A},\\mathcal{B}$ are $C^*$ -algebras. A homomorphism $\\phi :\\mathcal{B}\\to \\mathcal{A}$ is left-invertible if there is a (necessarily surjective) homomorphism $\\pi :\\mathcal{A}\\twoheadrightarrow \\mathcal{B}$ such that $\\pi \\circ \\phi = \\mathrm{id}_{\\mathcal{B}}$ . Clearly a left-invertible homomorphism is necessarily an embedding. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,675,918,735]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Definition 3.1. We say $\\mathcal{B}$ is a retract of $\\mathcal{A}$ if there is a left-invertible embedding from $\\mathcal{B}$ into $\\mathcal{A}$ . We say a subalgebra $\\mathcal{B}$ of $\\mathcal{A}$ is an inner retract if and only if there is a homomorphism $\\theta: \\mathcal{A} \\twoheadrightarrow \\mathcal{B}$ such that $\\theta|_{\\mathcal{B}} = \\mathrm{id}_{\\mathcal{B}}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,755,918,855]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The image of a left-invertible embedding $\\phi : \\mathcal{B} \\hookrightarrow \\mathcal{A}$ is an inner retract of $\\mathcal{A}$ . Note that $\\mathcal{B}$ is a retract of $\\mathcal{A}$ if and only if $\\mathcal{A}$ is a split-extension of $\\mathcal{B}$ . The next proposition contains some elementary facts about retracts of finite-dimensional $C^*$ -algebras and left-invertible maps between them. They follow from elementary facts about finite-dimensional $C^*$ -algebras, e.g., matrix algebras are simple. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,876,918,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proposition 3.2. A $C^*$ -algebra $\\mathcal{D}$ is a retract of a finite-dimensional $C^*$ -algebra $\\mathcal{E}$ if and only if $\\mathcal{E} \\cong \\mathcal{D} \\oplus \\mathcal{F}$ , for some finite-dimensional $C^*$ -algebra $\\mathcal{F}$ . In other words, $\\mathcal{D}$ is a retract of $\\mathcal{E}$ if and only if $\\mathcal{D}$ is isomorphic to an ideal of $\\mathcal{E}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[903,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[81,105,905,163]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Suppose $\\phi : \\mathcal{D} \\hookrightarrow \\mathcal{E}$ is a (unital) left-invertible embedding and $\\pi : \\mathcal{E} \\to \\mathcal{D}$ is a left inverse of $\\phi$ . Then $\\mathcal{E}$ can be written as $\\mathcal{E}_0 \\oplus \\mathcal{E}_1$ and there are $\\phi_0, \\phi_1$ such that $\\phi_0 : \\mathcal{D} \\to \\mathcal{E}_0$ is an isomorphism, $\\phi_1 : \\mathcal{D} \\to \\mathcal{E}_1$ is a (unital) homomorphism and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,183,569,222]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- $\\\\phi(d) = (\\\\phi_0(d), \\\\phi_1(d))$ , for every $d \\\\in \\\\mathcal{D}$ , \",\"- $\\\\pi(e_0, e_1) = \\\\phi_0^{-1}(e_0)$ , for every $(e_0, e_1) \\\\in \\\\mathcal{E}_0 \\\\oplus \\\\mathcal{E}_1$ . \"]","page_idx":"7","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[81,242,905,322]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Suppose $(\\mathcal{A}_n,\\phi_n^m)$ is a sequence where each connecting map $\\phi_n^m:\\mathcal{A}_n\\hookrightarrow \\mathcal{A}_m$ is left-invertible. Let $\\pi_n^{n + 1}:\\mathcal{A}_{n + 1}\\twoheadrightarrow \\mathcal{A}_n$ be a left inverse of $\\phi_n^{n + 1}$ , for each $n$ . For $m > n$ define $\\pi_n^m:\\mathcal{A}_m\\twoheadrightarrow \\mathcal{A}_n$ by $\\pi_n^m = \\pi_n^{n + 1}\\circ \\dots \\circ \\pi_{m - 1}^m$ . Then $\\pi_n^m$ is a left inverse of $\\phi_n^m$ which satisfies $\\pi_n^m\\circ \\pi_m^k = \\pi_n^k$ , for every $n\\leq m\\leq k$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,338,905,417]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Definition 3.3. We say $(\\mathcal{A}_n,\\phi_n^m)$ is a left-invertible sequence if each $\\phi_n^m$ is left-invertible and $\\phi_n^n = \\mathrm{id}_{\\mathcal{A}_n}$ . We call $(\\pi_n^m)$ a compatible left inverse of the left-invertible sequence $(\\mathcal{A}_n,\\phi_n^m)$ if $\\pi_n^m:\\mathcal{A}_m\\to \\mathcal{A}_n$ are surjective homomorphisms such that $\\pi_n^m\\circ \\pi_m^k = \\pi_n^k$ and $\\pi_n^m\\circ \\phi_n^m = \\mathrm{id}_{\\mathcal{A}_n}$ , for every $n\\leq m\\leq k$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[107,433,867,454]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The following simple lemma is true for arbitrary categories, see [10, Lemma 6.2]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,470,905,550]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 3.4. Suppose $(\\mathcal{A}_n,\\phi_n^m)$ is a left-invertible sequence of $C^*$ -algebras with a compatible left inverse $(\\pi_n^m)$ and $\\mathcal{A} = \\varinjlim (\\mathcal{A}_n,\\phi_n^m)$ . Then for every $n$ there are surjective homomorphisms $\\pi_n^\\infty : \\mathcal{A} \\to \\mathcal{A}_n$ such that $\\pi_n^\\infty \\circ \\phi_n^\\infty = \\mathrm{id}_{\\mathcal{A}_n}$ and $\\pi_n^m \\circ \\pi_m^\\infty = \\pi_n^\\infty$ for each $n \\leq m$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,566,903,605]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. First define $\\pi_n^\\infty$ on $\\bigcup_{i} \\phi_i^\\infty[\\mathcal{A}_i]$ , which is dense in $\\mathcal{A}$ . If $a = \\phi_m^\\infty(a_m)$ for some $m$ and $a_m \\in \\mathcal{A}_m$ , then let ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[346,622,635,670]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\pi_ {n} ^ {\\infty} (a) = \\left\\{ \\begin{array}{l l} \\pi_ {n} ^ {m} (a _ {m}) & \\text {i f} n \\leq m \\\\ \\phi_ {m} ^ {n} (a _ {m}) & \\text {i f} n > m \\end{array} \\right.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,685,903,723]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"These maps are well-defined (norm-decreasing) homomorphism, so they extend to $\\mathcal{A}$ and satisfy the requirements of the lemma. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,742,903,777]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In particular, each $\\mathcal{A}_n$ or any retract of it, is a retract of $\\mathcal{A}$ . The converse of this is also true. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,797,903,838]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 3.5. Suppose $(\\mathcal{A}_n,\\phi_n^m)$ is a left-invertible sequence of finite-dimensional $C^*$ -algebras with $\\mathcal{A} = \\varinjlim (\\mathcal{A}_n,\\phi_n^m)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[83,857,905,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(1) If $\\\\mathcal{D}$ is a finite-dimensional subalgebra of $\\\\mathcal{A}$ , then $\\\\mathcal{D}$ is contained in an inner retract of $\\\\mathcal{A}$ . \",\"(2) If $\\\\mathcal{D}$ is a finite-dimensional retract of $\\\\mathcal{A}$ , then there is $m \\\\in \\\\mathbb{N}$ such that $\\\\mathcal{D}$ is a retract of $\\\\mathcal{A}_{m'}$ for every $m' \\\\geq m$ . \"]","page_idx":"7","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[81,64,96,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,63,798,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,105,635,125]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Let $(\\pi_n^m)$ be a compatible left inverse of $(A_n,\\phi_n^m)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[87,126,916,220]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(1) If $\\\\mathcal{D}$ is a finite-dimensional subalgebra of $\\\\mathcal{A}$ , then for some $m \\\\in \\\\mathbb{N}$ and a unitary $u \\\\in \\\\widetilde{\\\\mathcal{A}}$ , it is contained in $u\\\\phi_m^\\\\infty[\\\\mathcal{A}_m]u^*$ (Lemma 2.1). The latter is an inner retract of $\\\\mathcal{A}$ . \",\"(2) If $\\\\mathcal{D}$ is a retract of $\\\\mathcal{A}$ , there is an embedding $\\\\phi : \\\\mathcal{D} \\\\hookrightarrow \\\\mathcal{A}$ with a left inverse $\\\\pi : \\\\mathcal{A} \\\\twoheadrightarrow \\\\mathcal{D}$ . Find $m$ and a unitary $u$ in $\\\\widetilde{\\\\mathcal{A}}$ such that $u^{*}\\\\phi[\\\\mathcal{D}]u \\\\subseteq \\\\phi_{m}^{\\\\infty}[\\\\mathcal{A}_{m}]$ . This implies that \"]","page_idx":"8","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[361,242,648,263]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\phi_ {m} ^ {\\infty} \\circ \\pi_ {m} ^ {\\infty} (u ^ {*} \\phi (d) u) = u ^ {*} \\phi (d) u\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,279,916,317]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"for every $d \\in \\mathcal{D}$ . Define $\\psi : \\mathcal{D} \\hookrightarrow \\mathcal{A}_m$ by $\\psi(d) = \\pi_m^\\infty(u^*\\phi(d)u)$ . Then $\\psi$ has a left inverse $\\theta : \\mathcal{A}_m \\twoheadrightarrow \\mathcal{D}$ defined by $\\theta(x) = \\pi(u\\phi_m^\\infty(x)u^*)$ , since for every $d \\in \\mathcal{D}$ we have ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[169,336,835,357]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\theta (\\psi (d)) = \\theta (\\pi_ {m} ^ {\\infty} (u ^ {*} \\phi (d) u)) = \\pi (u \\phi_ {m} ^ {\\infty} \\circ \\pi_ {m} ^ {\\infty} (u ^ {*} \\phi (d) u) u ^ {*}) = \\pi (\\phi (d)) = d.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,373,916,411]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Because $\\mathcal{A}_m$ is a retract of $\\mathcal{A}_{m'}$ , for every $m' \\geq m$ , we conclude that $\\mathcal{D}$ is also a retract of $\\mathcal{A}_{m'}$ . $\\square$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,430,918,647]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 3.6. It is not surprising that many AF-algebras are not limits of left-invertible sequences of finite-dimensional $C^*$ -algebras. This is because, for instance, such an AF-algebra has infinitely many ideals (unless it is finite-dimensional), and admits finite traces, as it maps onto finite-dimensional $C^*$ -algebras. Therefore, for example $\\mathcal{K}(\\ell_2)$ , the $C^*$ -algebra of all compact operators on $\\ell_2$ , and infinite-dimensional UHF-algebras are not limits of left-invertible sequences of finite-dimensional $C^*$ -algebras. Recall that a $C^*$ -algebra is stable if its tensor product with $\\mathcal{K}(\\ell_2)$ is isomorphic to itself. Blackadar's characterization of stable AF-algebras [2] (see also [16, Corollary 1.5.8]) states that a separable AF-algebra $\\mathcal{A}$ is stable if and only if no nonzero ideal of $\\mathcal{A}$ admits a nonzero finite (bounded) trace. Therefore no stable AF-algebra is the limit of a left-invertible sequence of finite-dimensional $C^*$ -algebras. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,664,916,723]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The following proposition gives another criteria to distinguish these AF-algebras. For example, it can be directly used to show that infinite-dimensional UHF-algebras are not limits of left-invertible sequences of finite-dimensional $C^*$ -algebras. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,741,918,842]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proposition 3.7. Suppose $\\mathcal{A}$ is an $AF$ -algebra isomorphic to the limit of a left-invertible sequence of finite-dimensional $C^*$ -algebras and $\\mathcal{A} = \\overline{\\bigcup_{n} \\mathcal{B}_{n}}$ for an increasing sequence $(\\mathcal{B}_n)$ of finite-dimensional subalgebras. Then there is an increasing sequence $(n_i)$ of natural numbers and an increasing sequence $(\\mathcal{C}_i)$ of finite-dimensional subalgebras of $\\mathcal{A}$ such that $\\mathcal{A} = \\overline{\\bigcup_{n} \\mathcal{C}_n}$ and $\\mathcal{B}_{n_i} \\subseteq \\mathcal{C}_i \\subseteq \\mathcal{B}_{n_{i+1}}$ and $\\mathcal{C}_i$ is an inner retract of $\\mathcal{C}_{i+1}$ for every $i \\in \\mathbb{N}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,857,916,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Suppose $\\mathcal{A}$ is the limit of a left-invertible direct sequence $(\\mathcal{A}_n, \\phi_n^m)$ of finite-dimensional $C^*$ -algebras. Theorem III.3.5 of [4], applied to sequences $(\\mathcal{B}_n)$ and $(\\phi_n^\\infty[\\mathcal{A}_n])$ , shows that there are sequences $(n_i)$ , $(m_i)$ of natural numbers and a unitary $u \\in \\widetilde{A}$ such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[903,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"9 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[355,105,623,126]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {B} _ {n _ {i}} \\subseteq u ^ {*} \\phi_ {m _ {i}} ^ {\\infty} [ \\mathcal {A} _ {m _ {i}} ] u \\subseteq \\mathcal {B} _ {n _ {i + 1}}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,142,490,161]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"for every $i\\in \\mathbb{N}$ . Let $\\mathcal{C}_i = u^*\\phi_{m_i}^\\infty [\\mathcal{A}_{m_i}]u$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,179,903,217]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, the next proposition shows that any AF-algebra is a quotient of an AF-algebra which is the limit of a left-invertible sequence of finite-dimensional $C^*$ -algebras. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,235,905,292]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proposition 3.8. For every (unital) $AF$ -algebra $\\mathcal{B}$ there is a (unital) $AF$ -algebra $\\mathcal{A} \\supseteq \\mathcal{B}$ which is the limit of a (unital) left-invertible sequence of finite-dimensional $C^*$ -algebras and $\\mathcal{A} / \\mathcal{J} \\cong \\mathcal{B}$ for an essential ideal $\\mathcal{J}$ of $\\mathcal{A}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,311,903,348]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Suppose $\\mathcal{B}$ is the limit of the sequence $(\\mathcal{B}_n, \\psi_n^m)$ of finite-dimensional $C^*$ -algebras and homomorphisms. Let $\\mathcal{A}$ denote the limit of the following diagram: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[241,364,663,511]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{c} \\mathcal {B} _ {1} \\xrightarrow [ i d ]{\\psi_ {1} ^ {2}} \\mathcal {B} _ {2} \\xrightarrow [ i d ]{\\psi_ {2} ^ {3}} \\mathcal {B} _ {3} \\xrightarrow [ i d ]{\\psi_ {3} ^ {4}} \\mathcal {B} _ {4} \\dots \\\\ \\mathcal {B} _ {1} \\xrightarrow [ i d ]{\\mathcal {B} _ {2}} \\mathcal {B} _ {1} \\xrightarrow [ i d ]{\\mathcal {B} _ {2}} \\mathcal {B} _ {2} \\dots \\\\ \\mathcal {B} _ {1} \\xrightarrow [ i d ]{\\mathcal {B} _ {2}} \\mathcal {B} _ {2} \\dots \\\\ \\mathcal {B} _ {1} \\xrightarrow [ i d ]{\\mathcal {B} _ {2}} \\mathcal {B} _ {1} \\dots \\\\ \\mathcal {B} _ {1} \\dots \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,526,907,604]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Then $\\mathcal{A}$ is an AF-algebra which contains $\\mathcal{B}$ and the connecting maps are left-invertible embeddings. The ideal $\\mathcal{J}$ corresponding to the (directed and hereditary) subdiagram of the above diagram which contains all the nodes except the ones on the top line is essential and clearly $\\mathcal{A} / \\mathcal{J} \\cong \\mathcal{B}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,625,475,642]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. AF-algebras with the Cantor property ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[77,663,905,800]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We define the notion of the \"Cantor property\" for an AF-algebra. These algebras have properties which are, in a sense, generalizations of the ones satisfied (some trivially) by $C(2^{\\mathbb{N}})$ . It is easier to state these properties using the notation for Bratteli diagrams that we fixed in Section 2. For example, every node of the Bratteli diagram of $C(2^{\\mathbb{N}})$ splits in two, which here is generalized to \"each node splits into at least two nodes with the same dimension at some further stage\", which of course guarantees that there are no minimal projections in the limit algebra. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,817,905,877]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Definition 4.1. We say an AF-algebra $\\mathcal{A}$ has the Cantor property if there is a sequence $(\\mathcal{A}_n,\\phi_n^m)$ of finite-dimensional $C^*$ -algebras and embeddings such that $\\mathcal{A} = \\varinjlim (\\mathcal{A}_n,\\phi_n^m)$ and the Bratteli diagram $\\mathfrak{D}$ of $(\\mathcal{A}_n,\\phi_n^m)$ has the following properties: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,895,903,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(D0) For every $(n,s)\\in \\mathfrak{D}$ there is $(n + 1,t)\\in \\mathfrak{D}$ such that $\\dim (n,s) = \\dim (n + 1,t)$ and $(n,s)\\to (n + 1,t)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,63,104,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,61,796,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubiš / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,105,916,244]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(D1) For every $(n,s)\\\\in \\\\mathfrak{D}$ there are distinct nodes $(m,t),(m,t^{\\\\prime})\\\\in \\\\mathfrak{D}$ , for some $m > n$ , such that $\\\\dim (n,s) = \\\\dim (m,t) = \\\\dim (m,t^{\\\\prime})$ and $(n,s)\\\\to (m,t)$ and $(n,s)\\\\to (m,t^{\\\\prime})$ . \",\"(D2) For every $(n, s_1), \\\\ldots, (n, s_k), (n', s') \\\\in \\\\mathfrak{D}$ and $\\\\{x_1, \\\\ldots, x_k\\\\} \\\\subseteq \\\\mathbb{N}$ such that $\\\\sum_{i=1}^{k} x_i \\\\dim(n, s_i) \\\\leq \\\\dim(n', s')$ , there is $m \\\\geq n$ such that for some $(m, t) \\\\in \\\\mathfrak{D}$ we have $\\\\dim(m, t) = \\\\dim(n', s')$ and there are exactly $x_i$ distinct paths from $(n, s_i)$ to $(m, t)$ in $\\\\mathfrak{D}$ . \"]","page_idx":"10","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[89,264,914,305]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Bratteli diagram of $C(2^{\\mathbb{N}})$ trivially satisfies these conditions and therefore $C(2^{\\mathbb{N}})$ has the Cantor property. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,327,918,508]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 4.2. Condition (D0) states that $(\\mathcal{A}_n,\\phi_n^m)$ is a left-invertible sequence. Dropping (D0) from Definition 4.1 does not change the definition (i.e., $\\mathcal{A}$ has the Cantor property if and only if it has a representing sequence satisfying (D1) and (D2)). This is because (D1) alone implies the existence of a left-invertible sequence with limit $\\mathcal{A}$ that still satisfies (D1) and (D2). In fact, $\\mathcal{A}$ has the Cantor property if and only if any representing sequence satisfies (D1) and (D2). However, we add (D0) for simplicity to make sure that $(\\mathcal{A}_n,\\phi_n^m)$ is already a left-invertible sequence, since, as we shall see later, being the limit of a left-invertible direct sequence of finite-dimensional $C^*$ -algebras is a crucial and helpful property of AF-algebras with the Cantor property. Condition (D2) can be rewritten as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,527,916,589]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(D2') For every ideal $\\mathcal{D}$ of some $\\mathcal{A}_n$ , if $M_{\\ell}$ is a retract of $\\mathcal{A}$ and $\\gamma : \\mathcal{D} \\hookrightarrow M_{\\ell}$ is an embedding, then there is $m \\geq n$ and $\\mathcal{A}_{m,t} \\subseteq \\mathcal{A}_m$ such that $\\mathcal{A}_{m,t} \\cong M_{\\ell}$ and $\\mathrm{Mult}_{\\phi_n^m}(\\mathcal{D}, \\mathcal{A}_{m,t}) = \\mathrm{Mult}_{\\gamma}(\\mathcal{D}, M_{\\ell})$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,608,914,647]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Definition 4.1 may be adjusted for unital AF-algebras where all the maps are considered to be unital. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,670,916,732]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Definition 4.3. A unital AF-algebra $\\mathcal{A}$ has the Cantor property if and only if it satisfies the conditions of Definition 4.1, where $\\phi_n^m$ are unital and in condition (D2) the inequality $\\sum_{i=1}^{k} x_i \\dim(n, s_i) \\leq \\dim(n', s')$ is replaced with equality. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,754,916,792]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proposition 4.4. Suppose $\\mathcal{A}$ is an $AF$ -algebra with Cantor property. If $\\mathcal{D}, \\mathcal{E}$ are finite-dimensional retracts of $\\mathcal{A}$ , then so is $\\mathcal{D} \\oplus \\mathcal{E}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,816,918,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Suppose $\\mathcal{D} = \\mathcal{D}_1 \\oplus \\mathcal{D}_2 \\oplus \\dots \\oplus \\mathcal{D}_l$ and $\\mathcal{E} = \\mathcal{E}_1 \\oplus \\mathcal{E}_2 \\oplus \\dots \\oplus \\mathcal{E}_k$ , where $\\mathcal{D}_i, \\mathcal{E}_i$ are isomorphic to matrix algebras. By Lemma 3.5 both $\\mathcal{D}$ and $\\mathcal{E}$ are retracts of some $\\mathcal{A}_m$ , which means that all $\\mathcal{D}_i$ and $\\mathcal{E}_i$ appear in $\\mathcal{A}_m$ as retracts (ideals). By (D1) and enlarging $m$ , if necessary, we can make sure these retracts in $\\mathcal{A}_m$ are orthogonal, meaning that $\\mathcal{A}_m \\cong \\mathcal{D} \\oplus \\mathcal{E} \\oplus \\mathcal{F}$ , for some finite-dimensional $C^*$ -algebra $\\mathcal{F}$ . Therefore $\\mathcal{D} \\oplus \\mathcal{E}$ is a retract of $\\mathcal{A}_m$ and as a result, it is a retract of $\\mathcal{A}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[895,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"11 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[77,105,905,185]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 4.5. Suppose $\\mathcal{A}$ is an $AF$ -algebra with the Cantor property, witnessed by $(\\mathcal{A}_n,\\phi_n^m)$ satisfying Definition 4.1 and $\\mathcal{E}$ is a finite-dimensional retract of $\\mathcal{A}$ . If $\\gamma :\\mathcal{A}_n\\hookrightarrow \\mathcal{E}$ is a left-invertible embedding then there are $m\\geq n$ and a left-invertible embedding $\\delta :\\mathcal{E}\\hookrightarrow \\mathcal{A}_m$ such that $\\delta \\circ \\gamma = \\phi_n^m$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,202,905,260]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Suppose $\\mathcal{A}_n = \\mathcal{A}_{n,1} \\oplus \\dots \\oplus \\mathcal{A}_{n,l}$ and $\\mathcal{E} = \\mathcal{E}_1 \\oplus \\mathcal{E}_2 \\oplus \\dots \\oplus \\mathcal{E}_k$ where $\\mathcal{E}_i$ and $\\mathcal{A}_{n,j}$ are all matrix algebras. Let $\\pi_i$ denote the canonical projection from $\\mathcal{E}$ onto $\\mathcal{E}_i$ . For every $i \\leq k$ put ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[344,279,638,300]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nY _ {i} = \\{j \\leq l: \\gamma [ \\mathcal {A} _ {n, j} ] \\cap \\mathcal {E} _ {i} \\neq 0 \\},\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,317,905,514]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and let $\\mathcal{A}_{n,Y_i} = \\bigoplus_{j\\in Y_i}\\mathcal{A}_{n,j}$ . Then $\\mathcal{A}_{n,Y_i}$ is an ideal (a retract) of $\\mathcal{A}_n$ and the map $\\gamma_{i}:\\mathcal{A}_{n,Y_{i}}\\hookrightarrow \\mathcal{E}_{i}$ , the restriction of $\\gamma$ to $\\mathcal{A}_{n,Y_i}$ composed with $\\pi_{i}$ , is an embedding. Since $\\mathcal{E}$ is a finite-dimensional retract of $\\mathcal{A}$ , it is a retract of some $\\mathcal{A}_{n'}$ (Lemma 3.5). So each $\\mathcal{E}_i$ is a retract of $\\mathcal{A}_{n'}$ . By applying (D2) for each $i\\leq k$ there are $m_{i}\\geq n$ and $(m_i,t_i)\\in \\mathfrak{D}$ such that $\\dim (m_i,t_i) = \\dim (\\mathcal{E}_i)$ and $\\mathrm{Mult}_{\\phi_n^{m_i}}(\\mathcal{A}_{n,Y_i},\\mathcal{A}_{m_i,t_i}) = \\mathrm{Mult}_{\\gamma_i}(\\mathcal{A}_{n,Y_i},\\mathcal{E}_i)$ . Let $m = \\max \\{m_i:i\\leq k\\}$ and by (D0) find $(m,s_i)$ such that $\\dim (m_i,t_i) = \\dim (m,s_i)$ and $(m_i,t_i)\\to (m,s_i)$ . Applying (D1) and possibly increasing $m$ allows us to make sure that $(m,s_i)\\neq (m,s_j)$ for distinct $i,j$ and therefore $\\mathcal{A}_{m,s_i}$ are pairwise orthogonal. Then $\\{\\mathcal{A}_{m,s_i}:i\\leq k\\}$ is a sequence of pairwise orthogonal subalgebras (retracts) of $\\mathcal{A}_m$ such that $\\mathcal{A}_{m,s_i}\\cong \\mathcal{E}_i$ and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[289,532,693,554]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathrm {M u l t} _ {\\phi_ {n} ^ {m}} (\\mathcal {A} _ {n, Y _ {i}}, \\mathcal {A} _ {m, s _ {i}}) = \\mathrm {M u l t} _ {\\gamma_ {i}} (\\mathcal {A} _ {n, Y _ {i}}, \\mathcal {E} _ {i}).\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,569,905,608]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"By Lemma 2.3 there are isomorphisms $\\delta_i : \\mathcal{E}_i \\hookrightarrow \\mathcal{A}_{m,s_i}$ such that $\\gamma_i \\circ \\delta_i$ is equal to the restriction of $\\phi_n^m$ to $\\mathcal{A}_{n,Y_i}$ projected onto $\\mathcal{A}_{m,s_i}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,610,905,685]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Suppose $1_{m}$ is the unit of $\\mathcal{A}_m$ and $q_{i}$ is the unit of $\\mathcal{A}_{m,s_i}$ . Each $q_{i}$ is a central projection of $\\mathcal{A}_m$ , because $\\mathcal{A}_{m,s_i}$ are ideals of $\\mathcal{A}_m$ . Since $\\gamma$ is left-invertible, for each $j \\leq l$ there is $k(j) \\leq k$ such that $\\mathcal{A}_{n,j} \\cong \\mathcal{E}_{k(j)}$ and $\\hat{\\gamma}_{j} = \\pi_{k(j)} \\circ \\gamma|_{\\mathcal{A}_{n,j}}$ is an isomorphism. Also for $j \\leq l$ let ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[340,705,642,727]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nX _ {j} = \\{i \\leq k: \\gamma [ \\mathcal {A} _ {n, j} ] \\cap \\mathcal {E} _ {i} \\neq 0 \\}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[79,742,177,758]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Note that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[83,782,306,841]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(1) $k(j)\\\\in X_{j}$ \",\"(2) $k(j^{\\\\prime})\\\\notin X_{j}$ if $j\\\\neq j^{\\\\prime}$ \",\"(3) $i\\\\in X_j\\\\Leftrightarrow j\\\\in Y_i$ \"]","page_idx":"11","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[77,860,897,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $\\hat{\\delta}_j: \\mathcal{E}_{k(j)} \\to (1_m - \\sum_{i \\in X_j} q_i) \\mathcal{A}_m(1_m - \\sum_{i \\in X_j} q_i)$ be the homomorphism defined by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[263,900,719,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\hat {\\delta} _ {j} (e) = (1 _ {m} - \\sum_ {i \\in X _ {j}} q _ {i}) \\phi_ {n} ^ {m} (\\hat {\\gamma} _ {j} ^ {- 1} (e)) (1 _ {m} - \\sum_ {i \\in X _ {j}} q _ {i}).\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,63,104,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"12 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,61,796,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubiš / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,105,304,125]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Define $\\delta :\\mathcal{E}\\hookrightarrow \\mathcal{A}_m$ by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,141,802,163]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\delta (e _ {1}, \\ldots , e _ {k}) = \\hat {\\delta} _ {1} (e _ {k (1)}) + \\dots + \\hat {\\delta} _ {l} (e _ {k (l)}) + \\delta_ {1} (e _ {1}) + \\dots + \\delta_ {k} (e _ {k}).\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,179,916,236]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Since each $\\delta_{i}$ is an isomorphism, it is clear that $\\delta$ is left-invertible. To check that $\\delta \\circ \\gamma = \\phi_n^m$ , by linearity of the maps it is enough to check it only for $\\bar{a} = (0,\\dots ,0,a_j,0,\\dots ,0)\\in \\mathcal{A}_n$ . If $\\gamma (\\bar{a}) = (e_1,\\ldots ,e_k)$ then ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[402,254,603,302]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\ne _ {i} = \\left\\{ \\begin{array}{l l} 0 & i \\not \\in X _ {j} \\\\ \\gamma_ {i} (\\bar {a}) & i \\in X _ {j} \\end{array} \\right.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,317,914,354]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"for $i \\leq k$ . Also note that $e_{k(j)} = \\hat{\\gamma}_j(a_j)$ . Assume $X_{j} = \\{r_{1},\\ldots ,r_{\\ell}\\}$ . Then by (1)-(3) we have ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[130,370,875,467]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\delta \\circ \\gamma (\\bar {a}) = \\hat {\\delta} _ {j} (\\hat {\\gamma} _ {j} (a _ {j})) + \\delta_ {r _ {1}} (\\gamma_ {r _ {1}} (\\bar {a})) + \\dots + \\delta_ {r _ {\\ell}} (\\gamma_ {r _ {\\ell}} (\\bar {a})) \\\\ = \\left(1 _ {m} - \\sum_ {i \\in X _ {j}} q _ {i}\\right) \\phi_ {n} ^ {m} (\\bar {a}) \\left(1 _ {m} - \\sum_ {i \\in X _ {j}} q _ {i}\\right) + q _ {r _ {1}} \\phi_ {n} ^ {m} (\\bar {a}) q _ {r _ {1}} + \\dots + q _ {r _ {\\ell}} \\phi_ {n} ^ {m} (\\bar {a}) q _ {r _ {\\ell}} \\\\ = \\phi_ {n} ^ {m} (\\bar {a}). \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,485,372,502]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This completes the proof. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,523,695,542]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.1. $AF$ -algebras with the Cantor property are $C(2^{\\mathbb{N}})$ -absorbing ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,561,916,620]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Suppose $\\mathcal{A}$ is an AF-algebra with Cantor property. Define $\\mathcal{A}^{\\mathcal{C}}$ to be the limit of the sequence $(\\mathcal{B}_n, \\psi_n^m)$ such that $\\mathcal{B}_n = \\bigoplus_{i \\leq 2^{n-1}} \\mathcal{A}_n \\cong \\mathbb{C}^{2^{n-1}} \\otimes \\mathcal{A}_n$ and $\\psi_n^{n+1} = \\bigoplus_{i \\leq 2^n} \\phi_n^{n+1}$ , as shown in the following diagram ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[308,636,914,898]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0654/11241661d9696d702575633b3052b394f5b3a6a48163159e781882143c03477a.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[89,914,702,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It is straightforward to check that $\\mathcal{A}^c\\cong \\mathcal{A}\\otimes C(2^{\\mathbb{N}})\\cong C(2^{\\mathbb{N}},\\mathcal{A})$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[895,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"13 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[77,105,466,125]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 4.6. $\\mathcal{A}^{\\mathcal{C}}$ has the Cantor property. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,141,907,217]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. We check that $(\\mathcal{B}_n, \\psi_n^m)$ satisfies (D0)-(D2). Each $\\psi_n^{n+1}$ is left-invertible, by Proposition 3.2 and since $\\phi_n^{n+1}$ is left-invertible, therefore (D0) holds. Conditions (D1) and (D2) are trivially satisfied by analyzing the Bratteli diagram (4.1), since $\\mathcal{A}$ satisfies them. $\\square$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,236,907,275]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 4.7. Suppose $\\mathcal{A}$ is an $AF$ -algebra with Cantor property. Then $\\mathcal{A} \\otimes C(2^{\\mathbb{N}})$ is isomorphic to $\\mathcal{A}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,291,907,351]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Identify $\\mathcal{A} \\otimes C(2^{\\mathbb{N}})$ with $\\mathcal{A}^{\\mathcal{C}}$ . Find sequences $(m_i)$ and $(n_i)$ of natural numbers and left-invertible embeddings $\\gamma_i : \\mathcal{A}_{n_i} \\hookrightarrow \\mathcal{B}_{m_{i+1}}$ and $\\delta_i : \\mathcal{B}_{n_i} \\hookrightarrow \\mathcal{A}_{m_i}$ such that $n_1 = m_1 = 1$ , $m_2 = 2$ and $\\gamma_1 = \\psi_1^2$ and the diagram below is commutative. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[139,364,905,448]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{c c c} \\mathcal {B} _ {1} \\xrightarrow {\\psi_ {1} ^ {2}} \\mathcal {B} _ {m _ {2}} \\xrightarrow {\\psi_ {m _ {2}} ^ {m _ {3}}} \\mathcal {B} _ {m _ {3}} \\xrightarrow {\\psi_ {m _ {3}} ^ {m _ {4}}} \\dots & \\mathcal {A} ^ {\\mathcal {C}} \\\\ \\Bigg \\| \\quad \\begin{array}{c c c} \\gamma_ {1} & \\searrow & \\searrow \\\\ & \\searrow & \\searrow \\\\ & \\phi_ {n _ {2}} ^ {n _ {2}} & \\end{array} \\Bigg \\| \\quad \\begin{array}{c c c} \\gamma_ {2} & \\searrow & \\searrow \\\\ & \\searrow & \\searrow \\\\ & \\phi_ {n _ {2}} ^ {n _ {3}} & \\end{array} \\Bigg \\| \\quad \\begin{array}{c c c} \\gamma_ {2} & \\searrow & \\searrow \\\\ & \\searrow & \\searrow \\\\ & \\phi_ {n _ {3}} ^ {n _ {4}} & \\end{array} \\Bigg \\| \\quad \\begin{array}{c c c} \\gamma_ {3} & \\searrow & \\searrow \\\\ & \\searrow & \\searrow \\\\ & \\phi_ {n _ {3}} ^ {n _ {4}} & \\end{array} \\Bigg \\| \\quad \\begin{array}{c c c} \\gamma_ {3} & \\searrow & \\searrow \\\\ & \\searrow & \\searrow \\\\ & \\phi_ {n _ {3}} ^ {n _ {4}} & - 1. 0 p t ] & \\end{array} \\\\ \\mathcal {A} _ {1} \\xrightarrow {\\gamma_ {1}} \\mathcal {A} _ {n _ {2}} \\xrightarrow {\\gamma_ {2}} \\mathcal {A} _ {n _ {3}} \\xrightarrow {\\phi_ {n _ {2}} ^ {n _ {3}}} \\dots & \\mathcal {\\downarrow} _ {\\phi} \\\\ & \\mathcal {A} \\end{array} \\tag {4.2}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,461,907,539]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The existence of such $\\gamma_{i}$ and $\\delta_{i}$ is guaranteed by Lemma 4.5, since each $\\mathcal{B}_i$ is a retract of $\\mathcal{A}$ , by Lemma 3.5 and Proposition 4.4, and of course each $\\mathcal{A}_i$ is a retract of $\\mathcal{B}_i$ . The universal property of inductive limits implies the existence of an isomorphism between $\\mathcal{A}$ and $\\mathcal{A}^{\\mathcal{C}}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,557,907,595]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 4.8. As we will see in section 7.2 the tensor products of two AF-algebras with Cantor property do not necessarily have the Cantor property. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,614,186,630]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.2. Ideals ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[77,652,907,770]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $\\mathcal{A} = \\varinjlim_{n}(\\mathcal{A}_n,\\phi_n^m)$ be an AF-algebra with Cantor property, such that the Bratteli diagram $\\mathfrak{D}$ of $(\\mathcal{A}_n,\\phi_n^m)$ satisfies (D0)-(D2) of Definition 4.1. Let $\\mathfrak{J}\\subseteq \\mathfrak{D}$ denote the Bratteli diagram of an ideal $\\mathcal{I}\\subseteq \\mathcal{A}$ . Put $\\mathcal{J}_n = \\bigoplus_{(n,s)\\in \\mathfrak{J}}\\mathcal{A}_{n,s}$ , which is an ideal (a retract) of $\\mathcal{A}_n$ . Then $\\mathcal{J} = \\varinjlim_{n}(\\mathcal{J}_n,\\phi_n^m|_{\\mathcal{J}_n})$ . It is automatic from the fact that $\\mathfrak{J}$ is a directed subdiagram of $\\mathfrak{D}$ that each $\\phi_n^m |_{\\mathcal{J}_n}:\\mathcal{J}_n\\hookrightarrow \\mathcal{J}_m$ is left-invertible and that $(\\mathcal{J}_n,\\phi_n^m|_{\\mathcal{J}_n})$ satisfies (D0)-(D2). In particular: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,786,907,825]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proposition 4.9. Any ideal of an $AF$ -algebra with Cantor property also has the Cantor property. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,841,907,880]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Here is another elementary fact about $C(2^{\\mathbb{N}})$ that is (essentially by Lemma 4.7) passed on to AF-algebras with Cantor property. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,897,907,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proposition 4.10. Suppose $\\mathcal{A}$ is an $AF$ -algebra with Cantor property and $\\mathcal{Q}$ is a quotient of $\\mathcal{A}$ . Then there is a surjection $\\eta : \\mathcal{A} \\twoheadrightarrow \\mathcal{Q}$ such that $\\ker(\\eta)$ is an essential ideal of $\\mathcal{A}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,64,104,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"14 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,63,796,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,105,918,289]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. It is enough to show that there is an essential ideal $\\mathcal{I}$ of $\\mathcal{A}$ such that $\\mathcal{A} / \\mathcal{I}$ is isomorphic to $\\mathcal{A}$ . In fact, we will show that there is an essential ideal $\\mathcal{I}$ of $\\mathcal{A}^{\\mathcal{C}}$ such that $\\mathcal{A}^{\\mathcal{C}} / \\mathcal{I}$ is isomorphic to $\\mathcal{A}$ . This is enough since $\\mathcal{A}^{\\mathcal{C}}$ is isomorphic to $\\mathcal{A}$ (Lemma 4.7). Let $\\mathfrak{D}$ be the Bratteli diagram of $\\mathcal{A}^{\\mathcal{C}}$ as in Diagram (4.1). Let $\\mathfrak{J}$ be the directed and hereditary subdiagram of $\\mathfrak{D}$ containing all the nodes in Diagram (4.1) except the lowest line. Being directed and hereditary, $\\mathfrak{J}$ corresponds to an ideal $\\mathcal{I}$ , which intersects any other directed and hereditary subdiagram of $\\mathfrak{D}$ . Therefore $\\mathcal{I}$ is an essential ideal of $\\mathcal{A}^{\\mathcal{C}}$ and $\\mathcal{A}^{\\mathcal{C}} / \\mathcal{I}$ is isomorphic to the limit of the sequence $\\mathcal{A}_1 \\xrightarrow{\\phi_1^2} \\mathcal{A}_2 \\xrightarrow{\\phi_2^3} \\mathcal{A}_3 \\xrightarrow{\\phi_3^4} \\ldots$ in the lowest line of Diagram (4.1), which is $\\mathcal{A}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,308,289,327]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5. Fraïssé categories ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,348,916,447]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Suppose $\\Re$ is a category of metric structures with non-expansive (1-Lipschitz) morphisms. We refer to objects and morphisms (arrows) of $\\Re$ by $\\Re$ -objects and $\\Re$ -arrows, respectively. We write $A \\in \\Re$ if $A$ is a $\\Re$ -object and $\\Re(A, B)$ to denote the set of all $\\Re$ -arrows from $A$ to $B \\in \\Re$ . The category $\\Re$ is metric-enriched or enriched over metric spaces if for every $\\Re$ -objects $A$ and $B$ there is a metric $d$ on $\\Re(A, B)$ satisfying ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[175,466,830,486]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nd (\\psi_ {0} \\circ \\phi , \\psi_ {1} \\circ \\phi) \\leq d (\\psi_ {0}, \\psi_ {1}) \\quad \\text {a n d} \\quad d (\\psi \\circ \\phi_ {0}, \\psi \\circ \\phi_ {0}) \\leq d (\\phi_ {0}, \\phi_ {1})\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,502,916,542]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"whenever the compositions make sense. We say $\\Re$ is enriched over complete metric spaces if $\\Re(A, B)$ is a complete metric space for every $\\Re$ -objects $A, B$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,542,916,580]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A $\\Re$ -sequence is a direct sequence in $\\Re$ , that is, a covariant functor from the category of all positive integers (treated as a poset) into $\\Re$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,582,916,641]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In our cases, $\\Re$ will always be a category of finite-dimensional $C^*$ -algebras with left-invertible embeddings. However, we would like to invoke the general theory of Fraïssé categories, which is possibly applicable to other similar contexts. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,660,543,677]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Definition 5.1. We say $\\Re$ is a Fraïssé category if ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[96,698,914,736]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(JEP) $\\Re$ has the joint embedding property: for $A, B \\in \\Re$ there is $C \\in \\Re$ such that $\\Re(A, C)$ and $\\Re(B, C)$ are nonempty. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,738,914,795]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(NAP) $\\Re$ has the near amalgamation property: for every $\\epsilon > 0$ , objects $A, B, C \\in \\Re$ , arrows $\\phi \\in \\Re(A, B)$ and $\\psi \\in \\Re(A, C)$ , there are $D \\in \\Re$ and $\\phi' \\in \\Re(B, D)$ and $\\psi' \\in \\Re(C, D)$ such that $d(\\phi' \\circ \\phi, \\psi' \\circ \\psi) < \\epsilon$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[96,798,826,814]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(SEP) $\\Re$ is separable: there is a countable dominating subcategory $\\mathfrak{C}$ , that is, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[167,817,914,875]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"for every $A\\\\in \\\\mathfrak{K}$ there is $C\\\\in \\\\mathfrak{C}$ and a $\\\\Re$ -arrow $\\\\phi :A\\\\to C$ \",\"- for every $\\\\epsilon > 0$ and a $\\\\mathfrak{K}$ -arrow $\\\\phi : A \\\\to B$ with $A \\\\in \\\\mathfrak{C}$ , there exist a $\\\\mathfrak{K}$ -arrow $\\\\psi : B \\\\to C$ with $\\\\mathcal{C} \\\\in \\\\mathfrak{C}$ and a $\\\\mathfrak{C}$ -arrow $\\\\alpha : A \\\\to C$ such that $d(\\\\alpha, \\\\psi \\\\circ \\\\phi) < \\\\epsilon$ . \"]","page_idx":"14","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[89,897,918,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Now suppose that $\\Re$ is contained in a bigger metric-enriched category $\\mathfrak{L}$ so that every sequence in $\\Re$ has a limit in $\\mathfrak{L}$ . We say that $\\Re \\subseteq \\mathfrak{L}$ has the almost factorization property if ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[895,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"15 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[77,105,907,164]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"given any sequence $(X_{n},f_{n}^{m})$ in $\\Re$ with limit $X_{\\infty}$ in $\\mathfrak{L}$ , for every $\\epsilon >0$ , for every $\\mathfrak{L}$ -arrow $g\\colon A\\to X_{\\infty}$ with $A\\in \\Re$ there is a $\\Re$ -arrow $g^{\\prime}\\colon A\\to X_{n}$ for some positive integer $n$ , such that $d(f_n^\\infty \\circ g',g)\\leq \\epsilon$ , where $f_{n}^{\\infty}\\colon X_{n}\\to X_{\\infty}$ comes from the limiting cocone. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,185,907,225]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 5.2. [11, Theorem 3.3] Suppose $\\Re$ is a Fraïssé category. Then there exists a sequence $(U_n,\\phi_n^m)$ in $\\Re$ satisfying ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,245,905,283]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(F) for every $n \\in \\mathbb{N}$ , for every $\\epsilon > 0$ and for every $\\Re$ -arrow $\\gamma : U_n \\to D$ , there are $m \\geq n$ and a $\\Re$ -arrow $\\delta : D \\to U_m$ such that $d(\\phi_n^m, \\delta \\circ \\gamma) < \\epsilon$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,304,907,482]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If $\\Re$ is a Fraïssé category, the $\\Re$ -sequence $(U_n, \\phi_n^m)$ from Theorem 5.2 is uniquely determined by the \"Fraïssé condition\" (F). That is, any two $\\Re$ -sequences satisfying (F) can be approximately intertwined (there is an approximate back-and-forth between them), and hence the limits of the sequences (typically in a bigger category containing $\\Re$ ) must be isomorphic (see [11, Theorem 3.5]). Therefore the $\\Re$ -sequence satisfying (F) is usually referred to as \"the\" Fraïssé sequence. The limit of the Fraïssé sequence is called the Fraïssé limit of the category $\\Re$ . In our case, $\\Re$ will be a category of finite-dimensional $C^*$ -algebras and the limit is just the inductive limit (also called colimit) in the category of all (or just separable) $C^*$ -algebras. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,502,907,561]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 5.3 (cf. [11]). Assume $\\Re$ is a Fraïssé category contained in a category $\\mathfrak{L}$ such that every sequence in $\\Re$ has a limit in $\\mathfrak{L}$ and every $\\mathfrak{L}$ -object is the limit of some sequence in $\\Re$ . Let $U \\in \\mathfrak{L}$ be the Fraïssé limit of $\\Re$ . Then ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,583,751,620]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- (uniqueness) $U$ is unique, up to isomorphisms. \",\"- (universality) For every $\\\\mathfrak{L}$ -object $B$ there is an $\\\\mathfrak{L}$ -arrow $\\\\phi : B \\\\to U$ . \"]","page_idx":"15","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[79,642,695,660]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Furthermore, if $\\Re \\subseteq \\mathfrak{L}$ has the almost factorization property then ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,680,907,720]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"- (almost $\\Re$ -homogeneity) For every $\\epsilon > 0$ , $\\Re$ -object $A$ and $\\mathfrak{L}$ -arrows $\\phi_i : A \\to U$ ( $i = 0,1$ ), there is an automorphism $\\eta : U \\to U$ such that $d(\\eta \\circ \\phi_0, \\phi_1) < \\epsilon$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[411,744,582,858]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0037/63d1e2144434cdb9e1cb46fd694f9bf90a18a1d2244cd443aeb7a466275c2b87.jpg","list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[81,63,104,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"16 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,61,796,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubiš / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[77,880,905,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Formally, the limit, or rather colimit of $(X_{n},f_{n}^{m})$ is a pair consisting of an $\\mathfrak{L}$ -object $X_{\\infty}$ and a sequence of $\\mathfrak{L}$ -arrows $f_{n}^{\\infty}\\colon X_{n}\\to X_{\\infty}$ satisfying suitable conditions. This sequence is called the (co-)limiting cocone. We use the word \"limit\" instead of \"colimit\" as we consider only covariant functors from the positive integers, called sequences. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[89,105,918,205]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Definition 5.4. Let $\\ddagger\\mathfrak{K}$ denote the category with the same objects as $\\mathfrak{K}$ , but a $\\ddagger\\mathfrak{K}$ -arrow from $A$ to $B$ is a pair $(\\phi, \\pi)$ where $\\phi, \\pi$ are $\\mathfrak{K}$ -arrows, $\\phi: A \\to B$ is left-invertible and $\\pi: B \\to A$ is a left inverse of $\\phi$ . We will denote such $\\ddagger\\mathfrak{K}$ -arrow by $(\\phi, \\pi): A \\to B$ . The composition is $(\\phi, \\pi) \\circ (\\phi', \\pi') = (\\phi \\circ \\phi', \\pi' \\circ \\pi)$ . The category $\\ddagger\\mathfrak{K}$ is usually called the category of embedding-projection pairs or briefly EP-pairs over $\\mathfrak{K}$ (see [10]). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,225,916,283]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Definition 5.5. We say $\\ddagger\\mathfrak{K}$ has the near proper amalgamation property if for every $\\epsilon > 0$ , objects $A, B, C \\in \\mathfrak{K}$ , arrows $(\\phi, \\pi) \\in \\ddagger\\mathfrak{K}(A, B)$ and $(\\psi, \\theta) \\in \\ddagger\\mathfrak{K}(A, C)$ , there are $D \\in \\ddagger\\mathfrak{K}$ and $(\\phi', \\pi') \\in \\ddagger\\mathfrak{K}(B, D)$ and $(\\psi', \\theta') \\in \\ddagger\\mathfrak{K}(C, D)$ such that the diagram ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[404,305,603,419]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0790/f198be4e62f64e7c2b31a5e7c4c53848a74e96eb0f80a558e24b1051b6f58ec6.jpg","list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[89,438,916,498]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"\"fully commutes\" up to $\\epsilon$ , meaning that $d(\\phi' \\circ \\phi, \\psi' \\circ \\psi)$ , $d(\\pi' \\circ \\pi, \\theta' \\circ \\theta)$ , $d(\\phi \\circ \\theta, \\pi' \\circ \\psi')$ and $d(\\psi \\circ \\pi, \\theta' \\circ \\phi')$ are all less than or equal to $\\epsilon$ . We say $\\S \\mathfrak{K}$ has the \"proper amalgamation property\" if $\\epsilon$ could be 0. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,517,916,577]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let us denote by $\\dagger \\Re$ the category of left-invertible $\\Re$ -arrows. In other words, $\\dagger \\Re$ is the image of $\\ddagger \\Re$ under the functor that forgets the left inverse, namely mapping $(\\phi, \\pi)$ to $\\phi$ . Note that all three categories $\\Re$ , $\\dagger \\Re$ , and $\\ddagger \\Re$ have the same objects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,595,918,675]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 5.6. Suppose $\\mathfrak{L}$ is enriched over complete metric spaces, $\\dagger \\Re$ is a Fraïssé category with Fraïssé limit $U$ , and $\\ddagger \\Re$ has the proper amalgamation property. Then for every $\\mathfrak{L}$ -object $B$ isomorphic to the limit of a sequence in $\\dagger \\Re$ there is a pair of $\\mathfrak{L}$ -arrows $\\alpha: B \\to U$ , $\\beta: U \\to B$ such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[441,698,563,717]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\beta \\circ \\alpha = \\operatorname {i d} _ {B}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,736,916,814]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Suppose $(U_n, \\phi_n^m)$ is a Fraïssé sequence in $\\dagger \\Re$ . Suppose first that the sequence satisfies (F) with $\\epsilon = 0$ and that $\\ddagger \\Re$ has the proper amalgamation property, namely with $\\epsilon = 0$ (this will be the case in the next section). In this case we do not use the fact that $\\mathfrak{L}$ is enriched over complete metric spaces. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,817,918,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Fix a $\\dagger\\mathfrak{K}$ -sequence $(B_n, \\psi_n^m)$ whose direct limit is $B$ . For each $n$ we may choose a left inverse $\\theta_n^{n+1}$ to $\\psi_n^{n+1}$ and next, setting $\\theta_n^m = \\theta_{m-1}^m \\circ \\dots \\circ \\theta_n^{n+1}$ for every $n < m$ , we obtain a $\\ddagger\\mathfrak{K}$ -sequence $(B_n, (\\psi_n^m, \\theta_n^m))$ whose direct limit is $B$ . Using (JEP) of $\\dagger\\mathfrak{K}$ and fixing arbitrary left inverses, find $F_1 \\in \\mathfrak{K}$ and $\\ddagger\\mathfrak{K}$ -arrows $(\\gamma_1, \\eta_1): U_1 \\to F_1$ and $(\\mu_1, \\nu_1): B_1 \\to F_1$ . By (F) and again fixing arbitrary left inverses, there are $n_1 \\geq 1$ and a $\\ddagger\\mathfrak{K}$ -arrow $(\\delta_1, \\lambda_1): F_1 \\to U_{n_1}$ such that $\\phi_1^{n_1} = \\delta_1 \\circ \\gamma_1$ (see Diagram (5.3) below). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[895,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"17 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[77,105,907,164]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Consider the composition arrow $(\\delta_1 \\circ \\mu_1, \\nu_1 \\circ \\lambda_1): B_1 \\to U_{n_1}$ and $(\\psi_1^2, \\theta_1^2): B_1 \\to B_2$ and use the proper amalgamation property to find $\\mathcal{F}_2 \\in \\Re$ and $\\ddagger\\Re$ -arrows $(\\mu_2, \\nu_2): B_2 \\to F_2$ and $(\\gamma_2, \\eta_2): U_{n_1} \\to F_2$ such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[226,180,903,201]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\gamma_ {2} \\circ \\delta_ {1} \\circ \\mu_ {1} = \\mu_ {2} \\circ \\psi_ {1} ^ {2} \\quad \\text {a n d} \\quad \\nu_ {2} \\circ \\gamma_ {2} = \\psi_ {1} ^ {2} \\circ \\nu_ {1} \\circ \\lambda_ {1}. \\tag {5.1}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[79,214,749,233]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Again using (F) we can find $n_2 \\geq n_1$ and $(\\delta_2, \\lambda_2): F_2 \\to U_{n_2}$ such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[423,251,901,272]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\phi_ {n _ {1}} ^ {n _ {2}} = \\delta_ {2} \\circ \\gamma_ {2}. \\tag {5.2}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,286,905,325]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Combining equations in (5.1) and (5.2) we have (also can be easily checked in Diagram (5.3)): ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[173,339,811,361]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\phi_ {n _ {1}} ^ {n _ {2}} \\circ \\delta_ {1} \\circ \\mu_ {1} = \\delta_ {2} \\circ \\mu_ {2} \\circ \\psi_ {1} ^ {2} \\qquad \\mathrm {a n d} \\qquad \\psi_ {1} ^ {2} \\circ \\nu_ {1} \\circ \\lambda_ {1} = \\nu_ {2} \\circ \\lambda_ {2} \\circ \\phi_ {n _ {1}} ^ {n _ {2}}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,376,907,433]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Again use the proper amalgamation property to find $F_{3} \\in \\mathfrak{K}$ and $(\\mu_3, \\nu_3): B_3 \\to F_3$ and $(\\gamma_3, \\eta_3): U_{n_2} \\to F_3$ . Follow the procedure, by finding $\\ddagger \\mathfrak{K}$ -arrow $(\\delta_3, \\lambda_3): F_3 \\to U_{n_3}$ , for some $n_3 \\geq n_2$ such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[177,450,805,470]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\phi_ {n _ {2}} ^ {n _ {3}} \\circ \\delta_ {2} \\circ \\mu_ {2} = \\delta_ {3} \\circ \\mu_ {3} \\circ \\psi_ {2} ^ {3} \\qquad \\text {a n d} \\qquad \\psi_ {2} ^ {3} \\circ \\nu_ {2} \\circ \\lambda_ {2} = \\nu_ {3} \\circ \\lambda_ {3} \\circ \\phi_ {n _ {2}} ^ {n _ {3}}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[111,476,903,632]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} U _ {1} \\xrightarrow {\\phi_ {1} ^ {n _ {1}}} U _ {n _ {1}} \\xrightarrow {\\phi_ {n _ {1}} ^ {n _ {2}}} U _ {n _ {2}} \\xrightarrow {\\phi_ {n _ {2}} ^ {n _ {3}}} U _ {n _ {3}} \\xrightarrow {\\phi_ {n _ {3}} ^ {n _ {4}}} \\dots U \\\\ B _ {1} \\xleftarrow {\\mu_ {1} \\nu_ {1} \\psi_ {1} ^ {2}} B _ {2} \\xleftarrow {\\mu_ {2} \\nu_ {2} \\psi_ {2} ^ {3}} B _ {3} \\xleftarrow {\\mu_ {3} \\nu_ {3} \\psi_ {3} ^ {4}} \\dots B \\end{array} \\Bigg | _ {\\beta}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,633,811,652]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $\\alpha_{i} = \\delta_{i}\\circ \\mu_{i}$ and $\\beta_{i}:\\nu_{i}\\circ \\lambda_{i}$ . By the construction, for every $i\\in \\mathbb{N}$ we have ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[211,667,770,689]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\phi_ {n _ {i}} ^ {n _ {i + 1}} \\circ \\alpha_ {i} = \\alpha_ {i + 1} \\circ \\psi_ {i} ^ {i + 1} \\quad \\text {a n d} \\quad \\psi_ {1} ^ {2} \\circ \\beta_ {i} = \\beta_ {i + 1} \\circ \\phi_ {n _ {i}} ^ {n _ {i + 1}}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,704,907,742]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and $\\beta_{i}$ is a left inverse of $\\alpha_{i}$ . Then $\\alpha = \\lim_{i}\\alpha_{i}$ is a well-defined arrow from $B$ to $U$ and $\\beta = \\lim_{i}\\beta_{i}$ is a well-defined arrow from $U$ onto $B$ such that $\\beta \\circ \\alpha = \\mathrm{id}_B$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,744,905,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, if $\\ddagger\\mathfrak{K}$ has the near proper amalgamation property and the sequence $(U_n,\\phi_n^m)$ satisfies (F) with arbitrary $\\epsilon >0$ , we repeat the arguments above, except that Diagram (5.3) is no longer commutative. On the other hand, at step $n$ we may choose $\\epsilon = 2^{-n}$ and then the arrows $\\alpha$ and $\\beta$ are obtained as limits of suitable Cauchy sequences in $\\mathfrak{L}(B,U)$ . This is the only place where we need to know that $\\mathfrak{L}$ is enriched over complete metric spaces. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,877,907,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let us mention that the concept of EP-pairs has been already used by Garbulińska-Wegrzyn [8] in the category of finite dimensional normed spaces, obtaining isometric uniqueness of a complementably universal Banach space. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,64,104,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"18 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,63,796,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[92,105,813,125]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6. Categories of finite-dimensional $C^*$ -algebras and left-invertible mappings ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,145,918,283]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this section $\\Re$ always denotes a (naturally metric-enriched) category whose objects are (not necessarily all) finite-dimensional $C^*$ -algebras, closed under isomorphisms, and $\\Re$ -arrows are left-invertible embeddings. For such $\\Re$ , let $\\mathfrak{L}\\Re$ denote the \"category of limits\" of $\\Re$ ; a category whose objects are limits of $\\Re$ -sequences and if $\\mathcal{B}$ and $\\mathcal{C}$ are $\\mathfrak{L}\\Re$ -objects, then an $\\mathfrak{L}\\Re$ -arrow from $\\mathcal{B}$ into $\\mathcal{C}$ is a left-invertible embedding $\\phi: \\mathcal{B} \\hookrightarrow \\mathcal{C}$ . Clearly $\\mathfrak{L}\\Re$ contains $\\Re$ as a full subcategory. The metric defined between $\\mathfrak{L}\\Re$ -arrows $\\phi$ and $\\psi$ with the same domain and codomain is $\\| \\phi - \\psi \\|$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,285,916,402]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For every such category $\\Re$ , let $\\widehat{\\mathfrak{K}}$ denote the category whose objects are exactly the objects of $\\Re$ , but the $\\widehat{\\mathfrak{K}}$ -morphisms are all homomorphisms between the objects. Then we can define the corresponding category of EP-pairs $\\ddagger \\widehat{\\mathfrak{K}}$ as in the previous section. In what follows, let us agree to write $\\ddagger \\mathfrak{K}$ instead of $\\ddagger \\widehat{\\mathfrak{K}}$ . Hence, the $\\ddagger \\mathfrak{K}$ -morphisms are of the form $(\\phi, \\pi)$ , where $\\phi$ is a $\\mathfrak{K}$ -morphism and $\\pi$ is a homomorphism which is a left inverse of $\\phi$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,422,916,541]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 6.1. If $\\Re$ is a category of finite-dimensional $C^*$ -algebras and embeddings, then it has the near amalgamation property (NAP) if and only if it has the amalgamation property ([5, Lemma 3.2]), namely, with $\\epsilon = 0$ . Similarly, the near proper amalgamation property of $\\ddagger \\Re$ is equivalent to the proper amalgamation property of $\\ddagger \\Re$ . Also in this case, the Fraïssé sequence $(\\mathcal{U}_n, \\phi_n^m)$ , whenever it exists for $\\Re$ , satisfies the Fraïssé condition (F) of Theorem 5.2 with $\\epsilon = 0$ . Therefore in this section (F) refers to the following condition. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,561,916,601]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(F) for every $n \\in \\mathbb{N}$ and for every $\\mathfrak{K}$ -arrow $\\gamma : \\mathcal{U}_n \\to \\mathcal{D}$ , there are $m \\geq n$ and $\\mathfrak{K}$ -arrow $\\delta : \\mathcal{D} \\to \\mathcal{U}_m$ such that $\\phi_n^m = \\delta \\circ \\gamma$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,620,640,639]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 6.2. $\\mathfrak{K} \\subseteq \\mathfrak{L}\\mathfrak{K}$ has the almost factorization property. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,658,918,797]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Suppose $\\mathcal{B} \\in \\mathfrak{L}\\mathfrak{K}$ is the limit of the $\\mathfrak{K}$ -sequence $(\\mathcal{B}_n, \\psi_n^m)$ and $(\\theta_n^m)$ is a compatible left inverse of $(\\psi_n^{n+1})$ . Assume $\\mathcal{D}$ is a $\\mathfrak{K}$ -object and $\\phi: \\mathcal{D} \\hookrightarrow \\mathcal{B}$ is an $\\mathfrak{L}\\mathfrak{K}$ -arrow with a left inverse $\\pi: \\mathcal{B} \\twoheadrightarrow \\mathcal{D}$ . For given $\\epsilon > 0$ , find $n$ and a unitary $u$ in $\\widetilde{\\mathcal{B}}$ such that $u^* \\phi[\\mathcal{D}] u \\subseteq \\psi_n^\\infty[\\mathcal{B}_n]$ and $\\|u - 1\\| < \\epsilon/2$ (Lemma 2.1). Define $\\psi: \\mathcal{D} \\hookrightarrow \\mathcal{B}_n$ by $\\psi(d) = \\theta_n^\\infty(u^* \\phi(d) u)$ . Then $\\psi$ has a left inverse $\\theta: \\mathcal{B}_n \\twoheadrightarrow \\mathcal{D}$ defined by $\\theta(x) = \\pi(u \\psi_n^\\infty(x) u^*)$ (see the proof of Lemma 3.5 (2)). Condition $\\|u - 1\\| < \\epsilon/2$ implies that $\\| \\psi_n^\\infty(\\psi(d)) - \\phi(d) \\| < \\epsilon$ , for every $d$ in the unit ball of $\\mathcal{D}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,817,346,836]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 6.3. $\\Re$ is separable. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,855,918,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. There are, up to isomorphisms, countably many $\\mathfrak{K}$ -objects, namely finite sums of matrix algebras. The set of all embeddings between two fixed finite-dimensional $C^*$ -algebras is a separable metric space. Thus, $\\mathfrak{K}$ trivially has a countable dominating subcategory. $\\square$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[895,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"19 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[104,105,698,125]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The following statement is a direct consequence of Lemma 5.6. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,144,905,202]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Corollary 6.4. Suppose $\\Re$ is a Fraïssé category of $C^*$ -algebras with the Fraïssé limit $\\mathcal{U}$ and $\\ddagger\\Re$ has the proper amalgamation property. Then $\\mathcal{U}$ is a split-extension of every $AF$ -algebra $\\mathcal{B}$ in $\\mathfrak{L}\\Re$ . In particular, $\\mathcal{U}$ maps onto any $AF$ -algebra in $\\mathfrak{L}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,225,595,242]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7. AF-algebras with Cantor property as Fraïssé limits ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[79,266,905,304]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Suppose $\\Re$ is a category of (not necessarily all) finite-dimensional $C^*$ -algebras, closed under isomorphisms, and $\\Re$ -arrows are left-invertible embeddings. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,325,775,342]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Definition 7.1. We say $\\Re$ is $\\oplus$ -stable if it satisfies the following conditions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,364,623,401]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(1) If $\\\\mathcal{D}$ is a $\\\\Re$ -object, then so is any retract (ideal) of $\\\\mathcal{D}$ , \",\"(2) $\\\\mathcal{D} \\\\oplus \\\\mathcal{E} \\\\in \\\\mathfrak{K}$ whenever $\\\\mathcal{D}, \\\\mathcal{E} \\\\in \\\\mathfrak{K}$ . \"]","page_idx":"19","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[77,423,905,501]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In general 0 is a retract of any $C^*$ -algebra and therefore it is the initial object of any $\\oplus$ -stable category, unless, when working with the unital categories (when all the $\\mathfrak{K}$ -arrows are unital), which in that case 0 is not a $\\mathfrak{K}$ -object anymore. Unital categories are briefly discussed in Section 9. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,522,905,560]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 7.2. Suppose $\\Re$ is a $\\oplus$ -stable category. Then $\\ddagger \\Re$ has the proper amalgamation property. In particular, $\\Re$ is a Fraïssé category. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,580,905,639]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Suppose $\\mathcal{D},\\mathcal{E}$ and $\\mathcal{F}$ are $\\Re$ -objects and $\\ddagger \\aleph$ -arrows $(\\phi ,\\pi):\\mathcal{D}\\to \\mathcal{E}$ and $(\\psi ,\\theta):$ $\\mathcal{D}\\rightarrow \\mathcal{F}$ are given. Since $\\phi$ and $\\psi$ are left-invertible, by Proposition 3.2 we can identify $\\mathcal{E}$ and $\\mathcal{F}$ with $\\mathcal{E}_0\\oplus \\mathcal{E}_1$ and $\\mathcal{F}_0\\oplus \\mathcal{F}_1$ , respectively, and find $\\phi_0,\\phi_1,\\psi_0,\\psi_1$ such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,658,721,738]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- $\\\\phi_0: \\\\mathcal{D} \\\\to \\\\mathcal{E}_0$ and $\\\\psi_0: \\\\mathcal{D} \\\\to \\\\mathcal{F}_0$ are isomorphisms, \",\"- $\\\\phi_1: \\\\mathcal{D} \\\\to \\\\mathcal{E}_1$ and $\\\\psi_1: \\\\mathcal{D} \\\\to \\\\mathcal{F}_1$ are homomorphisms, \",\"- $\\\\phi(d) = (\\\\phi_0(d), \\\\phi_1(d))$ and $\\\\psi(d) = (\\\\psi_0(d), \\\\psi_1(d))$ for every $d \\\\in \\\\mathcal{D}$ , \",\"- $\\\\pi(e_0, e_1) = \\\\phi_0^{-1}(e_0)$ and $\\\\theta(f_0, f_1) = \\\\psi_0^{-1}(f_0)$ . \"]","page_idx":"19","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[77,758,905,816]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Define homomorphisms $\\mu : \\mathcal{E} \\to \\mathcal{F}_1$ and $\\nu : \\mathcal{F} \\to \\mathcal{E}_1$ by $\\mu = \\psi_1 \\circ \\pi$ and $\\nu = \\phi_1 \\circ \\theta$ (see Diagram (7.1)). Since $\\Re$ is $\\oplus$ -stable $\\mathcal{D} \\oplus \\mathcal{E}_1 \\oplus \\mathcal{F}_1$ is a $\\Re$ -object. Define $\\Re$ -arrows $\\phi' : \\mathcal{E} \\hookrightarrow \\mathcal{D} \\oplus \\mathcal{E}_1 \\oplus \\mathcal{F}_1$ and $\\psi' : \\mathcal{F} \\hookrightarrow \\mathcal{D} \\oplus \\mathcal{E}_1 \\oplus \\mathcal{F}_1$ by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[327,836,653,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\phi^ {\\prime} (e _ {0}, e _ {1}) = (\\phi_ {0} ^ {- 1} (e _ {0}), e _ {1}, \\mu (e _ {0}, e _ {1}))\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,877,122,892]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[321,914,659,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\psi^ {\\prime} \\left(f _ {0}, f _ {1}\\right) = \\left(\\psi_ {0} ^ {- 1} \\left(f _ {0}\\right), \\nu \\left(f _ {0}, f _ {1}\\right), f _ {1}\\right).\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,64,104,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"20 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,63,796,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,105,329,123]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For every $d\\in \\mathcal{D}$ we have ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[188,144,817,164]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\phi^ {\\prime} (\\phi (d)) = \\phi^ {\\prime} (\\phi_ {0} (d), \\phi_ {1} (d)) = (d, \\phi_ {1} (d), \\mu (\\phi (d))) = (d, \\phi_ {1} (d), \\psi_ {1} (d))\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,183,134,200]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[179,219,916,363]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\psi^ {\\prime} (\\psi (d)) = \\psi^ {\\prime} (\\psi_ {0} (d), \\psi_ {1} (d)) = (d, \\nu (\\phi (d)), \\psi_ {1} (d)) = (d, \\phi_ {1} (d), \\psi_ {1} (d)). \\\\ \\mathcal {D} \\begin{array}{c} \\phi \\\\ \\pi \\\\ \\nu \\\\ \\psi \\\\ \\theta \\end{array} \\Bigg [ \\begin{array}{c} \\tilde {\\mu} \\\\ \\pi^ {\\prime} \\\\ \\psi^ {\\prime} \\\\ \\theta^ {\\prime} \\end{array} \\begin{array}{c} \\phi^ {\\prime} \\\\ \\tilde {\\mathcal {D}} \\oplus \\mathcal {E} _ {1} \\oplus \\mathcal {F} _ {1} \\end{array} \\tag {7.1} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,380,918,458]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Therefore $\\phi' \\circ \\phi = \\psi' \\circ \\psi$ . The map $\\pi': \\mathcal{D} \\oplus \\mathcal{E}_1 \\oplus \\mathcal{F}_1 \\to \\mathcal{E}$ defined by $\\pi'(d, e_1, f_1) = (\\phi_0(d), e_1)$ is a left inverse of $\\phi'$ . Similarly the map $\\theta': \\mathcal{D} \\oplus \\mathcal{E}_1 \\oplus \\mathcal{F}_1 \\to \\mathcal{F}$ defined by $\\theta'(d, e_1, f_1) = (\\psi_0(d), f_1)$ is a left inverse of $\\psi'$ . Therefore $(\\phi', \\pi') : \\mathcal{E} \\to \\mathcal{D} \\oplus \\mathcal{E}_1 \\oplus \\mathcal{F}_1$ and $(\\psi', \\theta') : \\mathcal{E} \\to \\mathcal{D} \\oplus \\mathcal{E}_1 \\oplus \\mathcal{F}_1$ are $\\Re$ -arrows. We have ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[336,479,668,526]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\pi \\circ \\pi^ {\\prime} (d, e _ {1}, f _ {1}) = \\pi (\\phi_ {0} (d), e _ {1}) = d, \\\\ \\theta \\circ \\theta^ {\\prime} (d, e _ {1}, f _ {1}) = \\theta (\\psi_ {0} (d), e _ {1}) = d. \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,544,346,561]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Hence $\\pi \\circ \\pi' = \\theta \\circ \\theta'$ . Also ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[190,580,813,627]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\theta^ {\\prime} \\circ \\phi^ {\\prime} \\left(e _ {0}, e _ {1}\\right) = \\theta^ {\\prime} \\left(\\phi_ {0} ^ {- 1} \\left(e _ {0}\\right), e _ {1}, \\mu \\left(e _ {0}, e _ {1}\\right)\\right) = \\left(\\psi_ {0} \\left(\\phi_ {0} ^ {- 1} \\left(e _ {0}\\right)\\right), \\mu \\left(e _ {0}, e _ {1}\\right)\\right) \\\\ = (\\psi_ {0} (\\pi (e _ {0}, e _ {1})), \\psi_ {1} (\\pi (e _ {0}, e _ {1}))) = \\psi (\\pi (e _ {0}, e _ {1})). \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,645,916,702]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"So $\\theta' \\circ \\phi' = \\psi \\circ \\pi$ and similarly we have $\\phi \\circ \\theta = \\pi' \\circ \\psi'$ . This shows that $\\ddagger\\mathfrak{K}$ has proper amalgamation property. Since $\\mathfrak{K}$ is separable and has an initial object, in particular, it is a Fraïssé category. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,725,916,761]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Therefore any $\\oplus$ -stable category $\\mathfrak{K}$ has a unique Fraïssé sequence; a $\\mathfrak{K}$ -sequence which satisfies (F). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,780,749,800]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Notation. Let $\\mathcal{A}_{\\mathfrak{K}}$ denote the Fraïssé limit of the $\\oplus$ -stable category $\\mathfrak{K}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,817,918,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The AF-algebra $\\mathcal{A}_{\\mathfrak{K}}$ is $\\mathfrak{K}$ -universal and almost $\\mathfrak{K}$ -homogeneous, by Theorem 5.3 and Lemma 6.2. In fact, $\\mathcal{A}_{\\mathfrak{K}}$ is $\\mathfrak{K}$ -homogeneous (where $\\epsilon$ is zero). To see this, suppose $\\mathcal{F}$ is a finite-dimensional $C^*$ -algebra in $\\mathfrak{K}$ and $\\phi_i: \\mathcal{F} \\hookrightarrow \\mathcal{A}$ ( $i = 0,1$ ) are left-invertible embeddings. By the almost $\\mathfrak{K}$ -homogeneity, there is an automorphism $\\eta: \\mathcal{A}_{\\mathfrak{K}} \\to \\mathcal{A}_{\\mathfrak{K}}$ such that $\\| \\eta \\circ \\phi_0 - \\phi_1 \\| < 1$ . There exists (Lemma 2.2) a unitary $u \\in \\widetilde{\\mathcal{A}}$ such that $\\mathrm{Ad}_u \\circ \\eta \\circ \\phi_0 = \\phi_1$ . The automorphism $\\mathrm{Ad}_u \\circ \\eta$ witnesses the $\\mathfrak{K}$ -homogeneity of $\\mathcal{A}_{\\mathfrak{K}}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[892,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"21 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[79,105,903,144]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Moreover, since $\\ddagger\\mathfrak{R}$ has the proper amalgamation property, every AF-algebra in $\\mathfrak{L}\\mathfrak{R}$ , is a retract of $\\mathcal{A}_{\\mathfrak{R}}$ (Corollary 6.4). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,167,582,185]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Corollary 7.3. Suppose $\\Re$ is a $\\oplus$ -stable category, then ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,205,907,304]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- (universality) Every $AF$ -algebra which is the limit of a $\\\\mathfrak{R}$ -sequence, is a retract of $\\\\mathcal{A}_{\\\\widehat{\\\\mathbb{R}}}$ . \",\"- (R-homogeneity) For every finite-dimensional $C^*$ -algebra $\\\\mathcal{F} \\\\in \\\\Re$ and left-invertible embeddings $\\\\phi_i : \\\\mathcal{F} \\\\hookrightarrow \\\\mathcal{A}_{\\\\Re}$ ( $i = 0,1$ ), there is an automorphism $\\\\eta : \\\\mathcal{A}_{\\\\Re} \\\\to \\\\mathcal{A}_{\\\\Re}$ such that $\\\\eta \\\\circ \\\\phi_0 = \\\\phi_1$ . \"]","page_idx":"21","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[104,325,871,344]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We will describe the structure of $\\mathcal{A}_{\\mathfrak{R}}$ by showing that it has the Cantor property. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,366,835,385]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 7.4. Suppose $\\Re$ is a $\\oplus$ -stable category, then $\\mathcal{A}_{\\Re}$ has the Cantor property. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,405,903,505]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Suppose $\\mathcal{A}_{\\mathfrak{K}} = \\varinjlim_{n}(\\mathcal{A}_{n},\\phi_{n}^{m})$ , where $(\\mathcal{A}_n,\\phi_n^m)$ is a $\\Re$ -sequence, i.e., $(\\mathcal{A}_n,\\phi_n^m)$ is a left-invertible sequence of finite-dimensional $C^*$ -algebras in $\\Re$ . Since $\\mathcal{A}_{\\mathfrak{K}}$ is the Fraïssé limit of $\\Re$ , we can suppose $(\\mathcal{A}_n,\\phi_n^m)$ satisfies (F). We claim that $(\\mathcal{A}_n,\\phi_n^m)$ satisfies (D0)-(D2) of Definition 4.1. Suppose $\\mathfrak{D}$ is the Bratteli diagram of $(\\mathcal{A}_n,\\phi_n^m)$ and $\\mathcal{A}_n = \\mathcal{A}_{n,1}\\oplus \\dots \\oplus \\mathcal{A}_{n,k_n}$ for every $n$ , such that each $\\mathcal{A}_{n,s}$ is a matrix algebra. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,505,903,625]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The condition (D0) is trivial since $\\phi_n^m$ are left-invertible. To see (D1), fix $\\mathcal{A}_{n,s}$ . Note that since $\\mathcal{A}_n$ is a $\\Re$ -object and $\\Re$ is $\\oplus$ -stable, we have $\\mathcal{A}_n \\oplus \\mathcal{A}_n \\in \\Re$ . Let $\\gamma : \\mathcal{A}_n \\hookrightarrow \\mathcal{A}_n \\oplus \\mathcal{A}_n$ be the left-invertible embedding defined by $\\gamma(a) = (a,a)$ . Use the Fraïssé condition (F) to find $\\delta : \\mathcal{A}_n \\oplus \\mathcal{A}_n \\hookrightarrow \\mathcal{A}_m$ , for some $m \\geq n$ , such that $\\delta \\circ \\gamma = \\phi_n^m$ . Since $\\delta$ is left-invertible, there are distinct $(m,t)$ and $(m,t')$ in $\\mathfrak{D}$ such that $\\mathcal{A}_{m,t} \\cong \\mathcal{A}_{m,t'} \\cong \\mathcal{A}_{n,s}$ . Then $\\delta \\circ \\gamma = \\phi_n^m$ implies that $(n,s) \\to (m,t)$ and $(n,s) \\to (m,t')$ in $\\mathfrak{D}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,626,903,725]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To see (D2) assume $\\mathcal{D} \\subseteq \\mathcal{A}_n$ is an ideal of $\\mathcal{A}_n$ and $M_{\\ell}$ is a retract of $\\mathcal{A}_{\\Re}$ and there is an embedding $\\gamma : \\mathcal{D} \\hookrightarrow M_{\\ell}$ . Suppose $\\mathcal{A}_n = \\mathcal{D} \\oplus \\mathcal{E}$ for some $\\mathcal{E}$ . Since $\\Re$ is $\\oplus$ -stable, $\\mathcal{D} \\oplus \\mathcal{E} \\oplus M_{\\ell}$ is a $\\Re$ -object. Therefore $\\gamma' : \\mathcal{D} \\oplus \\mathcal{E} \\hookrightarrow \\mathcal{D} \\oplus \\mathcal{E} \\oplus M_{\\ell}$ defined by $\\gamma'(d, e) = (d, e, \\gamma(d))$ is a $\\Re$ -arrow. Then by (F) there is a left-invertible embedding $\\delta': \\mathcal{D} \\oplus \\mathcal{E} \\oplus M_{\\ell} \\hookrightarrow \\mathcal{A}_m$ for some $m \\geq n$ , such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[432,750,899,766]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\delta^ {\\prime} \\circ \\gamma^ {\\prime} = \\phi_ {n} ^ {m}. \\tag {7.2}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[79,789,732,808]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Since $\\delta^\\prime$ is left-invertible, there is $(m,t)$ such that $\\dim (\\mathcal{A}_{m,t}) = \\ell$ and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[334,833,648,852]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\delta_ {m, t} = \\pi_ {\\mathcal {A} _ {m, t}} \\circ \\delta | _ {M _ {\\ell}}: M _ {\\ell} \\hookrightarrow \\mathcal {A} _ {m, t}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[79,873,811,892]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"is an isomorphism, where $\\pi_{\\mathcal{A}_{m,t}}: \\mathcal{A}_m \\twoheadrightarrow \\mathcal{A}_{m,t}$ is the canonical projection. Let ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[331,917,650,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\phi_ {m, t} = \\pi_ {\\mathcal {A} _ {m, t}} \\circ \\phi_ {n} ^ {m} | _ {\\mathcal {D}}: \\mathcal {D} \\rightarrow \\mathcal {A} _ {m, t}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,64,104,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"22 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,63,796,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,105,916,164]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"By definition of $\\gamma^\\prime$ and (7.2) it is clear that $\\phi_{m,t} = \\delta_{m,t}\\circ \\gamma$ and that $\\phi_{m,t}$ is also an embedding. By Lemma 2.3 we have $\\mathrm{Mult}_{\\phi_{m,t}}(\\mathcal{D},\\mathcal{A}_{m,t}) = c\\mathrm{Mult}_{\\gamma}(\\mathcal{D},M_{\\ell})$ for some natural number $c\\geq 1$ . Since $\\delta_{m,t}$ is an isomorphism, we have $c = 1$ . This proves (D2). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,186,916,245]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Next we show that every AF-algebra with Cantor property can be realized as the Fraïssé limit of a suitable $\\oplus$ -stable category of finite-dimensional $C^*$ -algebras and left-invertible embeddings. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,270,299,288]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7.1. The category $\\mathfrak{K}_A$ ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,311,916,391]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Suppose $\\mathcal{A}$ is an AF-algebra with Cantor property. Let $\\mathfrak{K}_{\\mathcal{A}}$ denote the category whose objects are finite-dimensional retracts of $\\mathcal{A}$ and $\\mathfrak{K}_{\\mathcal{A}}$ -arrows are left-invertible embeddings. Let $\\mathfrak{L}_{\\mathcal{A}}$ be the category whose objects are limits of $\\mathfrak{K}_{\\mathcal{A}}$ -sequences. If $\\mathcal{B}$ and $\\mathcal{C}$ are $\\mathfrak{L}_{\\mathcal{A}}$ -objects, an $\\mathfrak{L}_{\\mathcal{A}}$ -arrow from $\\mathcal{B}$ into $\\mathcal{C}$ is a left-invertible embedding $\\phi: \\mathcal{B} \\hookrightarrow \\mathcal{C}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,413,897,432]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 7.5. $\\mathfrak{K}_A$ is a Fraïssé category and $\\ddagger \\mathfrak{K}_A$ has the proper amalgamation property. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,454,916,492]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. By Theorem 7.2, it is enough to show that $\\mathfrak{K}_A$ is a $\\oplus$ -stable category. Condition (1) of Definition 7.1 is trivial. Condition (2) follows from Proposition 4.4. $\\square$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,514,914,554]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Again, Theorem 5.3 guarantees the existence of a unique $\\mathfrak{K}_{\\mathcal{A}}$ -universal and $\\mathfrak{K}_{\\mathcal{A}}$ -homogeneous AF-algebra in $\\mathfrak{L}_{\\mathcal{A}}$ , namely the Fraïssé limit of $\\mathfrak{K}_{\\mathcal{A}}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,575,505,594]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 7.6. The Fraïssé limit of $\\mathfrak{K}_A$ is $\\mathcal{A}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,614,916,714]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. There is a sequence $(\\mathcal{A}_n,\\phi_n^m)$ of finite-dimensional $C^*$ -algebras and embeddings such that $\\mathcal{A} = \\varinjlim (\\mathcal{A}_n,\\phi_n^m)$ satisfies (D0)-(D2) of Definition 4.1. First note that by (D0), $(\\mathcal{A}_n,\\phi_n^m)$ is a $\\mathfrak{K}_{\\mathcal{A}}$ -sequence and therefore $\\mathcal{A}$ is an $\\mathfrak{L}_{\\mathcal{A}}$ -object. In order to show that $\\mathcal{A}$ is the Fraïssé limit of $\\mathfrak{K}_{\\mathcal{A}}$ , we need to show that $(\\mathcal{A}_n,\\phi_n^m)$ satisfies condition (F). This is Lemma 4.5. $\\square$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,736,910,755]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 7.7. Suppose $\\Re$ is a $\\oplus$ -stable category. $\\mathcal{A}_{\\Re}$ is the unique $AF$ -algebra such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,777,880,814]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(1) it has the Cantor property, \",\"(2) a finite-dimensional $C^*$ -algebra is a retract of $\\\\mathcal{A}_{\\\\Re}$ if and only if it is a $\\\\Re$ -object. \"]","page_idx":"22","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[89,836,916,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. We have already shown that $\\mathcal{A}_{\\mathfrak{K}}$ has the Cantor property (Lemma 7.4). By Lemma 3.5(2), every finite-dimensional retract of $\\mathcal{A}_{\\mathfrak{K}}$ is a $\\mathfrak{K}$ -object and every finite-dimensional $C^*$ -algebra in $\\mathfrak{K}$ is a retract of $\\mathcal{A}_{\\mathfrak{K}}$ , by the $\\mathfrak{K}$ -universality of $\\mathcal{A}_{\\mathfrak{K}}$ . If $\\mathcal{A}$ is an AF-algebra satisfying (1) and (2), then by definition $\\mathfrak{K}_{\\mathcal{A}} = \\mathfrak{K}$ . The uniqueness of the Fraïssé limit and Theorem 7.6 imply that $\\mathcal{A} \\cong \\mathcal{A}_{\\mathfrak{K}}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[892,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"23 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[81,105,903,142]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Corollary 7.8. Two $AF$ -algebras with Cantor property are isomorphic if and only if they have the same set of matrix algebras as retracts. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[83,164,218,183]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7.2. Examples ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[81,204,903,360]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Corollary 7.8 shows that there is a one-to-one correspondence between AF-algebras with the Cantor property and the collections of (non-isomorphic) matrix algebras (hence, with the subsets of the natural numbers). More precisely, given any collection $X$ of nonisomorphic matrix algebras, let $\\mathfrak{K}_X$ denote the $\\oplus$ -stable category whose objects are finite direct sums of the matrix algebras in $\\mathfrak{K}_X$ (finite direct sums of a member of $X$ with itself are of course allowed) and left-invertible embeddings as arrows. Then the Fraïssé limit of $\\mathfrak{K}_X$ is the unique AF-algebra whose matrix algebra retracts are exactly the members of $X$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,361,903,439]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The class of AF-algebras with the Cantor property is not closed under direct sum (for instance, $(M_2\\oplus M_3)\\otimes C(2^{\\mathbb{N}})$ does not have the Cantor property, as its Bratteli diagram easily reveals, while $M_2\\otimes C(2^{\\mathbb{N}})$ and $M_3\\otimes C(2^{\\mathbb{N}})$ do). The following example shows that this class is also not closed under tensor product. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,442,903,757]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $\\mathcal{A}$ denote the unique AF-algebra with the Cantor property whose matrix algebra retracts are exactly $\\{M_2, M_3, M_5, M_{11}\\}$ . We claim that $\\mathcal{A} \\otimes \\mathcal{A}$ does not have the Cantor property. Suppose $\\mathcal{A} = \\varinjlim (\\mathcal{A}_n, \\phi_n^m)$ where the sequence satisfies (D0)-(D2) of Definition 4.1. Clearly $\\mathcal{A} \\otimes \\mathcal{A}$ is the limit of the left-invertible sequence $(\\mathcal{A}_n \\otimes \\mathcal{A}_n, \\phi_n^m \\otimes \\phi_n^m)$ . Therefore by Lemma 3.5 every matrix algebra retract of $\\mathcal{A} \\otimes \\mathcal{A}$ is isomorphic to $\\mathcal{D} \\otimes \\mathcal{E}$ , where $\\mathcal{D}, \\mathcal{E} \\in \\{M_2, M_3, M_5, M_{11}\\}$ . Take a retract of $\\mathcal{A}_n \\otimes \\mathcal{A}_n$ isomorphic to $M_3 \\otimes M_5$ (for large enough $n$ there is such a retract) and let $\\gamma: M_3 \\otimes M_5 \\to M_2 \\otimes M_{11}$ be an embedding of multiplicity 1. However, there is no embedding $\\phi \\otimes \\psi: M_3 \\otimes M_5 \\to M_{22} \\cong M_2 \\otimes M_{11}$ which corresponds to a path in the Bratteli diagram of the sequence $(\\mathcal{A}_n \\otimes \\mathcal{A}_n, \\phi_n^m \\otimes \\phi_n^m)$ . This is because the codomain of any such $\\phi$ should be either $M_3$ or $M_5$ or $M_{11}$ (since $\\phi$ corresponds to a path in the Bratteli diagram of the sequence $(\\mathcal{A}_n, \\phi_n^m)$ ) and similarly the codomain of $\\psi$ could only be $M_5$ or $M_{11}$ , while the tensor product of their codomains should be isomorphic to $M_{22}$ , which is not possible. Thus condition (D2) is satisfied neither by the sequence $(\\mathcal{A}_n \\otimes \\mathcal{A}_n, \\phi_n^m \\otimes \\phi_n^m)$ , nor by any sequence of finite-dimensional $C^*$ -algebras whose limit is $\\mathcal{A} \\otimes \\mathcal{A}$ (see Remark 4.2), which means that $\\mathcal{A} \\otimes \\mathcal{A}$ does not have the Cantor property. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,777,319,795]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8. Universal AF-algebras ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[81,817,903,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $\\mathfrak{F}$ denote the category of all finite-dimensional $C^*$ -algebras and left-invertible embeddings. The category $\\mathfrak{F}$ is $\\oplus$ -stable and therefore it is Fraïssé by Theorem 7.2. The Fraïssé limit $\\mathcal{A}_{\\mathfrak{F}}$ of this category has the universality property (Corollary 7.3) that any AF-algebra which is the limit of a left-invertible sequence of finite-dimensional $C^*$ -algebras can be embedded via a left-invertible embedding into $\\mathcal{A}_{\\mathfrak{F}}$ . In fact, $\\mathcal{A}_{\\mathfrak{F}}$ is surjectively universal in the category of all (separable) AF-algebras. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,64,102,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"24 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[190,63,794,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,105,916,144]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 8.1. There is a surjective homomorphism from $\\mathcal{A}_{\\mathfrak{F}}$ onto any separable $AF$ -algebra. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,169,918,291]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Suppose $\\mathcal{B}$ is a separable AF-algebra. Proposition 3.8 states that there is an AF-algebra $\\mathcal{A}$ , which is the limit of a left-invertible sequence of finite-dimensional $C^*$ -algebras and $\\mathcal{A} / \\mathcal{I} \\cong \\mathcal{B}$ , for some ideal $\\mathcal{I}$ . By the universality of $\\mathcal{A}_{\\mathfrak{F}}$ (Corollary 7.3) there is a left-invertible embedding $\\phi : \\mathcal{A} \\hookrightarrow \\mathcal{A}_{\\mathfrak{F}}$ . If $\\theta : \\mathcal{A}_{\\mathfrak{F}} \\twoheadrightarrow \\mathcal{A}$ is a left inverse of $\\phi$ then its composition with the quotient map $\\pi : \\mathcal{A} \\twoheadrightarrow \\mathcal{A} / \\mathcal{I}$ gives a surjective homomorphism from $\\mathcal{A}_{\\mathfrak{F}}$ onto $\\mathcal{B}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,314,916,377]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 8.2. Since $\\mathcal{A}_{\\mathfrak{F}}$ has the Cantor property (Lemma 7.4), it does not have any minimal projections. Therefore, for example, it cannot be isomorphic to $\\mathcal{A}_{\\mathfrak{F}} \\oplus \\mathbb{C}$ . Hence the property of being surjectively universal AF-algebra is not unique to $\\mathcal{A}_{\\mathfrak{F}}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,400,916,439]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Corollary 8.3. An $AF$ -algebra $\\mathcal{A}$ is surjectively universal if and only if $\\mathcal{A}_{\\mathfrak{F}}$ is a quotient of $\\mathcal{A}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,464,916,502]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 7.7 provides a characterization of $\\mathcal{A}_{\\mathfrak{F}}$ , up to isomorphism, in terms of its structure. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,529,916,567]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Corollary 8.4. $\\mathcal{A}_{\\mathfrak{F}}$ is the unique separable $AF$ -algebra with Cantor property such that every matrix algebra $M_{k}$ is a retract of $\\mathcal{A}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,570,916,630]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Equivalently, an $AF$ -algebra $\\mathcal{A}$ is isomorphic to $\\mathcal{A}_{\\mathfrak{F}}$ if and only if there is a sequence $(\\mathcal{A}_n, \\phi_n^m)$ of finite-dimensional $C^*$ -algebras and embeddings such that $\\mathcal{A} = \\varinjlim (\\mathcal{A}_n, \\phi_n^m)$ and the Bratteli diagram $\\mathfrak{D}$ of $(\\mathcal{A}_n, \\phi_n^m)$ satisfies (D0)-(D2) and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,650,663,670]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(D3) for every $k$ there is $(n, s) \\in \\mathfrak{D}$ such that $\\dim(n, s) = k$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,691,920,770]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 8.5. $\\mathcal{A}_{\\mathfrak{F}}$ is the unique $AF$ -algebra that is the limit of a left-invertible sequence of finite-dimensional $C^*$ -algebras and for any finite-dimensional $C^*$ -algebras $\\mathcal{D}, \\mathcal{E}$ and left-invertible embeddings $\\phi : \\mathcal{D} \\hookrightarrow \\mathcal{E}$ and $\\alpha : \\mathcal{D} \\hookrightarrow \\mathcal{A}_{\\mathfrak{F}}$ there is a left-invertible embedding $\\beta : \\mathcal{E} \\hookrightarrow \\mathcal{A}_{\\mathfrak{F}}$ such that $\\beta \\circ \\phi = \\alpha$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,795,918,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Suppose $\\mathcal{A}_{\\mathfrak{F}}$ is the limit of the Fraïssé $\\mathfrak{F}$ -sequence $(\\mathcal{A}_n, \\phi_n^m)$ . By definition, $\\alpha$ and $\\phi$ are $\\mathfrak{F}$ -arrows. There is (Lemma 6.2) a natural number $n$ and an $\\mathfrak{F}$ -arrow (a left-invertible embedding) $\\psi : \\mathcal{D} \\hookrightarrow \\mathcal{A}_n$ such that $\\| \\phi_n^\\infty \\circ \\psi - \\alpha \\| < 1$ . Use the amalgamation property to find a finite-dimensional $C^*$ -algebra $\\mathcal{G}$ and left-invertible embeddings $\\phi' : \\mathcal{E} \\hookrightarrow \\mathcal{G}$ and $\\psi' : \\mathcal{A}_n \\hookrightarrow \\mathcal{G}$ such that $\\phi' \\circ \\phi = \\psi' \\circ \\psi$ (see Diagram (8.1)). The Fraïssé condition (F) implies the existence of $m \\geq n$ and a left-invertible embedding $\\delta : \\mathcal{G} \\hookrightarrow \\mathcal{A}_m$ such that $\\delta \\circ \\psi' = \\phi_n^m$ . Let $\\beta' = \\phi_m^\\infty \\circ \\delta \\circ \\phi'$ . It is clearly left-invertible. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[892,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"25 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[139,100,903,227]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{c} \\mathcal {A} _ {1} \\xrightarrow {\\phi_ {1} ^ {2}} \\mathcal {A} _ {2} \\xrightarrow {\\phi_ {2} ^ {3}} \\dots \\xrightarrow {} \\mathcal {A} _ {n} \\xrightarrow {\\phi_ {n} ^ {m}} \\mathcal {A} _ {m} \\xrightarrow {\\phi_ {m} ^ {\\infty}} \\mathcal {A} _ {\\mathfrak {F}} \\\\ \\mathcal {D} \\xleftarrow {\\psi} \\quad \\begin{array}{c} \\phi^ {\\prime} \\uparrow \\\\ \\alpha \\end{array} \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[79,251,323,267]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For every $d$ in $\\mathcal{D}$ we have ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[104,289,875,311]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\beta^ {\\prime} \\circ \\phi (d) = \\phi_ {m} ^ {\\infty} \\circ \\delta \\circ \\phi^ {\\prime} \\circ \\phi (d) = \\phi_ {m} ^ {\\infty} \\circ \\delta \\circ \\psi^ {\\prime} \\circ \\psi (d) = \\phi_ {m} ^ {\\infty} \\circ \\phi_ {n} ^ {m} \\circ \\psi (d) = \\phi_ {n} ^ {\\infty} \\circ \\psi (d).\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,327,903,366]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Therefore $\\| \\beta' \\circ \\phi - \\alpha \\| < 1$ . Conjugating $\\beta'$ with a unitary in $\\widetilde{\\mathcal{A}}_{\\mathfrak{F}}$ gives the required left-invertible embedding $\\beta$ (Lemma 2.2). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,367,905,464]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For the uniqueness, suppose $\\mathcal{B}$ is the limit of a left-invertible sequence $(\\mathcal{B}_n,\\psi_n^m)$ of finite-dimensional $C^*$ -algebras, satisfying the assumption of the theorem. Using this assumption we can show that $(\\mathcal{B}_n,\\psi_n^m)$ satisfies the Fraïssé condition (F) and therefore $\\mathcal{B}$ is the Fraïssé limit of $\\mathfrak{F}$ . Uniqueness of the Fraïssé limit implies that $\\mathcal{B}$ is isomorphic to $\\mathcal{A}_{\\mathfrak{F}}$ . $\\square$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,485,903,523]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let us conclude this section with another example of a Fraïssé category of finite-dimensional $C^*$ -algebras. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,542,905,602]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 8.6. Note that a similar argument as in 7.2 shows that $\\mathcal{A}_{\\mathfrak{F}} \\otimes \\mathcal{A}_{\\mathfrak{F}}$ does not have the Cantor property. In particular, $\\mathcal{A}_{\\mathfrak{F}}$ is not self-absorbing, i.e., $\\mathcal{A}_{\\mathfrak{F}} \\otimes \\mathcal{A}_{\\mathfrak{F}}$ is not isomorphic to $\\mathcal{A}_{\\mathfrak{F}}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[79,623,387,641]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8.1. The universal UHF-algebra ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[104,663,608,680]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Recall that a UHF-algebra is the (inductive) limit of ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[349,700,635,730]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nM _ {k _ {1}} \\xrightarrow {\\phi_ {1} ^ {2}} M _ {k _ {2}} \\xrightarrow {\\phi_ {2} ^ {3}} M _ {k _ {3}} \\xrightarrow {\\phi_ {3} ^ {4}} \\ldots\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,747,905,805]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"of full matrix algebras, with unital connecting maps $\\phi_n^{n+1}$ . In particular $k_j|k_{j+1}$ for each $j$ . To each sequence of natural numbers $\\{k_j\\}_{j \\in \\mathbb{N}}$ (hence to the corresponding UHF-algebra) a supernatural number $n$ is associated, which is the formal product ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[419,823,563,861]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nn = \\prod_ {p \\text {p r i m e}} p ^ {n _ {p}}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,877,625,895]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $n_p \\in \\{0, 1, 2, \\ldots, \\infty\\}$ and for each prime number $p$ , ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[340,916,642,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nn _ {p} = \\sup \\{n: p ^ {n} | k _ {j} \\mathrm {f o r s o m e} j \\}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,64,104,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"26 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,63,796,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,105,918,201]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Also to each supernatural number $n$ there is an associated UHF-algebra denoted, as it is common, by $M_{n}$ (e.g., the CAR-algebra is $M_{2\\infty}$ ). Glimm [9] showed that a supernatural number is a complete invariant for the associated UHF-algebra. Recall that the universal UHF-algebra (see [16]), denoted by $\\mathcal{Q}$ , is the UHF-algebra associated to the supernatural number ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[421,217,584,258]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nn _ {\\infty} = \\prod_ {p \\mathrm {p r i m e}} p ^ {\\infty}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,270,817,289]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The universal UHF-algebra $\\mathcal{Q}$ is also the unique unital AF-algebra such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[329,308,680,329]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\langle K _ {0} (\\mathcal {Q}), K _ {0} (\\mathcal {Q}) _ {+}, [ 1 _ {\\mathcal {Q}} ] \\rangle \\cong \\langle \\mathbb {Q}, \\mathbb {Q} _ {+}, 1 \\rangle .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,345,916,402]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The multiplication of supernatural numbers is defined in the obvious way which means for supernatural numbers $n, m$ we have $M_{n} \\otimes M_{m} \\cong M_{nm}$ . This in particular implies that $\\mathcal{Q} \\otimes \\mathcal{M} \\cong \\mathcal{Q}$ , for any UHF-algebra $\\mathcal{M}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,404,918,561]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Now suppose $\\mathfrak{M}$ is the category of all nonzero matrix algebras and unital embeddings. Then $\\mathfrak{M}$ is a Fraïssé category. The only nontrivial part of the latter statement is to show that $\\mathfrak{M}$ has the amalgamation property, but this is quite easy since it is enough to make sure that the composition maps have the same multiplicities and then conjugating with a unitary makes sure that the composition maps are the same (this is similar to the proof of the amalgamation property in [5, Theorem 3.4]). The Fraïssé limit of $\\mathfrak{M}$ is $\\mathcal{Q}$ , since the universality property of the Fraïssé limit implies that the supernatural number associated to it must be $n_{\\infty}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,582,284,600]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"9. Unital categories ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,620,918,738]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The proof of Theorem 7.2 also shows that the category of all finite-dimensional $C^*$ -algebras (or any $\\oplus$ -stable category) and unital left-invertible embeddings has the (proper) amalgamation property. However, this category fails to have the joint embedding property (note that 0 is no longer an object of the category), since for example one cannot jointly embed $M_2$ and $M_3$ into a finite-dimensional $C^*$ -algebra with unital left-invertible maps. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,755,284,777]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"9.1. The category $\\widetilde{\\mathfrak{F}}$ ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,795,918,938]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $\\widetilde{\\mathfrak{F}}$ denote the category of all finite-dimensional $C^*$ -algebras isomorphic to $\\mathbb{C} \\oplus \\mathcal{D}$ , for a finite-dimensional $C^*$ -algebra $\\mathcal{D}$ , and unital left-invertible embeddings. This category is no longer $\\oplus$ -stable, however, a similar proof to the one of Theorem 7.2, where the maps are unital, shows that $\\sharp \\widetilde{\\mathfrak{F}}$ has the proper amalgamation property. Therefore $\\widetilde{\\mathfrak{F}}$ is a Fraïssé category, since $\\mathbb{C}$ is the initial object of this category and therefore the joint embedding property is a consequence of the amalgamation property. The Fraïssé limit $\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}$ of this category is a separable AF-algebra with the universality property that any ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[892,64,916,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"27 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[81,105,903,167]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"unital AF-algebra which can be obtained as the limit of a left-invertible unital sequence of finite-dimensional $C^*$ -algebras isomorphic to $\\mathbb{C} \\oplus \\mathcal{D}$ , can be embedded via a left-invertible unital embedding into $\\mathcal{A}_{\\widetilde{\\mathfrak{S}}}$ . The unital analogue of Theorem 8.1 states the following. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,188,903,230]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Corollary 9.1. For every unital separable $AF$ -algebra $\\mathcal{B}$ there is a surjective homomorphism from $\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}$ onto $\\mathcal{B}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,250,903,413]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Suppose $\\mathcal{B}$ is an arbitrary unital AF-algebra. Using Proposition 3.8 we can find a unital AF-algebra $\\mathcal{A} \\supseteq B$ which is the limit of a left-invertible unital sequence of finite-dimensional $C^*$ -algebras, such that $\\mathcal{B}$ is a quotient of $\\mathcal{A}$ . Thus $\\mathbb{C} \\oplus \\mathcal{A}$ is the limit of a unital left-invertible sequence of finite-dimensional $C^*$ -algebras of the form $\\mathbb{C} \\oplus \\mathcal{D}$ , for finite-dimensional $\\mathcal{D}$ . By the universality of $\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}$ , there is a left-invertible unital embedding from $\\mathbb{C} \\oplus \\mathcal{A}$ into $\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}$ . Since $\\mathcal{B}$ is a quotient of $\\mathcal{A}$ , there is a surjective homomorphism from $\\mathbb{C} \\oplus \\mathcal{A}$ onto $\\mathcal{B}$ . Combining the two surjections gives us a surjective homomorphism from $\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}$ onto $\\mathcal{B}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,433,903,539]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 9.2. Small adjustments in the proof of Lemma 7.4 show that $\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}$ has the Cantor property (in the sense of Definition 4.3). In fact, it is easy to check that $\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}$ is isomorphic to $\\widetilde{\\mathcal{A}}_{\\widetilde{\\mathfrak{F}}}$ , the unitization of $\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}$ . This, in particular, implies that $\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}$ is not unital. Since if it was unital, then $\\widetilde{\\mathcal{A}}_{\\widetilde{\\mathfrak{F}}}$ (and hence $\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}$ ) would be isomorphic to $\\mathcal{A}_{\\widetilde{\\mathfrak{F}}} \\oplus \\mathbb{C}$ , but this is not possible since $\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}$ has the Cantor property and therefore has no minimal projections. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,558,903,598]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Definition 9.3. We say $\\mathcal{D}$ is a unital-retract of the $C^*$ -algebra $\\mathcal{A}$ if there is a left-invertible unital embedding from $\\mathcal{D}$ into $\\mathcal{A}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[83,622,286,644]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"9.2. The category $\\widetilde{\\mathfrak{R}}_A$ ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[81,667,903,769]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If $\\mathcal{A}$ is a unital AF-algebra with Cantor property (Definition 4.3), then let $\\widetilde{\\mathfrak{K}}_{\\mathcal{A}}$ denote the category whose objects are finite-dimensional unital-retracts of $\\mathcal{A}$ and morphisms are unital left-invertible embeddings. This category is not $\\oplus$ -stable, since it does not satisfy condition (1) of Definition 7.1. However, $\\ddagger \\widetilde{\\mathfrak{K}}_{\\mathcal{A}}$ still has the proper amalgamations property. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,791,648,811]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proposition 9.4. $\\widehat{\\mathfrak{R}}_{\\mathcal{A}}$ has the proper amalgamation property. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,835,903,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. The proof is exactly the same as the proof of Lemma 7.2 where the maps are assumed to be unital. We only need to check that $\\mathcal{D} \\oplus \\mathcal{E}_1 \\oplus \\mathcal{F}_1$ is a unital-retract of $\\mathcal{A}$ . By Lemma 3.5, for some $m$ both $\\mathcal{E} \\cong \\mathcal{D} \\oplus \\mathcal{E}_1$ and $\\mathcal{F} \\cong \\mathcal{D} \\oplus \\mathcal{F}_1$ are unital-retracts of $\\mathcal{A}_m$ . An easy argument using Proposition 3.2 shows that $\\mathcal{D} \\oplus \\mathcal{E}_1 \\oplus \\mathcal{F}_1$ is also a unital-retract of $\\mathcal{A}_m$ and therefore a unital retract of $\\mathcal{A}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,64,104,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"28 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,61,796,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubiš / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,105,916,164]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Also $\\widetilde{\\mathfrak{K}}_{\\mathcal{A}}$ has a weakly initial object (by the next lemma). Therefore it is a Fraïssé category. Recall that an object is weakly initial in $\\mathfrak{K}$ if it has at least one $\\mathfrak{K}$ -arrow to any other object of $\\mathfrak{K}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,180,918,261]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 9.5. Suppose $\\mathcal{A}$ is a unital $AF$ -algebra with Cantor property. The category $\\widetilde{\\mathfrak{K}}_{\\mathcal{A}}$ has a weakly initial object, i.e., there is a finite-dimensional unital-retract of $\\mathcal{A}$ which can be mapped into any other finite-dimensional unital-retract of $\\mathcal{A}$ via a left-invertible unital embedding. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,276,916,420]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. Let $M_{k_1} \\oplus \\dots \\oplus M_{k_l}$ be an arbitrary $\\widetilde{\\mathcal{R}}_{\\mathcal{A}}$ -object. Suppose that $\\{k_1', \\ldots, k_t'\\}$ is the largest subset of $\\{k_1, \\ldots, k_l\\}$ such that $k_i'$ cannot be written as $\\sum_{\\substack{j \\leq n \\\\ j \\neq i}} x_j k_j'$ for any natural set numbers $\\{x_j : j \\leq n \\text{ and } j \\neq i\\}$ , for any $i \\leq t$ . Since $\\{k_1', \\ldots, k_t'\\}$ is the largest such subset, $\\mathcal{D} = M_{k_1'} \\oplus \\dots \\oplus M_{k_t'}$ is a unital-retract of $M_{k_1} \\oplus \\dots \\oplus M_{k_l}$ and therefore a unital-retract of $\\mathcal{A}$ . Suppose $\\mathcal{F}$ is an arbitrary $\\widetilde{\\mathcal{R}}_{\\mathcal{A}}$ -object. Let $(\\mathcal{A}_n, \\phi_n^m)$ be a $\\widetilde{\\mathcal{R}}_{\\mathcal{A}}$ -sequence with limit $\\mathcal{A}$ such that $\\mathcal{A}_1 \\cong \\mathcal{F}$ . Then $\\mathcal{D}$ is a unital-retract of some $\\mathcal{A}_m$ , so $\\mathcal{A}_m = \\dot{\\mathcal{D}} \\oplus \\mathcal{E}$ , for some $\\mathcal{E}$ and $\\dot{\\mathcal{D}} \\cong \\mathcal{D}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,423,918,555]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Fix $i \\leq t$ . Since $\\phi_1^m$ is a unital embedding, there is a subalgebra of $\\mathcal{F}$ isomorphic to $M_{n_1} \\oplus \\dots \\oplus M_{n_s}$ such that $\\sum_{j=1}^{s} y_j n_j = k_i'$ , for some $\\{y_1, \\ldots, y_s\\} \\subseteq \\mathbb{N}$ . We claim that exactly one $n_j$ is equal to $k_i'$ and the rest are zero. If not, then for every $j \\leq s$ we have $0 < n_j < k_i'$ . Since $\\phi_1^m$ is left-invertible, for every $j \\leq s$ a copy of $M_{n_j}$ appears as a summand of $\\mathcal{A}_m$ . Also because there is a unital embedding from $\\mathcal{D}$ into $\\mathcal{A}_m$ , for some $\\{x_1, \\ldots, x_r\\} \\subseteq \\mathbb{N}$ we have $n_j = \\sum_{\\substack{j' \\leq r \\\\ j' \\neq i}} x_{j'} k_{j'}'$ for every $j \\leq s$ . But then ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[398,570,608,632]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nk_{i}^{\\prime} = \\sum_{j = 1}^{s}\\sum_{\\substack{j^{\\prime}\\leq n\\\\ j^{\\prime}\\neq i}}x_{j^{\\prime}}y_{j}k_{j^{\\prime}}^{\\prime},\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[89,645,916,705]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"which is a contradiction with the choice of $k_{i}^{\\prime}$ . This means that $\\mathcal{F} = \\mathcal{F}_0 \\oplus \\mathcal{F}_1$ such that $\\mathcal{F}_0 \\cong \\mathcal{D}$ and there is a unital homomorphism from $\\mathcal{D}$ onto $\\dot{\\mathcal{F}}_1$ . Therefore $\\mathcal{D}$ is a unital-retract of $\\mathcal{F}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,720,916,782]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Corollary 9.6. Suppose $\\mathcal{A}$ is a unital $AF$ -algebra with Cantor property. The category $\\widetilde{\\mathfrak{K}}_{\\mathcal{A}}$ is a Fraïssé category and $\\ddagger \\widetilde{\\mathfrak{K}}_{\\mathcal{A}}$ has the proper amalgamation property. The Fraïssé limit of $\\widetilde{\\mathfrak{K}}_{\\mathcal{A}}$ is $\\mathcal{A}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,798,916,838]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proof. The proof of the fact that $\\mathcal{A}$ is the Fraïssé limit of $\\widetilde{\\mathfrak{K}}_{\\mathcal{A}}$ is same as Theorem 7.6, where all the maps are unital. $\\square$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,857,608,877]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10. Surjectively universal countable dimension groups ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,895,916,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A countable partially ordered abelian group $\\langle G, G^{+} \\rangle$ is a (countable) dimension group if it is isomorphic to the inductive limit of a sequence ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[892,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"29 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[359,98,623,123]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathbb {Z} ^ {r _ {1}} \\xrightarrow {\\alpha_ {1} ^ {2}} \\mathbb {Z} ^ {r _ {2}} \\xrightarrow {\\alpha_ {2} ^ {3}} \\mathbb {Z} ^ {r _ {3}} \\xrightarrow {\\alpha_ {3} ^ {4}} \\dots\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,142,903,183]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"for some natural numbers $r_n$ , where $\\alpha_i^j$ are positive group homomorphisms and $\\mathbb{Z}^r$ is equipped with the ordering given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[226,201,755,220]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left(\\mathbb {Z} ^ {r}\\right) ^ {+} = \\left\\{\\left(x _ {1}, x _ {2}, \\dots , x _ {r}\\right) \\in \\mathbb {Z} ^ {r}: x _ {i} \\geq 0 \\text {f o r} i = 1, \\dots , r \\right\\}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,239,905,298]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A partially ordered abelian group that is isomorphic to $\\langle \\mathbb{Z}^r, (\\mathbb{Z}^r)^+ \\rangle$ , for a non-negative integer $r$ , is usually called a simplicial group. A scale $S$ on the dimension group $\\langle G, G^+ \\rangle$ is a generating, upward directed and hereditary subset of $G^+$ (see [4, IV.3]). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,316,903,352]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Notation. If $\\langle G, S \\rangle$ is a scaled dimension group as above, we can recursively pick order-units ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[316,373,665,392]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\bar {u} _ {n} = \\left(u _ {n, 1}, u _ {n, 2}, \\dots , u _ {n, r _ {n}}\\right) \\in \\left(\\mathbb {Z} ^ {r _ {n}}\\right) ^ {+}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,410,905,491]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"of $\\mathbb{Z}^{r_n}$ such that $\\alpha_{n}^{n + 1}(\\bar{u}_{n})\\leq \\bar{u}_{n + 1}$ and $S = \\bigcup_{n}\\alpha_{n}^{\\infty}[[\\bar{0},\\bar{u}_{n}]]$ . Then we say the scaled dimension group $\\langle G,S\\rangle$ is the limit of the sequence $(\\mathbb{Z}^{r_n},\\bar{u}_n,\\alpha_n^m)$ . If $(\\bar{u}_n)$ can be chosen such that $\\alpha_{n}^{n + 1}(\\bar{u}_{n}) = \\bar{u}_{n + 1}$ for every $n\\in \\mathbb{N}$ , then $G$ has an order-unit $u = \\lim_{n}\\alpha_{n}^{\\infty}(\\bar{u}_{n})$ In this case we denote this dimension group with order-unit by $\\langle G,u\\rangle$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,507,905,605]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An isomorphism between scaled dimension groups is a positive group isomorphism which sends the scale of the domain to the scale of the codomain. Given a separable AF-algebra $\\mathcal{A}$ , its $K_{0}$ -group $\\langle K_0(\\mathcal{A}), K_0(\\mathcal{A})^+ \\rangle$ is a (countable) dimension group and conversely any dimension group is isomorphic to $K_{0}$ -group of a separable AF-algebra. The dimension range of $\\mathcal{A}$ , ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[263,625,717,645]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {D} (\\mathcal {A}) = \\{[ p ]: p \\text {i s a p r o j e c t i o n o f} \\mathcal {A} \\} \\subseteq K _ {0} (\\mathcal {A}) ^ {+}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[77,661,905,742]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"is a scale for $\\langle K_0(\\mathcal{A}),K_0(\\mathcal{A})^+\\rangle$ , and therefore $\\langle K_0(\\mathcal{A}),\\mathcal{D}(\\mathcal{A})\\rangle$ is a scaled dimension group. Conversely, every scaled dimension group is isomorphic to $\\langle K_0(\\mathcal{A}),\\mathcal{D}(\\mathcal{A})\\rangle$ for a separable AF-algebra $\\mathcal{A}$ . Elliott's classification of separable AF-algebras ([6]) states that $\\langle K_0(\\mathcal{A}),\\mathcal{D}(\\mathcal{A})\\rangle$ is a complete isomorphism invariant for the separable AF-algebra $\\mathcal{A}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[77,758,907,838]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 10.1 (Elliott [6]). Two separable $AF$ -algebras $\\mathcal{A}$ and $\\mathcal{B}$ are isomorphic if and only if their scaled dimension groups are isomorphic. If $\\mathcal{A}$ and $\\mathcal{B}$ are unital, then they are isomorphic if and only if $\\langle K_0(\\mathcal{A}), [1_{\\mathcal{A}}] \\rangle \\cong \\langle K_0(\\mathcal{B}), [1_{\\mathcal{B}}] \\rangle$ , as partially ordered abelian groups with order-units. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,857,513,876]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10.1. Surjectively universal dimension groups ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[77,897,903,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The universality property of $\\langle K_0(\\mathcal{A}_{\\mathfrak{F}}),\\mathcal{D}(\\mathcal{A}_{\\mathfrak{F}})\\rangle$ can be obtained by applying $K_{0}$ -functor to Theorem 8.1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,64,104,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"30 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,63,798,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[89,105,916,145]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Corollary 10.2. The scaled (countable) dimension group $\\langle K_0(\\mathcal{A}_{\\mathfrak{F}}),\\mathcal{D}(\\mathcal{A}_{\\mathfrak{F}})\\rangle$ maps onto any countable scaled dimension group. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[115,164,914,185]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"By applying $K_{0}$ -functor to Corollary 8.4, we immediately obtain the following result. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,202,918,242]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Corollary 10.3. $\\langle K_0(\\mathcal{A}_{\\mathfrak{F}}),\\mathcal{D}(\\mathcal{A}_{\\mathfrak{F}})\\rangle$ is the unique scaled dimension group which is the limit of a sequence $(\\mathbb{Z}^{r_n},\\bar{u}_n,\\alpha_n^m)$ (as in Notation above) satisfying the following conditions: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,261,916,401]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(1) for every $n \\\\in \\\\mathbb{N}$ and $1 \\\\leq i \\\\leq r_n$ there are $m \\\\geq n$ and $1 \\\\leq j, j' \\\\leq r_m$ such that $j \\\\neq j'$ , $u_{n,i} = u_{m,j} = u_{m,j'}$ and $\\\\pi_j \\\\circ \\\\alpha_n^m(u_{n,i}) = u_{m,j}$ and $\\\\pi_{j'} \\\\circ \\\\alpha_n^m(u_{n,i}) = u_{m,j'}$ , where $\\\\pi_j$ is the canonical projection from $\\\\mathbb{Z}^{r_m}$ onto its $j$ -th coordinate. \",\"(2) for every $n, n' \\\\in \\\\mathbb{N}, 1 \\\\leq i' \\\\leq r_{n'}$ and $\\\\{x_1, \\\\ldots, x_{r_n}\\\\} \\\\subseteq \\\\mathbb{N} \\\\cup \\\\{0\\\\}$ such that $\\\\sum_{i=1}^{r_n} x_i u_{n,i} \\\\leq u_{n',i'}$ there are $m \\\\geq n$ and $1 \\\\leq j \\\\leq r_m$ such that $u_{n',i'} \\\\leq u_{m,j}$ and $\\\\pi_j \\\\circ \\\\alpha_n^m(u_{n,i}) = x_i \\\\cdot u_{n,i}$ for every $i \\\\in \\\\{1, \\\\ldots, r_n\\\\}$ . \",\"(3) For every $k \\\\in \\\\mathbb{N}$ there are natural numbers $n$ and $1 \\\\leq i \\\\leq r_n$ such that $u_{n,i} = k$ . \"]","page_idx":"30","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[89,420,916,480]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Corollary 10.4. The (countable) dimension group with order-unit $\\langle K_0(\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}),[1_{\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}}]\\rangle$ maps onto (there is a surjective normalized positive group homomorphism) any countable dimension group with order-unit. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,500,916,558]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A similar characterization of the dimension group with order-unit $\\langle K_0(\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}),[1_{\\mathcal{A}_{\\widetilde{\\mathfrak{F}}}}]\\rangle$ holds where $\\alpha_{n}^{m}$ are order-unit preserving and in condition (2) of Corollary 10.3 the inequality $\\sum_{i = 1}^{r_n}x_iu_{n,i}\\leq u_{n',i'}$ is replaced with equality. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,580,265,598]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgments ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,620,916,658]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We would like to thank Ilijas Farah and Eva Pernecká for useful conversations and comments. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,682,199,698]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[100,719,914,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[1] I. Ben Yaacov, Fraïssé limits of metric structures, J. Symb. Log. 80 (2015) 100-115. \",\"[2] B.E. Blackadar, Traces on simple AF $C^*$ -algebras, J. Funct. Anal. 38 (2) (1980) 156-168. \",\"[3] O. Bratteli, Inductive limits of finite-dimensional $C^*$ -algebras, Trans. Am. Math. Soc. 171 (1972) 195-234. \",\"[4] K. Davidson, $C^*$ -Algebras by Example, Fields Institute Monographs, vol. 6, American Mathematical Society, Providence, RI, 1996. \",\"[5] C.J. Eagle, I. Farah, B. Hart, B. Kadets, V. Kalashnyk, M. Lupini, Fraïssé limits of $C^*$ -algebras, J. Symb. Log. 81 (2016) 755-773. \",\"[6] G.A. Elliott, On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Algebra 38 (1976) 29-44. \",\"[7] R. Fraïssé, Sur l'extension aux relations de quelques propriétés des ordres, Ann. Sci. Éc. Norm. Supér. (3) 71 (1954) 363-388. \",\"[8] J. Garbulińska-Wegrzyn, Isometric uniqueness of a complementably universal Banach space for Schauder decompositions, Banach J. Math. Anal. 8 (2014) 211-220. \",\"[9] J.G. Glimm, On a certain class of operator algebras, Trans. Am. Math. Soc. 95 (1960) 318-340. \"]","page_idx":"30","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[203,63,811,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[892,64,914,75]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"31 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[81,108,903,277]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[10] W. Kubis, Fraïssé sequences: category-theoretic approach to universal homogeneous structures, Ann. Pure Appl. Log. 165 (2014) 1755-1811. \",\"[11] W. Kubić, Metric-enriched categories and approximate Fraïssé limits, preprint, arXiv:1210.6506. \",\"[12] W. Kubis, S. Solecki, A proof of uniqueness of the Gurariš space, Isr. J. Math. 195 (2013) 449-456. \",\"[13] M. Lupini, Fraïssé limits in functional analysis, Adv. Math. 338 (2018) 93-174. \",\"[14] S. Masumoto, The Jiang-Su algebra as a Fraïssé limit, J. Symb. Log. 82 (2017) 1541-1559. \",\"[15] M. Rørdam, F. Larsen, N. Laustsen, An Introduction to K-Theory for $\\\\mathbf{C}^*$ -Algebras, vol. 49, Cambridge University Press, 2000. \",\"[16] M. Rørdam, E. Størmer, Classification of Nuclear $C^*$ -Algebras: Entropy in Operator Algebras, vol. 126, Springer, Berlin, 2002. \",\"[17] K. Schoretsanitis, Fraïssé theory for metric structures, Thesis (Ph.D.), University of Illinois at Urbana-Champaign, 2007. \"]","page_idx":"31","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[81,64,104,76]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"32 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,63,796,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 ","text_format":null,"text_level":null,"type":"header"}],"string":"[\n {\n \"bbox\": \"[92,263,404,289]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Universal AF-algebras \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,307,468,327]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Saeed Ghasemi a, Wiesław Kubiś a,b,* \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[790,267,852,311]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0149/9e456a09c85532a8fcb2c942e64b6f38c0a4436a4c51336963d5631572c0132f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[89,336,717,375]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"a Institute of Mathematics, Czech Academy of Sciences, Czechia \\\",\\\"$^{\\\\\\\\mathrm{b}}$ Institute of Mathematics, Cardinal Stefan Wyszynski University in Warsaw, Poland \\\"]\",\n \"page_idx\": \"0\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[92,408,316,422]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ARTICLE INFO \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,442,216,455]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article history: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,455,314,467]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received 26 September 2019 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,467,267,480]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Accepted 9 April 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,480,327,492]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Available online 18 April 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,494,340,505]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Communicated by Stefaan Vaes \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,517,141,529]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MSC: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,530,143,542]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"46L05 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,542,143,555]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"46L85 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,555,147,567]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"46M15 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,582,179,595]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,595,182,608]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"AF-algebra \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,608,222,620]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Cantor property \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,622,295,633]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Left-invertible embedding \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,635,190,645]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Fraissé limit \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[426,408,578,422]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABSTRACT \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[423,442,916,611]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We study the approximately finite-dimensional (AF) $C^*$ -algebras that appear as inductive limits of sequences of finite-dimensional $C^*$ -algebras and left-invertible embeddings. We show that there is such a separable AF-algebra $\\\\mathcal{A}_{\\\\mathfrak{F}}$ which is a split-extension of any finite-dimensional $C^*$ -algebra and has the property that any separable AF-algebra is isomorphic to a quotient of $\\\\mathcal{A}_{\\\\mathfrak{F}}$ . Equivalently, by Elliott's classification of separable AF-algebras, there are surjectively universal countable scaled (or with order-unit) dimension groups. This universality is a consequence of our result stating that $\\\\mathcal{A}_{\\\\mathfrak{F}}$ is the Fraissé limit of the category of all finite-dimensional $C^*$ -algebras and left-invertible embeddings. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[423,611,916,725]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"With the help of Fraïssé theory we describe the Bratteli diagram of $\\\\mathcal{A}_{\\\\mathfrak{F}}$ and provide conditions characterizing it up to isomorphisms. $\\\\mathcal{A}_{\\\\mathfrak{F}}$ belongs to a class of separable AF-algebras which are all Fraïssé limits of suitable categories of finite-dimensional $C^*$ -algebras, and resemble $C(2^{\\\\mathbb{N}})$ in many senses. For instance, they have no minimal projections, tensorially absorb $C(2^{\\\\mathbb{N}})$ (i.e. they are $C(2^{\\\\mathbb{N}})$ -stable) and satisfy similar homogeneity and universality properties as the Cantor set. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[593,725,914,738]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"© 2020 Elsevier Inc. All rights reserved. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[310,63,698,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[94,105,224,186]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[96,189,222,205]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ELSEVIER \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[353,107,661,120]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Contents lists available at ScienceDirect \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[304,142,708,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Journal of Functional Analysis \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[396,189,616,205]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.elsevier.com/locate/jfa \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[790,97,916,204]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"JOURNAL OF FUNCTIONAL ANALYSIS \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[92,823,914,852]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{\\\\text{念}}$ Research of the first author was supported by the GACR project 19-05271Y and RVO: 67985840. Research of the second author was supported by the GACR project 20-31529X and RVO: 67985840. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[102,852,293,866]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"* Corresponding author. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[119,867,492,880]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"E-mail address: kubis@math.cas.cz (W. Kubis). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[92,895,415,908]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1016/j.jfa.2020.108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[92,908,488,920]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"0022-1236/© 2020 Elsevier Inc. All rights reserved. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[79,107,235,122]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,142,905,475]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Operator algebraists often refer to (for good reasons, of course) the UHF-algebras such as CAR-algebra as the noncommutative analogues of the Cantor set $2^{\\\\mathbb{N}}$ , or more precisely the commutative $C^*$ -algebra $C(2^{\\\\mathbb{N}})$ . We introduce a different class of separable AF-algebras, we call them \\\"AF-algebras with Cantor property\\\" (Definition 4.1), which in some contexts are more suitable noncommutative analogues of $C(2^{\\\\mathbb{N}})$ . One of the main features of AF-algebras with Cantor property is that they are direct limits of sequences of finite-dimensional $C^*$ -algebras where the connecting maps are left-invertible homomorphisms. This property, for example, guarantees that if the algebra is infinite-dimensional, it has plenty of nontrivial ideals and quotients, while UHF-algebras are simple. The Cantor set is a \\\"special and unique\\\" space in the category of all compact (zero-dimensional) metrizable spaces in the sense that it bears some universality and homogeneity properties; it maps onto any compact (zero-dimensional) metrizable space and it has the homogeneity property that any homeomorphism between finite quotients lifts to a homeomorphism of the Cantor set (see [10]). Moreover, Cantor set is the unique compact zero-dimensional metrizable space with the property that (stated algebraically): for every $m, n \\\\in \\\\mathbb{N}$ and unital embeddings $\\\\phi: \\\\mathbb{C}^n \\\\to \\\\mathbb{C}^m$ and $\\\\alpha: \\\\mathbb{C}^n \\\\to C(2^{\\\\mathbb{N}})$ there is an embedding $\\\\beta: \\\\mathbb{C}^m \\\\to C(2^{\\\\mathbb{N}})$ such that the diagram \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[411,494,576,564]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{c} C (2 ^ {\\\\mathbb {N}}) \\\\\\\\ \\\\mathbb {C} ^ {n} \\\\xrightarrow {\\\\phi} \\\\mathbb {C} ^ {m} \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[79,579,905,852]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"commutes. Note that the map $\\\\phi$ in the above must be left-invertible and if $\\\\alpha$ is left-invertible then $\\\\beta$ can be chosen to be left-invertible. Recall that a homomorphism $\\\\phi : \\\\mathcal{B} \\\\to \\\\mathcal{A}$ is left-invertible if there is a homomorphism $\\\\pi : \\\\mathcal{A} \\\\to \\\\mathcal{B}$ such that $\\\\pi \\\\circ \\\\phi = \\\\mathrm{id}_{\\\\mathcal{B}}$ . The AF-algebras with Cantor property satisfy similar universality and homogeneity properties in their corresponding categories of finite-dimensional $C^*$ -algebras and left-invertible homomorphisms. Although, in general AF-algebras with Cantor property are not assumed to be unital, when restricted to the categories with unital maps, one can obtain the unital AF-algebras with same properties subject to the condition that maps are unital. For instance, the \\\"truly\\\" noncommutative AF-algebra with Cantor property $\\\\mathcal{A}_{\\\\mathfrak{F}}$ , that was mentioned in the abstract, is the unique (nonunital) AF-algebra which is the limit of a sequence of finite-dimensional $C^*$ -algebras and left-invertible homomorphisms (necessarily embeddings), with the property that for every finite-dimensional $C^*$ -algebras $\\\\mathcal{D}, \\\\mathcal{E}$ and (not necessarily unital) left-invertible embeddings $\\\\phi : \\\\mathcal{D} \\\\to \\\\mathcal{E}$ and $\\\\alpha : \\\\mathcal{D} \\\\to \\\\mathcal{A}_{\\\\mathfrak{F}}$ there is a left-invertible embedding $\\\\beta : \\\\mathcal{E} \\\\to \\\\mathcal{A}_{\\\\mathfrak{F}}$ such that the diagram \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[430,870,552,938]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{c} \\\\mathcal {A} _ {\\\\mathfrak {F}} \\\\\\\\ \\\\mathcal {D} \\\\xrightarrow {\\\\stackrel {\\\\alpha} {\\\\phi}} \\\\mathcal {E} \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,64,96,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,63,796,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,105,916,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"commutes (Theorem 8.5). One of our main results (Theorem 8.1) states that $\\\\mathcal{A}_{\\\\mathfrak{F}}$ maps surjectively onto any separable AF-algebra. However, this universality property is not unique to $\\\\mathcal{A}_{\\\\mathfrak{F}}$ (Remark 8.2). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,167,918,558]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The properties of the Cantor set that are mentioned above can be viewed as consequences of the fact that it is the \\\"Fraïssé limit\\\" of the class of all nonempty finite spaces and surjective maps (as well as the class of all nonempty compact metric spaces and continuous surjections); see [11]. The theory of Fraïssé limits was introduced by R. Fraïssé [7] in 1954 as a model-theoretic approach to the back-and-forth argument. Roughly speaking, Fraïssé theory establishes a correspondence between classes of finite (or finitely generated) models of a first-order language with certain properties (the joint-embedding property, the amalgamation property and having countably many isomorphism types), known as Fraïssé classes, and the unique (ultra-)homogeneous and universal countable structure, known as the Fraïssé limit, which can be represented as the union of a chain of models from the class. Fraïssé theory has been recently extended way beyond the countable first-order structures, in particular, covering some topological spaces, Banach spaces and, even more recently, some $C^*$ -algebras. Usually in these extensions the classical Fraïssé theory is replaced by its \\\"approximate\\\" version. Approximate Fraïssé theory was developed by Ben Yaacov [1] in continuous model theory (an earlier approach was developed in [17]) and independently, in the framework of metric-enriched categories, by the second author [11]. The Urysohn metric space, the separable infinite-dimensional Hilbert space [1], and the Gurarié space [12] are some of the other well-known examples of Fraïssé limits of metric structures (see also [13] for more on Fraïssé limits in functional analysis). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,561,920,797]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Fraïssé limits of $C^*$ -algebras are studied in [5] and [14], where it has been shown that the Jiang-Su algebra, all UHF algebras, and the hyperfinite $\\\\Pi_1$ -factor are Fraïssé limits of suitable classes of finitely generated $C^*$ -algebras with distinguished traces. Here we investigate the separable AF-algebras that arise as limits of Fraïssé classes of finite-dimensional $C^*$ -algebras. Apart from $C(2^{\\\\mathbb{N}})$ , which is the Fraïssé limit of the class of all commutative finite-dimensional $C^*$ -algebras and unital (automatically left-invertible) embeddings, all UHF-algebras [5, Theorem 3.4] and a class of simple monotracial AF-algebras described in [5, Theorem 3.9], are Fraïssé limits of classes of finite-dimensional $C^*$ -algebras. It is also worth noticing that the $C^*$ -algebra $\\\\mathcal{K}(H)$ of all compact operators on a separable Hilbert space $H$ and the universal UHF-algebra $\\\\mathcal{Q}$ (see Section 8.1) are both Fraïssé limits of, respectively, the category of all matrix algebras and (not necessarily unital) embeddings and the category of all matrix algebras and unital embeddings. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[87,798,918,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In general, however, obstacles arising from the existence of traces prevent many classes of finite-dimensional $C^*$ -algebras from having the amalgamation property ([5, Proposition 3.3]), therefore making it difficult to realize AF-algebras as Fraïssé limits of such classes. The AF-algebra $C(2^{\\\\mathbb{N}})$ is neither a UHF-algebra nor it is among AF-algebras considered in [5, Theorem 3.9]. Therefore, it is natural to ask whether $C(2^{\\\\mathbb{N}})$ belongs to any larger nontrivial class of AF-algebras whose elements are Fraïssé limits of some class of finite-dimensional $C^*$ -algebras. This was our initial motivation behind introducing the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[903,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[81,105,903,144]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"class of separable AF-algebras with Cantor property (Definition 4.1). This class properly contains the AF-algebras of the form $M_{n} \\\\otimes C(2^{\\\\mathbb{N}})$ , for any matrix algebra $M_{n}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,145,903,183]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If $\\\\mathcal{A}$ and $\\\\mathcal{B}$ are $C^*$ -algebras, $\\\\phi : \\\\mathcal{B} \\\\hookrightarrow \\\\mathcal{A}$ is a left-invertible embedding and $\\\\pi : \\\\mathcal{A} \\\\twoheadrightarrow \\\\mathcal{B}$ is a left inverse of $\\\\phi$ , then we have the short exact sequence \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[289,204,691,236]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n0 \\\\xrightarrow {} \\\\ker (\\\\pi) \\\\xrightarrow {\\\\iota} \\\\mathcal {A} \\\\xrightarrow [ \\\\phi ]{\\\\frac {\\\\pi}{\\\\iota}} \\\\mathcal {B} \\\\xrightarrow {} 0.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,255,903,333]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Therefore $\\\\mathcal{A}$ is a \\\"split-extension\\\" of $\\\\mathcal{B}$ . In this case we say $\\\\mathcal{B}$ is a \\\"retract\\\" of $\\\\mathcal{A}$ . It would be more convenient for us to say \\\" $\\\\mathcal{B}$ is a retract of $\\\\mathcal{A}$ \\\" rather than the more familiar phrase (for $C^*$ -algebraists) \\\" $\\\\mathcal{A}$ is a split-extension of $\\\\mathcal{B}$ \\\". In Section 3 we consider direct sequences of finite-dimensional $C^*$ -algebras \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[370,352,614,380]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {A} _ {1} \\\\xrightarrow {\\\\phi_ {1} ^ {2}} \\\\mathcal {A} _ {2} \\\\xrightarrow {\\\\phi_ {2} ^ {3}} \\\\mathcal {A} _ {3} \\\\xrightarrow {\\\\phi_ {3} ^ {4}} \\\\dots\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,398,903,577]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where each $\\\\phi_n^{n+1}$ is a left-invertible embedding. The AF-algebra $\\\\mathcal{A}$ that arises as the limit of this sequence has the property that every matrix algebra $M_k$ appearing as a direct-sum component (an ideal) of some $\\\\mathcal{A}_n$ is a retract of $\\\\mathcal{A}$ (equivalently, $\\\\mathcal{A}$ is a split-extension of each $\\\\mathcal{A}_n$ and such $M_k$ ). Moreover, every retract of $\\\\mathcal{A}$ which is a matrix algebra, appears as a direct-sum component of some $\\\\mathcal{A}_n$ (Lemma 3.5). The AF-algebras with Cantor property are defined and studied in Section 4. They are characterized by the set of their matrix algebra retracts. That is, two AF-algebras with Cantor property are isomorphic if and only if they have exactly the same matrix algebras as their retracts (Corollary 7.8), i.e., they are split-extensions of the same class of matrix algebras. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,579,903,776]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We will use the Fraïssé-theoretic framework of (metric-enriched) categories described in [11], rather than the (metric) model-theoretic approach to the Fraïssé theory. A brief introduction to Fraïssé categories is provided in Section 5. We show that (Theorem 7.2) any category of finite-dimensional $C^*$ -algebras and (not necessarily unital) left-invertible embeddings, which is closed under taking direct sums and ideals of its objects (we call these categories $\\\\oplus$ -stable) is a Fraïssé category. Moreover, Fraïssé limits of these categories have the Cantor property (Lemma 7.4) and in fact any AF-algebra $\\\\mathcal{A}$ with Cantor property can be realized as Fraïssé limit of such a category, where the objects of this category are precisely the finite-dimensional retracts of $\\\\mathcal{A}$ (see Definition 3.1 and Theorem 7.6). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,777,903,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In particular, the category $\\\\mathfrak{F}$ of all finite-dimensional $C^*$ -algebras and left-invertible embeddings is a Fraïssé category (Section 8). A priori, the Fraïssé limit $\\\\mathcal{A}_{\\\\mathfrak{F}}$ of this category is a separable AF-algebra with the universality property that any separable AF-algebra $\\\\mathcal{A}$ which is the limit of a sequence of finite-dimensional $C^*$ -algebras with left-invertible embeddings as connecting maps, can be embedded into $\\\\mathcal{A}_{\\\\mathfrak{F}}$ via a left-invertible embedding, i.e., $\\\\mathcal{A}_{\\\\mathfrak{F}}$ is a split-extension of $\\\\mathcal{A}$ . In particular, there is a surjective homomorphism $\\\\theta : \\\\mathcal{A}_{\\\\mathfrak{F}} \\\\twoheadrightarrow \\\\mathcal{A}$ . Also any separable AF-algebra is isomorphic to a quotient (by an essential ideal) of an AF-algebra which is the limit of a sequence of finite-dimensional $C^*$ - \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,64,96,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,63,796,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,105,916,144]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"algebras with left-invertible embeddings (Proposition 3.8). Combining the two quotient maps, we have the following result, which is later restated as Theorem 8.1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,164,916,204]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 1.1. The category of all finite-dimensional $C^*$ -algebras and left-invertible embeddings is a Fraïssé category. Its Fraïssé limit $\\\\mathcal{A}_{\\\\mathfrak{F}}$ is a separable $AF$ -algebra such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[102,225,912,280]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- $\\\\\\\\mathcal{A}_{\\\\\\\\mathfrak{F}}$ is a split-extension of any $AF$ -algebra which is the limit of a sequence of finite-dimensional $C^*$ -algebras and left-invertible connecting maps. \\\",\\\"- there is a surjective homomorphism from $\\\\\\\\mathcal{A}_{\\\\\\\\mathfrak{F}}$ onto any separable $AF$ -algebra. \\\"]\",\n \"page_idx\": \"4\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[89,302,916,420]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Bratteli diagram of $\\\\mathcal{A}_{\\\\mathfrak{F}}$ is described in Proposition 8.4, using the fact that it has the Cantor property. It is the unique AF-algebra with Cantor property which is a split-extension of every finite-dimensional $C^*$ -algebra. The unital versions of these results are given in Section 9 (with a bit of extra work, since unlike $\\\\mathfrak{F}$ , the category of all finite-dimensional $C^*$ -algebras and unital left-invertible maps is not a Fraïssé category, namely, it lacks the joint embedding property). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,422,916,480]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Separable AF-algebras are famously characterized [6] by their $K_{0}$ -invariants which are scaled countable dimension groups (with order-unit, in the unital case). By applying the $K_{0}$ -functor to Theorem 1.1 we have the following result. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,500,916,539]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Corollary 1.2. There is a scaled countable dimension group (with order-unit) which maps onto any scaled countable dimension group (with order-unit). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,558,914,594]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The corresponding characterizations of these dimension groups are mentioned in Section 10. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,598,916,675]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, this paper could have been written entirely in the language of partially ordered abelian groups, where the categories of \\\"simplicial groups\\\" and left-invertible positive embeddings replace our categories. However, we do not see any clear advantage in doing so. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,698,250,714]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. Preliminaries \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,738,918,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Recall that an approximately finite-dimensional (AF) algebra is a $C^*$ -algebra which is an inductive limit of a sequence of finite-dimensional $C^*$ -algebras. We review a few basic facts about separable AF-algebras. The background needed regarding AF-algebras is quite elementary and [4] is more than sufficient. The AF-algebras that are considered here are always separable and therefore by \\\"AF-algebra\\\" we always mean \\\"separable AF-algebra\\\". AF-algebras can be characterized up to isomorphisms by their Bratteli diagrams [3]. However, there is no efficient way (at least visually) to decide whether two Bratteli diagrams are isomorphic, i.e., they correspond to isomorphic AF-algebras. A much better characterization of AF-algebras uses $K$ -theory. To each $C^*$ -algebra the $K_0$ -functor assigns a partially ordered abelian group (its $K_0$ -group) which turns out to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[903,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[79,105,905,183]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"be a complete invariant for AF-algebras [6]. Moreover, there is a complete description of all possible $K_{0}$ -groups of AF-algebras. Namely, a partially ordered abelian group is isomorphic to the $K_{0}$ -group of an AF-algebra if and only if it is a countable dimension group. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,185,905,342]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We mostly use the notation from [4] with minor adjustments. Let $M_{k}$ denote the $C^*$ -algebra of all $k \\\\times k$ matrices over $\\\\mathbb{C}$ . Suppose $\\\\mathcal{A} = \\\\varinjlim (\\\\mathcal{A}_n, \\\\phi_n^m)$ is an AF-algebra with Bratteli diagram $\\\\mathfrak{D}$ such that each $\\\\mathcal{A}_n \\\\cong \\\\mathcal{A}_{n,1} \\\\oplus \\\\dots \\\\oplus \\\\mathcal{A}_{n,\\\\ell}$ , is a finite-dimensional $C^*$ -algebra and each $\\\\mathcal{A}_{n,s}$ is a full matrix algebra. The node of $\\\\mathfrak{D}$ corresponding to $\\\\mathcal{A}_{n,s}$ is \\\"officially\\\" denoted by $(n,s)$ , while intrinsically it carries over a natural number $\\\\dim(n,s)$ , which represents the dimension of the matrix algebra $\\\\mathcal{A}_{n,s}$ , i.e. $\\\\mathcal{A}_{n,s} \\\\cong M_{\\\\dim(n,s)}$ . For $(n,s), (m,t) \\\\in \\\\mathfrak{D}$ we write $(n,s) \\\\to (m,t)$ if $(n,t)$ is connected $(m,t)$ by at least one path in $\\\\mathfrak{D}$ , i.e. if $\\\\phi_n^m$ sends $\\\\mathcal{A}_{n,s}$ faithfully into $\\\\mathcal{A}_{m,t}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,344,905,482]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The ideals of AF-algebras are also AF-algebras and they can be recognized from the Bratteli diagram of the algebra. Namely, the Bratteli diagrams of ideals correspond to directed and hereditary subsets of the Bratteli diagram of the algebra (see [4, Theorem III.4.2]). Recall that an essential ideal $\\\\mathcal{I}$ of $\\\\mathcal{A}$ is an ideal which has nonzero intersections with every nonzero ideal of $\\\\mathcal{A}$ . Suppose $\\\\mathfrak{D}$ is the Bratteli diagram for an AF-algebra $\\\\mathcal{A}$ and $\\\\mathcal{I}$ is an ideal of $\\\\mathcal{A}$ whose Bratteli diagram corresponds to $\\\\mathfrak{J} \\\\subseteq \\\\mathfrak{D}$ . Then $\\\\mathcal{I}$ is essential if and only if for every $(n,s) \\\\in \\\\mathfrak{D}$ there is $(m,t) \\\\in \\\\mathfrak{J}$ such that $(n,s) \\\\to (m,t)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,483,905,560]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If $\\\\mathcal{D} = \\\\mathcal{D}_1 \\\\oplus \\\\dots \\\\oplus \\\\mathcal{D}_l$ and $\\\\mathcal{E} = \\\\mathcal{E}_1 \\\\oplus \\\\dots \\\\oplus \\\\mathcal{E}_k$ are finite-dimensional $C^*$ -algebras where $\\\\mathcal{D}_i$ and $\\\\mathcal{E}_j$ are matrix algebras and $\\\\phi : \\\\mathcal{D} \\\\to \\\\mathcal{E}$ is a homomorphism, we denote the \\\"multiplicity of $\\\\mathcal{D}_i$ in $\\\\mathcal{E}_j$ along $\\\\phi$ \\\" by $\\\\mathrm{Mult}_{\\\\phi}(\\\\mathcal{D}_i, \\\\mathcal{E}_j)$ . Also let $\\\\mathrm{Mult}_{\\\\phi}(\\\\mathcal{D}, \\\\mathcal{E}_j)$ denote the tuple \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[301,580,680,602]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left(\\\\operatorname {M u l t} _ {\\\\phi} \\\\left(\\\\mathcal {D} _ {1}, \\\\mathcal {E} _ {j}\\\\right), \\\\dots , \\\\operatorname {M u l t} _ {\\\\phi} \\\\left(\\\\mathcal {D} _ {l}, \\\\mathcal {E} _ {j}\\\\right)\\\\right) \\\\in \\\\mathbb {N} ^ {l}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,620,905,700]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Suppose $\\\\pi_j: \\\\mathcal{E} \\\\to \\\\mathcal{E}_j$ is the canonical projection. If $\\\\mathrm{Mult}_{\\\\phi}(\\\\mathcal{D}, \\\\mathcal{E}_j) = (x_1, \\\\ldots, x_l)$ then the group homomorphism $K_0(\\\\pi_j \\\\circ \\\\phi): \\\\mathbb{Z}^l \\\\to \\\\mathbb{Z}$ sends $(y_1, \\\\ldots, y_l)$ to $\\\\sum_{i \\\\leq l} x_i y_i$ . Therefore if $\\\\phi, \\\\psi: \\\\mathcal{D} \\\\to \\\\mathcal{E}$ are homomorphisms, we have $K_0(\\\\phi) = K_0(\\\\psi)$ if and only if $\\\\mathrm{Mult}_{\\\\phi}(\\\\mathcal{D}, \\\\mathcal{E}_j) = \\\\mathrm{Mult}_{\\\\psi}(\\\\mathcal{D}, \\\\mathcal{E}_j)$ for every $j \\\\leq k$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,700,903,758]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The following well known facts about AF-algebras will be used several times throughout the article. We denote the unitization of $\\\\mathcal{A}$ by $\\\\widetilde{\\\\mathcal{A}}$ and if $u$ is a unitary in $\\\\widetilde{\\\\mathcal{A}}$ , then $\\\\mathrm{Ad}_u$ denotes the inner automorphisms of $\\\\mathcal{A}$ given by $a \\\\to u^*au$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,777,905,857]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 2.1. [4, Lemma III.3.2] Suppose $\\\\epsilon > 0$ and $\\\\{\\\\mathcal{A}_n\\\\}$ is an increasing sequence of finite-dimensional $C^*$ -algebras such that $\\\\mathcal{A} = \\\\overline{\\\\bigcup \\\\mathcal{A}_n}$ . If $\\\\mathcal{F}$ is a finite-dimensional subalgebra of $\\\\mathcal{A}$ , then there are $m \\\\in \\\\mathbb{N}$ and a unitary $u$ in $\\\\widetilde{\\\\mathcal{A}}$ such that $u^* \\\\mathcal{F} u \\\\subseteq \\\\mathcal{A}_m$ and $\\\\|1 - u\\\\| < \\\\epsilon$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,876,905,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 2.2. Suppose $\\\\mathcal{D}$ is a finite-dimensional $C^*$ -algebra, $\\\\mathcal{A}$ is a separable $AF$ -algebra and $\\\\phi, \\\\psi : \\\\mathcal{D} \\\\to \\\\mathcal{A}$ are homomorphisms such that $\\\\| \\\\phi - \\\\psi \\\\| < 1$ . Then there is a unitary $u \\\\in \\\\widetilde{\\\\mathcal{A}}$ such that $\\\\mathrm{Ad}_u \\\\circ \\\\psi = \\\\phi$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,64,96,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,63,798,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,105,918,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. We have $K_{0}(\\\\phi) = K_{0}(\\\\psi)$ , since otherwise for some nonzero projection $p$ in $\\\\mathcal{D}$ the dimensions of the projections $\\\\phi(p)$ and $\\\\psi(p)$ differ and hence $\\\\| \\\\psi - \\\\phi \\\\| \\\\geq 1$ . Therefore there is a unitary $u$ in $\\\\widetilde{\\\\mathcal{A}}$ such that $\\\\mathrm{Ad}_u \\\\circ \\\\psi = \\\\phi$ , by [15, Lemma 7.3.2]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,186,918,245]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 2.3. Suppose $\\\\mathcal{D} = \\\\mathcal{D}_1 \\\\oplus \\\\dots \\\\oplus \\\\mathcal{D}_l$ is a finite-dimensional $C^*$ -algebra, where each $\\\\mathcal{D}_i$ is a matrix algebra. Assume $\\\\gamma : \\\\mathcal{D} \\\\hookrightarrow M_k$ and $\\\\phi : \\\\mathcal{D} \\\\hookrightarrow M_\\\\ell$ are embeddings. The following are equivalent. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,264,916,345]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(1) There is an embedding $\\\\\\\\delta : M_k \\\\\\\\hookrightarrow M_\\\\\\\\ell$ such that $\\\\\\\\delta \\\\\\\\circ \\\\\\\\gamma = \\\\\\\\phi$ . \\\",\\\"(2) There is an embedding $\\\\\\\\delta : M_k \\\\\\\\hookrightarrow M_\\\\\\\\ell$ such that $\\\\\\\\| \\\\\\\\delta \\\\\\\\circ \\\\\\\\gamma - \\\\\\\\phi \\\\\\\\| < 1$ . \\\",\\\"(3) There is a natural number $c \\\\\\\\geq 1$ such that $\\\\\\\\ell \\\\\\\\geq ck$ and $\\\\\\\\mathrm{Mult}_{\\\\\\\\phi}(\\\\\\\\mathcal{D}, M_{\\\\\\\\ell}) = c \\\\\\\\mathrm{Mult}_{\\\\\\\\gamma}(\\\\\\\\mathcal{D}, M_{k})$ . \\\"]\",\n \"page_idx\": \"6\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[89,364,719,385]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. (1) trivially implies (2). To see $(2)\\\\Rightarrow (3)$ , note that we have \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,408,732,429]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\operatorname {M u l t} _ {\\\\phi} \\\\left(\\\\mathcal {D} _ {i}, M _ {\\\\ell}\\\\right) = \\\\operatorname {M u l t} _ {\\\\delta} \\\\left(M _ {k}, M _ {\\\\ell}\\\\right) \\\\operatorname {M u l t} _ {\\\\gamma} \\\\left(\\\\mathcal {D} _ {i}, M _ {k}\\\\right),\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,450,918,529]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"for every $i \\\\leq l$ , since otherwise $\\\\| \\\\delta \\\\circ \\\\gamma - \\\\phi \\\\| \\\\geq 1$ . Let $c = \\\\mathrm{Mult}_{\\\\delta}(M_k, M_\\\\ell)$ . To see $(3) \\\\Rightarrow (1)$ , let $\\\\delta': M_k \\\\to M_l$ be the embedding which sends an element of $M_k$ to $c$ many identical copies of it along the diagonal of $M_\\\\ell$ . Then we have $K_0(\\\\phi) = K_0(\\\\delta' \\\\circ \\\\gamma)$ , by the assumption of (3). Therefore there is a unitary $u$ in $M_\\\\ell$ such that $\\\\mathrm{Ad}_u \\\\circ \\\\delta' \\\\circ \\\\gamma = \\\\phi$ . Let $\\\\delta = \\\\mathrm{Ad}_u \\\\circ \\\\delta'$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,552,584,572]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. AF-algebras with left-invertible connecting maps \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,595,918,655]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Suppose $\\\\mathcal{A},\\\\mathcal{B}$ are $C^*$ -algebras. A homomorphism $\\\\phi :\\\\mathcal{B}\\\\to \\\\mathcal{A}$ is left-invertible if there is a (necessarily surjective) homomorphism $\\\\pi :\\\\mathcal{A}\\\\twoheadrightarrow \\\\mathcal{B}$ such that $\\\\pi \\\\circ \\\\phi = \\\\mathrm{id}_{\\\\mathcal{B}}$ . Clearly a left-invertible homomorphism is necessarily an embedding. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,675,918,735]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Definition 3.1. We say $\\\\mathcal{B}$ is a retract of $\\\\mathcal{A}$ if there is a left-invertible embedding from $\\\\mathcal{B}$ into $\\\\mathcal{A}$ . We say a subalgebra $\\\\mathcal{B}$ of $\\\\mathcal{A}$ is an inner retract if and only if there is a homomorphism $\\\\theta: \\\\mathcal{A} \\\\twoheadrightarrow \\\\mathcal{B}$ such that $\\\\theta|_{\\\\mathcal{B}} = \\\\mathrm{id}_{\\\\mathcal{B}}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,755,918,855]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The image of a left-invertible embedding $\\\\phi : \\\\mathcal{B} \\\\hookrightarrow \\\\mathcal{A}$ is an inner retract of $\\\\mathcal{A}$ . Note that $\\\\mathcal{B}$ is a retract of $\\\\mathcal{A}$ if and only if $\\\\mathcal{A}$ is a split-extension of $\\\\mathcal{B}$ . The next proposition contains some elementary facts about retracts of finite-dimensional $C^*$ -algebras and left-invertible maps between them. They follow from elementary facts about finite-dimensional $C^*$ -algebras, e.g., matrix algebras are simple. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,876,918,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proposition 3.2. A $C^*$ -algebra $\\\\mathcal{D}$ is a retract of a finite-dimensional $C^*$ -algebra $\\\\mathcal{E}$ if and only if $\\\\mathcal{E} \\\\cong \\\\mathcal{D} \\\\oplus \\\\mathcal{F}$ , for some finite-dimensional $C^*$ -algebra $\\\\mathcal{F}$ . In other words, $\\\\mathcal{D}$ is a retract of $\\\\mathcal{E}$ if and only if $\\\\mathcal{D}$ is isomorphic to an ideal of $\\\\mathcal{E}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[903,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[81,105,905,163]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Suppose $\\\\phi : \\\\mathcal{D} \\\\hookrightarrow \\\\mathcal{E}$ is a (unital) left-invertible embedding and $\\\\pi : \\\\mathcal{E} \\\\to \\\\mathcal{D}$ is a left inverse of $\\\\phi$ . Then $\\\\mathcal{E}$ can be written as $\\\\mathcal{E}_0 \\\\oplus \\\\mathcal{E}_1$ and there are $\\\\phi_0, \\\\phi_1$ such that $\\\\phi_0 : \\\\mathcal{D} \\\\to \\\\mathcal{E}_0$ is an isomorphism, $\\\\phi_1 : \\\\mathcal{D} \\\\to \\\\mathcal{E}_1$ is a (unital) homomorphism and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,183,569,222]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- $\\\\\\\\phi(d) = (\\\\\\\\phi_0(d), \\\\\\\\phi_1(d))$ , for every $d \\\\\\\\in \\\\\\\\mathcal{D}$ , \\\",\\\"- $\\\\\\\\pi(e_0, e_1) = \\\\\\\\phi_0^{-1}(e_0)$ , for every $(e_0, e_1) \\\\\\\\in \\\\\\\\mathcal{E}_0 \\\\\\\\oplus \\\\\\\\mathcal{E}_1$ . \\\"]\",\n \"page_idx\": \"7\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[81,242,905,322]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Suppose $(\\\\mathcal{A}_n,\\\\phi_n^m)$ is a sequence where each connecting map $\\\\phi_n^m:\\\\mathcal{A}_n\\\\hookrightarrow \\\\mathcal{A}_m$ is left-invertible. Let $\\\\pi_n^{n + 1}:\\\\mathcal{A}_{n + 1}\\\\twoheadrightarrow \\\\mathcal{A}_n$ be a left inverse of $\\\\phi_n^{n + 1}$ , for each $n$ . For $m > n$ define $\\\\pi_n^m:\\\\mathcal{A}_m\\\\twoheadrightarrow \\\\mathcal{A}_n$ by $\\\\pi_n^m = \\\\pi_n^{n + 1}\\\\circ \\\\dots \\\\circ \\\\pi_{m - 1}^m$ . Then $\\\\pi_n^m$ is a left inverse of $\\\\phi_n^m$ which satisfies $\\\\pi_n^m\\\\circ \\\\pi_m^k = \\\\pi_n^k$ , for every $n\\\\leq m\\\\leq k$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,338,905,417]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Definition 3.3. We say $(\\\\mathcal{A}_n,\\\\phi_n^m)$ is a left-invertible sequence if each $\\\\phi_n^m$ is left-invertible and $\\\\phi_n^n = \\\\mathrm{id}_{\\\\mathcal{A}_n}$ . We call $(\\\\pi_n^m)$ a compatible left inverse of the left-invertible sequence $(\\\\mathcal{A}_n,\\\\phi_n^m)$ if $\\\\pi_n^m:\\\\mathcal{A}_m\\\\to \\\\mathcal{A}_n$ are surjective homomorphisms such that $\\\\pi_n^m\\\\circ \\\\pi_m^k = \\\\pi_n^k$ and $\\\\pi_n^m\\\\circ \\\\phi_n^m = \\\\mathrm{id}_{\\\\mathcal{A}_n}$ , for every $n\\\\leq m\\\\leq k$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,433,867,454]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The following simple lemma is true for arbitrary categories, see [10, Lemma 6.2]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,470,905,550]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 3.4. Suppose $(\\\\mathcal{A}_n,\\\\phi_n^m)$ is a left-invertible sequence of $C^*$ -algebras with a compatible left inverse $(\\\\pi_n^m)$ and $\\\\mathcal{A} = \\\\varinjlim (\\\\mathcal{A}_n,\\\\phi_n^m)$ . Then for every $n$ there are surjective homomorphisms $\\\\pi_n^\\\\infty : \\\\mathcal{A} \\\\to \\\\mathcal{A}_n$ such that $\\\\pi_n^\\\\infty \\\\circ \\\\phi_n^\\\\infty = \\\\mathrm{id}_{\\\\mathcal{A}_n}$ and $\\\\pi_n^m \\\\circ \\\\pi_m^\\\\infty = \\\\pi_n^\\\\infty$ for each $n \\\\leq m$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,566,903,605]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. First define $\\\\pi_n^\\\\infty$ on $\\\\bigcup_{i} \\\\phi_i^\\\\infty[\\\\mathcal{A}_i]$ , which is dense in $\\\\mathcal{A}$ . If $a = \\\\phi_m^\\\\infty(a_m)$ for some $m$ and $a_m \\\\in \\\\mathcal{A}_m$ , then let \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[346,622,635,670]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\pi_ {n} ^ {\\\\infty} (a) = \\\\left\\\\{ \\\\begin{array}{l l} \\\\pi_ {n} ^ {m} (a _ {m}) & \\\\text {i f} n \\\\leq m \\\\\\\\ \\\\phi_ {m} ^ {n} (a _ {m}) & \\\\text {i f} n > m \\\\end{array} \\\\right.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,685,903,723]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"These maps are well-defined (norm-decreasing) homomorphism, so they extend to $\\\\mathcal{A}$ and satisfy the requirements of the lemma. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,742,903,777]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In particular, each $\\\\mathcal{A}_n$ or any retract of it, is a retract of $\\\\mathcal{A}$ . The converse of this is also true. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,797,903,838]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 3.5. Suppose $(\\\\mathcal{A}_n,\\\\phi_n^m)$ is a left-invertible sequence of finite-dimensional $C^*$ -algebras with $\\\\mathcal{A} = \\\\varinjlim (\\\\mathcal{A}_n,\\\\phi_n^m)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[83,857,905,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(1) If $\\\\\\\\mathcal{D}$ is a finite-dimensional subalgebra of $\\\\\\\\mathcal{A}$ , then $\\\\\\\\mathcal{D}$ is contained in an inner retract of $\\\\\\\\mathcal{A}$ . \\\",\\\"(2) If $\\\\\\\\mathcal{D}$ is a finite-dimensional retract of $\\\\\\\\mathcal{A}$ , then there is $m \\\\\\\\in \\\\\\\\mathbb{N}$ such that $\\\\\\\\mathcal{D}$ is a retract of $\\\\\\\\mathcal{A}_{m'}$ for every $m' \\\\\\\\geq m$ . \\\"]\",\n \"page_idx\": \"7\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[81,64,96,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,63,798,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,105,635,125]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Let $(\\\\pi_n^m)$ be a compatible left inverse of $(A_n,\\\\phi_n^m)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[87,126,916,220]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(1) If $\\\\\\\\mathcal{D}$ is a finite-dimensional subalgebra of $\\\\\\\\mathcal{A}$ , then for some $m \\\\\\\\in \\\\\\\\mathbb{N}$ and a unitary $u \\\\\\\\in \\\\\\\\widetilde{\\\\\\\\mathcal{A}}$ , it is contained in $u\\\\\\\\phi_m^\\\\\\\\infty[\\\\\\\\mathcal{A}_m]u^*$ (Lemma 2.1). The latter is an inner retract of $\\\\\\\\mathcal{A}$ . \\\",\\\"(2) If $\\\\\\\\mathcal{D}$ is a retract of $\\\\\\\\mathcal{A}$ , there is an embedding $\\\\\\\\phi : \\\\\\\\mathcal{D} \\\\\\\\hookrightarrow \\\\\\\\mathcal{A}$ with a left inverse $\\\\\\\\pi : \\\\\\\\mathcal{A} \\\\\\\\twoheadrightarrow \\\\\\\\mathcal{D}$ . Find $m$ and a unitary $u$ in $\\\\\\\\widetilde{\\\\\\\\mathcal{A}}$ such that $u^{*}\\\\\\\\phi[\\\\\\\\mathcal{D}]u \\\\\\\\subseteq \\\\\\\\phi_{m}^{\\\\\\\\infty}[\\\\\\\\mathcal{A}_{m}]$ . This implies that \\\"]\",\n \"page_idx\": \"8\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[361,242,648,263]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\phi_ {m} ^ {\\\\infty} \\\\circ \\\\pi_ {m} ^ {\\\\infty} (u ^ {*} \\\\phi (d) u) = u ^ {*} \\\\phi (d) u\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,279,916,317]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"for every $d \\\\in \\\\mathcal{D}$ . Define $\\\\psi : \\\\mathcal{D} \\\\hookrightarrow \\\\mathcal{A}_m$ by $\\\\psi(d) = \\\\pi_m^\\\\infty(u^*\\\\phi(d)u)$ . Then $\\\\psi$ has a left inverse $\\\\theta : \\\\mathcal{A}_m \\\\twoheadrightarrow \\\\mathcal{D}$ defined by $\\\\theta(x) = \\\\pi(u\\\\phi_m^\\\\infty(x)u^*)$ , since for every $d \\\\in \\\\mathcal{D}$ we have \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[169,336,835,357]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\theta (\\\\psi (d)) = \\\\theta (\\\\pi_ {m} ^ {\\\\infty} (u ^ {*} \\\\phi (d) u)) = \\\\pi (u \\\\phi_ {m} ^ {\\\\infty} \\\\circ \\\\pi_ {m} ^ {\\\\infty} (u ^ {*} \\\\phi (d) u) u ^ {*}) = \\\\pi (\\\\phi (d)) = d.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,373,916,411]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Because $\\\\mathcal{A}_m$ is a retract of $\\\\mathcal{A}_{m'}$ , for every $m' \\\\geq m$ , we conclude that $\\\\mathcal{D}$ is also a retract of $\\\\mathcal{A}_{m'}$ . $\\\\square$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,430,918,647]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 3.6. It is not surprising that many AF-algebras are not limits of left-invertible sequences of finite-dimensional $C^*$ -algebras. This is because, for instance, such an AF-algebra has infinitely many ideals (unless it is finite-dimensional), and admits finite traces, as it maps onto finite-dimensional $C^*$ -algebras. Therefore, for example $\\\\mathcal{K}(\\\\ell_2)$ , the $C^*$ -algebra of all compact operators on $\\\\ell_2$ , and infinite-dimensional UHF-algebras are not limits of left-invertible sequences of finite-dimensional $C^*$ -algebras. Recall that a $C^*$ -algebra is stable if its tensor product with $\\\\mathcal{K}(\\\\ell_2)$ is isomorphic to itself. Blackadar's characterization of stable AF-algebras [2] (see also [16, Corollary 1.5.8]) states that a separable AF-algebra $\\\\mathcal{A}$ is stable if and only if no nonzero ideal of $\\\\mathcal{A}$ admits a nonzero finite (bounded) trace. Therefore no stable AF-algebra is the limit of a left-invertible sequence of finite-dimensional $C^*$ -algebras. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,664,916,723]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The following proposition gives another criteria to distinguish these AF-algebras. For example, it can be directly used to show that infinite-dimensional UHF-algebras are not limits of left-invertible sequences of finite-dimensional $C^*$ -algebras. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,741,918,842]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proposition 3.7. Suppose $\\\\mathcal{A}$ is an $AF$ -algebra isomorphic to the limit of a left-invertible sequence of finite-dimensional $C^*$ -algebras and $\\\\mathcal{A} = \\\\overline{\\\\bigcup_{n} \\\\mathcal{B}_{n}}$ for an increasing sequence $(\\\\mathcal{B}_n)$ of finite-dimensional subalgebras. Then there is an increasing sequence $(n_i)$ of natural numbers and an increasing sequence $(\\\\mathcal{C}_i)$ of finite-dimensional subalgebras of $\\\\mathcal{A}$ such that $\\\\mathcal{A} = \\\\overline{\\\\bigcup_{n} \\\\mathcal{C}_n}$ and $\\\\mathcal{B}_{n_i} \\\\subseteq \\\\mathcal{C}_i \\\\subseteq \\\\mathcal{B}_{n_{i+1}}$ and $\\\\mathcal{C}_i$ is an inner retract of $\\\\mathcal{C}_{i+1}$ for every $i \\\\in \\\\mathbb{N}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,857,916,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Suppose $\\\\mathcal{A}$ is the limit of a left-invertible direct sequence $(\\\\mathcal{A}_n, \\\\phi_n^m)$ of finite-dimensional $C^*$ -algebras. Theorem III.3.5 of [4], applied to sequences $(\\\\mathcal{B}_n)$ and $(\\\\phi_n^\\\\infty[\\\\mathcal{A}_n])$ , shows that there are sequences $(n_i)$ , $(m_i)$ of natural numbers and a unitary $u \\\\in \\\\widetilde{A}$ such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[903,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"9 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[355,105,623,126]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {B} _ {n _ {i}} \\\\subseteq u ^ {*} \\\\phi_ {m _ {i}} ^ {\\\\infty} [ \\\\mathcal {A} _ {m _ {i}} ] u \\\\subseteq \\\\mathcal {B} _ {n _ {i + 1}}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,142,490,161]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"for every $i\\\\in \\\\mathbb{N}$ . Let $\\\\mathcal{C}_i = u^*\\\\phi_{m_i}^\\\\infty [\\\\mathcal{A}_{m_i}]u$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,179,903,217]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, the next proposition shows that any AF-algebra is a quotient of an AF-algebra which is the limit of a left-invertible sequence of finite-dimensional $C^*$ -algebras. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,235,905,292]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proposition 3.8. For every (unital) $AF$ -algebra $\\\\mathcal{B}$ there is a (unital) $AF$ -algebra $\\\\mathcal{A} \\\\supseteq \\\\mathcal{B}$ which is the limit of a (unital) left-invertible sequence of finite-dimensional $C^*$ -algebras and $\\\\mathcal{A} / \\\\mathcal{J} \\\\cong \\\\mathcal{B}$ for an essential ideal $\\\\mathcal{J}$ of $\\\\mathcal{A}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,311,903,348]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Suppose $\\\\mathcal{B}$ is the limit of the sequence $(\\\\mathcal{B}_n, \\\\psi_n^m)$ of finite-dimensional $C^*$ -algebras and homomorphisms. Let $\\\\mathcal{A}$ denote the limit of the following diagram: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[241,364,663,511]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{c} \\\\mathcal {B} _ {1} \\\\xrightarrow [ i d ]{\\\\psi_ {1} ^ {2}} \\\\mathcal {B} _ {2} \\\\xrightarrow [ i d ]{\\\\psi_ {2} ^ {3}} \\\\mathcal {B} _ {3} \\\\xrightarrow [ i d ]{\\\\psi_ {3} ^ {4}} \\\\mathcal {B} _ {4} \\\\dots \\\\\\\\ \\\\mathcal {B} _ {1} \\\\xrightarrow [ i d ]{\\\\mathcal {B} _ {2}} \\\\mathcal {B} _ {1} \\\\xrightarrow [ i d ]{\\\\mathcal {B} _ {2}} \\\\mathcal {B} _ {2} \\\\dots \\\\\\\\ \\\\mathcal {B} _ {1} \\\\xrightarrow [ i d ]{\\\\mathcal {B} _ {2}} \\\\mathcal {B} _ {2} \\\\dots \\\\\\\\ \\\\mathcal {B} _ {1} \\\\xrightarrow [ i d ]{\\\\mathcal {B} _ {2}} \\\\mathcal {B} _ {1} \\\\dots \\\\\\\\ \\\\mathcal {B} _ {1} \\\\dots \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,526,907,604]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Then $\\\\mathcal{A}$ is an AF-algebra which contains $\\\\mathcal{B}$ and the connecting maps are left-invertible embeddings. The ideal $\\\\mathcal{J}$ corresponding to the (directed and hereditary) subdiagram of the above diagram which contains all the nodes except the ones on the top line is essential and clearly $\\\\mathcal{A} / \\\\mathcal{J} \\\\cong \\\\mathcal{B}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,625,475,642]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. AF-algebras with the Cantor property \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,663,905,800]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We define the notion of the \\\"Cantor property\\\" for an AF-algebra. These algebras have properties which are, in a sense, generalizations of the ones satisfied (some trivially) by $C(2^{\\\\mathbb{N}})$ . It is easier to state these properties using the notation for Bratteli diagrams that we fixed in Section 2. For example, every node of the Bratteli diagram of $C(2^{\\\\mathbb{N}})$ splits in two, which here is generalized to \\\"each node splits into at least two nodes with the same dimension at some further stage\\\", which of course guarantees that there are no minimal projections in the limit algebra. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,817,905,877]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Definition 4.1. We say an AF-algebra $\\\\mathcal{A}$ has the Cantor property if there is a sequence $(\\\\mathcal{A}_n,\\\\phi_n^m)$ of finite-dimensional $C^*$ -algebras and embeddings such that $\\\\mathcal{A} = \\\\varinjlim (\\\\mathcal{A}_n,\\\\phi_n^m)$ and the Bratteli diagram $\\\\mathfrak{D}$ of $(\\\\mathcal{A}_n,\\\\phi_n^m)$ has the following properties: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,895,903,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(D0) For every $(n,s)\\\\in \\\\mathfrak{D}$ there is $(n + 1,t)\\\\in \\\\mathfrak{D}$ such that $\\\\dim (n,s) = \\\\dim (n + 1,t)$ and $(n,s)\\\\to (n + 1,t)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,63,104,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,61,796,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubiš / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,105,916,244]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(D1) For every $(n,s)\\\\\\\\in \\\\\\\\mathfrak{D}$ there are distinct nodes $(m,t),(m,t^{\\\\\\\\prime})\\\\\\\\in \\\\\\\\mathfrak{D}$ , for some $m > n$ , such that $\\\\\\\\dim (n,s) = \\\\\\\\dim (m,t) = \\\\\\\\dim (m,t^{\\\\\\\\prime})$ and $(n,s)\\\\\\\\to (m,t)$ and $(n,s)\\\\\\\\to (m,t^{\\\\\\\\prime})$ . \\\",\\\"(D2) For every $(n, s_1), \\\\\\\\ldots, (n, s_k), (n', s') \\\\\\\\in \\\\\\\\mathfrak{D}$ and $\\\\\\\\{x_1, \\\\\\\\ldots, x_k\\\\\\\\} \\\\\\\\subseteq \\\\\\\\mathbb{N}$ such that $\\\\\\\\sum_{i=1}^{k} x_i \\\\\\\\dim(n, s_i) \\\\\\\\leq \\\\\\\\dim(n', s')$ , there is $m \\\\\\\\geq n$ such that for some $(m, t) \\\\\\\\in \\\\\\\\mathfrak{D}$ we have $\\\\\\\\dim(m, t) = \\\\\\\\dim(n', s')$ and there are exactly $x_i$ distinct paths from $(n, s_i)$ to $(m, t)$ in $\\\\\\\\mathfrak{D}$ . \\\"]\",\n \"page_idx\": \"10\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[89,264,914,305]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Bratteli diagram of $C(2^{\\\\mathbb{N}})$ trivially satisfies these conditions and therefore $C(2^{\\\\mathbb{N}})$ has the Cantor property. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,327,918,508]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 4.2. Condition (D0) states that $(\\\\mathcal{A}_n,\\\\phi_n^m)$ is a left-invertible sequence. Dropping (D0) from Definition 4.1 does not change the definition (i.e., $\\\\mathcal{A}$ has the Cantor property if and only if it has a representing sequence satisfying (D1) and (D2)). This is because (D1) alone implies the existence of a left-invertible sequence with limit $\\\\mathcal{A}$ that still satisfies (D1) and (D2). In fact, $\\\\mathcal{A}$ has the Cantor property if and only if any representing sequence satisfies (D1) and (D2). However, we add (D0) for simplicity to make sure that $(\\\\mathcal{A}_n,\\\\phi_n^m)$ is already a left-invertible sequence, since, as we shall see later, being the limit of a left-invertible direct sequence of finite-dimensional $C^*$ -algebras is a crucial and helpful property of AF-algebras with the Cantor property. Condition (D2) can be rewritten as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,527,916,589]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(D2') For every ideal $\\\\mathcal{D}$ of some $\\\\mathcal{A}_n$ , if $M_{\\\\ell}$ is a retract of $\\\\mathcal{A}$ and $\\\\gamma : \\\\mathcal{D} \\\\hookrightarrow M_{\\\\ell}$ is an embedding, then there is $m \\\\geq n$ and $\\\\mathcal{A}_{m,t} \\\\subseteq \\\\mathcal{A}_m$ such that $\\\\mathcal{A}_{m,t} \\\\cong M_{\\\\ell}$ and $\\\\mathrm{Mult}_{\\\\phi_n^m}(\\\\mathcal{D}, \\\\mathcal{A}_{m,t}) = \\\\mathrm{Mult}_{\\\\gamma}(\\\\mathcal{D}, M_{\\\\ell})$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,608,914,647]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Definition 4.1 may be adjusted for unital AF-algebras where all the maps are considered to be unital. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,670,916,732]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Definition 4.3. A unital AF-algebra $\\\\mathcal{A}$ has the Cantor property if and only if it satisfies the conditions of Definition 4.1, where $\\\\phi_n^m$ are unital and in condition (D2) the inequality $\\\\sum_{i=1}^{k} x_i \\\\dim(n, s_i) \\\\leq \\\\dim(n', s')$ is replaced with equality. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,754,916,792]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proposition 4.4. Suppose $\\\\mathcal{A}$ is an $AF$ -algebra with Cantor property. If $\\\\mathcal{D}, \\\\mathcal{E}$ are finite-dimensional retracts of $\\\\mathcal{A}$ , then so is $\\\\mathcal{D} \\\\oplus \\\\mathcal{E}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,816,918,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Suppose $\\\\mathcal{D} = \\\\mathcal{D}_1 \\\\oplus \\\\mathcal{D}_2 \\\\oplus \\\\dots \\\\oplus \\\\mathcal{D}_l$ and $\\\\mathcal{E} = \\\\mathcal{E}_1 \\\\oplus \\\\mathcal{E}_2 \\\\oplus \\\\dots \\\\oplus \\\\mathcal{E}_k$ , where $\\\\mathcal{D}_i, \\\\mathcal{E}_i$ are isomorphic to matrix algebras. By Lemma 3.5 both $\\\\mathcal{D}$ and $\\\\mathcal{E}$ are retracts of some $\\\\mathcal{A}_m$ , which means that all $\\\\mathcal{D}_i$ and $\\\\mathcal{E}_i$ appear in $\\\\mathcal{A}_m$ as retracts (ideals). By (D1) and enlarging $m$ , if necessary, we can make sure these retracts in $\\\\mathcal{A}_m$ are orthogonal, meaning that $\\\\mathcal{A}_m \\\\cong \\\\mathcal{D} \\\\oplus \\\\mathcal{E} \\\\oplus \\\\mathcal{F}$ , for some finite-dimensional $C^*$ -algebra $\\\\mathcal{F}$ . Therefore $\\\\mathcal{D} \\\\oplus \\\\mathcal{E}$ is a retract of $\\\\mathcal{A}_m$ and as a result, it is a retract of $\\\\mathcal{A}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[895,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"11 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[77,105,905,185]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 4.5. Suppose $\\\\mathcal{A}$ is an $AF$ -algebra with the Cantor property, witnessed by $(\\\\mathcal{A}_n,\\\\phi_n^m)$ satisfying Definition 4.1 and $\\\\mathcal{E}$ is a finite-dimensional retract of $\\\\mathcal{A}$ . If $\\\\gamma :\\\\mathcal{A}_n\\\\hookrightarrow \\\\mathcal{E}$ is a left-invertible embedding then there are $m\\\\geq n$ and a left-invertible embedding $\\\\delta :\\\\mathcal{E}\\\\hookrightarrow \\\\mathcal{A}_m$ such that $\\\\delta \\\\circ \\\\gamma = \\\\phi_n^m$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,202,905,260]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Suppose $\\\\mathcal{A}_n = \\\\mathcal{A}_{n,1} \\\\oplus \\\\dots \\\\oplus \\\\mathcal{A}_{n,l}$ and $\\\\mathcal{E} = \\\\mathcal{E}_1 \\\\oplus \\\\mathcal{E}_2 \\\\oplus \\\\dots \\\\oplus \\\\mathcal{E}_k$ where $\\\\mathcal{E}_i$ and $\\\\mathcal{A}_{n,j}$ are all matrix algebras. Let $\\\\pi_i$ denote the canonical projection from $\\\\mathcal{E}$ onto $\\\\mathcal{E}_i$ . For every $i \\\\leq k$ put \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[344,279,638,300]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nY _ {i} = \\\\{j \\\\leq l: \\\\gamma [ \\\\mathcal {A} _ {n, j} ] \\\\cap \\\\mathcal {E} _ {i} \\\\neq 0 \\\\},\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,317,905,514]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and let $\\\\mathcal{A}_{n,Y_i} = \\\\bigoplus_{j\\\\in Y_i}\\\\mathcal{A}_{n,j}$ . Then $\\\\mathcal{A}_{n,Y_i}$ is an ideal (a retract) of $\\\\mathcal{A}_n$ and the map $\\\\gamma_{i}:\\\\mathcal{A}_{n,Y_{i}}\\\\hookrightarrow \\\\mathcal{E}_{i}$ , the restriction of $\\\\gamma$ to $\\\\mathcal{A}_{n,Y_i}$ composed with $\\\\pi_{i}$ , is an embedding. Since $\\\\mathcal{E}$ is a finite-dimensional retract of $\\\\mathcal{A}$ , it is a retract of some $\\\\mathcal{A}_{n'}$ (Lemma 3.5). So each $\\\\mathcal{E}_i$ is a retract of $\\\\mathcal{A}_{n'}$ . By applying (D2) for each $i\\\\leq k$ there are $m_{i}\\\\geq n$ and $(m_i,t_i)\\\\in \\\\mathfrak{D}$ such that $\\\\dim (m_i,t_i) = \\\\dim (\\\\mathcal{E}_i)$ and $\\\\mathrm{Mult}_{\\\\phi_n^{m_i}}(\\\\mathcal{A}_{n,Y_i},\\\\mathcal{A}_{m_i,t_i}) = \\\\mathrm{Mult}_{\\\\gamma_i}(\\\\mathcal{A}_{n,Y_i},\\\\mathcal{E}_i)$ . Let $m = \\\\max \\\\{m_i:i\\\\leq k\\\\}$ and by (D0) find $(m,s_i)$ such that $\\\\dim (m_i,t_i) = \\\\dim (m,s_i)$ and $(m_i,t_i)\\\\to (m,s_i)$ . Applying (D1) and possibly increasing $m$ allows us to make sure that $(m,s_i)\\\\neq (m,s_j)$ for distinct $i,j$ and therefore $\\\\mathcal{A}_{m,s_i}$ are pairwise orthogonal. Then $\\\\{\\\\mathcal{A}_{m,s_i}:i\\\\leq k\\\\}$ is a sequence of pairwise orthogonal subalgebras (retracts) of $\\\\mathcal{A}_m$ such that $\\\\mathcal{A}_{m,s_i}\\\\cong \\\\mathcal{E}_i$ and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[289,532,693,554]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathrm {M u l t} _ {\\\\phi_ {n} ^ {m}} (\\\\mathcal {A} _ {n, Y _ {i}}, \\\\mathcal {A} _ {m, s _ {i}}) = \\\\mathrm {M u l t} _ {\\\\gamma_ {i}} (\\\\mathcal {A} _ {n, Y _ {i}}, \\\\mathcal {E} _ {i}).\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,569,905,608]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"By Lemma 2.3 there are isomorphisms $\\\\delta_i : \\\\mathcal{E}_i \\\\hookrightarrow \\\\mathcal{A}_{m,s_i}$ such that $\\\\gamma_i \\\\circ \\\\delta_i$ is equal to the restriction of $\\\\phi_n^m$ to $\\\\mathcal{A}_{n,Y_i}$ projected onto $\\\\mathcal{A}_{m,s_i}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,610,905,685]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Suppose $1_{m}$ is the unit of $\\\\mathcal{A}_m$ and $q_{i}$ is the unit of $\\\\mathcal{A}_{m,s_i}$ . Each $q_{i}$ is a central projection of $\\\\mathcal{A}_m$ , because $\\\\mathcal{A}_{m,s_i}$ are ideals of $\\\\mathcal{A}_m$ . Since $\\\\gamma$ is left-invertible, for each $j \\\\leq l$ there is $k(j) \\\\leq k$ such that $\\\\mathcal{A}_{n,j} \\\\cong \\\\mathcal{E}_{k(j)}$ and $\\\\hat{\\\\gamma}_{j} = \\\\pi_{k(j)} \\\\circ \\\\gamma|_{\\\\mathcal{A}_{n,j}}$ is an isomorphism. Also for $j \\\\leq l$ let \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[340,705,642,727]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nX _ {j} = \\\\{i \\\\leq k: \\\\gamma [ \\\\mathcal {A} _ {n, j} ] \\\\cap \\\\mathcal {E} _ {i} \\\\neq 0 \\\\}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[79,742,177,758]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Note that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[83,782,306,841]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(1) $k(j)\\\\\\\\in X_{j}$ \\\",\\\"(2) $k(j^{\\\\\\\\prime})\\\\\\\\notin X_{j}$ if $j\\\\\\\\neq j^{\\\\\\\\prime}$ \\\",\\\"(3) $i\\\\\\\\in X_j\\\\\\\\Leftrightarrow j\\\\\\\\in Y_i$ \\\"]\",\n \"page_idx\": \"11\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[77,860,897,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $\\\\hat{\\\\delta}_j: \\\\mathcal{E}_{k(j)} \\\\to (1_m - \\\\sum_{i \\\\in X_j} q_i) \\\\mathcal{A}_m(1_m - \\\\sum_{i \\\\in X_j} q_i)$ be the homomorphism defined by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[263,900,719,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\hat {\\\\delta} _ {j} (e) = (1 _ {m} - \\\\sum_ {i \\\\in X _ {j}} q _ {i}) \\\\phi_ {n} ^ {m} (\\\\hat {\\\\gamma} _ {j} ^ {- 1} (e)) (1 _ {m} - \\\\sum_ {i \\\\in X _ {j}} q _ {i}).\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,63,104,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"12 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,61,796,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubiš / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,105,304,125]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Define $\\\\delta :\\\\mathcal{E}\\\\hookrightarrow \\\\mathcal{A}_m$ by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,141,802,163]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\delta (e _ {1}, \\\\ldots , e _ {k}) = \\\\hat {\\\\delta} _ {1} (e _ {k (1)}) + \\\\dots + \\\\hat {\\\\delta} _ {l} (e _ {k (l)}) + \\\\delta_ {1} (e _ {1}) + \\\\dots + \\\\delta_ {k} (e _ {k}).\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,179,916,236]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Since each $\\\\delta_{i}$ is an isomorphism, it is clear that $\\\\delta$ is left-invertible. To check that $\\\\delta \\\\circ \\\\gamma = \\\\phi_n^m$ , by linearity of the maps it is enough to check it only for $\\\\bar{a} = (0,\\\\dots ,0,a_j,0,\\\\dots ,0)\\\\in \\\\mathcal{A}_n$ . If $\\\\gamma (\\\\bar{a}) = (e_1,\\\\ldots ,e_k)$ then \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[402,254,603,302]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\ne _ {i} = \\\\left\\\\{ \\\\begin{array}{l l} 0 & i \\\\not \\\\in X _ {j} \\\\\\\\ \\\\gamma_ {i} (\\\\bar {a}) & i \\\\in X _ {j} \\\\end{array} \\\\right.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,317,914,354]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"for $i \\\\leq k$ . Also note that $e_{k(j)} = \\\\hat{\\\\gamma}_j(a_j)$ . Assume $X_{j} = \\\\{r_{1},\\\\ldots ,r_{\\\\ell}\\\\}$ . Then by (1)-(3) we have \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[130,370,875,467]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\delta \\\\circ \\\\gamma (\\\\bar {a}) = \\\\hat {\\\\delta} _ {j} (\\\\hat {\\\\gamma} _ {j} (a _ {j})) + \\\\delta_ {r _ {1}} (\\\\gamma_ {r _ {1}} (\\\\bar {a})) + \\\\dots + \\\\delta_ {r _ {\\\\ell}} (\\\\gamma_ {r _ {\\\\ell}} (\\\\bar {a})) \\\\\\\\ = \\\\left(1 _ {m} - \\\\sum_ {i \\\\in X _ {j}} q _ {i}\\\\right) \\\\phi_ {n} ^ {m} (\\\\bar {a}) \\\\left(1 _ {m} - \\\\sum_ {i \\\\in X _ {j}} q _ {i}\\\\right) + q _ {r _ {1}} \\\\phi_ {n} ^ {m} (\\\\bar {a}) q _ {r _ {1}} + \\\\dots + q _ {r _ {\\\\ell}} \\\\phi_ {n} ^ {m} (\\\\bar {a}) q _ {r _ {\\\\ell}} \\\\\\\\ = \\\\phi_ {n} ^ {m} (\\\\bar {a}). \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,485,372,502]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This completes the proof. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,523,695,542]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.1. $AF$ -algebras with the Cantor property are $C(2^{\\\\mathbb{N}})$ -absorbing \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,561,916,620]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Suppose $\\\\mathcal{A}$ is an AF-algebra with Cantor property. Define $\\\\mathcal{A}^{\\\\mathcal{C}}$ to be the limit of the sequence $(\\\\mathcal{B}_n, \\\\psi_n^m)$ such that $\\\\mathcal{B}_n = \\\\bigoplus_{i \\\\leq 2^{n-1}} \\\\mathcal{A}_n \\\\cong \\\\mathbb{C}^{2^{n-1}} \\\\otimes \\\\mathcal{A}_n$ and $\\\\psi_n^{n+1} = \\\\bigoplus_{i \\\\leq 2^n} \\\\phi_n^{n+1}$ , as shown in the following diagram \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[308,636,914,898]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0654/11241661d9696d702575633b3052b394f5b3a6a48163159e781882143c03477a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[89,914,702,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It is straightforward to check that $\\\\mathcal{A}^c\\\\cong \\\\mathcal{A}\\\\otimes C(2^{\\\\mathbb{N}})\\\\cong C(2^{\\\\mathbb{N}},\\\\mathcal{A})$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[895,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"13 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[77,105,466,125]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 4.6. $\\\\mathcal{A}^{\\\\mathcal{C}}$ has the Cantor property. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,141,907,217]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. We check that $(\\\\mathcal{B}_n, \\\\psi_n^m)$ satisfies (D0)-(D2). Each $\\\\psi_n^{n+1}$ is left-invertible, by Proposition 3.2 and since $\\\\phi_n^{n+1}$ is left-invertible, therefore (D0) holds. Conditions (D1) and (D2) are trivially satisfied by analyzing the Bratteli diagram (4.1), since $\\\\mathcal{A}$ satisfies them. $\\\\square$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,236,907,275]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 4.7. Suppose $\\\\mathcal{A}$ is an $AF$ -algebra with Cantor property. Then $\\\\mathcal{A} \\\\otimes C(2^{\\\\mathbb{N}})$ is isomorphic to $\\\\mathcal{A}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,291,907,351]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Identify $\\\\mathcal{A} \\\\otimes C(2^{\\\\mathbb{N}})$ with $\\\\mathcal{A}^{\\\\mathcal{C}}$ . Find sequences $(m_i)$ and $(n_i)$ of natural numbers and left-invertible embeddings $\\\\gamma_i : \\\\mathcal{A}_{n_i} \\\\hookrightarrow \\\\mathcal{B}_{m_{i+1}}$ and $\\\\delta_i : \\\\mathcal{B}_{n_i} \\\\hookrightarrow \\\\mathcal{A}_{m_i}$ such that $n_1 = m_1 = 1$ , $m_2 = 2$ and $\\\\gamma_1 = \\\\psi_1^2$ and the diagram below is commutative. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[139,364,905,448]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{c c c} \\\\mathcal {B} _ {1} \\\\xrightarrow {\\\\psi_ {1} ^ {2}} \\\\mathcal {B} _ {m _ {2}} \\\\xrightarrow {\\\\psi_ {m _ {2}} ^ {m _ {3}}} \\\\mathcal {B} _ {m _ {3}} \\\\xrightarrow {\\\\psi_ {m _ {3}} ^ {m _ {4}}} \\\\dots & \\\\mathcal {A} ^ {\\\\mathcal {C}} \\\\\\\\ \\\\Bigg \\\\| \\\\quad \\\\begin{array}{c c c} \\\\gamma_ {1} & \\\\searrow & \\\\searrow \\\\\\\\ & \\\\searrow & \\\\searrow \\\\\\\\ & \\\\phi_ {n _ {2}} ^ {n _ {2}} & \\\\end{array} \\\\Bigg \\\\| \\\\quad \\\\begin{array}{c c c} \\\\gamma_ {2} & \\\\searrow & \\\\searrow \\\\\\\\ & \\\\searrow & \\\\searrow \\\\\\\\ & \\\\phi_ {n _ {2}} ^ {n _ {3}} & \\\\end{array} \\\\Bigg \\\\| \\\\quad \\\\begin{array}{c c c} \\\\gamma_ {2} & \\\\searrow & \\\\searrow \\\\\\\\ & \\\\searrow & \\\\searrow \\\\\\\\ & \\\\phi_ {n _ {3}} ^ {n _ {4}} & \\\\end{array} \\\\Bigg \\\\| \\\\quad \\\\begin{array}{c c c} \\\\gamma_ {3} & \\\\searrow & \\\\searrow \\\\\\\\ & \\\\searrow & \\\\searrow \\\\\\\\ & \\\\phi_ {n _ {3}} ^ {n _ {4}} & \\\\end{array} \\\\Bigg \\\\| \\\\quad \\\\begin{array}{c c c} \\\\gamma_ {3} & \\\\searrow & \\\\searrow \\\\\\\\ & \\\\searrow & \\\\searrow \\\\\\\\ & \\\\phi_ {n _ {3}} ^ {n _ {4}} & - 1. 0 p t ] & \\\\end{array} \\\\\\\\ \\\\mathcal {A} _ {1} \\\\xrightarrow {\\\\gamma_ {1}} \\\\mathcal {A} _ {n _ {2}} \\\\xrightarrow {\\\\gamma_ {2}} \\\\mathcal {A} _ {n _ {3}} \\\\xrightarrow {\\\\phi_ {n _ {2}} ^ {n _ {3}}} \\\\dots & \\\\mathcal {\\\\downarrow} _ {\\\\phi} \\\\\\\\ & \\\\mathcal {A} \\\\end{array} \\\\tag {4.2}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,461,907,539]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The existence of such $\\\\gamma_{i}$ and $\\\\delta_{i}$ is guaranteed by Lemma 4.5, since each $\\\\mathcal{B}_i$ is a retract of $\\\\mathcal{A}$ , by Lemma 3.5 and Proposition 4.4, and of course each $\\\\mathcal{A}_i$ is a retract of $\\\\mathcal{B}_i$ . The universal property of inductive limits implies the existence of an isomorphism between $\\\\mathcal{A}$ and $\\\\mathcal{A}^{\\\\mathcal{C}}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,557,907,595]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 4.8. As we will see in section 7.2 the tensor products of two AF-algebras with Cantor property do not necessarily have the Cantor property. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,614,186,630]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.2. Ideals \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,652,907,770]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $\\\\mathcal{A} = \\\\varinjlim_{n}(\\\\mathcal{A}_n,\\\\phi_n^m)$ be an AF-algebra with Cantor property, such that the Bratteli diagram $\\\\mathfrak{D}$ of $(\\\\mathcal{A}_n,\\\\phi_n^m)$ satisfies (D0)-(D2) of Definition 4.1. Let $\\\\mathfrak{J}\\\\subseteq \\\\mathfrak{D}$ denote the Bratteli diagram of an ideal $\\\\mathcal{I}\\\\subseteq \\\\mathcal{A}$ . Put $\\\\mathcal{J}_n = \\\\bigoplus_{(n,s)\\\\in \\\\mathfrak{J}}\\\\mathcal{A}_{n,s}$ , which is an ideal (a retract) of $\\\\mathcal{A}_n$ . Then $\\\\mathcal{J} = \\\\varinjlim_{n}(\\\\mathcal{J}_n,\\\\phi_n^m|_{\\\\mathcal{J}_n})$ . It is automatic from the fact that $\\\\mathfrak{J}$ is a directed subdiagram of $\\\\mathfrak{D}$ that each $\\\\phi_n^m |_{\\\\mathcal{J}_n}:\\\\mathcal{J}_n\\\\hookrightarrow \\\\mathcal{J}_m$ is left-invertible and that $(\\\\mathcal{J}_n,\\\\phi_n^m|_{\\\\mathcal{J}_n})$ satisfies (D0)-(D2). In particular: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,786,907,825]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proposition 4.9. Any ideal of an $AF$ -algebra with Cantor property also has the Cantor property. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,841,907,880]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Here is another elementary fact about $C(2^{\\\\mathbb{N}})$ that is (essentially by Lemma 4.7) passed on to AF-algebras with Cantor property. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,897,907,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proposition 4.10. Suppose $\\\\mathcal{A}$ is an $AF$ -algebra with Cantor property and $\\\\mathcal{Q}$ is a quotient of $\\\\mathcal{A}$ . Then there is a surjection $\\\\eta : \\\\mathcal{A} \\\\twoheadrightarrow \\\\mathcal{Q}$ such that $\\\\ker(\\\\eta)$ is an essential ideal of $\\\\mathcal{A}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,64,104,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"14 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,63,796,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,105,918,289]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. It is enough to show that there is an essential ideal $\\\\mathcal{I}$ of $\\\\mathcal{A}$ such that $\\\\mathcal{A} / \\\\mathcal{I}$ is isomorphic to $\\\\mathcal{A}$ . In fact, we will show that there is an essential ideal $\\\\mathcal{I}$ of $\\\\mathcal{A}^{\\\\mathcal{C}}$ such that $\\\\mathcal{A}^{\\\\mathcal{C}} / \\\\mathcal{I}$ is isomorphic to $\\\\mathcal{A}$ . This is enough since $\\\\mathcal{A}^{\\\\mathcal{C}}$ is isomorphic to $\\\\mathcal{A}$ (Lemma 4.7). Let $\\\\mathfrak{D}$ be the Bratteli diagram of $\\\\mathcal{A}^{\\\\mathcal{C}}$ as in Diagram (4.1). Let $\\\\mathfrak{J}$ be the directed and hereditary subdiagram of $\\\\mathfrak{D}$ containing all the nodes in Diagram (4.1) except the lowest line. Being directed and hereditary, $\\\\mathfrak{J}$ corresponds to an ideal $\\\\mathcal{I}$ , which intersects any other directed and hereditary subdiagram of $\\\\mathfrak{D}$ . Therefore $\\\\mathcal{I}$ is an essential ideal of $\\\\mathcal{A}^{\\\\mathcal{C}}$ and $\\\\mathcal{A}^{\\\\mathcal{C}} / \\\\mathcal{I}$ is isomorphic to the limit of the sequence $\\\\mathcal{A}_1 \\\\xrightarrow{\\\\phi_1^2} \\\\mathcal{A}_2 \\\\xrightarrow{\\\\phi_2^3} \\\\mathcal{A}_3 \\\\xrightarrow{\\\\phi_3^4} \\\\ldots$ in the lowest line of Diagram (4.1), which is $\\\\mathcal{A}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,308,289,327]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5. Fraïssé categories \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,348,916,447]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Suppose $\\\\Re$ is a category of metric structures with non-expansive (1-Lipschitz) morphisms. We refer to objects and morphisms (arrows) of $\\\\Re$ by $\\\\Re$ -objects and $\\\\Re$ -arrows, respectively. We write $A \\\\in \\\\Re$ if $A$ is a $\\\\Re$ -object and $\\\\Re(A, B)$ to denote the set of all $\\\\Re$ -arrows from $A$ to $B \\\\in \\\\Re$ . The category $\\\\Re$ is metric-enriched or enriched over metric spaces if for every $\\\\Re$ -objects $A$ and $B$ there is a metric $d$ on $\\\\Re(A, B)$ satisfying \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[175,466,830,486]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nd (\\\\psi_ {0} \\\\circ \\\\phi , \\\\psi_ {1} \\\\circ \\\\phi) \\\\leq d (\\\\psi_ {0}, \\\\psi_ {1}) \\\\quad \\\\text {a n d} \\\\quad d (\\\\psi \\\\circ \\\\phi_ {0}, \\\\psi \\\\circ \\\\phi_ {0}) \\\\leq d (\\\\phi_ {0}, \\\\phi_ {1})\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,502,916,542]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"whenever the compositions make sense. We say $\\\\Re$ is enriched over complete metric spaces if $\\\\Re(A, B)$ is a complete metric space for every $\\\\Re$ -objects $A, B$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,542,916,580]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A $\\\\Re$ -sequence is a direct sequence in $\\\\Re$ , that is, a covariant functor from the category of all positive integers (treated as a poset) into $\\\\Re$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,582,916,641]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In our cases, $\\\\Re$ will always be a category of finite-dimensional $C^*$ -algebras with left-invertible embeddings. However, we would like to invoke the general theory of Fraïssé categories, which is possibly applicable to other similar contexts. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,660,543,677]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Definition 5.1. We say $\\\\Re$ is a Fraïssé category if \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[96,698,914,736]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(JEP) $\\\\Re$ has the joint embedding property: for $A, B \\\\in \\\\Re$ there is $C \\\\in \\\\Re$ such that $\\\\Re(A, C)$ and $\\\\Re(B, C)$ are nonempty. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,738,914,795]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(NAP) $\\\\Re$ has the near amalgamation property: for every $\\\\epsilon > 0$ , objects $A, B, C \\\\in \\\\Re$ , arrows $\\\\phi \\\\in \\\\Re(A, B)$ and $\\\\psi \\\\in \\\\Re(A, C)$ , there are $D \\\\in \\\\Re$ and $\\\\phi' \\\\in \\\\Re(B, D)$ and $\\\\psi' \\\\in \\\\Re(C, D)$ such that $d(\\\\phi' \\\\circ \\\\phi, \\\\psi' \\\\circ \\\\psi) < \\\\epsilon$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[96,798,826,814]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(SEP) $\\\\Re$ is separable: there is a countable dominating subcategory $\\\\mathfrak{C}$ , that is, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[167,817,914,875]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"for every $A\\\\\\\\in \\\\\\\\mathfrak{K}$ there is $C\\\\\\\\in \\\\\\\\mathfrak{C}$ and a $\\\\\\\\Re$ -arrow $\\\\\\\\phi :A\\\\\\\\to C$ \\\",\\\"- for every $\\\\\\\\epsilon > 0$ and a $\\\\\\\\mathfrak{K}$ -arrow $\\\\\\\\phi : A \\\\\\\\to B$ with $A \\\\\\\\in \\\\\\\\mathfrak{C}$ , there exist a $\\\\\\\\mathfrak{K}$ -arrow $\\\\\\\\psi : B \\\\\\\\to C$ with $\\\\\\\\mathcal{C} \\\\\\\\in \\\\\\\\mathfrak{C}$ and a $\\\\\\\\mathfrak{C}$ -arrow $\\\\\\\\alpha : A \\\\\\\\to C$ such that $d(\\\\\\\\alpha, \\\\\\\\psi \\\\\\\\circ \\\\\\\\phi) < \\\\\\\\epsilon$ . \\\"]\",\n \"page_idx\": \"14\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[89,897,918,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Now suppose that $\\\\Re$ is contained in a bigger metric-enriched category $\\\\mathfrak{L}$ so that every sequence in $\\\\Re$ has a limit in $\\\\mathfrak{L}$ . We say that $\\\\Re \\\\subseteq \\\\mathfrak{L}$ has the almost factorization property if \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[895,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"15 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[77,105,907,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"given any sequence $(X_{n},f_{n}^{m})$ in $\\\\Re$ with limit $X_{\\\\infty}$ in $\\\\mathfrak{L}$ , for every $\\\\epsilon >0$ , for every $\\\\mathfrak{L}$ -arrow $g\\\\colon A\\\\to X_{\\\\infty}$ with $A\\\\in \\\\Re$ there is a $\\\\Re$ -arrow $g^{\\\\prime}\\\\colon A\\\\to X_{n}$ for some positive integer $n$ , such that $d(f_n^\\\\infty \\\\circ g',g)\\\\leq \\\\epsilon$ , where $f_{n}^{\\\\infty}\\\\colon X_{n}\\\\to X_{\\\\infty}$ comes from the limiting cocone. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,185,907,225]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 5.2. [11, Theorem 3.3] Suppose $\\\\Re$ is a Fraïssé category. Then there exists a sequence $(U_n,\\\\phi_n^m)$ in $\\\\Re$ satisfying \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,245,905,283]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(F) for every $n \\\\in \\\\mathbb{N}$ , for every $\\\\epsilon > 0$ and for every $\\\\Re$ -arrow $\\\\gamma : U_n \\\\to D$ , there are $m \\\\geq n$ and a $\\\\Re$ -arrow $\\\\delta : D \\\\to U_m$ such that $d(\\\\phi_n^m, \\\\delta \\\\circ \\\\gamma) < \\\\epsilon$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,304,907,482]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If $\\\\Re$ is a Fraïssé category, the $\\\\Re$ -sequence $(U_n, \\\\phi_n^m)$ from Theorem 5.2 is uniquely determined by the \\\"Fraïssé condition\\\" (F). That is, any two $\\\\Re$ -sequences satisfying (F) can be approximately intertwined (there is an approximate back-and-forth between them), and hence the limits of the sequences (typically in a bigger category containing $\\\\Re$ ) must be isomorphic (see [11, Theorem 3.5]). Therefore the $\\\\Re$ -sequence satisfying (F) is usually referred to as \\\"the\\\" Fraïssé sequence. The limit of the Fraïssé sequence is called the Fraïssé limit of the category $\\\\Re$ . In our case, $\\\\Re$ will be a category of finite-dimensional $C^*$ -algebras and the limit is just the inductive limit (also called colimit) in the category of all (or just separable) $C^*$ -algebras. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,502,907,561]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 5.3 (cf. [11]). Assume $\\\\Re$ is a Fraïssé category contained in a category $\\\\mathfrak{L}$ such that every sequence in $\\\\Re$ has a limit in $\\\\mathfrak{L}$ and every $\\\\mathfrak{L}$ -object is the limit of some sequence in $\\\\Re$ . Let $U \\\\in \\\\mathfrak{L}$ be the Fraïssé limit of $\\\\Re$ . Then \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,583,751,620]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- (uniqueness) $U$ is unique, up to isomorphisms. \\\",\\\"- (universality) For every $\\\\\\\\mathfrak{L}$ -object $B$ there is an $\\\\\\\\mathfrak{L}$ -arrow $\\\\\\\\phi : B \\\\\\\\to U$ . \\\"]\",\n \"page_idx\": \"15\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[79,642,695,660]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Furthermore, if $\\\\Re \\\\subseteq \\\\mathfrak{L}$ has the almost factorization property then \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,680,907,720]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"- (almost $\\\\Re$ -homogeneity) For every $\\\\epsilon > 0$ , $\\\\Re$ -object $A$ and $\\\\mathfrak{L}$ -arrows $\\\\phi_i : A \\\\to U$ ( $i = 0,1$ ), there is an automorphism $\\\\eta : U \\\\to U$ such that $d(\\\\eta \\\\circ \\\\phi_0, \\\\phi_1) < \\\\epsilon$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[411,744,582,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0037/63d1e2144434cdb9e1cb46fd694f9bf90a18a1d2244cd443aeb7a466275c2b87.jpg\",\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[81,63,104,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"16 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,61,796,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubiš / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[77,880,905,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Formally, the limit, or rather colimit of $(X_{n},f_{n}^{m})$ is a pair consisting of an $\\\\mathfrak{L}$ -object $X_{\\\\infty}$ and a sequence of $\\\\mathfrak{L}$ -arrows $f_{n}^{\\\\infty}\\\\colon X_{n}\\\\to X_{\\\\infty}$ satisfying suitable conditions. This sequence is called the (co-)limiting cocone. We use the word \\\"limit\\\" instead of \\\"colimit\\\" as we consider only covariant functors from the positive integers, called sequences. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[89,105,918,205]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Definition 5.4. Let $\\\\ddagger\\\\mathfrak{K}$ denote the category with the same objects as $\\\\mathfrak{K}$ , but a $\\\\ddagger\\\\mathfrak{K}$ -arrow from $A$ to $B$ is a pair $(\\\\phi, \\\\pi)$ where $\\\\phi, \\\\pi$ are $\\\\mathfrak{K}$ -arrows, $\\\\phi: A \\\\to B$ is left-invertible and $\\\\pi: B \\\\to A$ is a left inverse of $\\\\phi$ . We will denote such $\\\\ddagger\\\\mathfrak{K}$ -arrow by $(\\\\phi, \\\\pi): A \\\\to B$ . The composition is $(\\\\phi, \\\\pi) \\\\circ (\\\\phi', \\\\pi') = (\\\\phi \\\\circ \\\\phi', \\\\pi' \\\\circ \\\\pi)$ . The category $\\\\ddagger\\\\mathfrak{K}$ is usually called the category of embedding-projection pairs or briefly EP-pairs over $\\\\mathfrak{K}$ (see [10]). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,225,916,283]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Definition 5.5. We say $\\\\ddagger\\\\mathfrak{K}$ has the near proper amalgamation property if for every $\\\\epsilon > 0$ , objects $A, B, C \\\\in \\\\mathfrak{K}$ , arrows $(\\\\phi, \\\\pi) \\\\in \\\\ddagger\\\\mathfrak{K}(A, B)$ and $(\\\\psi, \\\\theta) \\\\in \\\\ddagger\\\\mathfrak{K}(A, C)$ , there are $D \\\\in \\\\ddagger\\\\mathfrak{K}$ and $(\\\\phi', \\\\pi') \\\\in \\\\ddagger\\\\mathfrak{K}(B, D)$ and $(\\\\psi', \\\\theta') \\\\in \\\\ddagger\\\\mathfrak{K}(C, D)$ such that the diagram \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[404,305,603,419]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0790/f198be4e62f64e7c2b31a5e7c4c53848a74e96eb0f80a558e24b1051b6f58ec6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[89,438,916,498]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\\\"fully commutes\\\" up to $\\\\epsilon$ , meaning that $d(\\\\phi' \\\\circ \\\\phi, \\\\psi' \\\\circ \\\\psi)$ , $d(\\\\pi' \\\\circ \\\\pi, \\\\theta' \\\\circ \\\\theta)$ , $d(\\\\phi \\\\circ \\\\theta, \\\\pi' \\\\circ \\\\psi')$ and $d(\\\\psi \\\\circ \\\\pi, \\\\theta' \\\\circ \\\\phi')$ are all less than or equal to $\\\\epsilon$ . We say $\\\\S \\\\mathfrak{K}$ has the \\\"proper amalgamation property\\\" if $\\\\epsilon$ could be 0. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,517,916,577]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let us denote by $\\\\dagger \\\\Re$ the category of left-invertible $\\\\Re$ -arrows. In other words, $\\\\dagger \\\\Re$ is the image of $\\\\ddagger \\\\Re$ under the functor that forgets the left inverse, namely mapping $(\\\\phi, \\\\pi)$ to $\\\\phi$ . Note that all three categories $\\\\Re$ , $\\\\dagger \\\\Re$ , and $\\\\ddagger \\\\Re$ have the same objects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,595,918,675]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 5.6. Suppose $\\\\mathfrak{L}$ is enriched over complete metric spaces, $\\\\dagger \\\\Re$ is a Fraïssé category with Fraïssé limit $U$ , and $\\\\ddagger \\\\Re$ has the proper amalgamation property. Then for every $\\\\mathfrak{L}$ -object $B$ isomorphic to the limit of a sequence in $\\\\dagger \\\\Re$ there is a pair of $\\\\mathfrak{L}$ -arrows $\\\\alpha: B \\\\to U$ , $\\\\beta: U \\\\to B$ such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[441,698,563,717]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\beta \\\\circ \\\\alpha = \\\\operatorname {i d} _ {B}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,736,916,814]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Suppose $(U_n, \\\\phi_n^m)$ is a Fraïssé sequence in $\\\\dagger \\\\Re$ . Suppose first that the sequence satisfies (F) with $\\\\epsilon = 0$ and that $\\\\ddagger \\\\Re$ has the proper amalgamation property, namely with $\\\\epsilon = 0$ (this will be the case in the next section). In this case we do not use the fact that $\\\\mathfrak{L}$ is enriched over complete metric spaces. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,817,918,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Fix a $\\\\dagger\\\\mathfrak{K}$ -sequence $(B_n, \\\\psi_n^m)$ whose direct limit is $B$ . For each $n$ we may choose a left inverse $\\\\theta_n^{n+1}$ to $\\\\psi_n^{n+1}$ and next, setting $\\\\theta_n^m = \\\\theta_{m-1}^m \\\\circ \\\\dots \\\\circ \\\\theta_n^{n+1}$ for every $n < m$ , we obtain a $\\\\ddagger\\\\mathfrak{K}$ -sequence $(B_n, (\\\\psi_n^m, \\\\theta_n^m))$ whose direct limit is $B$ . Using (JEP) of $\\\\dagger\\\\mathfrak{K}$ and fixing arbitrary left inverses, find $F_1 \\\\in \\\\mathfrak{K}$ and $\\\\ddagger\\\\mathfrak{K}$ -arrows $(\\\\gamma_1, \\\\eta_1): U_1 \\\\to F_1$ and $(\\\\mu_1, \\\\nu_1): B_1 \\\\to F_1$ . By (F) and again fixing arbitrary left inverses, there are $n_1 \\\\geq 1$ and a $\\\\ddagger\\\\mathfrak{K}$ -arrow $(\\\\delta_1, \\\\lambda_1): F_1 \\\\to U_{n_1}$ such that $\\\\phi_1^{n_1} = \\\\delta_1 \\\\circ \\\\gamma_1$ (see Diagram (5.3) below). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[895,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"17 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[77,105,907,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Consider the composition arrow $(\\\\delta_1 \\\\circ \\\\mu_1, \\\\nu_1 \\\\circ \\\\lambda_1): B_1 \\\\to U_{n_1}$ and $(\\\\psi_1^2, \\\\theta_1^2): B_1 \\\\to B_2$ and use the proper amalgamation property to find $\\\\mathcal{F}_2 \\\\in \\\\Re$ and $\\\\ddagger\\\\Re$ -arrows $(\\\\mu_2, \\\\nu_2): B_2 \\\\to F_2$ and $(\\\\gamma_2, \\\\eta_2): U_{n_1} \\\\to F_2$ such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[226,180,903,201]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\gamma_ {2} \\\\circ \\\\delta_ {1} \\\\circ \\\\mu_ {1} = \\\\mu_ {2} \\\\circ \\\\psi_ {1} ^ {2} \\\\quad \\\\text {a n d} \\\\quad \\\\nu_ {2} \\\\circ \\\\gamma_ {2} = \\\\psi_ {1} ^ {2} \\\\circ \\\\nu_ {1} \\\\circ \\\\lambda_ {1}. \\\\tag {5.1}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[79,214,749,233]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Again using (F) we can find $n_2 \\\\geq n_1$ and $(\\\\delta_2, \\\\lambda_2): F_2 \\\\to U_{n_2}$ such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[423,251,901,272]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\phi_ {n _ {1}} ^ {n _ {2}} = \\\\delta_ {2} \\\\circ \\\\gamma_ {2}. \\\\tag {5.2}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,286,905,325]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Combining equations in (5.1) and (5.2) we have (also can be easily checked in Diagram (5.3)): \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[173,339,811,361]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\phi_ {n _ {1}} ^ {n _ {2}} \\\\circ \\\\delta_ {1} \\\\circ \\\\mu_ {1} = \\\\delta_ {2} \\\\circ \\\\mu_ {2} \\\\circ \\\\psi_ {1} ^ {2} \\\\qquad \\\\mathrm {a n d} \\\\qquad \\\\psi_ {1} ^ {2} \\\\circ \\\\nu_ {1} \\\\circ \\\\lambda_ {1} = \\\\nu_ {2} \\\\circ \\\\lambda_ {2} \\\\circ \\\\phi_ {n _ {1}} ^ {n _ {2}}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,376,907,433]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Again use the proper amalgamation property to find $F_{3} \\\\in \\\\mathfrak{K}$ and $(\\\\mu_3, \\\\nu_3): B_3 \\\\to F_3$ and $(\\\\gamma_3, \\\\eta_3): U_{n_2} \\\\to F_3$ . Follow the procedure, by finding $\\\\ddagger \\\\mathfrak{K}$ -arrow $(\\\\delta_3, \\\\lambda_3): F_3 \\\\to U_{n_3}$ , for some $n_3 \\\\geq n_2$ such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[177,450,805,470]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\phi_ {n _ {2}} ^ {n _ {3}} \\\\circ \\\\delta_ {2} \\\\circ \\\\mu_ {2} = \\\\delta_ {3} \\\\circ \\\\mu_ {3} \\\\circ \\\\psi_ {2} ^ {3} \\\\qquad \\\\text {a n d} \\\\qquad \\\\psi_ {2} ^ {3} \\\\circ \\\\nu_ {2} \\\\circ \\\\lambda_ {2} = \\\\nu_ {3} \\\\circ \\\\lambda_ {3} \\\\circ \\\\phi_ {n _ {2}} ^ {n _ {3}}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[111,476,903,632]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} U _ {1} \\\\xrightarrow {\\\\phi_ {1} ^ {n _ {1}}} U _ {n _ {1}} \\\\xrightarrow {\\\\phi_ {n _ {1}} ^ {n _ {2}}} U _ {n _ {2}} \\\\xrightarrow {\\\\phi_ {n _ {2}} ^ {n _ {3}}} U _ {n _ {3}} \\\\xrightarrow {\\\\phi_ {n _ {3}} ^ {n _ {4}}} \\\\dots U \\\\\\\\ B _ {1} \\\\xleftarrow {\\\\mu_ {1} \\\\nu_ {1} \\\\psi_ {1} ^ {2}} B _ {2} \\\\xleftarrow {\\\\mu_ {2} \\\\nu_ {2} \\\\psi_ {2} ^ {3}} B _ {3} \\\\xleftarrow {\\\\mu_ {3} \\\\nu_ {3} \\\\psi_ {3} ^ {4}} \\\\dots B \\\\end{array} \\\\Bigg | _ {\\\\beta}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,633,811,652]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $\\\\alpha_{i} = \\\\delta_{i}\\\\circ \\\\mu_{i}$ and $\\\\beta_{i}:\\\\nu_{i}\\\\circ \\\\lambda_{i}$ . By the construction, for every $i\\\\in \\\\mathbb{N}$ we have \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[211,667,770,689]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\phi_ {n _ {i}} ^ {n _ {i + 1}} \\\\circ \\\\alpha_ {i} = \\\\alpha_ {i + 1} \\\\circ \\\\psi_ {i} ^ {i + 1} \\\\quad \\\\text {a n d} \\\\quad \\\\psi_ {1} ^ {2} \\\\circ \\\\beta_ {i} = \\\\beta_ {i + 1} \\\\circ \\\\phi_ {n _ {i}} ^ {n _ {i + 1}}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,704,907,742]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and $\\\\beta_{i}$ is a left inverse of $\\\\alpha_{i}$ . Then $\\\\alpha = \\\\lim_{i}\\\\alpha_{i}$ is a well-defined arrow from $B$ to $U$ and $\\\\beta = \\\\lim_{i}\\\\beta_{i}$ is a well-defined arrow from $U$ onto $B$ such that $\\\\beta \\\\circ \\\\alpha = \\\\mathrm{id}_B$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,744,905,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, if $\\\\ddagger\\\\mathfrak{K}$ has the near proper amalgamation property and the sequence $(U_n,\\\\phi_n^m)$ satisfies (F) with arbitrary $\\\\epsilon >0$ , we repeat the arguments above, except that Diagram (5.3) is no longer commutative. On the other hand, at step $n$ we may choose $\\\\epsilon = 2^{-n}$ and then the arrows $\\\\alpha$ and $\\\\beta$ are obtained as limits of suitable Cauchy sequences in $\\\\mathfrak{L}(B,U)$ . This is the only place where we need to know that $\\\\mathfrak{L}$ is enriched over complete metric spaces. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,877,907,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let us mention that the concept of EP-pairs has been already used by Garbulińska-Wegrzyn [8] in the category of finite dimensional normed spaces, obtaining isometric uniqueness of a complementably universal Banach space. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,64,104,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,63,796,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[92,105,813,125]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6. Categories of finite-dimensional $C^*$ -algebras and left-invertible mappings \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,145,918,283]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this section $\\\\Re$ always denotes a (naturally metric-enriched) category whose objects are (not necessarily all) finite-dimensional $C^*$ -algebras, closed under isomorphisms, and $\\\\Re$ -arrows are left-invertible embeddings. For such $\\\\Re$ , let $\\\\mathfrak{L}\\\\Re$ denote the \\\"category of limits\\\" of $\\\\Re$ ; a category whose objects are limits of $\\\\Re$ -sequences and if $\\\\mathcal{B}$ and $\\\\mathcal{C}$ are $\\\\mathfrak{L}\\\\Re$ -objects, then an $\\\\mathfrak{L}\\\\Re$ -arrow from $\\\\mathcal{B}$ into $\\\\mathcal{C}$ is a left-invertible embedding $\\\\phi: \\\\mathcal{B} \\\\hookrightarrow \\\\mathcal{C}$ . Clearly $\\\\mathfrak{L}\\\\Re$ contains $\\\\Re$ as a full subcategory. The metric defined between $\\\\mathfrak{L}\\\\Re$ -arrows $\\\\phi$ and $\\\\psi$ with the same domain and codomain is $\\\\| \\\\phi - \\\\psi \\\\|$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,285,916,402]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For every such category $\\\\Re$ , let $\\\\widehat{\\\\mathfrak{K}}$ denote the category whose objects are exactly the objects of $\\\\Re$ , but the $\\\\widehat{\\\\mathfrak{K}}$ -morphisms are all homomorphisms between the objects. Then we can define the corresponding category of EP-pairs $\\\\ddagger \\\\widehat{\\\\mathfrak{K}}$ as in the previous section. In what follows, let us agree to write $\\\\ddagger \\\\mathfrak{K}$ instead of $\\\\ddagger \\\\widehat{\\\\mathfrak{K}}$ . Hence, the $\\\\ddagger \\\\mathfrak{K}$ -morphisms are of the form $(\\\\phi, \\\\pi)$ , where $\\\\phi$ is a $\\\\mathfrak{K}$ -morphism and $\\\\pi$ is a homomorphism which is a left inverse of $\\\\phi$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,422,916,541]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 6.1. If $\\\\Re$ is a category of finite-dimensional $C^*$ -algebras and embeddings, then it has the near amalgamation property (NAP) if and only if it has the amalgamation property ([5, Lemma 3.2]), namely, with $\\\\epsilon = 0$ . Similarly, the near proper amalgamation property of $\\\\ddagger \\\\Re$ is equivalent to the proper amalgamation property of $\\\\ddagger \\\\Re$ . Also in this case, the Fraïssé sequence $(\\\\mathcal{U}_n, \\\\phi_n^m)$ , whenever it exists for $\\\\Re$ , satisfies the Fraïssé condition (F) of Theorem 5.2 with $\\\\epsilon = 0$ . Therefore in this section (F) refers to the following condition. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,561,916,601]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(F) for every $n \\\\in \\\\mathbb{N}$ and for every $\\\\mathfrak{K}$ -arrow $\\\\gamma : \\\\mathcal{U}_n \\\\to \\\\mathcal{D}$ , there are $m \\\\geq n$ and $\\\\mathfrak{K}$ -arrow $\\\\delta : \\\\mathcal{D} \\\\to \\\\mathcal{U}_m$ such that $\\\\phi_n^m = \\\\delta \\\\circ \\\\gamma$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,620,640,639]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 6.2. $\\\\mathfrak{K} \\\\subseteq \\\\mathfrak{L}\\\\mathfrak{K}$ has the almost factorization property. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,658,918,797]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Suppose $\\\\mathcal{B} \\\\in \\\\mathfrak{L}\\\\mathfrak{K}$ is the limit of the $\\\\mathfrak{K}$ -sequence $(\\\\mathcal{B}_n, \\\\psi_n^m)$ and $(\\\\theta_n^m)$ is a compatible left inverse of $(\\\\psi_n^{n+1})$ . Assume $\\\\mathcal{D}$ is a $\\\\mathfrak{K}$ -object and $\\\\phi: \\\\mathcal{D} \\\\hookrightarrow \\\\mathcal{B}$ is an $\\\\mathfrak{L}\\\\mathfrak{K}$ -arrow with a left inverse $\\\\pi: \\\\mathcal{B} \\\\twoheadrightarrow \\\\mathcal{D}$ . For given $\\\\epsilon > 0$ , find $n$ and a unitary $u$ in $\\\\widetilde{\\\\mathcal{B}}$ such that $u^* \\\\phi[\\\\mathcal{D}] u \\\\subseteq \\\\psi_n^\\\\infty[\\\\mathcal{B}_n]$ and $\\\\|u - 1\\\\| < \\\\epsilon/2$ (Lemma 2.1). Define $\\\\psi: \\\\mathcal{D} \\\\hookrightarrow \\\\mathcal{B}_n$ by $\\\\psi(d) = \\\\theta_n^\\\\infty(u^* \\\\phi(d) u)$ . Then $\\\\psi$ has a left inverse $\\\\theta: \\\\mathcal{B}_n \\\\twoheadrightarrow \\\\mathcal{D}$ defined by $\\\\theta(x) = \\\\pi(u \\\\psi_n^\\\\infty(x) u^*)$ (see the proof of Lemma 3.5 (2)). Condition $\\\\|u - 1\\\\| < \\\\epsilon/2$ implies that $\\\\| \\\\psi_n^\\\\infty(\\\\psi(d)) - \\\\phi(d) \\\\| < \\\\epsilon$ , for every $d$ in the unit ball of $\\\\mathcal{D}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,817,346,836]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 6.3. $\\\\Re$ is separable. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,855,918,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. There are, up to isomorphisms, countably many $\\\\mathfrak{K}$ -objects, namely finite sums of matrix algebras. The set of all embeddings between two fixed finite-dimensional $C^*$ -algebras is a separable metric space. Thus, $\\\\mathfrak{K}$ trivially has a countable dominating subcategory. $\\\\square$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[895,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"19 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[104,105,698,125]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The following statement is a direct consequence of Lemma 5.6. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,144,905,202]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Corollary 6.4. Suppose $\\\\Re$ is a Fraïssé category of $C^*$ -algebras with the Fraïssé limit $\\\\mathcal{U}$ and $\\\\ddagger\\\\Re$ has the proper amalgamation property. Then $\\\\mathcal{U}$ is a split-extension of every $AF$ -algebra $\\\\mathcal{B}$ in $\\\\mathfrak{L}\\\\Re$ . In particular, $\\\\mathcal{U}$ maps onto any $AF$ -algebra in $\\\\mathfrak{L}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,225,595,242]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7. AF-algebras with Cantor property as Fraïssé limits \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,266,905,304]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Suppose $\\\\Re$ is a category of (not necessarily all) finite-dimensional $C^*$ -algebras, closed under isomorphisms, and $\\\\Re$ -arrows are left-invertible embeddings. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,325,775,342]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Definition 7.1. We say $\\\\Re$ is $\\\\oplus$ -stable if it satisfies the following conditions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,364,623,401]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(1) If $\\\\\\\\mathcal{D}$ is a $\\\\\\\\Re$ -object, then so is any retract (ideal) of $\\\\\\\\mathcal{D}$ , \\\",\\\"(2) $\\\\\\\\mathcal{D} \\\\\\\\oplus \\\\\\\\mathcal{E} \\\\\\\\in \\\\\\\\mathfrak{K}$ whenever $\\\\\\\\mathcal{D}, \\\\\\\\mathcal{E} \\\\\\\\in \\\\\\\\mathfrak{K}$ . \\\"]\",\n \"page_idx\": \"19\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[77,423,905,501]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In general 0 is a retract of any $C^*$ -algebra and therefore it is the initial object of any $\\\\oplus$ -stable category, unless, when working with the unital categories (when all the $\\\\mathfrak{K}$ -arrows are unital), which in that case 0 is not a $\\\\mathfrak{K}$ -object anymore. Unital categories are briefly discussed in Section 9. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,522,905,560]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 7.2. Suppose $\\\\Re$ is a $\\\\oplus$ -stable category. Then $\\\\ddagger \\\\Re$ has the proper amalgamation property. In particular, $\\\\Re$ is a Fraïssé category. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,580,905,639]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Suppose $\\\\mathcal{D},\\\\mathcal{E}$ and $\\\\mathcal{F}$ are $\\\\Re$ -objects and $\\\\ddagger \\\\aleph$ -arrows $(\\\\phi ,\\\\pi):\\\\mathcal{D}\\\\to \\\\mathcal{E}$ and $(\\\\psi ,\\\\theta):$ $\\\\mathcal{D}\\\\rightarrow \\\\mathcal{F}$ are given. Since $\\\\phi$ and $\\\\psi$ are left-invertible, by Proposition 3.2 we can identify $\\\\mathcal{E}$ and $\\\\mathcal{F}$ with $\\\\mathcal{E}_0\\\\oplus \\\\mathcal{E}_1$ and $\\\\mathcal{F}_0\\\\oplus \\\\mathcal{F}_1$ , respectively, and find $\\\\phi_0,\\\\phi_1,\\\\psi_0,\\\\psi_1$ such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,658,721,738]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- $\\\\\\\\phi_0: \\\\\\\\mathcal{D} \\\\\\\\to \\\\\\\\mathcal{E}_0$ and $\\\\\\\\psi_0: \\\\\\\\mathcal{D} \\\\\\\\to \\\\\\\\mathcal{F}_0$ are isomorphisms, \\\",\\\"- $\\\\\\\\phi_1: \\\\\\\\mathcal{D} \\\\\\\\to \\\\\\\\mathcal{E}_1$ and $\\\\\\\\psi_1: \\\\\\\\mathcal{D} \\\\\\\\to \\\\\\\\mathcal{F}_1$ are homomorphisms, \\\",\\\"- $\\\\\\\\phi(d) = (\\\\\\\\phi_0(d), \\\\\\\\phi_1(d))$ and $\\\\\\\\psi(d) = (\\\\\\\\psi_0(d), \\\\\\\\psi_1(d))$ for every $d \\\\\\\\in \\\\\\\\mathcal{D}$ , \\\",\\\"- $\\\\\\\\pi(e_0, e_1) = \\\\\\\\phi_0^{-1}(e_0)$ and $\\\\\\\\theta(f_0, f_1) = \\\\\\\\psi_0^{-1}(f_0)$ . \\\"]\",\n \"page_idx\": \"19\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[77,758,905,816]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Define homomorphisms $\\\\mu : \\\\mathcal{E} \\\\to \\\\mathcal{F}_1$ and $\\\\nu : \\\\mathcal{F} \\\\to \\\\mathcal{E}_1$ by $\\\\mu = \\\\psi_1 \\\\circ \\\\pi$ and $\\\\nu = \\\\phi_1 \\\\circ \\\\theta$ (see Diagram (7.1)). Since $\\\\Re$ is $\\\\oplus$ -stable $\\\\mathcal{D} \\\\oplus \\\\mathcal{E}_1 \\\\oplus \\\\mathcal{F}_1$ is a $\\\\Re$ -object. Define $\\\\Re$ -arrows $\\\\phi' : \\\\mathcal{E} \\\\hookrightarrow \\\\mathcal{D} \\\\oplus \\\\mathcal{E}_1 \\\\oplus \\\\mathcal{F}_1$ and $\\\\psi' : \\\\mathcal{F} \\\\hookrightarrow \\\\mathcal{D} \\\\oplus \\\\mathcal{E}_1 \\\\oplus \\\\mathcal{F}_1$ by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[327,836,653,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\phi^ {\\\\prime} (e _ {0}, e _ {1}) = (\\\\phi_ {0} ^ {- 1} (e _ {0}), e _ {1}, \\\\mu (e _ {0}, e _ {1}))\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,877,122,892]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[321,914,659,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\psi^ {\\\\prime} \\\\left(f _ {0}, f _ {1}\\\\right) = \\\\left(\\\\psi_ {0} ^ {- 1} \\\\left(f _ {0}\\\\right), \\\\nu \\\\left(f _ {0}, f _ {1}\\\\right), f _ {1}\\\\right).\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,64,104,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"20 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,63,796,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,105,329,123]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For every $d\\\\in \\\\mathcal{D}$ we have \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[188,144,817,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\phi^ {\\\\prime} (\\\\phi (d)) = \\\\phi^ {\\\\prime} (\\\\phi_ {0} (d), \\\\phi_ {1} (d)) = (d, \\\\phi_ {1} (d), \\\\mu (\\\\phi (d))) = (d, \\\\phi_ {1} (d), \\\\psi_ {1} (d))\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,183,134,200]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[179,219,916,363]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\psi^ {\\\\prime} (\\\\psi (d)) = \\\\psi^ {\\\\prime} (\\\\psi_ {0} (d), \\\\psi_ {1} (d)) = (d, \\\\nu (\\\\phi (d)), \\\\psi_ {1} (d)) = (d, \\\\phi_ {1} (d), \\\\psi_ {1} (d)). \\\\\\\\ \\\\mathcal {D} \\\\begin{array}{c} \\\\phi \\\\\\\\ \\\\pi \\\\\\\\ \\\\nu \\\\\\\\ \\\\psi \\\\\\\\ \\\\theta \\\\end{array} \\\\Bigg [ \\\\begin{array}{c} \\\\tilde {\\\\mu} \\\\\\\\ \\\\pi^ {\\\\prime} \\\\\\\\ \\\\psi^ {\\\\prime} \\\\\\\\ \\\\theta^ {\\\\prime} \\\\end{array} \\\\begin{array}{c} \\\\phi^ {\\\\prime} \\\\\\\\ \\\\tilde {\\\\mathcal {D}} \\\\oplus \\\\mathcal {E} _ {1} \\\\oplus \\\\mathcal {F} _ {1} \\\\end{array} \\\\tag {7.1} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,380,918,458]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Therefore $\\\\phi' \\\\circ \\\\phi = \\\\psi' \\\\circ \\\\psi$ . The map $\\\\pi': \\\\mathcal{D} \\\\oplus \\\\mathcal{E}_1 \\\\oplus \\\\mathcal{F}_1 \\\\to \\\\mathcal{E}$ defined by $\\\\pi'(d, e_1, f_1) = (\\\\phi_0(d), e_1)$ is a left inverse of $\\\\phi'$ . Similarly the map $\\\\theta': \\\\mathcal{D} \\\\oplus \\\\mathcal{E}_1 \\\\oplus \\\\mathcal{F}_1 \\\\to \\\\mathcal{F}$ defined by $\\\\theta'(d, e_1, f_1) = (\\\\psi_0(d), f_1)$ is a left inverse of $\\\\psi'$ . Therefore $(\\\\phi', \\\\pi') : \\\\mathcal{E} \\\\to \\\\mathcal{D} \\\\oplus \\\\mathcal{E}_1 \\\\oplus \\\\mathcal{F}_1$ and $(\\\\psi', \\\\theta') : \\\\mathcal{E} \\\\to \\\\mathcal{D} \\\\oplus \\\\mathcal{E}_1 \\\\oplus \\\\mathcal{F}_1$ are $\\\\Re$ -arrows. We have \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[336,479,668,526]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\pi \\\\circ \\\\pi^ {\\\\prime} (d, e _ {1}, f _ {1}) = \\\\pi (\\\\phi_ {0} (d), e _ {1}) = d, \\\\\\\\ \\\\theta \\\\circ \\\\theta^ {\\\\prime} (d, e _ {1}, f _ {1}) = \\\\theta (\\\\psi_ {0} (d), e _ {1}) = d. \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,544,346,561]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Hence $\\\\pi \\\\circ \\\\pi' = \\\\theta \\\\circ \\\\theta'$ . Also \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[190,580,813,627]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\theta^ {\\\\prime} \\\\circ \\\\phi^ {\\\\prime} \\\\left(e _ {0}, e _ {1}\\\\right) = \\\\theta^ {\\\\prime} \\\\left(\\\\phi_ {0} ^ {- 1} \\\\left(e _ {0}\\\\right), e _ {1}, \\\\mu \\\\left(e _ {0}, e _ {1}\\\\right)\\\\right) = \\\\left(\\\\psi_ {0} \\\\left(\\\\phi_ {0} ^ {- 1} \\\\left(e _ {0}\\\\right)\\\\right), \\\\mu \\\\left(e _ {0}, e _ {1}\\\\right)\\\\right) \\\\\\\\ = (\\\\psi_ {0} (\\\\pi (e _ {0}, e _ {1})), \\\\psi_ {1} (\\\\pi (e _ {0}, e _ {1}))) = \\\\psi (\\\\pi (e _ {0}, e _ {1})). \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,645,916,702]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"So $\\\\theta' \\\\circ \\\\phi' = \\\\psi \\\\circ \\\\pi$ and similarly we have $\\\\phi \\\\circ \\\\theta = \\\\pi' \\\\circ \\\\psi'$ . This shows that $\\\\ddagger\\\\mathfrak{K}$ has proper amalgamation property. Since $\\\\mathfrak{K}$ is separable and has an initial object, in particular, it is a Fraïssé category. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,725,916,761]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Therefore any $\\\\oplus$ -stable category $\\\\mathfrak{K}$ has a unique Fraïssé sequence; a $\\\\mathfrak{K}$ -sequence which satisfies (F). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,780,749,800]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Notation. Let $\\\\mathcal{A}_{\\\\mathfrak{K}}$ denote the Fraïssé limit of the $\\\\oplus$ -stable category $\\\\mathfrak{K}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,817,918,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The AF-algebra $\\\\mathcal{A}_{\\\\mathfrak{K}}$ is $\\\\mathfrak{K}$ -universal and almost $\\\\mathfrak{K}$ -homogeneous, by Theorem 5.3 and Lemma 6.2. In fact, $\\\\mathcal{A}_{\\\\mathfrak{K}}$ is $\\\\mathfrak{K}$ -homogeneous (where $\\\\epsilon$ is zero). To see this, suppose $\\\\mathcal{F}$ is a finite-dimensional $C^*$ -algebra in $\\\\mathfrak{K}$ and $\\\\phi_i: \\\\mathcal{F} \\\\hookrightarrow \\\\mathcal{A}$ ( $i = 0,1$ ) are left-invertible embeddings. By the almost $\\\\mathfrak{K}$ -homogeneity, there is an automorphism $\\\\eta: \\\\mathcal{A}_{\\\\mathfrak{K}} \\\\to \\\\mathcal{A}_{\\\\mathfrak{K}}$ such that $\\\\| \\\\eta \\\\circ \\\\phi_0 - \\\\phi_1 \\\\| < 1$ . There exists (Lemma 2.2) a unitary $u \\\\in \\\\widetilde{\\\\mathcal{A}}$ such that $\\\\mathrm{Ad}_u \\\\circ \\\\eta \\\\circ \\\\phi_0 = \\\\phi_1$ . The automorphism $\\\\mathrm{Ad}_u \\\\circ \\\\eta$ witnesses the $\\\\mathfrak{K}$ -homogeneity of $\\\\mathcal{A}_{\\\\mathfrak{K}}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[892,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"21 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[79,105,903,144]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Moreover, since $\\\\ddagger\\\\mathfrak{R}$ has the proper amalgamation property, every AF-algebra in $\\\\mathfrak{L}\\\\mathfrak{R}$ , is a retract of $\\\\mathcal{A}_{\\\\mathfrak{R}}$ (Corollary 6.4). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,167,582,185]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Corollary 7.3. Suppose $\\\\Re$ is a $\\\\oplus$ -stable category, then \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,205,907,304]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- (universality) Every $AF$ -algebra which is the limit of a $\\\\\\\\mathfrak{R}$ -sequence, is a retract of $\\\\\\\\mathcal{A}_{\\\\\\\\widehat{\\\\\\\\mathbb{R}}}$ . \\\",\\\"- (R-homogeneity) For every finite-dimensional $C^*$ -algebra $\\\\\\\\mathcal{F} \\\\\\\\in \\\\\\\\Re$ and left-invertible embeddings $\\\\\\\\phi_i : \\\\\\\\mathcal{F} \\\\\\\\hookrightarrow \\\\\\\\mathcal{A}_{\\\\\\\\Re}$ ( $i = 0,1$ ), there is an automorphism $\\\\\\\\eta : \\\\\\\\mathcal{A}_{\\\\\\\\Re} \\\\\\\\to \\\\\\\\mathcal{A}_{\\\\\\\\Re}$ such that $\\\\\\\\eta \\\\\\\\circ \\\\\\\\phi_0 = \\\\\\\\phi_1$ . \\\"]\",\n \"page_idx\": \"21\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[104,325,871,344]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We will describe the structure of $\\\\mathcal{A}_{\\\\mathfrak{R}}$ by showing that it has the Cantor property. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,366,835,385]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 7.4. Suppose $\\\\Re$ is a $\\\\oplus$ -stable category, then $\\\\mathcal{A}_{\\\\Re}$ has the Cantor property. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,405,903,505]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Suppose $\\\\mathcal{A}_{\\\\mathfrak{K}} = \\\\varinjlim_{n}(\\\\mathcal{A}_{n},\\\\phi_{n}^{m})$ , where $(\\\\mathcal{A}_n,\\\\phi_n^m)$ is a $\\\\Re$ -sequence, i.e., $(\\\\mathcal{A}_n,\\\\phi_n^m)$ is a left-invertible sequence of finite-dimensional $C^*$ -algebras in $\\\\Re$ . Since $\\\\mathcal{A}_{\\\\mathfrak{K}}$ is the Fraïssé limit of $\\\\Re$ , we can suppose $(\\\\mathcal{A}_n,\\\\phi_n^m)$ satisfies (F). We claim that $(\\\\mathcal{A}_n,\\\\phi_n^m)$ satisfies (D0)-(D2) of Definition 4.1. Suppose $\\\\mathfrak{D}$ is the Bratteli diagram of $(\\\\mathcal{A}_n,\\\\phi_n^m)$ and $\\\\mathcal{A}_n = \\\\mathcal{A}_{n,1}\\\\oplus \\\\dots \\\\oplus \\\\mathcal{A}_{n,k_n}$ for every $n$ , such that each $\\\\mathcal{A}_{n,s}$ is a matrix algebra. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,505,903,625]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The condition (D0) is trivial since $\\\\phi_n^m$ are left-invertible. To see (D1), fix $\\\\mathcal{A}_{n,s}$ . Note that since $\\\\mathcal{A}_n$ is a $\\\\Re$ -object and $\\\\Re$ is $\\\\oplus$ -stable, we have $\\\\mathcal{A}_n \\\\oplus \\\\mathcal{A}_n \\\\in \\\\Re$ . Let $\\\\gamma : \\\\mathcal{A}_n \\\\hookrightarrow \\\\mathcal{A}_n \\\\oplus \\\\mathcal{A}_n$ be the left-invertible embedding defined by $\\\\gamma(a) = (a,a)$ . Use the Fraïssé condition (F) to find $\\\\delta : \\\\mathcal{A}_n \\\\oplus \\\\mathcal{A}_n \\\\hookrightarrow \\\\mathcal{A}_m$ , for some $m \\\\geq n$ , such that $\\\\delta \\\\circ \\\\gamma = \\\\phi_n^m$ . Since $\\\\delta$ is left-invertible, there are distinct $(m,t)$ and $(m,t')$ in $\\\\mathfrak{D}$ such that $\\\\mathcal{A}_{m,t} \\\\cong \\\\mathcal{A}_{m,t'} \\\\cong \\\\mathcal{A}_{n,s}$ . Then $\\\\delta \\\\circ \\\\gamma = \\\\phi_n^m$ implies that $(n,s) \\\\to (m,t)$ and $(n,s) \\\\to (m,t')$ in $\\\\mathfrak{D}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,626,903,725]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To see (D2) assume $\\\\mathcal{D} \\\\subseteq \\\\mathcal{A}_n$ is an ideal of $\\\\mathcal{A}_n$ and $M_{\\\\ell}$ is a retract of $\\\\mathcal{A}_{\\\\Re}$ and there is an embedding $\\\\gamma : \\\\mathcal{D} \\\\hookrightarrow M_{\\\\ell}$ . Suppose $\\\\mathcal{A}_n = \\\\mathcal{D} \\\\oplus \\\\mathcal{E}$ for some $\\\\mathcal{E}$ . Since $\\\\Re$ is $\\\\oplus$ -stable, $\\\\mathcal{D} \\\\oplus \\\\mathcal{E} \\\\oplus M_{\\\\ell}$ is a $\\\\Re$ -object. Therefore $\\\\gamma' : \\\\mathcal{D} \\\\oplus \\\\mathcal{E} \\\\hookrightarrow \\\\mathcal{D} \\\\oplus \\\\mathcal{E} \\\\oplus M_{\\\\ell}$ defined by $\\\\gamma'(d, e) = (d, e, \\\\gamma(d))$ is a $\\\\Re$ -arrow. Then by (F) there is a left-invertible embedding $\\\\delta': \\\\mathcal{D} \\\\oplus \\\\mathcal{E} \\\\oplus M_{\\\\ell} \\\\hookrightarrow \\\\mathcal{A}_m$ for some $m \\\\geq n$ , such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[432,750,899,766]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\delta^ {\\\\prime} \\\\circ \\\\gamma^ {\\\\prime} = \\\\phi_ {n} ^ {m}. \\\\tag {7.2}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[79,789,732,808]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Since $\\\\delta^\\\\prime$ is left-invertible, there is $(m,t)$ such that $\\\\dim (\\\\mathcal{A}_{m,t}) = \\\\ell$ and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[334,833,648,852]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\delta_ {m, t} = \\\\pi_ {\\\\mathcal {A} _ {m, t}} \\\\circ \\\\delta | _ {M _ {\\\\ell}}: M _ {\\\\ell} \\\\hookrightarrow \\\\mathcal {A} _ {m, t}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[79,873,811,892]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"is an isomorphism, where $\\\\pi_{\\\\mathcal{A}_{m,t}}: \\\\mathcal{A}_m \\\\twoheadrightarrow \\\\mathcal{A}_{m,t}$ is the canonical projection. Let \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[331,917,650,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\phi_ {m, t} = \\\\pi_ {\\\\mathcal {A} _ {m, t}} \\\\circ \\\\phi_ {n} ^ {m} | _ {\\\\mathcal {D}}: \\\\mathcal {D} \\\\rightarrow \\\\mathcal {A} _ {m, t}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,64,104,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"22 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,63,796,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,105,916,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"By definition of $\\\\gamma^\\\\prime$ and (7.2) it is clear that $\\\\phi_{m,t} = \\\\delta_{m,t}\\\\circ \\\\gamma$ and that $\\\\phi_{m,t}$ is also an embedding. By Lemma 2.3 we have $\\\\mathrm{Mult}_{\\\\phi_{m,t}}(\\\\mathcal{D},\\\\mathcal{A}_{m,t}) = c\\\\mathrm{Mult}_{\\\\gamma}(\\\\mathcal{D},M_{\\\\ell})$ for some natural number $c\\\\geq 1$ . Since $\\\\delta_{m,t}$ is an isomorphism, we have $c = 1$ . This proves (D2). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,186,916,245]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Next we show that every AF-algebra with Cantor property can be realized as the Fraïssé limit of a suitable $\\\\oplus$ -stable category of finite-dimensional $C^*$ -algebras and left-invertible embeddings. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,270,299,288]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7.1. The category $\\\\mathfrak{K}_A$ \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,311,916,391]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Suppose $\\\\mathcal{A}$ is an AF-algebra with Cantor property. Let $\\\\mathfrak{K}_{\\\\mathcal{A}}$ denote the category whose objects are finite-dimensional retracts of $\\\\mathcal{A}$ and $\\\\mathfrak{K}_{\\\\mathcal{A}}$ -arrows are left-invertible embeddings. Let $\\\\mathfrak{L}_{\\\\mathcal{A}}$ be the category whose objects are limits of $\\\\mathfrak{K}_{\\\\mathcal{A}}$ -sequences. If $\\\\mathcal{B}$ and $\\\\mathcal{C}$ are $\\\\mathfrak{L}_{\\\\mathcal{A}}$ -objects, an $\\\\mathfrak{L}_{\\\\mathcal{A}}$ -arrow from $\\\\mathcal{B}$ into $\\\\mathcal{C}$ is a left-invertible embedding $\\\\phi: \\\\mathcal{B} \\\\hookrightarrow \\\\mathcal{C}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,413,897,432]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 7.5. $\\\\mathfrak{K}_A$ is a Fraïssé category and $\\\\ddagger \\\\mathfrak{K}_A$ has the proper amalgamation property. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,454,916,492]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. By Theorem 7.2, it is enough to show that $\\\\mathfrak{K}_A$ is a $\\\\oplus$ -stable category. Condition (1) of Definition 7.1 is trivial. Condition (2) follows from Proposition 4.4. $\\\\square$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,514,914,554]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Again, Theorem 5.3 guarantees the existence of a unique $\\\\mathfrak{K}_{\\\\mathcal{A}}$ -universal and $\\\\mathfrak{K}_{\\\\mathcal{A}}$ -homogeneous AF-algebra in $\\\\mathfrak{L}_{\\\\mathcal{A}}$ , namely the Fraïssé limit of $\\\\mathfrak{K}_{\\\\mathcal{A}}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,575,505,594]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 7.6. The Fraïssé limit of $\\\\mathfrak{K}_A$ is $\\\\mathcal{A}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,614,916,714]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. There is a sequence $(\\\\mathcal{A}_n,\\\\phi_n^m)$ of finite-dimensional $C^*$ -algebras and embeddings such that $\\\\mathcal{A} = \\\\varinjlim (\\\\mathcal{A}_n,\\\\phi_n^m)$ satisfies (D0)-(D2) of Definition 4.1. First note that by (D0), $(\\\\mathcal{A}_n,\\\\phi_n^m)$ is a $\\\\mathfrak{K}_{\\\\mathcal{A}}$ -sequence and therefore $\\\\mathcal{A}$ is an $\\\\mathfrak{L}_{\\\\mathcal{A}}$ -object. In order to show that $\\\\mathcal{A}$ is the Fraïssé limit of $\\\\mathfrak{K}_{\\\\mathcal{A}}$ , we need to show that $(\\\\mathcal{A}_n,\\\\phi_n^m)$ satisfies condition (F). This is Lemma 4.5. $\\\\square$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,736,910,755]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 7.7. Suppose $\\\\Re$ is a $\\\\oplus$ -stable category. $\\\\mathcal{A}_{\\\\Re}$ is the unique $AF$ -algebra such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,777,880,814]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(1) it has the Cantor property, \\\",\\\"(2) a finite-dimensional $C^*$ -algebra is a retract of $\\\\\\\\mathcal{A}_{\\\\\\\\Re}$ if and only if it is a $\\\\\\\\Re$ -object. \\\"]\",\n \"page_idx\": \"22\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[89,836,916,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. We have already shown that $\\\\mathcal{A}_{\\\\mathfrak{K}}$ has the Cantor property (Lemma 7.4). By Lemma 3.5(2), every finite-dimensional retract of $\\\\mathcal{A}_{\\\\mathfrak{K}}$ is a $\\\\mathfrak{K}$ -object and every finite-dimensional $C^*$ -algebra in $\\\\mathfrak{K}$ is a retract of $\\\\mathcal{A}_{\\\\mathfrak{K}}$ , by the $\\\\mathfrak{K}$ -universality of $\\\\mathcal{A}_{\\\\mathfrak{K}}$ . If $\\\\mathcal{A}$ is an AF-algebra satisfying (1) and (2), then by definition $\\\\mathfrak{K}_{\\\\mathcal{A}} = \\\\mathfrak{K}$ . The uniqueness of the Fraïssé limit and Theorem 7.6 imply that $\\\\mathcal{A} \\\\cong \\\\mathcal{A}_{\\\\mathfrak{K}}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[892,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[81,105,903,142]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Corollary 7.8. Two $AF$ -algebras with Cantor property are isomorphic if and only if they have the same set of matrix algebras as retracts. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[83,164,218,183]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7.2. Examples \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,204,903,360]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Corollary 7.8 shows that there is a one-to-one correspondence between AF-algebras with the Cantor property and the collections of (non-isomorphic) matrix algebras (hence, with the subsets of the natural numbers). More precisely, given any collection $X$ of nonisomorphic matrix algebras, let $\\\\mathfrak{K}_X$ denote the $\\\\oplus$ -stable category whose objects are finite direct sums of the matrix algebras in $\\\\mathfrak{K}_X$ (finite direct sums of a member of $X$ with itself are of course allowed) and left-invertible embeddings as arrows. Then the Fraïssé limit of $\\\\mathfrak{K}_X$ is the unique AF-algebra whose matrix algebra retracts are exactly the members of $X$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,361,903,439]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The class of AF-algebras with the Cantor property is not closed under direct sum (for instance, $(M_2\\\\oplus M_3)\\\\otimes C(2^{\\\\mathbb{N}})$ does not have the Cantor property, as its Bratteli diagram easily reveals, while $M_2\\\\otimes C(2^{\\\\mathbb{N}})$ and $M_3\\\\otimes C(2^{\\\\mathbb{N}})$ do). The following example shows that this class is also not closed under tensor product. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,442,903,757]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $\\\\mathcal{A}$ denote the unique AF-algebra with the Cantor property whose matrix algebra retracts are exactly $\\\\{M_2, M_3, M_5, M_{11}\\\\}$ . We claim that $\\\\mathcal{A} \\\\otimes \\\\mathcal{A}$ does not have the Cantor property. Suppose $\\\\mathcal{A} = \\\\varinjlim (\\\\mathcal{A}_n, \\\\phi_n^m)$ where the sequence satisfies (D0)-(D2) of Definition 4.1. Clearly $\\\\mathcal{A} \\\\otimes \\\\mathcal{A}$ is the limit of the left-invertible sequence $(\\\\mathcal{A}_n \\\\otimes \\\\mathcal{A}_n, \\\\phi_n^m \\\\otimes \\\\phi_n^m)$ . Therefore by Lemma 3.5 every matrix algebra retract of $\\\\mathcal{A} \\\\otimes \\\\mathcal{A}$ is isomorphic to $\\\\mathcal{D} \\\\otimes \\\\mathcal{E}$ , where $\\\\mathcal{D}, \\\\mathcal{E} \\\\in \\\\{M_2, M_3, M_5, M_{11}\\\\}$ . Take a retract of $\\\\mathcal{A}_n \\\\otimes \\\\mathcal{A}_n$ isomorphic to $M_3 \\\\otimes M_5$ (for large enough $n$ there is such a retract) and let $\\\\gamma: M_3 \\\\otimes M_5 \\\\to M_2 \\\\otimes M_{11}$ be an embedding of multiplicity 1. However, there is no embedding $\\\\phi \\\\otimes \\\\psi: M_3 \\\\otimes M_5 \\\\to M_{22} \\\\cong M_2 \\\\otimes M_{11}$ which corresponds to a path in the Bratteli diagram of the sequence $(\\\\mathcal{A}_n \\\\otimes \\\\mathcal{A}_n, \\\\phi_n^m \\\\otimes \\\\phi_n^m)$ . This is because the codomain of any such $\\\\phi$ should be either $M_3$ or $M_5$ or $M_{11}$ (since $\\\\phi$ corresponds to a path in the Bratteli diagram of the sequence $(\\\\mathcal{A}_n, \\\\phi_n^m)$ ) and similarly the codomain of $\\\\psi$ could only be $M_5$ or $M_{11}$ , while the tensor product of their codomains should be isomorphic to $M_{22}$ , which is not possible. Thus condition (D2) is satisfied neither by the sequence $(\\\\mathcal{A}_n \\\\otimes \\\\mathcal{A}_n, \\\\phi_n^m \\\\otimes \\\\phi_n^m)$ , nor by any sequence of finite-dimensional $C^*$ -algebras whose limit is $\\\\mathcal{A} \\\\otimes \\\\mathcal{A}$ (see Remark 4.2), which means that $\\\\mathcal{A} \\\\otimes \\\\mathcal{A}$ does not have the Cantor property. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,777,319,795]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8. Universal AF-algebras \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,817,903,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $\\\\mathfrak{F}$ denote the category of all finite-dimensional $C^*$ -algebras and left-invertible embeddings. The category $\\\\mathfrak{F}$ is $\\\\oplus$ -stable and therefore it is Fraïssé by Theorem 7.2. The Fraïssé limit $\\\\mathcal{A}_{\\\\mathfrak{F}}$ of this category has the universality property (Corollary 7.3) that any AF-algebra which is the limit of a left-invertible sequence of finite-dimensional $C^*$ -algebras can be embedded via a left-invertible embedding into $\\\\mathcal{A}_{\\\\mathfrak{F}}$ . In fact, $\\\\mathcal{A}_{\\\\mathfrak{F}}$ is surjectively universal in the category of all (separable) AF-algebras. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,64,102,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"24 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[190,63,794,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,105,916,144]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 8.1. There is a surjective homomorphism from $\\\\mathcal{A}_{\\\\mathfrak{F}}$ onto any separable $AF$ -algebra. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,169,918,291]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Suppose $\\\\mathcal{B}$ is a separable AF-algebra. Proposition 3.8 states that there is an AF-algebra $\\\\mathcal{A}$ , which is the limit of a left-invertible sequence of finite-dimensional $C^*$ -algebras and $\\\\mathcal{A} / \\\\mathcal{I} \\\\cong \\\\mathcal{B}$ , for some ideal $\\\\mathcal{I}$ . By the universality of $\\\\mathcal{A}_{\\\\mathfrak{F}}$ (Corollary 7.3) there is a left-invertible embedding $\\\\phi : \\\\mathcal{A} \\\\hookrightarrow \\\\mathcal{A}_{\\\\mathfrak{F}}$ . If $\\\\theta : \\\\mathcal{A}_{\\\\mathfrak{F}} \\\\twoheadrightarrow \\\\mathcal{A}$ is a left inverse of $\\\\phi$ then its composition with the quotient map $\\\\pi : \\\\mathcal{A} \\\\twoheadrightarrow \\\\mathcal{A} / \\\\mathcal{I}$ gives a surjective homomorphism from $\\\\mathcal{A}_{\\\\mathfrak{F}}$ onto $\\\\mathcal{B}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,314,916,377]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 8.2. Since $\\\\mathcal{A}_{\\\\mathfrak{F}}$ has the Cantor property (Lemma 7.4), it does not have any minimal projections. Therefore, for example, it cannot be isomorphic to $\\\\mathcal{A}_{\\\\mathfrak{F}} \\\\oplus \\\\mathbb{C}$ . Hence the property of being surjectively universal AF-algebra is not unique to $\\\\mathcal{A}_{\\\\mathfrak{F}}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,400,916,439]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Corollary 8.3. An $AF$ -algebra $\\\\mathcal{A}$ is surjectively universal if and only if $\\\\mathcal{A}_{\\\\mathfrak{F}}$ is a quotient of $\\\\mathcal{A}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,464,916,502]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 7.7 provides a characterization of $\\\\mathcal{A}_{\\\\mathfrak{F}}$ , up to isomorphism, in terms of its structure. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,529,916,567]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Corollary 8.4. $\\\\mathcal{A}_{\\\\mathfrak{F}}$ is the unique separable $AF$ -algebra with Cantor property such that every matrix algebra $M_{k}$ is a retract of $\\\\mathcal{A}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,570,916,630]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Equivalently, an $AF$ -algebra $\\\\mathcal{A}$ is isomorphic to $\\\\mathcal{A}_{\\\\mathfrak{F}}$ if and only if there is a sequence $(\\\\mathcal{A}_n, \\\\phi_n^m)$ of finite-dimensional $C^*$ -algebras and embeddings such that $\\\\mathcal{A} = \\\\varinjlim (\\\\mathcal{A}_n, \\\\phi_n^m)$ and the Bratteli diagram $\\\\mathfrak{D}$ of $(\\\\mathcal{A}_n, \\\\phi_n^m)$ satisfies (D0)-(D2) and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,650,663,670]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(D3) for every $k$ there is $(n, s) \\\\in \\\\mathfrak{D}$ such that $\\\\dim(n, s) = k$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,691,920,770]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 8.5. $\\\\mathcal{A}_{\\\\mathfrak{F}}$ is the unique $AF$ -algebra that is the limit of a left-invertible sequence of finite-dimensional $C^*$ -algebras and for any finite-dimensional $C^*$ -algebras $\\\\mathcal{D}, \\\\mathcal{E}$ and left-invertible embeddings $\\\\phi : \\\\mathcal{D} \\\\hookrightarrow \\\\mathcal{E}$ and $\\\\alpha : \\\\mathcal{D} \\\\hookrightarrow \\\\mathcal{A}_{\\\\mathfrak{F}}$ there is a left-invertible embedding $\\\\beta : \\\\mathcal{E} \\\\hookrightarrow \\\\mathcal{A}_{\\\\mathfrak{F}}$ such that $\\\\beta \\\\circ \\\\phi = \\\\alpha$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,795,918,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Suppose $\\\\mathcal{A}_{\\\\mathfrak{F}}$ is the limit of the Fraïssé $\\\\mathfrak{F}$ -sequence $(\\\\mathcal{A}_n, \\\\phi_n^m)$ . By definition, $\\\\alpha$ and $\\\\phi$ are $\\\\mathfrak{F}$ -arrows. There is (Lemma 6.2) a natural number $n$ and an $\\\\mathfrak{F}$ -arrow (a left-invertible embedding) $\\\\psi : \\\\mathcal{D} \\\\hookrightarrow \\\\mathcal{A}_n$ such that $\\\\| \\\\phi_n^\\\\infty \\\\circ \\\\psi - \\\\alpha \\\\| < 1$ . Use the amalgamation property to find a finite-dimensional $C^*$ -algebra $\\\\mathcal{G}$ and left-invertible embeddings $\\\\phi' : \\\\mathcal{E} \\\\hookrightarrow \\\\mathcal{G}$ and $\\\\psi' : \\\\mathcal{A}_n \\\\hookrightarrow \\\\mathcal{G}$ such that $\\\\phi' \\\\circ \\\\phi = \\\\psi' \\\\circ \\\\psi$ (see Diagram (8.1)). The Fraïssé condition (F) implies the existence of $m \\\\geq n$ and a left-invertible embedding $\\\\delta : \\\\mathcal{G} \\\\hookrightarrow \\\\mathcal{A}_m$ such that $\\\\delta \\\\circ \\\\psi' = \\\\phi_n^m$ . Let $\\\\beta' = \\\\phi_m^\\\\infty \\\\circ \\\\delta \\\\circ \\\\phi'$ . It is clearly left-invertible. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[892,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"25 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[139,100,903,227]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{c} \\\\mathcal {A} _ {1} \\\\xrightarrow {\\\\phi_ {1} ^ {2}} \\\\mathcal {A} _ {2} \\\\xrightarrow {\\\\phi_ {2} ^ {3}} \\\\dots \\\\xrightarrow {} \\\\mathcal {A} _ {n} \\\\xrightarrow {\\\\phi_ {n} ^ {m}} \\\\mathcal {A} _ {m} \\\\xrightarrow {\\\\phi_ {m} ^ {\\\\infty}} \\\\mathcal {A} _ {\\\\mathfrak {F}} \\\\\\\\ \\\\mathcal {D} \\\\xleftarrow {\\\\psi} \\\\quad \\\\begin{array}{c} \\\\phi^ {\\\\prime} \\\\uparrow \\\\\\\\ \\\\alpha \\\\end{array} \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[79,251,323,267]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For every $d$ in $\\\\mathcal{D}$ we have \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[104,289,875,311]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\beta^ {\\\\prime} \\\\circ \\\\phi (d) = \\\\phi_ {m} ^ {\\\\infty} \\\\circ \\\\delta \\\\circ \\\\phi^ {\\\\prime} \\\\circ \\\\phi (d) = \\\\phi_ {m} ^ {\\\\infty} \\\\circ \\\\delta \\\\circ \\\\psi^ {\\\\prime} \\\\circ \\\\psi (d) = \\\\phi_ {m} ^ {\\\\infty} \\\\circ \\\\phi_ {n} ^ {m} \\\\circ \\\\psi (d) = \\\\phi_ {n} ^ {\\\\infty} \\\\circ \\\\psi (d).\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,327,903,366]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Therefore $\\\\| \\\\beta' \\\\circ \\\\phi - \\\\alpha \\\\| < 1$ . Conjugating $\\\\beta'$ with a unitary in $\\\\widetilde{\\\\mathcal{A}}_{\\\\mathfrak{F}}$ gives the required left-invertible embedding $\\\\beta$ (Lemma 2.2). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,367,905,464]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For the uniqueness, suppose $\\\\mathcal{B}$ is the limit of a left-invertible sequence $(\\\\mathcal{B}_n,\\\\psi_n^m)$ of finite-dimensional $C^*$ -algebras, satisfying the assumption of the theorem. Using this assumption we can show that $(\\\\mathcal{B}_n,\\\\psi_n^m)$ satisfies the Fraïssé condition (F) and therefore $\\\\mathcal{B}$ is the Fraïssé limit of $\\\\mathfrak{F}$ . Uniqueness of the Fraïssé limit implies that $\\\\mathcal{B}$ is isomorphic to $\\\\mathcal{A}_{\\\\mathfrak{F}}$ . $\\\\square$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,485,903,523]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let us conclude this section with another example of a Fraïssé category of finite-dimensional $C^*$ -algebras. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,542,905,602]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 8.6. Note that a similar argument as in 7.2 shows that $\\\\mathcal{A}_{\\\\mathfrak{F}} \\\\otimes \\\\mathcal{A}_{\\\\mathfrak{F}}$ does not have the Cantor property. In particular, $\\\\mathcal{A}_{\\\\mathfrak{F}}$ is not self-absorbing, i.e., $\\\\mathcal{A}_{\\\\mathfrak{F}} \\\\otimes \\\\mathcal{A}_{\\\\mathfrak{F}}$ is not isomorphic to $\\\\mathcal{A}_{\\\\mathfrak{F}}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[79,623,387,641]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8.1. The universal UHF-algebra \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[104,663,608,680]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Recall that a UHF-algebra is the (inductive) limit of \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[349,700,635,730]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nM _ {k _ {1}} \\\\xrightarrow {\\\\phi_ {1} ^ {2}} M _ {k _ {2}} \\\\xrightarrow {\\\\phi_ {2} ^ {3}} M _ {k _ {3}} \\\\xrightarrow {\\\\phi_ {3} ^ {4}} \\\\ldots\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,747,905,805]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"of full matrix algebras, with unital connecting maps $\\\\phi_n^{n+1}$ . In particular $k_j|k_{j+1}$ for each $j$ . To each sequence of natural numbers $\\\\{k_j\\\\}_{j \\\\in \\\\mathbb{N}}$ (hence to the corresponding UHF-algebra) a supernatural number $n$ is associated, which is the formal product \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[419,823,563,861]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nn = \\\\prod_ {p \\\\text {p r i m e}} p ^ {n _ {p}}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,877,625,895]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $n_p \\\\in \\\\{0, 1, 2, \\\\ldots, \\\\infty\\\\}$ and for each prime number $p$ , \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[340,916,642,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nn _ {p} = \\\\sup \\\\{n: p ^ {n} | k _ {j} \\\\mathrm {f o r s o m e} j \\\\}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,64,104,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"26 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,63,796,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,105,918,201]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Also to each supernatural number $n$ there is an associated UHF-algebra denoted, as it is common, by $M_{n}$ (e.g., the CAR-algebra is $M_{2\\\\infty}$ ). Glimm [9] showed that a supernatural number is a complete invariant for the associated UHF-algebra. Recall that the universal UHF-algebra (see [16]), denoted by $\\\\mathcal{Q}$ , is the UHF-algebra associated to the supernatural number \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[421,217,584,258]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nn _ {\\\\infty} = \\\\prod_ {p \\\\mathrm {p r i m e}} p ^ {\\\\infty}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,270,817,289]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The universal UHF-algebra $\\\\mathcal{Q}$ is also the unique unital AF-algebra such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[329,308,680,329]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\langle K _ {0} (\\\\mathcal {Q}), K _ {0} (\\\\mathcal {Q}) _ {+}, [ 1 _ {\\\\mathcal {Q}} ] \\\\rangle \\\\cong \\\\langle \\\\mathbb {Q}, \\\\mathbb {Q} _ {+}, 1 \\\\rangle .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,345,916,402]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The multiplication of supernatural numbers is defined in the obvious way which means for supernatural numbers $n, m$ we have $M_{n} \\\\otimes M_{m} \\\\cong M_{nm}$ . This in particular implies that $\\\\mathcal{Q} \\\\otimes \\\\mathcal{M} \\\\cong \\\\mathcal{Q}$ , for any UHF-algebra $\\\\mathcal{M}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,404,918,561]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Now suppose $\\\\mathfrak{M}$ is the category of all nonzero matrix algebras and unital embeddings. Then $\\\\mathfrak{M}$ is a Fraïssé category. The only nontrivial part of the latter statement is to show that $\\\\mathfrak{M}$ has the amalgamation property, but this is quite easy since it is enough to make sure that the composition maps have the same multiplicities and then conjugating with a unitary makes sure that the composition maps are the same (this is similar to the proof of the amalgamation property in [5, Theorem 3.4]). The Fraïssé limit of $\\\\mathfrak{M}$ is $\\\\mathcal{Q}$ , since the universality property of the Fraïssé limit implies that the supernatural number associated to it must be $n_{\\\\infty}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,582,284,600]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"9. Unital categories \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,620,918,738]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The proof of Theorem 7.2 also shows that the category of all finite-dimensional $C^*$ -algebras (or any $\\\\oplus$ -stable category) and unital left-invertible embeddings has the (proper) amalgamation property. However, this category fails to have the joint embedding property (note that 0 is no longer an object of the category), since for example one cannot jointly embed $M_2$ and $M_3$ into a finite-dimensional $C^*$ -algebra with unital left-invertible maps. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,755,284,777]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"9.1. The category $\\\\widetilde{\\\\mathfrak{F}}$ \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,795,918,938]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $\\\\widetilde{\\\\mathfrak{F}}$ denote the category of all finite-dimensional $C^*$ -algebras isomorphic to $\\\\mathbb{C} \\\\oplus \\\\mathcal{D}$ , for a finite-dimensional $C^*$ -algebra $\\\\mathcal{D}$ , and unital left-invertible embeddings. This category is no longer $\\\\oplus$ -stable, however, a similar proof to the one of Theorem 7.2, where the maps are unital, shows that $\\\\sharp \\\\widetilde{\\\\mathfrak{F}}$ has the proper amalgamation property. Therefore $\\\\widetilde{\\\\mathfrak{F}}$ is a Fraïssé category, since $\\\\mathbb{C}$ is the initial object of this category and therefore the joint embedding property is a consequence of the amalgamation property. The Fraïssé limit $\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}$ of this category is a separable AF-algebra with the universality property that any \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[892,64,916,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"27 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[81,105,903,167]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"unital AF-algebra which can be obtained as the limit of a left-invertible unital sequence of finite-dimensional $C^*$ -algebras isomorphic to $\\\\mathbb{C} \\\\oplus \\\\mathcal{D}$ , can be embedded via a left-invertible unital embedding into $\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{S}}}$ . The unital analogue of Theorem 8.1 states the following. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,188,903,230]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Corollary 9.1. For every unital separable $AF$ -algebra $\\\\mathcal{B}$ there is a surjective homomorphism from $\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}$ onto $\\\\mathcal{B}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,250,903,413]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Suppose $\\\\mathcal{B}$ is an arbitrary unital AF-algebra. Using Proposition 3.8 we can find a unital AF-algebra $\\\\mathcal{A} \\\\supseteq B$ which is the limit of a left-invertible unital sequence of finite-dimensional $C^*$ -algebras, such that $\\\\mathcal{B}$ is a quotient of $\\\\mathcal{A}$ . Thus $\\\\mathbb{C} \\\\oplus \\\\mathcal{A}$ is the limit of a unital left-invertible sequence of finite-dimensional $C^*$ -algebras of the form $\\\\mathbb{C} \\\\oplus \\\\mathcal{D}$ , for finite-dimensional $\\\\mathcal{D}$ . By the universality of $\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}$ , there is a left-invertible unital embedding from $\\\\mathbb{C} \\\\oplus \\\\mathcal{A}$ into $\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}$ . Since $\\\\mathcal{B}$ is a quotient of $\\\\mathcal{A}$ , there is a surjective homomorphism from $\\\\mathbb{C} \\\\oplus \\\\mathcal{A}$ onto $\\\\mathcal{B}$ . Combining the two surjections gives us a surjective homomorphism from $\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}$ onto $\\\\mathcal{B}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,433,903,539]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 9.2. Small adjustments in the proof of Lemma 7.4 show that $\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}$ has the Cantor property (in the sense of Definition 4.3). In fact, it is easy to check that $\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}$ is isomorphic to $\\\\widetilde{\\\\mathcal{A}}_{\\\\widetilde{\\\\mathfrak{F}}}$ , the unitization of $\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}$ . This, in particular, implies that $\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}$ is not unital. Since if it was unital, then $\\\\widetilde{\\\\mathcal{A}}_{\\\\widetilde{\\\\mathfrak{F}}}$ (and hence $\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}$ ) would be isomorphic to $\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}} \\\\oplus \\\\mathbb{C}$ , but this is not possible since $\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}$ has the Cantor property and therefore has no minimal projections. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,558,903,598]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Definition 9.3. We say $\\\\mathcal{D}$ is a unital-retract of the $C^*$ -algebra $\\\\mathcal{A}$ if there is a left-invertible unital embedding from $\\\\mathcal{D}$ into $\\\\mathcal{A}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[83,622,286,644]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"9.2. The category $\\\\widetilde{\\\\mathfrak{R}}_A$ \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,667,903,769]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If $\\\\mathcal{A}$ is a unital AF-algebra with Cantor property (Definition 4.3), then let $\\\\widetilde{\\\\mathfrak{K}}_{\\\\mathcal{A}}$ denote the category whose objects are finite-dimensional unital-retracts of $\\\\mathcal{A}$ and morphisms are unital left-invertible embeddings. This category is not $\\\\oplus$ -stable, since it does not satisfy condition (1) of Definition 7.1. However, $\\\\ddagger \\\\widetilde{\\\\mathfrak{K}}_{\\\\mathcal{A}}$ still has the proper amalgamations property. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,791,648,811]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proposition 9.4. $\\\\widehat{\\\\mathfrak{R}}_{\\\\mathcal{A}}$ has the proper amalgamation property. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,835,903,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. The proof is exactly the same as the proof of Lemma 7.2 where the maps are assumed to be unital. We only need to check that $\\\\mathcal{D} \\\\oplus \\\\mathcal{E}_1 \\\\oplus \\\\mathcal{F}_1$ is a unital-retract of $\\\\mathcal{A}$ . By Lemma 3.5, for some $m$ both $\\\\mathcal{E} \\\\cong \\\\mathcal{D} \\\\oplus \\\\mathcal{E}_1$ and $\\\\mathcal{F} \\\\cong \\\\mathcal{D} \\\\oplus \\\\mathcal{F}_1$ are unital-retracts of $\\\\mathcal{A}_m$ . An easy argument using Proposition 3.2 shows that $\\\\mathcal{D} \\\\oplus \\\\mathcal{E}_1 \\\\oplus \\\\mathcal{F}_1$ is also a unital-retract of $\\\\mathcal{A}_m$ and therefore a unital retract of $\\\\mathcal{A}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,64,104,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"28 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,61,796,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubiš / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,105,916,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Also $\\\\widetilde{\\\\mathfrak{K}}_{\\\\mathcal{A}}$ has a weakly initial object (by the next lemma). Therefore it is a Fraïssé category. Recall that an object is weakly initial in $\\\\mathfrak{K}$ if it has at least one $\\\\mathfrak{K}$ -arrow to any other object of $\\\\mathfrak{K}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,180,918,261]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 9.5. Suppose $\\\\mathcal{A}$ is a unital $AF$ -algebra with Cantor property. The category $\\\\widetilde{\\\\mathfrak{K}}_{\\\\mathcal{A}}$ has a weakly initial object, i.e., there is a finite-dimensional unital-retract of $\\\\mathcal{A}$ which can be mapped into any other finite-dimensional unital-retract of $\\\\mathcal{A}$ via a left-invertible unital embedding. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,276,916,420]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. Let $M_{k_1} \\\\oplus \\\\dots \\\\oplus M_{k_l}$ be an arbitrary $\\\\widetilde{\\\\mathcal{R}}_{\\\\mathcal{A}}$ -object. Suppose that $\\\\{k_1', \\\\ldots, k_t'\\\\}$ is the largest subset of $\\\\{k_1, \\\\ldots, k_l\\\\}$ such that $k_i'$ cannot be written as $\\\\sum_{\\\\substack{j \\\\leq n \\\\\\\\ j \\\\neq i}} x_j k_j'$ for any natural set numbers $\\\\{x_j : j \\\\leq n \\\\text{ and } j \\\\neq i\\\\}$ , for any $i \\\\leq t$ . Since $\\\\{k_1', \\\\ldots, k_t'\\\\}$ is the largest such subset, $\\\\mathcal{D} = M_{k_1'} \\\\oplus \\\\dots \\\\oplus M_{k_t'}$ is a unital-retract of $M_{k_1} \\\\oplus \\\\dots \\\\oplus M_{k_l}$ and therefore a unital-retract of $\\\\mathcal{A}$ . Suppose $\\\\mathcal{F}$ is an arbitrary $\\\\widetilde{\\\\mathcal{R}}_{\\\\mathcal{A}}$ -object. Let $(\\\\mathcal{A}_n, \\\\phi_n^m)$ be a $\\\\widetilde{\\\\mathcal{R}}_{\\\\mathcal{A}}$ -sequence with limit $\\\\mathcal{A}$ such that $\\\\mathcal{A}_1 \\\\cong \\\\mathcal{F}$ . Then $\\\\mathcal{D}$ is a unital-retract of some $\\\\mathcal{A}_m$ , so $\\\\mathcal{A}_m = \\\\dot{\\\\mathcal{D}} \\\\oplus \\\\mathcal{E}$ , for some $\\\\mathcal{E}$ and $\\\\dot{\\\\mathcal{D}} \\\\cong \\\\mathcal{D}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,423,918,555]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Fix $i \\\\leq t$ . Since $\\\\phi_1^m$ is a unital embedding, there is a subalgebra of $\\\\mathcal{F}$ isomorphic to $M_{n_1} \\\\oplus \\\\dots \\\\oplus M_{n_s}$ such that $\\\\sum_{j=1}^{s} y_j n_j = k_i'$ , for some $\\\\{y_1, \\\\ldots, y_s\\\\} \\\\subseteq \\\\mathbb{N}$ . We claim that exactly one $n_j$ is equal to $k_i'$ and the rest are zero. If not, then for every $j \\\\leq s$ we have $0 < n_j < k_i'$ . Since $\\\\phi_1^m$ is left-invertible, for every $j \\\\leq s$ a copy of $M_{n_j}$ appears as a summand of $\\\\mathcal{A}_m$ . Also because there is a unital embedding from $\\\\mathcal{D}$ into $\\\\mathcal{A}_m$ , for some $\\\\{x_1, \\\\ldots, x_r\\\\} \\\\subseteq \\\\mathbb{N}$ we have $n_j = \\\\sum_{\\\\substack{j' \\\\leq r \\\\\\\\ j' \\\\neq i}} x_{j'} k_{j'}'$ for every $j \\\\leq s$ . But then \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[398,570,608,632]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nk_{i}^{\\\\prime} = \\\\sum_{j = 1}^{s}\\\\sum_{\\\\substack{j^{\\\\prime}\\\\leq n\\\\\\\\ j^{\\\\prime}\\\\neq i}}x_{j^{\\\\prime}}y_{j}k_{j^{\\\\prime}}^{\\\\prime},\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[89,645,916,705]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"which is a contradiction with the choice of $k_{i}^{\\\\prime}$ . This means that $\\\\mathcal{F} = \\\\mathcal{F}_0 \\\\oplus \\\\mathcal{F}_1$ such that $\\\\mathcal{F}_0 \\\\cong \\\\mathcal{D}$ and there is a unital homomorphism from $\\\\mathcal{D}$ onto $\\\\dot{\\\\mathcal{F}}_1$ . Therefore $\\\\mathcal{D}$ is a unital-retract of $\\\\mathcal{F}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,720,916,782]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Corollary 9.6. Suppose $\\\\mathcal{A}$ is a unital $AF$ -algebra with Cantor property. The category $\\\\widetilde{\\\\mathfrak{K}}_{\\\\mathcal{A}}$ is a Fraïssé category and $\\\\ddagger \\\\widetilde{\\\\mathfrak{K}}_{\\\\mathcal{A}}$ has the proper amalgamation property. The Fraïssé limit of $\\\\widetilde{\\\\mathfrak{K}}_{\\\\mathcal{A}}$ is $\\\\mathcal{A}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,798,916,838]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proof. The proof of the fact that $\\\\mathcal{A}$ is the Fraïssé limit of $\\\\widetilde{\\\\mathfrak{K}}_{\\\\mathcal{A}}$ is same as Theorem 7.6, where all the maps are unital. $\\\\square$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,857,608,877]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10. Surjectively universal countable dimension groups \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,895,916,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A countable partially ordered abelian group $\\\\langle G, G^{+} \\\\rangle$ is a (countable) dimension group if it is isomorphic to the inductive limit of a sequence \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[892,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"29 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[359,98,623,123]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathbb {Z} ^ {r _ {1}} \\\\xrightarrow {\\\\alpha_ {1} ^ {2}} \\\\mathbb {Z} ^ {r _ {2}} \\\\xrightarrow {\\\\alpha_ {2} ^ {3}} \\\\mathbb {Z} ^ {r _ {3}} \\\\xrightarrow {\\\\alpha_ {3} ^ {4}} \\\\dots\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,142,903,183]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"for some natural numbers $r_n$ , where $\\\\alpha_i^j$ are positive group homomorphisms and $\\\\mathbb{Z}^r$ is equipped with the ordering given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[226,201,755,220]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left(\\\\mathbb {Z} ^ {r}\\\\right) ^ {+} = \\\\left\\\\{\\\\left(x _ {1}, x _ {2}, \\\\dots , x _ {r}\\\\right) \\\\in \\\\mathbb {Z} ^ {r}: x _ {i} \\\\geq 0 \\\\text {f o r} i = 1, \\\\dots , r \\\\right\\\\}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,239,905,298]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A partially ordered abelian group that is isomorphic to $\\\\langle \\\\mathbb{Z}^r, (\\\\mathbb{Z}^r)^+ \\\\rangle$ , for a non-negative integer $r$ , is usually called a simplicial group. A scale $S$ on the dimension group $\\\\langle G, G^+ \\\\rangle$ is a generating, upward directed and hereditary subset of $G^+$ (see [4, IV.3]). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,316,903,352]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Notation. If $\\\\langle G, S \\\\rangle$ is a scaled dimension group as above, we can recursively pick order-units \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[316,373,665,392]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\bar {u} _ {n} = \\\\left(u _ {n, 1}, u _ {n, 2}, \\\\dots , u _ {n, r _ {n}}\\\\right) \\\\in \\\\left(\\\\mathbb {Z} ^ {r _ {n}}\\\\right) ^ {+}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,410,905,491]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"of $\\\\mathbb{Z}^{r_n}$ such that $\\\\alpha_{n}^{n + 1}(\\\\bar{u}_{n})\\\\leq \\\\bar{u}_{n + 1}$ and $S = \\\\bigcup_{n}\\\\alpha_{n}^{\\\\infty}[[\\\\bar{0},\\\\bar{u}_{n}]]$ . Then we say the scaled dimension group $\\\\langle G,S\\\\rangle$ is the limit of the sequence $(\\\\mathbb{Z}^{r_n},\\\\bar{u}_n,\\\\alpha_n^m)$ . If $(\\\\bar{u}_n)$ can be chosen such that $\\\\alpha_{n}^{n + 1}(\\\\bar{u}_{n}) = \\\\bar{u}_{n + 1}$ for every $n\\\\in \\\\mathbb{N}$ , then $G$ has an order-unit $u = \\\\lim_{n}\\\\alpha_{n}^{\\\\infty}(\\\\bar{u}_{n})$ In this case we denote this dimension group with order-unit by $\\\\langle G,u\\\\rangle$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,507,905,605]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An isomorphism between scaled dimension groups is a positive group isomorphism which sends the scale of the domain to the scale of the codomain. Given a separable AF-algebra $\\\\mathcal{A}$ , its $K_{0}$ -group $\\\\langle K_0(\\\\mathcal{A}), K_0(\\\\mathcal{A})^+ \\\\rangle$ is a (countable) dimension group and conversely any dimension group is isomorphic to $K_{0}$ -group of a separable AF-algebra. The dimension range of $\\\\mathcal{A}$ , \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[263,625,717,645]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {D} (\\\\mathcal {A}) = \\\\{[ p ]: p \\\\text {i s a p r o j e c t i o n o f} \\\\mathcal {A} \\\\} \\\\subseteq K _ {0} (\\\\mathcal {A}) ^ {+}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[77,661,905,742]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"is a scale for $\\\\langle K_0(\\\\mathcal{A}),K_0(\\\\mathcal{A})^+\\\\rangle$ , and therefore $\\\\langle K_0(\\\\mathcal{A}),\\\\mathcal{D}(\\\\mathcal{A})\\\\rangle$ is a scaled dimension group. Conversely, every scaled dimension group is isomorphic to $\\\\langle K_0(\\\\mathcal{A}),\\\\mathcal{D}(\\\\mathcal{A})\\\\rangle$ for a separable AF-algebra $\\\\mathcal{A}$ . Elliott's classification of separable AF-algebras ([6]) states that $\\\\langle K_0(\\\\mathcal{A}),\\\\mathcal{D}(\\\\mathcal{A})\\\\rangle$ is a complete isomorphism invariant for the separable AF-algebra $\\\\mathcal{A}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,758,907,838]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 10.1 (Elliott [6]). Two separable $AF$ -algebras $\\\\mathcal{A}$ and $\\\\mathcal{B}$ are isomorphic if and only if their scaled dimension groups are isomorphic. If $\\\\mathcal{A}$ and $\\\\mathcal{B}$ are unital, then they are isomorphic if and only if $\\\\langle K_0(\\\\mathcal{A}), [1_{\\\\mathcal{A}}] \\\\rangle \\\\cong \\\\langle K_0(\\\\mathcal{B}), [1_{\\\\mathcal{B}}] \\\\rangle$ , as partially ordered abelian groups with order-units. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,857,513,876]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10.1. Surjectively universal dimension groups \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[77,897,903,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The universality property of $\\\\langle K_0(\\\\mathcal{A}_{\\\\mathfrak{F}}),\\\\mathcal{D}(\\\\mathcal{A}_{\\\\mathfrak{F}})\\\\rangle$ can be obtained by applying $K_{0}$ -functor to Theorem 8.1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,64,104,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"30 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,63,798,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[89,105,916,145]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Corollary 10.2. The scaled (countable) dimension group $\\\\langle K_0(\\\\mathcal{A}_{\\\\mathfrak{F}}),\\\\mathcal{D}(\\\\mathcal{A}_{\\\\mathfrak{F}})\\\\rangle$ maps onto any countable scaled dimension group. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[115,164,914,185]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"By applying $K_{0}$ -functor to Corollary 8.4, we immediately obtain the following result. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,202,918,242]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Corollary 10.3. $\\\\langle K_0(\\\\mathcal{A}_{\\\\mathfrak{F}}),\\\\mathcal{D}(\\\\mathcal{A}_{\\\\mathfrak{F}})\\\\rangle$ is the unique scaled dimension group which is the limit of a sequence $(\\\\mathbb{Z}^{r_n},\\\\bar{u}_n,\\\\alpha_n^m)$ (as in Notation above) satisfying the following conditions: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,261,916,401]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(1) for every $n \\\\\\\\in \\\\\\\\mathbb{N}$ and $1 \\\\\\\\leq i \\\\\\\\leq r_n$ there are $m \\\\\\\\geq n$ and $1 \\\\\\\\leq j, j' \\\\\\\\leq r_m$ such that $j \\\\\\\\neq j'$ , $u_{n,i} = u_{m,j} = u_{m,j'}$ and $\\\\\\\\pi_j \\\\\\\\circ \\\\\\\\alpha_n^m(u_{n,i}) = u_{m,j}$ and $\\\\\\\\pi_{j'} \\\\\\\\circ \\\\\\\\alpha_n^m(u_{n,i}) = u_{m,j'}$ , where $\\\\\\\\pi_j$ is the canonical projection from $\\\\\\\\mathbb{Z}^{r_m}$ onto its $j$ -th coordinate. \\\",\\\"(2) for every $n, n' \\\\\\\\in \\\\\\\\mathbb{N}, 1 \\\\\\\\leq i' \\\\\\\\leq r_{n'}$ and $\\\\\\\\{x_1, \\\\\\\\ldots, x_{r_n}\\\\\\\\} \\\\\\\\subseteq \\\\\\\\mathbb{N} \\\\\\\\cup \\\\\\\\{0\\\\\\\\}$ such that $\\\\\\\\sum_{i=1}^{r_n} x_i u_{n,i} \\\\\\\\leq u_{n',i'}$ there are $m \\\\\\\\geq n$ and $1 \\\\\\\\leq j \\\\\\\\leq r_m$ such that $u_{n',i'} \\\\\\\\leq u_{m,j}$ and $\\\\\\\\pi_j \\\\\\\\circ \\\\\\\\alpha_n^m(u_{n,i}) = x_i \\\\\\\\cdot u_{n,i}$ for every $i \\\\\\\\in \\\\\\\\{1, \\\\\\\\ldots, r_n\\\\\\\\}$ . \\\",\\\"(3) For every $k \\\\\\\\in \\\\\\\\mathbb{N}$ there are natural numbers $n$ and $1 \\\\\\\\leq i \\\\\\\\leq r_n$ such that $u_{n,i} = k$ . \\\"]\",\n \"page_idx\": \"30\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[89,420,916,480]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Corollary 10.4. The (countable) dimension group with order-unit $\\\\langle K_0(\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}),[1_{\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}}]\\\\rangle$ maps onto (there is a surjective normalized positive group homomorphism) any countable dimension group with order-unit. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,500,916,558]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A similar characterization of the dimension group with order-unit $\\\\langle K_0(\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}),[1_{\\\\mathcal{A}_{\\\\widetilde{\\\\mathfrak{F}}}}]\\\\rangle$ holds where $\\\\alpha_{n}^{m}$ are order-unit preserving and in condition (2) of Corollary 10.3 the inequality $\\\\sum_{i = 1}^{r_n}x_iu_{n,i}\\\\leq u_{n',i'}$ is replaced with equality. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,580,265,598]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgments \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,620,916,658]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We would like to thank Ilijas Farah and Eva Pernecká for useful conversations and comments. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,682,199,698]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[100,719,914,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[1] I. Ben Yaacov, Fraïssé limits of metric structures, J. Symb. Log. 80 (2015) 100-115. \\\",\\\"[2] B.E. Blackadar, Traces on simple AF $C^*$ -algebras, J. Funct. Anal. 38 (2) (1980) 156-168. \\\",\\\"[3] O. Bratteli, Inductive limits of finite-dimensional $C^*$ -algebras, Trans. Am. Math. Soc. 171 (1972) 195-234. \\\",\\\"[4] K. Davidson, $C^*$ -Algebras by Example, Fields Institute Monographs, vol. 6, American Mathematical Society, Providence, RI, 1996. \\\",\\\"[5] C.J. Eagle, I. Farah, B. Hart, B. Kadets, V. Kalashnyk, M. Lupini, Fraïssé limits of $C^*$ -algebras, J. Symb. Log. 81 (2016) 755-773. \\\",\\\"[6] G.A. Elliott, On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Algebra 38 (1976) 29-44. \\\",\\\"[7] R. Fraïssé, Sur l'extension aux relations de quelques propriétés des ordres, Ann. Sci. Éc. Norm. Supér. (3) 71 (1954) 363-388. \\\",\\\"[8] J. Garbulińska-Wegrzyn, Isometric uniqueness of a complementably universal Banach space for Schauder decompositions, Banach J. Math. Anal. 8 (2014) 211-220. \\\",\\\"[9] J.G. Glimm, On a certain class of operator algebras, Trans. Am. Math. Soc. 95 (1960) 318-340. \\\"]\",\n \"page_idx\": \"30\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[203,63,811,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[892,64,914,75]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"31 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[81,108,903,277]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[10] W. Kubis, Fraïssé sequences: category-theoretic approach to universal homogeneous structures, Ann. Pure Appl. Log. 165 (2014) 1755-1811. \\\",\\\"[11] W. Kubić, Metric-enriched categories and approximate Fraïssé limits, preprint, arXiv:1210.6506. \\\",\\\"[12] W. Kubis, S. Solecki, A proof of uniqueness of the Gurariš space, Isr. J. Math. 195 (2013) 449-456. \\\",\\\"[13] M. Lupini, Fraïssé limits in functional analysis, Adv. Math. 338 (2018) 93-174. \\\",\\\"[14] S. Masumoto, The Jiang-Su algebra as a Fraïssé limit, J. Symb. Log. 82 (2017) 1541-1559. \\\",\\\"[15] M. Rørdam, F. Larsen, N. Laustsen, An Introduction to K-Theory for $\\\\\\\\mathbf{C}^*$ -Algebras, vol. 49, Cambridge University Press, 2000. \\\",\\\"[16] M. Rørdam, E. Størmer, Classification of Nuclear $C^*$ -Algebras: Entropy in Operator Algebras, vol. 126, Springer, Berlin, 2002. \\\",\\\"[17] K. Schoretsanitis, Fraïssé theory for metric structures, Thesis (Ph.D.), University of Illinois at Urbana-Champaign, 2007. \\\"]\",\n \"page_idx\": \"31\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[81,64,104,76]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"32 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,63,796,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"S. Ghasemi, W. Kubis / Journal of Functional Analysis 279 (2020) 108590 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1016/j.jfa.2020.108590"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Physics/Mathematics and Computational Science"},"sha256":{"kind":"string","value":"01c0d5d76e66cbb923c2ea3c5b4467e84b7a7b784864c6424a8f8f27b177a58c"},"title":{"kind":"string","value":"Universal AF-algebras"}}},{"rowIdx":262,"cells":{"abstract":{"kind":"string","value":"While the development of dye-sensitized solar cells (DSSCs) has been ongoing for more than 30 years, the currently obtained efficiency is unsatisfactory. However, the study of DSSC development has produced a fundamental understanding of cell performance and inspired other devices, such as perovskite cell solar cells. DSSCs consist of a dye-sensitized photoanode, a counter electrode, and a redox couple in the electrolyte system. Each of the components has an important role and cofunctions with each other to obtain a high power conversion efficiency. Various modifications to each DSSC component have been applied to improve their performance. Additionally, to generate improvements, the effort to reduce production costs has been crucial. The utilization of natural sources for DSSC components is a possible solution to this issue. The utilization of natural resources also aims to increase the value of the natural resource itself. In this review, the applications of various natural sources for DSSC components are described, as well as the modification efforts that have been made to enhance their performance. The discussion covers the utilization of natural dye for sensitizer dyes in liquid DSSC applications: (1) utilization of biopolymers for quasi-solid DSSC electrolytes, (2) green synthesis methods for photoanode semiconductors, and (3) development of natural carbon counter electrodes. The detailed factors that influence improvements in cell performance are also addressed."},"author":{"kind":"string","value":"Yuly Kusumawati|Aulia S. Hutama|Diana V. Wellia|Riki Subagyo"},"content_list":{"kind":"list like","value":[{"bbox":"[58,184,174,197]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Review article ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,206,529,226]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Natural resources for dye-sensitized solar cells ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[838,208,890,247]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0007/78026f383237e705af19a3e21bedad8fef44412254bdcf1638d2ce62b956972e.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,240,640,259]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Yuly Kusumawati a,\\*, Aulia S. Hutama b, Diana V. Wellia c, Riki Subagyo a ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,266,801,298]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"$^{a}$ Department of Chemistry, Institut Teknologi Sepuluh Nopember, Sukolilo Campus, Surabaya, 60111, Indonesia \",\"$^{b}$ Department of Chemistry, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Jalan Sekip Utara, Bulaksumur, Yogyakarta, 55281, Indonesia \",\"$^{c}$ Department of Chemistry, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Padang, 24516, Indonesia \"]","page_idx":"0","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[58,327,193,339]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ARTICLEINFO ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[58,353,109,363]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,365,181,374]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dye sensitized solar cells ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,375,146,385]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Natural resources ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,385,117,395]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biopolymer ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,397,184,406]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Natural counter electrode ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,408,137,417]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green synthesis ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[334,327,435,339]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABSTRACT ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[332,353,937,522]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"While the development of dye-sensitized solar cells (DSSCs) has been ongoing for more than 30 years, the currently obtained efficiency is unsatisfactory. However, the study of DSSC development has produced a fundamental understanding of cell performance and inspired other devices, such as perovskite cell solar cells. DSSCs consist of a dye-sensitized photoanode, a counter electrode, and a redox couple in the electrolyte system. Each of the components has an important role and cofunctions with each other to obtain a high power conversion efficiency. Various modifications to each DSSC component have been applied to improve their performance. Additionally, to generate improvements, the effort to reduce production costs has been crucial. The utilization of natural sources for DSSC components is a possible solution to this issue. The utilization of natural resources also aims to increase the value of the natural resource itself. In this review, the applications of various natural sources for DSSC components are described, as well as the modification efforts that have been made to enhance their performance. The discussion covers the utilization of natural dye for sensitizer dyes in liquid DSSC applications: (1) utilization of biopolymers for quasi-solid DSSC electrolytes, (2) green synthesis methods for photoanode semiconductors, and (3) development of natural carbon counter electrodes. The detailed factors that influence improvements in cell performance are also addressed. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,559,163,571]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,585,485,689]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Multiple renewable energy sources must be developed to meet rapidly increasing energy demand and human population growth. Countries around the world should utilize their natural resources as renewable energy to ensure sustainability. Solar energy is an abundant resource available in many countries. It has enabled continuous growth in the development of solar cells in recent decades. Among solar technologies, dye-sensitized solar cells (DSSCs) are photovoltaic devices that have attracted much attention since the 1990s. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,691,485,795]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 1 presents a model of DSSC structure and function. It consists of two electrodes. One electrode is an oxide-semiconductor mesoporous layer deposited onto fluorine-doped tin oxide (FTO) glass and sensitized by a dye, which acts as a photoanode. The other is platinized FTO glass as a cathode, also called a counter electrode. An electrolyte system is placed between these two electrodes. The most common DSSC liquid electrolyte consists of an $\\mathrm{I}_3 / \\mathrm{T}^-$ redox couple dissolved in an organic solvent such as acetonitrile. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,796,485,823]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Electricity in the DSSC is produced by the electron transfer process displayed in the inset section in Figure 1. When the dye - which acts ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,559,937,742]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"as a sensitizer in DSSC - receives solar radiation, the electron from the highest occupied molecular orbital (HOMO) excites the lowest unoccupied molecular orbital (LUMO). Electrons are subsequently injected into the oxide semiconductor conduction band. After that, the electrons travel to the external circuit through the anode and cathode. Once the electrons arrive at the external circuit, they change the redox couple species state from oxidized to reduced. The electrons obtained from the reversal of the redox couple utilize dye regeneration. This cycle is repeated until electricity is gathered. General article reviews have already been published on the primary or fundamental concepts of DSSCs [1, 2, 3], the electron transfer mechanism in DSSCs [4, 5, 6, 7], and recent progress about DSSC development [8, 9, 10, 11], which will be beneficial for readers who need additional information. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,744,937,822]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The assessed performance for the DSSC is the light-to-electricity conversion efficiency or power conversion efficiency (PCE, $\\%$ ). The PCE is contributed by the photoanode, counter electrode, electrolyte, and dye employed in the DSSC device. The PCE is proportional to the short circuit current density $(J_{sc})$ , open-circuit voltage $(V_{oc})$ , and fill factor $(FF)$ as follows. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[428,42,569,55]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[60,74,161,158]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CellPress ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[388,76,628,89]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Contents lists available at ScienceDirect ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[463,105,549,126]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[371,145,643,160]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"journal homepage: www.cell.com/heliyon ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[852,76,936,160]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[67,844,201,856]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"* Corresponding author. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[80,856,418,867]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"E-mail address: y_kusumawati@chem.its.ac.id (Y. Kusumawati). ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[57,876,319,887]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1016/j.heliyon.2021.e08436 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[58,889,598,901]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received 28 August 2021; Received in revised form 14 October 2021; Accepted 16 November 2021 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[58,902,937,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2405-8440/© 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[163,66,836,290]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 1. A model of dye-sensitized solar-cell structure and function. (Red/Ox = the coupled redox species for example $\\\\mathrm{I}_3\\\\mathbin{\\\\text{一}}/\\\\mathrm{T}$ ; VB = Valence band; CB = Conduction band). \"]","image_footnote":"[]","img_path":"images/0876/36f9eaf855edc4a9cad11636fc6e3be44459162573027363be8b781f95483561.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,339,485,353]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\eta \\sim J _ {s c} \\times V _ {o c} \\times F F \\tag {1}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[57,358,485,490]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The short circuit current $(J_{\\mathrm{sc}})$ correlates with both the photoanode and counter electrode performance. The value of $J_{\\mathrm{sc}}$ can be increased by improving the efficiency of light harvesting. The improvement can be conducted, for instance, by finding a proper sensitizer that can more strongly attach to $\\mathrm{TiO_2}$ surfaces or pores [12]. The counter electrode has a crucial role in catalyzing the redox couple in the electrolyte solution. The reduced species will be transported to the photoanode, reduce the oxidized dye, and continue the light absorption cycle. Therefore, a counter electrode with high electrocatalytic activity, charge transport activity, and low resistance is highly desirable to increase the $J_{\\mathrm{sc}}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,490,485,530]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The open-circuit voltage $(V_{oc})$ is the difference in the Fermi level of electrons in $\\mathrm{TiO}_2(E_F)$ and the redox potential of the electrolyte $(E_{redox})$ over the charge $(q)$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,539,485,566]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV _ {o c} = \\frac {\\left(E _ {F} - E _ {r e d o x}\\right)}{q} \\tag {2}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[57,572,485,668]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theoretically, $V_{oc}$ can reach up to 1.6 V. However, due to the energy mismatches between the $E_{redox}$ and HOMO levels of the dye and between the conduction band level $(E_c)$ of TiO2 and the LUMO of the dye, the maximum voltage is reduced to $\\frac{(E_c - E_{redox})}{q}$ [13]. The $V_{oc}$ can be tuned by several means. An example of this is putting additives into the electrolyte to shift the conduction band level of TiO2 and/or proper choice of $\\mathrm{I}^{-}$ salt source [14, 15, 16]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,669,485,761]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The $FF$ depends on the serial resistance and shunt resistance of the devices. Serial resistance in DSSCs is the resistance of the electron transfer process in the external circuit to the counter electrode. Shunt resistance is the resistance of the back electron transfer to the photoanode. Therefore, to increase the $FF$ value, the serial resistance must be minimal, while the shunt resistance must be maximal. The DSSCs first published by Grätzel in 1991 gained a cell PCE of $7.1 - 7.9\\%$ [17]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,761,485,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For the last three decades, increasing the PCE has remained a challenge in enhancing DSSC performance. Ideally, DSSC improvement requires the optimization of all device components. For example, the oxide semiconductor layer of the photoanode is expected to have a mesoporous structure to immobilize a maximum amount of dye to absorb adequate solar light [18, 19]. To have a mesoporous structure, various methods have been proposed. Surfactants are the most straightforward templating agents to control the surface area of the resulting semiconductors [20, 21, 22]. The use of sodium dodecyl sulfate in the oxide synthesis step can improve the cell performance to $6.08\\%$ compared to the $4.06\\%$ cell performance when using $\\mathrm{TiO_2}$ P25 [20]. The template-free semiconductor synthesis method, with controllable size and surface area, can also be carried out to synthesize the oxide photoanodes. This has been ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,339,937,457]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"demonstrated by Hosni et al., who prepared a zinc oxide nanotubes with a diameter of $35\\mathrm{nm}$ [23]. The layer of this particle is highly porous, which is beneficial for DSSC performance. Another method for photoanode improvement is to prepare an oxide semiconductor with a one-dimensional structure. It has been proven that the one-dimensional structure will be beneficial for electron transport within the oxide matrix [23, 24, 25, 26]. Zhang et al. developed a $\\mathrm{TiO_2}$ nanotube DSSC, and they obtained a satisfactory PCE of $9.86\\%$ . The necks formed between $\\mathrm{TiO_2}$ nanotube particles are responsible for charge transport [27]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,457,937,718]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dye sensitizer optimization has been studied to improve cell performance and reduce the cell production cost. Metal-free organic dyes have become an alternative to classical organo-ruthenium complexes due to multiple advantages, such as low cost, tunable properties, and high molar extinction coefficients [28]. Dye design works usually utilize quantum chemical calculations in conjunction with the experimental works. Quantum chemical calculations are pivotal in predicting the electronic properties of dyes to provide a molecular-level explanation of the electronic process. Experimental and theoretical molecular engineering has been carried out to arrange the donor (D), $\\pi$ -spacer ( $\\pi$ -conjugation section of the dye) and acceptor (A) units to obtain either D- $\\pi$ -A [29], D-A- $\\pi$ -A [30], or D-D- $\\pi$ -A structures [31]. Despite the endeavor, not all results were satisfactory. For example, the D- $\\pi$ -A thiophene dyes developed by Babu et al. only achieved a PCE of $4.24\\%$ . On the other hand, Wang et al. succeeded in preparing a D-A- $\\pi$ -A-based DSSC and produced a PCE value of $9.83\\%$ . The study of the binding of dyes onto the oxide surface is also vital to ensure an efficient electron injection process [32, 33]. Additionally, it is important to tune the HOMO and LUMO levels of the dyes to obtain an efficient intramolecular charge transfer process and electron injection into the photoanode. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,721,937,878]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Studies on electrolytes focus on finding alternatives to iodine/triiodide liquid-based electrolyte solution, which presents. This has led to a replacement of the $\\mathrm{I}_3 / \\mathrm{I}^-$ redox couple by other redox couples, such as $\\mathrm{Co}^{2+} / \\mathrm{Co}^{3+}$ [34, 35, 36], nitroxide radicals [37, 38], copper complexes [39, 40], thiolate/disulfide [41], and ferrocenium/ferrocene [42, 43]. In addition, to overcome electrolyte leakage, quasi-solid DSSCs, which use a polymer gel as an electrolyte medium, have been considered [44, 45, 46]. Unfortunately, quasi-solid DSSCs have not shown a better PCE value than liquid DSSCs, with PCE values ranging from $4\\%$ to $5\\%$ [44]. A few have a PEC value of $7\\%$ , such as a PAN (polyacrylonitrile)-based DSSC combined with RbI and tetrahexylammonium iodide salt developed by Bandara et al. [47]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,880,937,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For the counter electrode component, research has been focused on finding a platinum substitute. It is evident that platinum-based DSSC show superior performance as catalyst for the reduction of $\\Gamma_{3}$ to $\\Gamma^{-}$ . However, since it is a noble metal, the production cost of platinum-based ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,42,154,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[494,952,502,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[57,65,485,223]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"DSSCs are expensive [48, 49]. Various materials have then been proposed to replace platinum, such as carbon-based materials, including allotrope graphene [50, 51, 52, 53] or carbon nanotubes [54, 55], conductive polymers such as PEDOT [56], metal-organic frameworks (MOF) [49, 57], and perovskites [58, 59]. Research on counter electrodes also focuses on flexible counter electrodes to extend DSSC applications [60, 61]. In general, most nonplatinum counter electrode-based DSSCs have a lower PCE than the platinum DSSCs. However, some materials outperform the platinum materials and appear to be promising for further development [48, 62]. For instance, the graphene nanoplate-based counter electrode prepared by Kakiage et al. has a PCE value of $14.7\\%$ [53]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,223,485,341]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The best performance of DSSC currently recorded is one that uses copper complex redox couple-based electrolytes developed by Zhang et al. This cell employs a sensitizer constructed by a bulky donor N-(2',4'- bis (dodecyloxy)-[1,1'-biphenyl]-4-yl)-2',4'-bis(dodecyloxy)-N-phenyl[1,1'-biphenyl]-4-amine and an electron acceptor 4-(benzo[c] [1, 2, 5] thiadiazol-4-yl) benzoic acid coupled with the PEDOT (poly(3,4-ethylenedioxythiophene) counter electrode. This cell shows a PCE value of $34.5\\%$ under warm white fluorescent light at 1000 lux. Based on these results, the cell is the best cell for ambient light device applications [63]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,343,487,593]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To improve DSSC performance and decrease their cost, the utilization of natural resources has attracted much attention. Natural resources aim to achieve sustainability and reliability and support an eco-friendly environment [64, 65]. In this review, the current progress on natural resource utilization in DSSC development is presented. Although Mariotti et al. [66] recently reviewed the development of eco-friendly and cost-effective materials for DSSCs, the point of view of that work is slightly different from the current review. In the present review, the natural resources as material sources that build DSSCs will be further elaborated on. The purposes of this review are to describe the utilization of natural resources in DSSCs and their shortcomings. The discussion will point out the natural resource utilization in each DSSC component: natural dyes for sensitizers, natural polymers for quasi-solid DSSC electrolytes, and natural carbon for counter electrodes. In most DSSCs, $\\mathrm{TiO_2}$ and ZnO photoanode are usually taken from either commercial sources or chemically and physically controlled synthetic procedures. Here, we also present the possibility of preparing photoanodes from the oxides obtained through green synthesis with controllable structures and morphologies. Figure 2 presents the illustration of the scope of this review. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,607,284,620]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. Natural dye for sensitizer DSSC ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,633,487,713]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The sensitizer is one of the vital components in DSSCs. It aids in capturing visible to near-infrared light over a broad spectrum range with high molar extinction coefficients. It must also produce good charge separation to avoid electron recombination and efficient electron injection into oxide semiconductors [67]. Ruthenium-based dyes have shown good performance in fulfilling sensitizer requirements. Due to their rare ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,65,937,211]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"availability and high cost, alternative dyes have been developed to replace ruthenium complex dyes [68]. Natural dyes offer good opportunities. They have been considered due to their high molar extinction coefficient and their abundant availability [68, 69]. Families of natural dyes that have been explored for sensitizers applications in DSSCs include betanin or betalain [70, 71, 72, 73, 74, 75, 76, 77, 78], chlorophyll [72, 73, 74, 75, 76, 77, 78, 79, 80], and anthocyanin [28, 88, 89, 90, 91, 92, 93, 94]. The cosensitization of two dyes is also of high interest to enhance their performance [95, 96]. In the following sections, we present details of the various families of natural dyes and explain multiple research efforts undertaken to overcome their limitations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,225,589,235]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.1. Betanin ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,250,937,369]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Betanins are a category of pigments that belong to the betalain class. The betanin structure is presented in Figure 3. In their chemical structure, betalains contain an N-heterocyclic bearing hydroxyl functional group. Betalain compounds are divided into betacyanins, red-violet pigments, and betaxanthin, yellow pigments. Approximately $75 - 95\\%$ of red-violet pigments are composed of betanin. Notably, this pigment can be extracted from Caryophyllales plants [66, 97]. Betanins have inspired researchers to utilize these compounds for sensitizers in DSSCs [70, 71, 72, 73, 74, 75, 76, 77, 78]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,370,937,540]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The betanin sensitizer was first reported in 2005 by a research group from Uppsala University [80]. Unfortunately, the DSSC performance was still considered relatively poor. They conducted the research using an unsealed cell and reported a poor performance with a very low $J_{SC}$ , even with an $FF$ value in the same range of the standard ruthenium dye cell. Among the tested cells, the use of an ethanol solvent for the electrolyte showed the best result [80]. In 2011, Sandquist et al. from Washington State University reported a relatively higher PCE of the betanin-based DSSC than the previous study [71]. They made improvements by using 3-methoxypropionate (MPN) as the electrolyte solvent and employing a blocking layer. Their improvement led to a PCE of $2.7\\%$ [71]. This report showed that using MPN as an electrolyte solvent gives a better result than acetonitrile. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,540,937,646]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Table 1 summarizes the results of betanin-based DSSCs. It highlights the efforts and modifications that have been conducted thus far. Based on Table 1, we can conclude that the factors that have to be considered to develop betanin-based DSSCs are (1) the extraction process of the dyes [70, 71, 72]; (2) the immersion system for sensitizing the photoanode [71, 72, 73]; (3) the incorporation of a small amount of metal/cation to tune the electronic properties of the photoanode [73, 74, 77]; and (4) the choice of the electrolyte system [70, 72, 74, 77]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,646,937,712]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Table 1 shows that most PCEs of the betanin-based DSSCs do not exceed $3\\%$ . The best result was obtained for cells using medium-pressure liquid chromatography-extracted betanin [71]. Incorporating Ag and Au nanoparticles into the photoanode can also enhance light absorption due to the surface plasmon resonance effect [74, 77]. Moreover, Au ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[166,742,831,914]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 2. The illustration of natural resources for DSSC application. \"]","image_footnote":"[]","img_path":"images/0856/55e61d7a30d41fd68242b023305b7ee5a1dc4ab967b6082b7fa1f500d6224e71.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[58,42,157,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[494,952,504,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[255,65,480,337]","code_body":null,"code_caption":null,"image_caption":"[\"(a) \"]","image_footnote":"[]","img_path":"images/0691/093bdf2ad69a4552a940d5ee8a5b5281d78b40333d7a4f69eefbcc7ecf45cd4d.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[512,64,736,336]","code_body":null,"code_caption":null,"image_caption":"[\"(b) \"]","image_footnote":"[]","img_path":"images/0890/753642f648bf614b83ad016bda612cd27d7c3c451fb6c4eddcf51249a4ca473c.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[201,424,457,733]","code_body":null,"code_caption":null,"image_caption":"[\"(c) \"]","image_footnote":"[]","img_path":"images/0392/fd2ffe66b4da2a6485cf5babcaad63e3d6db14ac6164f45f76f3f6fb37f9a9e4.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[485,443,789,728]","code_body":null,"code_caption":null,"image_caption":"[\"(d) \",\"Figure 3. Structure of (a) Betalain and (b) Betanin and structure of the constituent pigment, namely (c) betacyanin and (d) betaxanthin. \"]","image_footnote":"[]","img_path":"images/0514/611d15fa01fc5fd13f10483b519d3d78c2ef16d18afefef1ba3028c3381d87d0.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,795,485,873]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"incorporation provokes a Schottky barrier effect at the Au and $\\mathrm{TiO_2}$ interface. This effect can reduce the charge recombination from the oxide conduction band to the LUMO of dyes or electrolyte species [77]. Maintaining the acidic condition of the solvent upon the extraction process or photoanode immersion can also be considered since the structure of betanin is known to be influenced by the solution pH [73]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,875,485,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Multiple experimental and computational studies have also been performed to gain insights into the intramolecular electronic properties of betanin and the charge electron mechanism on the $\\mathrm{TiO_2}$ surface. Many findings explain betanin limitations that should help to find solutions for ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,795,937,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"cell improvement. Knorr et al. reported that during the recombination process of electron injection, a radical species is formed. This radical species provokes betanin oxidation [98]. Damayanti et al. revealed that one of the three carboxyl moieties of betanin limits the betanin charge transfer to the oxide semiconductor [99]. Based on these findings, betanin modification can be carried out to develop a betanin-based DSSC. Dye aggregation is also prominent in betanin-based DSSC performance. This phenomenon can either be beneficial or detrimental to cell performance. The absorbed photon energy will be partly lost due to thermal processes and noncharge collection [100]. In contrast, Treat et al. found ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,42,154,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[494,952,502,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[60,63,931,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0841/89d8212cb6250485ca906f892ae96b2d5c5bf1a3c782fdcd9199d7196003909f.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":"<table><tr><td>No</td><td>Source</td><td>Pigmen</td><td>Solvent of extraction</td><td>Technique of purification</td><td>Photoanode</td><td>Counter electrode</td><td>Redox couple</td><td>Electrolyte solvent</td><td>JSC(mA/cm2)</td><td>VOC(V)</td><td>FF</td><td>η(%)</td><td>Referen-ce</td></tr><tr><td rowspan=\"3\">1</td><td rowspan=\"3\">Red beetroot (Beta vulgaris)</td><td rowspan=\"3\">Betanin</td><td rowspan=\"3\">0.1 M HCl in ethanol</td><td rowspan=\"3\">Collum chromatography (Waters MCX ion-exchange column or Sephadex G25) for purifying</td><td rowspan=\"3\">P25 TiO2</td><td rowspan=\"3\">Pt</td><td rowspan=\"3\">I2, LiI</td><td>acetonitrile (ACN)</td><td>0.52</td><td>0.27</td><td>0.47</td><td>0.07</td><td rowspan=\"3\">[70]</td></tr><tr><td>3-methoxypropinitrile (MPN)</td><td>0.89</td><td>0.26</td><td>0.47</td><td>0.11</td></tr><tr><td>3-methoxypropinitrile (MPN) with HCl and 4-tert-Butylpyridine (TBP)</td><td>2.42</td><td>0.44</td><td>0.63</td><td>0.67</td></tr><tr><td rowspan=\"6\">2</td><td rowspan=\"6\">Red beetroot (Beta vulgaris)</td><td rowspan=\"6\">Betanin</td><td rowspan=\"6\">Potassium phosphate buffer</td><td rowspan=\"6\">Develop the reverse-phase medium pressure liquid chromatography for purifying the extracted betanine</td><td>P25 TiO2 without bloking layer</td><td rowspan=\"6\">Pt</td><td rowspan=\"6\">I2, LiI</td><td rowspan=\"3\">acetonitrile (ACN)</td><td>10.55</td><td>0.35</td><td>0.57</td><td>2.04</td><td rowspan=\"6\">[71]</td></tr><tr><td>P25 TiO2 with TiCl4post treated</td><td>9.34</td><td>0.44</td><td>0.57</td><td>2.27</td></tr><tr><td>P25 TiO2 with bloking layer</td><td>13.91</td><td>0.36</td><td>0.56</td><td>2.71</td></tr><tr><td>P25 TiO2 without bloking layer</td><td rowspan=\"3\">3-methoxypropinitrile (MPN)</td><td>7.64</td><td>0.39</td><td>0.51</td><td>1.46</td></tr><tr><td>P25 TiO2 with TiCl4post treated</td><td>10.13</td><td>0.36</td><td>0.55</td><td>1.93</td></tr><tr><td>P25 TiO2 with bloking layer</td><td>8.61</td><td>0.44</td><td>0.61</td><td>2.22</td></tr><tr><td rowspan=\"6\">3</td><td rowspan=\"6\">Red beetroot (Beta vulgaris)</td><td rowspan=\"6\">Betalain</td><td>Water-HCl</td><td rowspan=\"3\">-</td><td rowspan=\"3\">The TiO2 porous film electrode was manufactured by using the sol-gel method, starting from the commercial titanium(IV)</td><td rowspan=\"6\">Pt</td><td rowspan=\"6\">I2, KI</td><td rowspan=\"6\">Ethyleneglicole:acetonitrile (4:1, volume ratio)</td><td>0.38</td><td>0.36</td><td>0.69</td><td>0.12</td><td rowspan=\"6\">[72]</td></tr><tr><td>Water-ascorbic acid</td><td>0.39</td><td>0.35</td><td>0.62</td><td>0.11</td></tr><tr><td>Methanol-HCl</td><td>0.09</td><td>0.36</td><td>0.65</td><td>0.03</td></tr><tr><td>Water-HCl</td><td rowspan=\"3\">pressure liquid chromatography (MPLC) for purifying</td><td rowspan=\"3\">oxide, anatase, nanopowder <25 nm, from Sigma-Aldrich, and titanium isopropoxide (Sigma-Aldrich)</td><td>2.95</td><td>0.36</td><td>0.30</td><td>0.40</td></tr><tr><td>Water-ascorbic acid</td><td>0.42</td><td>0.40</td><td>0.56</td><td>0.12</td></tr><tr><td>Methanol-HCl</td><td>0.16</td><td>0.37</td><td>0.65</td><td>0.05</td></tr><tr><td rowspan=\"3\">4</td><td rowspan=\"3\">Paper flower (Bougainville glabra)</td><td rowspan=\"3\">Betaxanthin betacyanine</td><td>Water-HCl pH = 5.70</td><td rowspan=\"3\">-</td><td rowspan=\"3\">TiO2film from blending P25 and Triton x-100</td><td rowspan=\"3\">Pt</td><td rowspan=\"3\">-</td><td rowspan=\"3\">-</td><td>2.27</td><td>0.41</td><td>0.61</td><td>0.57</td><td rowspan=\"3\">[73]</td></tr><tr><td>Water-HCl pH = 3</td><td>3.72</td><td>0.44</td><td>0.59</td><td>0.98</td></tr><tr><td>Water-HCl pH = 1.23</td><td>1.13</td><td>0.44</td><td>0.43</td><td>0.21</td></tr><tr><td rowspan=\"2\">5</td><td rowspan=\"2\">Beetroot (Beta vulgaris)</td><td rowspan=\"2\">Betanin</td><td rowspan=\"2\">Potassium phosphate buffer</td><td rowspan=\"2\">Develop the reverse-phase medium pressure liquid chromatography for purifying the extracted betanine</td><td>TiO2</td><td rowspan=\"2\">Pt</td><td rowspan=\"2\">I2, LiI</td><td rowspan=\"2\">N-methyl-2-pyrrolidone (NMP) solvent with 6% by weight polyvinylidene fluoride (PVDF)</td><td>1.47</td><td>0.49</td><td>0.63</td><td>0.58</td><td rowspan=\"2\">[74]</td></tr><tr><td>AgNPs coated onto TiO2</td><td>1.65</td><td>0.51</td><td>0.64</td><td>0.68</td></tr><tr><td>6</td><td>Bracks of paper flower (Bougainville glabra)</td><td>Betaxanthin betacyanine</td><td>Acetone-water</td><td>-</td><td>TiO2NPs</td><td>Pt</td><td>I2, LiI, TBP</td><td>3-methoxypropinitrile (MPN)</td><td>-</td><td>-</td><td>0.59</td><td>0.25</td><td>[75]</td></tr><tr><td rowspan=\"2\">7</td><td rowspan=\"2\">Sicilian prickly pears (Opuntia ficus indica) Blackberry()</td><td rowspan=\"2\">Betalain (the dominant pigmen is betaxantin)</td><td rowspan=\"2\">Ethanol and HCl/ carboxylic acid/tartaric acid as acids and co-adsorbers.</td><td rowspan=\"2\">-</td><td rowspan=\"2\">TiO2nanocrystalline</td><td rowspan=\"2\">Pt</td><td rowspan=\"2\">GuNCS, TBP</td><td rowspan=\"2\">Acetonitrile:valeronitrile (85:15)</td><td>7.85</td><td>0.38</td><td>0.62</td><td>1.87</td><td rowspan=\"2\">[76]</td></tr><tr><td>5.85</td><td>0.32</td><td>0.57</td><td>1.07</td></tr><tr><td rowspan=\"3\">8</td><td rowspan=\"3\">Red Beetroot (Beta vulgaris)</td><td rowspan=\"3\">Betanin</td><td rowspan=\"3\">Water-HCl</td><td rowspan=\"3\">-</td><td rowspan=\"3\">ZnO/Au</td><td rowspan=\"3\">Pt</td><td rowspan=\"3\">I2, KI</td><td>Water</td><td>0.05</td><td>0.25</td><td>0.33</td><td>0.48</td><td rowspan=\"3\">[77]</td></tr><tr><td>Asetonitrile</td><td>0.99</td><td>0.15</td><td>0.21</td><td>2.99</td></tr><tr><td>PVA</td><td>0.01</td><td>0.06</td><td>0.29</td><td>0.01</td></tr><tr><td>9</td><td>Red boot (Beta vulgaris L.)</td><td>Betanin</td><td>Ethanol-HCl</td><td>Sephadex DEAE A25 column and Phenomenon Strata C18 SPE Column</td><td>TiO2</td><td>Pt</td><td>I2, LiI</td><td>Acetonitrile</td><td>14</td><td>0.38</td><td>-</td><td>3.00</td><td>[78]</td></tr></table>","table_caption":"[\"Table 1. The summarized results on betanine-based DSSCs. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[944,60,954,157]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[944,815,954,937]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[37,495,45,504]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[57,65,487,119]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"that aggregated dye induces a broadened absorbance spectrum, increasing the light-harvesting efficiency [78]. A comprehensive review of the dye aggregation phenomena and their implications for DSSC performance can be found in Ref. [101]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,132,159,145]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.2. Chlorophyll ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,158,485,433]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Chlorophylls are a family of pigments classified into chlorin family. They consist of a tetrapyrrole derivative as a chelating ligand and an $\\mathrm{Mg}^{2+}$ ion as a central ion. Based on the ligand structure, chlorophyll is divided into chlorophyll-a, chlorophyll-b, chlorophyll-c1, chlorophyll-c2, and chlorophyll-f. The motivation to consider chlorophyll as natural DSSC sensitizers is to mimic the photosynthesis phenomenon. Based on our records, Kay et al. were the first to investigate chlorophyll-based DSSCs in 1993. They also compared the cell performance with a modified chlorophyll in which a $\\mathrm{Cu}^{2+}$ ion replaced the $\\mathrm{Mg}^{2+}$ ion. They reported the following cell parameters: $J_{SC}$ of $9.4\\mathrm{mAcm}^{-2}$ , $V_{OC}$ of $0.52\\mathrm{V}$ , and PCE of $2.6\\%$ . This best result was obtained with the addition of a coadsorbate using polyhydroxyl compounds such as glucose, glycerol, or sorbitol [79]. Coadsorbates were used to reduce electron recombination from the couple redox species to the photoanode surface. We also noted that even though Kay et al. were the first group to develop chlorophyll-based DSSCs, Cu-chlorophyll $\\mathrm{TiO}_2$ sensitization was first observed by Kamat et al. in 1986. They investigated the photoelectrochemical mechanism in a sensitized $\\mathrm{TiO}_2$ system using laser flash photolysis, time-resolved microwave absorption, and spectrofluorometry techniques. For these experiments, they measured the sample in dispersion form [102]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,435,485,645]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the next decade, research on chlorophyll-based DSSCs was continued by Amao et al. They used a dye derived from chlorophyll extracted from Spirulina, namely, Chl-e6. The obtained results were not satisfactory since the $J_{SC}$ was only $0.305\\mathrm{mAcm}^{-2}$ and the $V_{OC}$ was 0.426 V [80]. Wang and coworkers reported research results on chlorophyll-based DSSCs in Refs. [103, 104, 105, 106]. They developed DSSCs using a modified chlorophyll as a photosensitizer. They added a natural conjugated redox spacer to prevent the recombination of electrons with the oxidized sensitizer. Approximately $30\\%$ of the cell performance was improved after performing this modification [82, 103]. They also compared the performance of chlorophyll-based DSSCs using $\\mathrm{TiO_2}$ and $\\mathrm{ZnO}$ photoanodes. They concluded that the limitation of chlorophyll-ZnO-based DSSCs was caused by far location of the molecular orbital involved in the electron excitation process from the anchoring site [105]. A complete summary of the research on chlorophyll-based DSSCs is summarized in Table 2. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,646,487,791]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Many works have already focused on applying chlorophyll dye in DSSCs due to its role in the photosynthesis process. There have also been many reports on the utilization of synthetic porphyrin-sensitized DSSCs. The first was due to Jasieniak et al. from Flinders University, Australia, in 2004. They did not obtain a satisfactory result at that time, and their best cell efficiency was only $0.69\\%$ [107]. Impressively, in 2011, Yella et al. succeeded in preparing DSSCs based on multiple synthetic porphyrin dyes with a cobalt redox couple. The efficiency of their device reached $12\\%$ [108]. This promising result suggests the need for further investigation in the utilization of porphyrin dyes as sensitizers in DSSC applications. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,805,171,817]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.3. Anthocyanins ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,831,487,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Research on the application of anthocyanins as natural dyes in DSSCs is relatively abundant. These dyes are present in almost all colorful fruit and flowers and offer a large panel of potentially interesting dyes for DSSC applications. By looking at their chemical structure, anthocyanins have hydroxyl moieties, and some of them possess a catechol group [109]. They can act as anchoring groups to attach the dye onto the semiconductor surface. The catechol group showed better performance as an anchoring group than the carboxylic group because the latter ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,65,937,119]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"presents an electron-withdrawing character [110]. Table 3 summarizes the main published results on anthocyanin utilization as a sensitizer for DSSCs. This table shows that the anthocyanin performance is still lower than that of the chlorophyll derivative dyes. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,132,685,145]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.4. Remarks on natural dyes ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,158,937,316]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the last twenty years, reports from the scientific community on using natural dyes as a sensitizer for DSSCs have given unsatisfactory results in terms of efficiency. Many works have reported efficiencies below $2\\%$ [70, 83, 89]. Some of them have succeeded in reaching a PCE of $5\\%$ [82]. The motivations to develop natural dyes for sensitizers in DSSCs are their abundant availability, environmental friendliness, cost effectiveness, and biodegradable. Unfortunately, no one reported a PCE higher than $10\\%$ for natural dyes based on our record. Most of them have relatively low PCE values of approximately $3 - 4\\%$ . The deficiency of natural dyes lies in their stability. They also easily agglomerate, and then the photogenerated charges are not efficiently collected [111]. Almost all of them attach poorly to the oxide semiconductor surface [69, 99]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,317,937,423]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The incorporation of natural dyes in working DSSC devices remains a challenging task. Chlorophyll derivatives display the best performance among the outlined dyes, making chlorophyll derivative dyes the most researched compared to others. The strong performance of chlorophyll inspires synthetic chlorophyll-based dyes, which are no longer natural dyes. However, the lack of research on the other dyes presents the opportunity for further investigations, as the derivatives of the other dyes have not been much explored. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,436,742,448]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. Biopolymer for quasi-solid DSSC ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,462,778,475]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1. Development of biopolymer used in DSSC ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,488,937,593]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The first DSSC employed a liquid electrolyte that contained a redox couple. The utilization of a liquid electrolyte faces various problems, including solvent leakages, desorption of dye attached to the photoanode, and some practical issues of sealing [112, 113]. These reasons encouraged many researchers to develop quasi-solid electrolytes. They notably developed polymers, and among them, biopolymers have attracted much attention in line with sustainability issues and the utilization of natural resources. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,593,937,751]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Research on the utilization of biopolymers for DSSC applications started in 2010. The initial study was carried out by Buraidah et al., who used a chitosan biopolymer for solid electrolytes. The composition of $27.5\\%$ chitosan, $22.5\\%$ $\\mathrm{NH_4I}$ , and $50\\%$ BMII $(w\\%)$ produced a good conductivity of $3.34\\times 10^{-5}\\mathrm{Scm}^{-1}$ , which at the time was comparable with other polymer cells [114]. In the following years, Buraidaeh et al. developed copolymer chitosan and poly(vinyl alcohol) (PVA) to improve polymer electrolyte conductivity [115]. Several reports emerged during the same period where agarose had been used for quasi-solid DSSCs [116]. Several biopolymers that have been widely developed for quasi-solid DSSCs in the past were agarose, carrageenan, cellulose, and chitin/chitosan [117]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,752,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A more comprehensive list of the previous research is summarized in Table 4. Figure 4 presents a map of conductivity and cell performance of various biopolymer-based DSSCs. Among natural biopolymers, agarose and cellulose show promising results. Their cell efficiency value ranges from 4.5 to $7\\%$ . Table 4 also mentions various modifications that have been carried out to improve cell performance. The presence of an ionic liquid can increase the conductivity and improve the charge transfer. Singh et al. investigated the influence of a 1-ethyl-3-methylimidazolium ionic liquid in an agarose-based electrolyte. This ionic liquid increased the short circuit current from $1\\mathrm{mAcm}^{-2}$ to $3.3\\mathrm{mAcm}^{-2}$ . Moreover, Huang et al. showed that the presence of a 1-methyl-3-hexylimidazolium iodide (MHII) ionic liquid in cyanoethylated hydroxypropyl cellulose (CN-HPC) reduced the charge recombination between redox couple species and the oxide semiconductor surface due to the bulky structure of ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,42,157,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[494,952,504,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[60,87,931,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0715/e721b707196df13da6dc28664fe3a5c2e48f1e0a0c3fb8e5b249ee52906caf79.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":"<table><tr><td>No</td><td>Sources</td><td>Solvent of extraction</td><td>Modification</td><td>Photoanodes</td><td>Counter electrode</td><td>Redox couple</td><td>Electrolyte Solvent</td><td>JSC(mA/cm2)</td><td>VOC(V)</td><td>FF</td><td>η(%)</td><td>Reference</td></tr><tr><td>1</td><td>Commercial chlorophyll from Sigma</td><td>-</td><td>Replaced Mg2+with Cu2+</td><td>TiO2</td><td>Pt-foil</td><td>KI, I2</td><td>80%ethylene carbonate and 20% propylene carbonate</td><td>0.54</td><td>0.42</td><td>-</td><td>2.6</td><td>[80]</td></tr><tr><td>2</td><td>Commercial chlorine-e6 derived from chlorophyll extracted from Spirulina</td><td>-</td><td>-</td><td>TiO2nanocrystalline</td><td>C-OTE</td><td>KI, I2</td><td>Ethylene glycol/acetonitrile</td><td>0.305</td><td>0.43</td><td>0.45</td><td>0.73</td><td>[79]</td></tr><tr><td rowspan=\"6\">3</td><td>Spinach leave (Spinacia oleracea L.)</td><td>Ethanol T=50 °C</td><td>-</td><td>TiO2nanofluid</td><td>Plate of lower conductive glass</td><td>I-/I3</td><td>Acetonitrile</td><td>0.467</td><td>0.55</td><td>0.51</td><td>0.13</td><td>[81]</td></tr><tr><td rowspan=\"5\">Ipomoea (Ipomoea carnea)</td><td>Ethanol T=50 °C</td><td></td><td></td><td></td><td></td><td></td><td>0.914</td><td>0.54</td><td>0.56</td><td>0.28</td><td></td></tr><tr><td>Ethanol T=50 °C</td><td></td><td></td><td></td><td></td><td></td><td>0.915</td><td>0.51</td><td>0.55</td><td>0.25</td><td></td></tr><tr><td>Ethanol T=50 °C</td><td></td><td></td><td></td><td></td><td></td><td>0.982</td><td>0.54</td><td>0.56</td><td>0.29</td><td></td></tr><tr><td>Ethanol T=50 °C</td><td></td><td></td><td></td><td></td><td></td><td>1.120</td><td>0.57</td><td>0.59</td><td>0.32</td><td></td></tr><tr><td>Ethanol T=50 °C</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\"5\">4</td><td rowspan=\"5\">Spirulina geileri</td><td rowspan=\"5\">Methanol Modification function group (hydrocarbon) by transesterification using methyl esther</td><td rowspan=\"5\">Chlorine-1 (methyl) Chlorine-2 (hexyl) Chlorine-3 (dodecyl) Chlorine-4 (2-butyloctyl) Chlorine-5 (cholesteryl)</td><td rowspan=\"5\">TiO2NPs</td><td rowspan=\"5\">Pt wire</td><td rowspan=\"5\">BMII, I2, Additive: GNCS, TPB</td><td rowspan=\"5\">Acetonitrile-valeronitrile</td><td>15</td><td>0.60</td><td>0.72</td><td>6.5</td><td>[82]</td></tr><tr><td>15.5</td><td>0.62</td><td>0.73</td><td>7.0</td><td></td></tr><tr><td>17.4</td><td>0.64</td><td>0.72</td><td>8.0</td><td></td></tr><tr><td>13.9</td><td>0.65</td><td>0.74</td><td>6.6</td><td></td></tr><tr><td>13.6</td><td>0.64</td><td>0.70</td><td>6.1</td><td></td></tr><tr><td>5</td><td>Pomegranate leaves (Punica granatum L.)</td><td>Ethanol</td><td>-</td><td>TiO2NPs</td><td>Pt-thin film on FTO</td><td>I2, LiI Additive: TBP</td><td>Acetonitrile</td><td>2.05</td><td>0.56</td><td>0.52</td><td>0.59</td><td>[83]</td></tr><tr><td>6</td><td>Pandan leaves (Pandanus amaryllifolius)</td><td>Ethanol-tartaric acid</td><td>-</td><td>TiO2</td><td>Pt-FTO</td><td>NaI</td><td>PVDF-HFP</td><td>1.91</td><td>0.48</td><td>0.56</td><td>0.51</td><td>[84]</td></tr><tr><td rowspan=\"2\">7</td><td rowspan=\"2\">Spinach (Spinacia oleracea L.)</td><td rowspan=\"2\">Ethanol using ultrasonic technique water using ultrasonic technique</td><td rowspan=\"2\">-</td><td rowspan=\"2\">TiO2</td><td rowspan=\"2\">Graphite-ITO</td><td rowspan=\"2\">I-/I3</td><td rowspan=\"2\">Acetonitrile</td><td>0.32</td><td>0.38</td><td>0.36</td><td>1-2</td><td>[85]</td></tr><tr><td>0.35</td><td>0.44</td><td>0.49</td><td></td><td></td></tr><tr><td rowspan=\"5\">8</td><td rowspan=\"5\">Marigold leaves (Tagetes patula)</td><td rowspan=\"5\">Water</td><td rowspan=\"5\">Effect dipping time of ZnS in dye solution</td><td>ZnS (0 h)</td><td rowspan=\"5\">Graphite</td><td rowspan=\"5\">S2/Sn2</td><td rowspan=\"5\">NaOH-Na2S</td><td>0.297</td><td>0.21</td><td>0.30</td><td>0.05</td><td>[86]</td></tr><tr><td>ZnS (2 h)</td><td>0.400</td><td>0.23</td><td>0.21</td><td>0.05</td><td></td></tr><tr><td>ZnS (4 h)</td><td>0.463</td><td>0.29</td><td>0.28</td><td>0.10</td><td></td></tr><tr><td>ZnS (6 h)</td><td>0.520</td><td>0.24</td><td>0.24</td><td>0.09</td><td></td></tr><tr><td>ZnS (8 h)</td><td>0.533</td><td>0.30</td><td>0.31</td><td>0.12</td><td></td></tr><tr><td rowspan=\"6\">9</td><td rowspan=\"6\">Bryophyte</td><td rowspan=\"6\">Ethanol</td><td rowspan=\"6\">-</td><td rowspan=\"6\">TiO2</td><td rowspan=\"6\">Pt-FTO</td><td>TPAI(2%)-I2(0.17%w/w)</td><td rowspan=\"6\">PAN-EC-PC</td><td>0.94</td><td>0.63</td><td>0.75</td><td>0.45</td><td>[87]</td></tr><tr><td>TPAI(4%)-I2(0.34%w/w)</td><td>4.08</td><td>0.54</td><td>0.58</td><td>1.27</td><td></td></tr><tr><td>TPAI(6%)-I2(0.51%w/w)</td><td>5.51</td><td>0.53</td><td>0.53</td><td>1.52</td><td></td></tr><tr><td>TPAI(8%)-I2(0.68%w/w)</td><td>6.10</td><td>0.53</td><td>0.51</td><td>1.66</td><td></td></tr><tr><td>TPAI(10%)-I2(0.85%w/w)</td><td>5.78</td><td>0.6</td><td>0.57</td><td>1.97</td><td></td></tr><tr><td>TPAI(12%)-I2(0.97%w/w)</td><td>5.96</td><td>0.62</td><td>0.50</td><td>1.86</td><td></td></tr></table>","table_caption":"[\"Table 2. The summarized research on chlorophyll-based DSSCs. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[944,58,955,157]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[944,815,954,937]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[58,90,937,590]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0221/63928f3a95074ce1941d8c0281f6576edaf41e8e7c625bc3b7facc82c61192e4.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":"<table><tr><td>No</td><td>Sources</td><td>Solvent of extraction</td><td>Photoanode</td><td>Counter electrode</td><td>Redox couple</td><td>Solvent of electrolyte</td><td>JSC(mA/cm2)</td><td>VOC(V)</td><td>FF</td><td>η(%)</td><td>Reference</td></tr><tr><td rowspan=\"2\">1</td><td rowspan=\"2\">Henna leaves(Lawsonia inermis)</td><td>Ethanol</td><td rowspan=\"2\">TiO2</td><td rowspan=\"2\">Pt</td><td rowspan=\"2\">KI, I2</td><td rowspan=\"2\">Ethylene glycol-acetonitrile</td><td>1.87</td><td>0.59</td><td>0.58</td><td>0.66</td><td rowspan=\"2\">[88]</td></tr><tr><td>Ethanol-water</td><td>1.35</td><td>0.59</td><td>0.65</td><td>0.52</td></tr><tr><td rowspan=\"4\">2</td><td rowspan=\"4\">Canna indicaSalvia splendensCow berry (Vaccinium vitis-idaea)Solanum nigrum</td><td rowspan=\"4\">Ethanol-water</td><td rowspan=\"4\">TiO2</td><td rowspan=\"4\">Pt</td><td rowspan=\"4\">Lil, I2,TBP and BMII</td><td rowspan=\"4\">Acetonitrile-valeronitrile</td><td>0.82</td><td>0.54</td><td>0.59</td><td>0.29</td><td rowspan=\"4\">[89]</td></tr><tr><td>0.7</td><td>0.56</td><td>0.61</td><td>0.26</td></tr><tr><td>0.4</td><td>0.56</td><td>0.54</td><td>0.13</td></tr><tr><td>1.01</td><td>0.54</td><td>0.51</td><td>0.31</td></tr><tr><td rowspan=\"4\">3</td><td rowspan=\"4\">Mulberry Fruits(Morus nigra)</td><td rowspan=\"4\">Metanol:water:acetic-acid:25:21:4</td><td rowspan=\"4\">P25 TiO2</td><td>Purified SWCNTs</td><td rowspan=\"4\">I-/I3-</td><td rowspan=\"4\">Acetonitrile</td><td>2.65</td><td>0.59</td><td>0.51</td><td>0.67</td><td rowspan=\"4\">[90]</td></tr><tr><td>SWCNTs</td><td>2.41</td><td>0.47</td><td>0.38</td><td>0.42</td></tr><tr><td>Purified MWCNTs</td><td>3.12</td><td>0.48</td><td>0.39</td><td>0.52</td></tr><tr><td>MWCNTs</td><td>1.71</td><td>0.51</td><td>0.44</td><td>0.39</td></tr><tr><td rowspan=\"4\">4</td><td rowspan=\"4\">Roselle (Hibiscus sabdariffa)</td><td rowspan=\"4\">Citric acid</td><td>TiO2</td><td rowspan=\"4\">Pt</td><td rowspan=\"4\">I-/I3-</td><td rowspan=\"4\">Acetonitrile</td><td>4.8</td><td>0.45</td><td>0.43</td><td>0.92</td><td rowspan=\"4\">[28]</td></tr><tr><td>Na-TiO2(6%)</td><td>5.5</td><td>0.55</td><td>0.55</td><td>1.65</td></tr><tr><td>Na(6%)-Yeast (4%)-TiO2</td><td>6.2</td><td>0.58</td><td>0.60</td><td>2.17</td></tr><tr><td>Na(6%)-Yeast (6%)-TiO2</td><td>6.9</td><td>0.62</td><td>0.56</td><td>2.40</td></tr><tr><td rowspan=\"4\">5</td><td rowspan=\"4\">Mangosteen pericarp(Garcinia mangostanaL.)</td><td>Methanol:HCl (99:1) + add benzoic acid (1:0)</td><td rowspan=\"4\">TiO2NTs</td><td rowspan=\"4\">Pt</td><td rowspan=\"4\">I-/I3-</td><td rowspan=\"4\">Acetonitrile</td><td>0.0069</td><td>0.26</td><td>0.39</td><td>0.23</td><td rowspan=\"4\">[91]</td></tr><tr><td>Methanol:HCl (99:1) + add benzoic acid (1:0.5)</td><td>0.0125</td><td>0.16</td><td>0.36</td><td>0.23</td></tr><tr><td>Methanol:HCl (99:1) + add benzoic acid (1:0.8)</td><td>0.0043</td><td>0.31</td><td>0.66</td><td>0.29</td></tr><tr><td>Methanol:HCl (99:1) + add benzoic acid (1:1)</td><td>0.0065</td><td>0.36</td><td>0.48</td><td>0.37</td></tr><tr><td rowspan=\"2\">6</td><td rowspan=\"2\">Seduduk fruit(Malabrichum MelastomaL)</td><td>Ethanol-HCl</td><td rowspan=\"2\">P25 TiO2</td><td rowspan=\"2\">C</td><td rowspan=\"2\">NaI2</td><td rowspan=\"2\">PEG</td><td rowspan=\"2\">-</td><td rowspan=\"2\">-</td><td rowspan=\"2\">-</td><td>0.62</td><td rowspan=\"2\">[92]</td></tr><tr><td>Ethanol-HCl with salicylic acid</td><td>1.32</td></tr><tr><td>7</td><td>Vaccinium meridionale</td><td>Ethanol-water bu proculation method</td><td>P25 TiO2</td><td>Pt</td><td>KI, I2,KClO4</td><td>Acetonitrile</td><td>-</td><td>-</td><td>-</td><td>-</td><td>[93]</td></tr><tr><td rowspan=\"2\">8</td><td rowspan=\"2\">Jabuticaba fruits(Plinia cauliflora)</td><td rowspan=\"2\">Absolute ethanol</td><td>TiO2(doctorblade)</td><td rowspan=\"2\">C</td><td rowspan=\"2\">I2, KI</td><td rowspan=\"2\">PVP</td><td>0.23</td><td>0.35</td><td>0.23</td><td>0.08</td><td rowspan=\"2\">[94]</td></tr><tr><td>TiO2(spin coating)</td><td>0.38</td><td>0.41</td><td>0.29</td><td>0.13</td></tr></table>","table_caption":"[\"Table 3. The summarized research on anthocyanin based DSSCs. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[57,614,487,694]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MHII compared to $\\mathrm{I}^{-}$ [118]. The addition of $\\mathrm{Co}_3\\mathrm{O}_4$ , NiO, and $\\mathrm{TiO}_2$ nanoparticles can also improve conductivity [119]. The presence of cross-linking networks between nanoparticles and polymers facilitates ion transport within the polymer matrix. The addition of nanoparticles can also be detrimental due to the formation of nanoparticle aggregates [120]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,712,391,725]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2. Structural aspects of biopolymer for quasi-solid DSSC ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,738,485,829]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"All of the biopolymers mentioned previously, which are widely applied to polymer gel electrolytes, are polysaccharides. These biopolymers consist of the hexa-pyranose building block of D-glucose as a monomer with various glycosidic linkages, either $\\alpha$ -1,3 or $\\beta$ -1,4. In chitin or chitosan, D-glucose is substituted by amine or acetyl amine groups. Table 5 presents the chemical structure information and conductivity of these biopolymers. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,829,485,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The hydroxyl groups in polymer chains are responsible for establishing the bond with the ionic species in the electrolyte, which subsequently contributes to the ionic conductivity [121, 122, 123]. Furthermore, the functional groups on the polymer chain play an essential role in creating the bond with the liquid as a dispersed phase in the gelation process [124]. The gel polymer electrolyte system in a DSSC consists of the polymer matrix and liquid. The polymer matrix acts as the immobilizer or dispersion medium, while the liquid functions as a ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,614,937,718]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"dispersed phase. Liquid can also function as a solvent for ionic species or redox couples. The interaction of these three components is vital for charges to be transferred to ensure good cell performance. One of the studies on this topic was conducted by Shih et al., where the interfacial interaction of iodide as a redox couple and agarose as a polymer matrix was investigated. The XPS study confirmed the formation of polyiodide in the electrolyte, which benefited the charge transfer channels after adding $\\mathrm{TiO_2}$ nanoparticles into the electrolyte gel system [119]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,720,937,851]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Molecular-level studies concerning this background are necessary. Unfortunately, only a small number of previous studies that are relevant to natural polymer systems were found. Yoon et al. theoretically observed the interaction between the ionic liquid 1-propyl-3-methyl imidazolium iodide (PMII) and the synthetic polymer poly(styrene-block-ethylene oxide-block-styrene) (SEOS) to investigate the complex structure of PMII and SEOS during the interaction stages. This experiment will then be used to explain the typical bonding and charge transfer [125]. Thus, to do so, further studies in natural polymer systems are still needed. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,870,781,883]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.3. Remarks on biopolymer quasi solid DSSCs ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,897,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Biopolymer electrolytes for DSSCs have been chosen as a solution to overcome the shortcomings of liquid electrolytes, such as solvent volatilization, poor stability due to leakage or counter electrode corrosion, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,42,154,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[494,952,502,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[63,92,931,860]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0437/5b3d1cd864c5a9637fd944185079ed2def2d4b6301c0e77a48b581e0c13912f7.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":"<table><tr><td>No</td><td>Biopolymer as Gel electrolyte</td><td>Modification biopolymer</td><td>Electrolyte solvent</td><td>Redox couple</td><td>Photoanode</td><td>Counter electrode</td><td>Dye</td><td>Conductivity (mS/cm)</td><td>JSC(mA/cm2)</td><td>VOC(V)</td><td>FF</td><td>η(%)</td><td>Reference</td></tr><tr><td rowspan=\"39\">1</td><td rowspan=\"39\">Agarose</td><td>Ratio agarose (%)</td><td rowspan=\"14\">1-methyl-2-pyrrolidinone (NMP)</td><td rowspan=\"14\">I2,LiI</td><td rowspan=\"14\">P25 TiO2</td><td rowspan=\"14\">Pt</td><td rowspan=\"14\">-</td><td></td><td></td><td></td><td></td><td></td><td rowspan=\"14\">[116]</td></tr><tr><td>1</td><td>0.28</td><td>6.16</td><td>0.58</td><td>0.67</td><td>3.20</td></tr><tr><td>1.5</td><td>0.39</td><td>7.56</td><td>0.62</td><td>0.63</td><td>3.97</td></tr><tr><td>2</td><td>0.36</td><td>8.24</td><td>0.60</td><td>0.62</td><td>4.14</td></tr><tr><td>2.5</td><td>0.32</td><td>5.16</td><td>0.63</td><td>0.69</td><td>3.01</td></tr><tr><td>3</td><td>0.65</td><td>5.32</td><td>0.62</td><td>0.64</td><td>2.83</td></tr><tr><td>4</td><td>-</td><td>4.44</td><td>0.63</td><td>0.72</td><td>2.73</td></tr><tr><td>5</td><td>0.66</td><td>2.12</td><td>0.68</td><td>0.78</td><td>1.49</td></tr><tr><td>Ratio TiO2 in agarose (%)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0</td><td>0.30</td><td>7.76</td><td>0.66</td><td>0.53</td><td>3.77</td></tr><tr><td>2.5</td><td>0.44</td><td>10.96</td><td>0.55</td><td>0.57</td><td>4.74</td></tr><tr><td>5</td><td>0.51</td><td>8.84</td><td>0.55</td><td>0.56</td><td>4.45</td></tr><tr><td>7.5</td><td>0.33</td><td>9.20</td><td>0.55</td><td>0.52</td><td>3.64</td></tr><tr><td>10</td><td>0.34</td><td>9.04</td><td>0.57</td><td>0.48</td><td>3.42</td></tr><tr><td rowspan=\"8\">-</td><td rowspan=\"8\">NMP</td><td>10%LiI, I2</td><td rowspan=\"8\">P25 TiO2</td><td rowspan=\"8\">Pt</td><td rowspan=\"8\">N719</td><td>1.99</td><td rowspan=\"8\" colspan=\"4\">Not measured</td><td rowspan=\"8\">[212]</td></tr><tr><td>15%LiI, I2</td><td>3.16</td></tr><tr><td>20%LiI, I2</td><td>3.98</td></tr><tr><td>25%LiI, I2</td><td>2.39</td></tr><tr><td>30%LiI, I2</td><td>3.31</td></tr><tr><td>35%LiI, I2</td><td>3.89</td></tr><tr><td>65%LiI, I2</td><td>5.62</td></tr><tr><td>85%LiI, I2</td><td>5.62</td></tr><tr><td rowspan=\"5\">-</td><td>DMSO/PC</td><td rowspan=\"5\">GuSCN, NMBI, I2</td><td rowspan=\"5\">P25 TiO2</td><td rowspan=\"5\">Pt</td><td rowspan=\"5\">N719</td><td>14.2</td><td>4.65</td><td>0.73</td><td>0.58</td><td>1.97</td><td rowspan=\"5\">[213]</td></tr><tr><td>DMSO/4EG</td><td>4.4</td><td>3.69</td><td>0.65</td><td>0.57</td><td>1.38</td></tr><tr><td>DMSO/3EG</td><td>4.6</td><td>4.01</td><td>0.61</td><td>0.57</td><td>1.39</td></tr><tr><td>DMSO/PEG</td><td>6.2</td><td>3.21</td><td>0.58</td><td>0.57</td><td>1.06</td></tr><tr><td>DMSO (20v%)</td><td>5.0</td><td>3.69</td><td>0.58</td><td>0.54</td><td>1.15</td></tr><tr><td rowspan=\"4\">0.5% agarose</td><td rowspan=\"9\">PC/DMSO (8:2)</td><td>MPII</td><td rowspan=\"9\">Double-layer TiO2</td><td rowspan=\"9\">Pt</td><td rowspan=\"9\">N719</td><td rowspan=\"9\">-</td><td>11.73</td><td>0.70</td><td>0.64</td><td>5.25</td><td rowspan=\"9\">[214]</td></tr><tr><td>AEII</td><td>11.71</td><td>0.72</td><td>0.65</td><td>5.45</td></tr><tr><td>APII</td><td>11.53</td><td>0.70</td><td>0.62</td><td>4.97</td></tr><tr><td>DAIII</td><td>11.84</td><td>0.70</td><td>0.60</td><td>4.96</td></tr><tr><td>0wt% agarose</td><td rowspan=\"5\">AEII</td><td>12.26</td><td>0.66</td><td>0.60</td><td>4.97</td></tr><tr><td>0.5wt% agarose</td><td>11.71</td><td>0.72</td><td>0.65</td><td>5.45</td></tr><tr><td>0.65wt% agarose</td><td>11.45</td><td>0.76</td><td>0.68</td><td>5.89</td></tr><tr><td>0.8wt% agarose</td><td>11.82</td><td>0.75</td><td>0.64</td><td>5.68</td></tr><tr><td>1.0wt% agarose</td><td>11.96</td><td>0.70</td><td>0.63</td><td>5.31</td></tr><tr><td>0 mT NiO-agarose</td><td rowspan=\"3\">NMP</td><td rowspan=\"3\">LiI, I2</td><td rowspan=\"3\">P25 TiO2</td><td rowspan=\"3\">Pt</td><td rowspan=\"3\">N719</td><td rowspan=\"3\">-</td><td>4.5</td><td>0.77</td><td>0.45</td><td>1.61</td><td rowspan=\"3\">[215]</td></tr><tr><td>14 mT NiO-agarose</td><td>4.7</td><td>0.80</td><td>0.56</td><td>2.32</td></tr><tr><td>25 mT NiO-agarose</td><td>5.9</td><td>0.74</td><td>0.64</td><td>2.95</td></tr></table>","table_caption":"[\"Table 4. The summary of various researches reported on the biopolymer-based quasi solid DSSC. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[846,868,930,882]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(continued on next page) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[944,58,955,157]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[944,815,954,937]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[60,90,931,915]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0844/17fa711c1f4b12dbd4721bf760e41118a3b4760bbf2c5bcd72a562e23f97348e.jpg","list_items":null,"page_idx":"9","sub_type":null,"table_body":"<table><tr><td>No</td><td>Biopolymer as Gel electrolyte</td><td>Modification biopolymer</td><td>Electrolyte solvent</td><td>Redox couple</td><td>Photoanode</td><td>Counter electrode</td><td>Dye</td><td>Conductivity (mS/cm)</td><td>JSC(mA/cm2)</td><td>VOC(V)</td><td>FF</td><td>η(%)</td><td>Reference</td></tr><tr><td></td><td></td><td>35 mT NiO-agarose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6.0</td><td>0.77</td><td>0.62</td><td>2.94</td><td></td></tr><tr><td></td><td></td><td>45 mT NiO-agarose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4.2</td><td>0.76</td><td>0.61</td><td>2.24</td><td></td></tr><tr><td></td><td></td><td>55 mT NiO-agarose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.5</td><td>0.78</td><td>0.70</td><td>1.37</td><td></td></tr><tr><td></td><td></td><td>-</td><td>PC/DMSO</td><td>AEII, GuSCN, NMBI, I2</td><td>a-TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>10.39</td><td>0.80</td><td>0.71</td><td>5.89</td><td>[216]</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>a-TiO2+30% PEG (0 min)</td><td></td><td></td><td></td><td>13.29</td><td>0.74</td><td>0.66</td><td>6.54</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>a-TiO2+30% PEG (30 min)</td><td></td><td></td><td></td><td>14.18</td><td>0.74</td><td>0.69</td><td>7.18</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>a-TiO2+30% PEG (60 min)</td><td></td><td></td><td></td><td>14.32</td><td>0.75</td><td>0.69</td><td>7.43</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>a-TiO2+30% PEG (90 min)</td><td></td><td></td><td></td><td>14.57</td><td>0.73</td><td>0.68</td><td>7.28</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>a-TiO2+30% PEG (120 min)</td><td></td><td></td><td></td><td>13.89</td><td>0.74</td><td>0.68</td><td>7.04</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>a-TiO2+30% PEG (150 min)</td><td></td><td></td><td></td><td>11.36</td><td>0.68</td><td>0.65</td><td>4.98</td><td></td></tr><tr><td></td><td></td><td>TiO2-agarose</td><td>NMP</td><td>LiI, I2</td><td>TiO2 NPs</td><td>Pt</td><td>N719</td><td>2.66</td><td>5.28</td><td>0.61</td><td>0.55</td><td>1.71</td><td>[120]</td></tr><tr><td></td><td></td><td>Co3O4-agarose</td><td></td><td></td><td></td><td></td><td></td><td>4.37</td><td>7.24</td><td>0.64</td><td>0.46</td><td>2.11</td><td></td></tr><tr><td></td><td></td><td>NiO-agarose</td><td></td><td></td><td></td><td></td><td></td><td>3.33</td><td>6.20</td><td>0.63</td><td>0.52</td><td>2.02</td><td></td></tr><tr><td></td><td></td><td>-</td><td>NMP/MPN</td><td>LiI, I2, PMI, NMBI</td><td>TiO2 NPs</td><td>Pt</td><td>Ruthenizer 520-DN</td><td>14.09</td><td>10.7</td><td>0.82</td><td>-</td><td>4.9</td><td>[119]</td></tr><tr><td></td><td></td><td>Agarose</td><td></td><td></td><td></td><td></td><td></td><td>8.31</td><td>10.7</td><td>0.78</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td></td><td>TiO2-agarose</td><td></td><td></td><td></td><td></td><td></td><td>12.12</td><td>11.8</td><td>0.80</td><td>-</td><td>5.1</td><td></td></tr><tr><td></td><td></td><td>-</td><td>DMSO</td><td>KI, I2</td><td>TiO2</td><td>Pt</td><td>N3 dye</td><td>-</td><td>1.00</td><td>0.57</td><td>0.56</td><td>0.33</td><td>[217]</td></tr><tr><td></td><td></td><td></td><td></td><td>KI, I2, IL</td><td></td><td></td><td></td><td></td><td>1.90</td><td>0.75</td><td>0.77</td><td>0.47</td><td></td></tr><tr><td></td><td></td><td></td><td>DMF</td><td>KI, I2</td><td></td><td></td><td></td><td></td><td>1.00</td><td>0.63</td><td>0.60</td><td>0.72</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>KI, I2, IL</td><td></td><td></td><td></td><td></td><td>3.30</td><td>0.62</td><td>0.66</td><td>1.36</td><td></td></tr><tr><td>2</td><td>Kappa-Carrageenan</td><td>Carboxymethyl kappa-carrageenan/wt-carboxymethyl cellulose:NH4(I (30% wt)</td><td>Acetic acid</td><td>NH4I, I2</td><td>TiO2</td><td>Pt</td><td>N719</td><td>2.41</td><td>0.42</td><td>0.50</td><td>0.64</td><td>0.13</td><td>[218]</td></tr><tr><td></td><td></td><td>Carboxymethyl kappa-carrageenan/wt-carboxymethyl cellulose:LiI (10% wt)</td><td>Acetic acid</td><td>LiI, I2</td><td>TiO2</td><td>Pt</td><td>N719</td><td>1.66</td><td>0.05</td><td>0.50</td><td>0.90</td><td>0.02</td><td>[219]</td></tr><tr><td></td><td></td><td>Carboxymethyl kappa-carrageenan/wt-carboxymethyl cellulose:LiI (20% wt)</td><td></td><td></td><td></td><td></td><td></td><td>2.73</td><td>0.12</td><td>0.49</td><td>0.80</td><td>0.05</td><td></td></tr><tr><td></td><td></td><td>Carboxymethyl kappa-carrageenan/wt-carboxymethyl cellulose:LiI (30% wt)</td><td></td><td></td><td></td><td></td><td></td><td>3.89</td><td>0.40</td><td>0.49</td><td>0.57</td><td>0.11</td><td></td></tr><tr><td>3</td><td>Iota Carrageenan</td><td>-</td><td>Water</td><td>NaI, I2</td><td>TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>2.58</td><td>0.41</td><td>0.60</td><td>0.63</td><td>[220]</td></tr><tr><td></td><td></td><td>Iota carrageenan +10%wt ionic liquid</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3.63</td><td>0.43</td><td>0.42</td><td>0.64</td><td></td></tr><tr><td></td><td></td><td>Iota carrageenan +20%wt ionic liquid</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.71</td><td>0.45</td><td>0.54</td><td>0.65</td><td></td></tr><tr><td></td><td></td><td>Iota carrageenan +30%wt ionic liquid</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3.38</td><td>0.46</td><td>0.47</td><td>0.72</td><td></td></tr><tr><td></td><td></td><td>Iota carrageenan +40%wt ionic liquid</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1.74</td><td>0.43</td><td>0.54</td><td>0.40</td><td></td></tr><tr><td>4</td><td>Chitosan</td><td>27.5%wt chitosan</td><td>DMF</td><td>22.5% wt NH4I - 50%wt I2</td><td>TiO2</td><td>Pt</td><td>Anthocyanin</td><td>1.51</td><td>0.76</td><td>0.38</td><td>0.48</td><td>0.14</td><td>[114]</td></tr><tr><td></td><td></td><td>11%wt chitosan</td><td></td><td>9% wt NH4I - 80%wt I2</td><td></td><td></td><td></td><td>3.02</td><td>0.90</td><td>0.37</td><td>0.45</td><td>0.15</td><td></td></tr><tr><td></td><td></td><td>11%wt of chitosan-PEO (ratio 30:70)</td><td></td><td>9% wt NH4I - 80%wt I2</td><td></td><td></td><td></td><td>5.52</td><td>1.21</td><td>0.40</td><td>0.47</td><td>0.23</td><td></td></tr><tr><td></td><td></td><td>adding PEG as plasticizer</td><td>Formic acid</td><td>KI, I2</td><td>Bi2Ti2O7</td><td>Pt</td><td>N719</td><td>-</td><td>2.72</td><td>0.63</td><td>0.36</td><td>0.73</td><td>[221]</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Bi2Ti2O7: 2% Sm</td><td></td><td></td><td></td><td>3.65</td><td>0.69</td><td>0.49</td><td>1.45</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Bi2Ti2O7: 2% Eu</td><td></td><td></td><td></td><td>8.42</td><td>0.72</td><td>0.39</td><td>2.77</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Bi2Ti2O7: 2% Gd</td><td></td><td></td><td></td><td>8.36</td><td>0.72</td><td>0.55</td><td>3.88</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Bi2Ti2O7: 2% Dy</td><td></td><td></td><td></td><td>8.83</td><td>0.74</td><td>0.50</td><td>3.86</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Bi2Ti2O7: 2% Ho</td><td></td><td></td><td></td><td>5.90</td><td>0.72</td><td>0.52</td><td>2.58</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Bi2Ti2O7: 2% Er</td><td></td><td></td><td></td><td>6.36</td><td>0.67</td><td>0.43</td><td>2.18</td><td></td></tr><tr><td></td><td></td><td>Chitosan</td><td>Acetic acid</td><td>KI, I2</td><td>TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>1.29</td><td>0.62</td><td>0.82</td><td>0.66</td><td>[222]</td></tr><tr><td></td><td></td><td>Chitosan NPs by ultrasonication methods</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.18</td><td>0.58</td><td>0.78</td><td>0.99</td><td></td></tr><tr><td></td><td></td><td>Chitosan NPs by ionic gelatin methods</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3.66</td><td>0.55</td><td>0.61</td><td>1.23</td><td></td></tr><tr><td></td><td></td><td>Hexanoyl chitosan/PVC</td><td>THF</td><td>20%NaI, I2</td><td>TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>5.31</td><td>0.63</td><td>0.54</td><td>1.80</td><td>[223]</td></tr><tr><td></td><td></td><td></td><td></td><td>30%NaI, I2</td><td></td><td></td><td></td><td></td><td>8.62</td><td>0.58</td><td>0.59</td><td>2.93</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>40%NaI, I2</td><td></td><td></td><td></td><td></td><td>6.32</td><td>0.67</td><td>0.62</td><td>2.59</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>30%NaI, I2, GuSCN, TBP</td><td></td><td></td><td></td><td></td><td>17.69</td><td>0.65</td><td>0.46</td><td>5.31</td><td></td></tr><tr><td></td><td></td><td>Cellulose</td><td>-</td><td>Acetonitrile</td><td>LII, I2, TBP, TBAI</td><td>TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>17.05</td><td>0.67</td><td>0.57</td><td>[224]</td></tr><tr><td></td><td></td><td>Adding 3.5 wt% ethyl cellulose as gelator</td><td></td><td></td><td></td><td></td><td></td><td></td><td>14.94</td><td>0.70</td><td>0.61</td><td>6.37</td><td></td></tr><tr><td></td><td></td><td>Adding 5.8 wt% ethyl cellulose as gelator</td><td></td><td></td><td></td><td></td><td></td><td></td><td>14.91</td><td>0.68</td><td>0.59</td><td>5.98</td><td></td></tr><tr><td></td><td></td><td>Adding 8.8 wt% ethyl cellulose as gelator</td><td></td><td></td><td></td><td></td><td></td><td></td><td>14.23</td><td>0.68</td><td>0.57</td><td>5.51</td><td></td></tr><tr><td></td><td></td><td>Grafted cellulose</td><td>-</td><td>KI, I2</td><td>TiO2</td><td>Pt</td><td>Ru dye</td><td></td><td>12.65</td><td>0.71</td><td>0.61</td><td>5.51</td><td>[225]</td></tr><tr><td></td><td></td><td>CN-HPC (cyanoethylated hydroxypropyl cellulose)</td><td>MPN</td><td>MHII, LII, I2, TBP</td><td>TiO2 adding MgO</td><td>Pt</td><td>N719</td><td>-</td><td>13.67</td><td>0.74</td><td>0.69</td><td>7.02</td><td>[118]</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>SD2</td><td></td><td>12.17</td><td>0.74</td><td>0.75</td><td>6.76</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>MHII, LII, I2, TBP</td><td></td><td></td><td>N719</td><td></td><td>14.40</td><td>0.76</td><td>0.70</td><td>7.55</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>SD2</td><td></td><td>12.65</td><td>0.78</td><td>0.75</td><td>7.40</td><td></td></tr><tr><td></td><td></td><td>3% micro-cellulose</td><td>-</td><td>LII, I2, MPI, EMISCN, TBP</td><td>TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>5.45</td><td>0.54</td><td>0.60</td><td>1.75</td><td>[226]</td></tr><tr><td></td><td></td><td>4% micro-cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5.42</td><td>0.53</td><td>0.57</td><td>1.64</td><td></td></tr><tr><td></td><td></td><td>5% micro-cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7.37</td><td>0.61</td><td>0.58</td><td>2.69</td><td></td></tr><tr><td></td><td></td><td>6% micro-cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7.47</td><td>0.58</td><td>0.61</td><td>2.62</td><td></td></tr><tr><td></td><td></td><td>0%-Nanoscale microfibrillated cellulose</td><td>Acetonitrile</td><td>NaI, I2, TBP</td><td>TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>11.7</td><td>0.65</td><td>0.59</td><td>4.42</td><td>[227]</td></tr><tr><td></td><td></td><td>5%-Nanoscale microfibrillated cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>11.9</td><td>0.68</td><td>0.58</td><td>4.71</td><td></td></tr><tr><td></td><td></td><td>10%-Nanoscale microfibrillated cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12.3</td><td>0.71</td><td>0.59</td><td>5.11</td><td></td></tr><tr><td></td><td></td><td>20%-Nanoscale microfibrillated cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>13.2</td><td>0.73</td><td>0.60</td><td>5.84</td><td></td></tr><tr><td></td><td></td><td>30%-Nanoscale microfibrillated cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>15.2</td><td>0.76</td><td>0.61</td><td>7.03</td><td></td></tr><tr><td></td><td></td><td>0%-cellulose nanocrystall</td><td>water</td><td>NaI, I2, TBP</td><td>TiO2</td><td>Pt</td><td>Cu based dye</td><td>-</td><td>0.3</td><td>0.63</td><td>0.48</td><td>0.08</td><td>[228]</td></tr><tr><td></td><td></td><td>5%-cellulose nanocrystal</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1.9</td><td>0.49</td><td>0.27</td><td>0.26</td><td></td></tr><tr><td></td><td></td><td>10%-cellulose nanocrystal</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.5</td><td>0.51</td><td>0.30</td><td>0.39</td><td></td></tr><tr><td></td><td></td><td>20%-cellulose nanocrystal</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.6</td><td>0.53</td><td>0.39</td><td>0.54</td><td></td></tr><tr><td></td><td></td><td>40%-cellulose nanocrystall</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.3</td><td>0.57</td><td>0.67</td><td>0.89</td><td></td></tr><tr><td></td><td></td><td>60%-cellulose nanocrystal</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.8</td><td>0.57</td><td>0.60</td><td>0.96</td><td></td></tr><tr><td></td><td></td><td>80%-cellulose nanocrystal</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.8</td><td>0.58</td><td>0.66</td><td>1.09</td><td></td></tr><tr><td></td><td></td><td>100%-cellulose nanocrystall</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.0</td><td>0.60</td><td>0.50</td><td>0.61</td><td></td></tr><tr><td></td><td></td><td>Hydroxylpropyl cellulose (HPC) and EC/PC as plasticizer</td><td>-</td><td>NaI</td><td>P25 TiO2</td><td>Pt</td><td>N719</td><td>4.94</td><td>13.65</td><td>0.49</td><td>0.58</td><td>3.94</td><td>[229]</td></tr><tr><td></td><td></td><td></td><td></td><td>NaI-40%wtMPII</td><td></td><td></td><td></td><td>5.85</td><td>11.69</td><td>0.58</td><td>0.62</td><td>4.23</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>NaI-60%wtMPII</td><td></td><td></td><td></td><td>5.79</td><td>12.72</td><td>0.55</td><td>0.61</td><td>4.27</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>NaI-80%wtMPII</td><td></td><td></td><td></td><td>5.93</td><td>13.20</td><td>0.58</td><td>0.63</td><td>4.80</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>NaI-100%wtMPII</td><td></td><td></td><td></td><td>6.49</td><td>14.71</td><td>0.57</td><td>0.63</td><td>5.19</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>NaI-100%wtMPII</td><td></td><td></td><td></td><td>7.37</td><td>13.73</td><td>0.61</td><td>0.69</td><td>5.79</td><td></td></tr><tr><td></td><td></td><td>Cellulose nanocrystal blend with POEGMA</td><td>Sulfuric acid</td><td>HSE-EL, MPN</td><td>TiO2</td><td>Pt</td><td>Dyesol (Ru dye)</td><td>-</td><td>13.6</td><td>0.69</td><td>0.53</td><td>4.98</td><td>[230]</td></tr></table>","table_caption":"[\"Table 4 (continued) \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[944,60,954,156]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[37,492,45,505]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[944,816,954,937]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[846,922,929,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(continued on next page) ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[60,78,931,899]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":"[\"\"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[944,60,954,156]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. 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Kusumawati et al. ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[944,816,954,937]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[161,66,505,428]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0305/91c4fe4f9063462a12d6bc989291ce08b0800bbb2d4078a97b21b694a1955800.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[509,68,836,428]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 4. The map of conductivity towards the cell performance various biopolymer based DSSC. \"]","image_footnote":"[]","img_path":"images/1016/9c6e2a869f43026e37d928e85e26e0d61e19f0044d606d068a5e63b1dbf02c99.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[58,491,937,825]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0126/eb8f909c9be215cf52fa98a18fe2b935d33133fca157b6425ee3832dc82448b8.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":"<table><tr><td>Biopolymer</td><td>Monomer unit</td><td>Linkage</td><td>Dimer</td><td>Electrolyte</td><td>Conductivity value (S/cm)</td><td>Referen-ce</td></tr><tr><td>Agarose</td><td>[HOH]</td><td>α-1,3 β-1,4</td><td>[HOH]</td><td>LiI/I2(2.5 wt%)</td><td>3.94 × 10-4</td><td>[116]</td></tr><tr><td rowspan=\"3\">Carrageenan</td><td rowspan=\"2\">[OSSO]</td><td rowspan=\"2\">α-1,3 β-1,4</td><td>[O3SO]</td><td>-</td><td>2.79 × 10-6</td><td>[231]</td></tr><tr><td>[O3SO]</td><td>NH4I/I2</td><td>2.41 × 10-3</td><td>[218]</td></tr><tr><td>[OSO]</td><td>β-1,4</td><td>[O3SO]</td><td>MgTf2: AmNTFSI (27:10 wt%)</td><td>9.25 × 10-5</td><td>[232]</td></tr><tr><td rowspan=\"2\">Cellulose</td><td rowspan=\"2\">[HOH]</td><td rowspan=\"2\">β-1,4</td><td>[HOH]</td><td>-</td><td>9.33 × 10-9</td><td rowspan=\"2\">[233]</td></tr><tr><td>[HOH]</td><td>(NH4)2CO3(11 wt%)</td><td>2.28 × 10-6</td></tr><tr><td>Chitin</td><td>[HOH]</td><td>β-1,4</td><td>[HOH]</td><td>-</td><td>1.55 × 10-9</td><td>[234]</td></tr><tr><td>Chitosan</td><td>[HOH]</td><td>β-1,4</td><td>[HOH]</td><td>NH4I/I2</td><td>5.52 × 10-3</td><td>[114]</td></tr></table>","table_caption":"[\"Table 5. The most used biopolymers as electrolyte in quasi-solid DSSC. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[57,858,487,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and dye photodegradation. The improvement of biopolymers for quasisolid DSSCs is focused on increasing ionic transport through the polymer matrix. As mentioned in the previous section, the modeling or computational studies will be a good choice to study the interaction of responsible species involved in charge transfer. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,858,808,871]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. Natural carbon for DSSC counter electrode ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,883,937,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The high cost and rarity of platinum as the counter electrode in DSSCs prompts one to replace the noble metal with an alternative conducting material with a relative or similar efficiency. However, platinum-based ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,42,154,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[492,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"13 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[57,65,485,145]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"DSSCs remain the benchmark for assessing the performance of DSSCs [48, 62]. Thus far, several materials have been employed as alternative replacements of platinum as the counter electrode. These include carbonaceous materials [62, 126], conducting polymers [127, 128], transition metal carbides, nitrides, oxides, sulfides [129], and alloys [130]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,143,485,288]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Among the proposed materials for the platinum replacement of the DSSC counter electrode, carbonaceous or carbon-based materials remain one of the most studied platinum-replacement counter electrode candidates for DSSCs [62] due to their remarkable intrinsic chemical and physical characteristics, such as a high surface area, high catalytic activity, high electrical conductivity, excellent thermal stability, and good corrosion resistance, accompanied by their beneficial economic and environmental aspects. Due to the versatility of carbon-based materials, they are employed not only as counter electrodes in DSSCs but also as electrodes in electrochemical capacitors (supercapacitors) [131], and Li-ion batteries [132]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,288,485,486]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The usage of carbon-based materials dates back to the original formulation of the DSSC by the Grätzel research group [133]. Grätzel and coworkers employed a graphite powder/carbon black composite attached to a $\\mathrm{SnO}_2$ (TO) substrate as a counter electrode with a standard DSSC arrangement of $\\mathrm{I}_2 / \\mathrm{I}_3$ electrolyte and $\\mathrm{TiO}_2$ (anatase) photoelectrode, achieving a power conversion efficiency (PCE) of $6.7\\%$ . The encouraging results on the PCE of the low-cost carbon-based counter electrode prompted researchers to further develop the carbon-based counter electrodes by employing new microstructures of carbon materials such as porous carbon, carbon nanotube, graphene, and carbon nanofiber [61, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157], modifying of the existing phases such as doping or functionalizing with heteroatoms [158, 159, 160, 161] or incorporating with other materials like silica [162]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,486,485,645]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the context of the current review, natural products such as biomass have become essential sources of carbon-based materials. Biomasses are undoubtedly rich in carbonaceous materials, yet their low retrieval cost and high availability make them promising candidates for the mass production of carbon-based materials and waste valorization. There are at least 60 different biomass sources for carbon-based electrodes employed in supercapacitors, Li-ion batteries, and fuel cells, as summarized in a recent review [163]. In environmental applications, biomass-derived carbon materials have become routinely employed as adsorbents for dyes, heavy metals, and so on [164, 165] in water and wastewater, owing to their large surface area and active adsorption sites. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,646,485,815]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This section will discuss natural product-derived counter electrodes to gain insight into the relationship between the synthetic method, structure, and performance in DSSC cells. Figure 5 and Table 6 show the available literature on counter electrodes from various biomasses, wastes, and commercial biomasses, which will be included in the discussion. Interestingly, most of, if not all, the literature comes from authors who reside in Asia, more specifically, East and Southeast Asian countries. Due to the high diversity of primary natural resources from these regions, the current review results may benefit researchers from these countries to valorize natural products as more functional materials. It is worth mentioning that the natural products discussed here are not necessarily waste but also commercially produced biomass such as humic acid and ovalbumin. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,831,453,844]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.1. Preparation of counter electrode materials from natural products ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,857,485,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As listed in Table 6, a wealth of natural product resources is available for counter electrodes. Describing detailed procedures of the material extraction and counter electrode fabrication for each study would be too exhaustive. Nevertheless, this subsection will present the general trend of the resulting products with each of the preparation routes of counter electrode materials. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,66,934,380]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 5. Typical sources for counter electrode materials from natural products based on the number of available articles. \"]","image_footnote":"[]","img_path":"images/1007/8120a52346fb46f8096e15e079c603809b59c0858273fe7ef52c99f2f02436ef.jpg","list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[510,466,936,802]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0193/691ae89198394b180278721972a793080f78747dac81fff84d2be1737fb842a5.jpg","list_items":null,"page_idx":"13","sub_type":null,"table_body":"<table><tr><td>Type</td><td>Source</td><td>References</td></tr><tr><td rowspan=\"12\">Agricultural biomass</td><td>Rice husk</td><td>[165, 235, 236]</td></tr><tr><td>Coconut shell</td><td>[170, 237, 238]</td></tr><tr><td>Pumpkin stem</td><td>[183]</td></tr><tr><td>Mangosteen peel</td><td>[167]</td></tr><tr><td>Pine cone flower</td><td>[239]</td></tr><tr><td>Various leaves</td><td>[240, 241, 242]</td></tr><tr><td>Various woods</td><td>[241, 243]</td></tr><tr><td>Sunflower stalk</td><td>[173]</td></tr><tr><td>Aloe peel</td><td>[174, 175, 176, 177, 178, 179, 180]</td></tr><tr><td>Kelp</td><td>[244]</td></tr><tr><td>Orange fiber</td><td>[185]</td></tr><tr><td>Pomelo peel</td><td>[181]</td></tr><tr><td rowspan=\"2\">Animal biomass</td><td>Fish</td><td>[166, 245]</td></tr><tr><td>Human hair</td><td>[246]</td></tr><tr><td rowspan=\"4\">Post-consumer waste</td><td>Ground coffee</td><td>[188]</td></tr><tr><td>Facial tissue</td><td>[241]</td></tr><tr><td>Paper</td><td>[241]</td></tr><tr><td>Carton</td><td>[182]</td></tr><tr><td rowspan=\"5\">Commercial biomass</td><td>Bagasse</td><td>[171]</td></tr><tr><td>Table sugar</td><td>[184]</td></tr><tr><td>Sucrose</td><td>[184]</td></tr><tr><td>Humic acid</td><td>[247]</td></tr><tr><td>Ovalbumin</td><td>[248]</td></tr></table>","table_caption":"[\"Table 6. Various available sources for carbon electrode derived from natural products. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[507,815,937,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It seems evident that natural product resources mostly contain carbon obtained from macromolecule constituents. As seen from Figure 6, the extracted materials for counter electrodes from the literature are primarily carbon-based materials, with several types ranging from porous carbon to biochar, depending on the preparation route and sources. They can be categorized based on different chemical compositions, porous sizes, and surface areas. Other extracted materials include silicon or silica-based materials, such as rice husk ash, which seem to gain less attention due to more unsatisfactory DSSC performance than carbon-based materials. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,42,157,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[492,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"14 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[184,66,811,534]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 6. Typical counter electrode materials extracted from natural products and from literature. \"]","image_footnote":"[]","img_path":"images/0939/c29951f23caa91be1e1251b5f9f710d3540007353763659ff6e45fb859537215.jpg","list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,578,485,788]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The types of extracted carbon-based materials based on morphology are explained in greater detail in this section. These materials can be divided into two groups: inactivate carbon material and porous carbon material. However, the naming for the former is somehow quite ambiguous across the literature. Inactivate carbon material in this review refers to carbon material that is mainly prepared by carbonization techniques, such as heat treatment (pyrolysis), without any further treatment apart from washing and/or drying. By this definition, the simple \"carbon material,\" amorphous carbon material, and biochar listed in Table 7 belong to this group. Spherical carbon materials can also be categorized into this group. The second group seems to have a more obvious definition. The carbon-based materials in this group have porous structures, as revealed mostly by SEM images, and quantitatively, the total porous size. More specifically, the materials usually have a mesoporous structure. According to the morphology, activated carbon and porous carbon belong to the second group of carbon-based materials. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,789,485,934]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Generally, the preparation of carbon-based counter electrode materials usually involves several procedures, including pretreatment, carbonization, and activation. Figure 7 summarizes the general procedure for preparing carbon-based counter electrode materials. The pretreatment step is conducted to remove impurities and water, which can be achieved by washing, drying, and mechanical treatments such as cutting, grinding, and sieving. The second procedure is carbonization, which occurs through high-temperature annealing under an inert atmosphere (pyrolysis) and hydrothermal carbonization. The former carbonization technique will yield amorphous carbon, charcoal, and biochar, while the latter gives the spherical carbon morphology. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,578,937,697]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Depending on the intended final target material, further activation and carbonization may be conducted to enhance the surface area and develop the pores, carried out by either physical or chemical activation to prepare \"porous carbon\". The resulting \"inactivate carbon material\" is usually mixed with chemical activators such as KOH and $\\mathrm{ZnCl}_2$ , followed by further heating at high temperatures. The base can react with the carbon to develop pores within the carbon structure. Simultaneous physical activation and carbonization, along with chemical activation, can be carried out by microwave treatment. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,697,937,868]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"One issue regarding the utilization of natural products is their inhomogeneous content, which can bring either benefits or drawback to the extraction processes of the intended counter electrode material and DSSC performance. The impurities contained in the source have to be removed using harsh chemicals if necessary. On the other hand, impurities can also benefit DSSC performance due to the introduction of defective sites into the counter electrode structure, enhancing the electrocatalytic activities. Another issue is the reproducibility of the material extracted from the natural product, where the material obtained can have a different structure, morphology, and surface area. However, there seems to be a consistent preparation route for porous carbon. While the resulting materials have a quantitatively different surface area, the characterization reveals that they belong to a similar class of porous carbon. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,883,833,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.2. The performance of the natural carbon-based DSSC ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,910,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Table 7 lists the photovoltaic performances of DSSC devices that used counter electrodes derived from natural products. Before further ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,42,154,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[492,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"15 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[58,85,937,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0992/fce8ed385b57e05c757558c3a39e9116722b9ecf4febc5e06dc25d99544c403d.jpg","list_items":null,"page_idx":"15","sub_type":null,"table_body":"<table><tr><td rowspan=\"2\">Source</td><td rowspan=\"2\">Counter electrode material</td><td colspan=\"4\">Natural product-based counter electrode</td><td colspan=\"4\">Pt counter electrode</td><td rowspan=\"2\">Electrolyte solution</td><td rowspan=\"2\">Photoanode/Dye</td><td rowspan=\"2\">Reference</td></tr><tr><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η(%)</td><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η(%)</td></tr><tr><td>Rice husk</td><td>Porous carbon</td><td>14.53</td><td>0.680</td><td>64</td><td>6.32</td><td>14.61</td><td>0.69</td><td>66</td><td>6.69</td><td>LiI/2/1-methyl-3-hexylimidazolium iodide/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N3</td><td>[165]</td></tr><tr><td>Rice husk</td><td>ACs/Acetylene Black</td><td>15.01</td><td>0.73</td><td>60</td><td>6.57</td><td>15.20</td><td>0.74</td><td>64</td><td>7.20</td><td>LiI/2/1-methyl-3-propyl imidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile and valeronitrile (85:15)</td><td>TiO2/N719</td><td>[235]</td></tr><tr><td>Rice husk</td><td>Nano-Si@ACs/Acetylene Black</td><td>15.50</td><td>0.76</td><td>67</td><td>8.01</td><td>15.20</td><td>0.74</td><td>64</td><td>7.20</td><td>LiI/2/1-methyl-3-propyl imidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile and valeronitrile (85:15)</td><td>TiO2/N719</td><td>[235]</td></tr><tr><td>Rice husk</td><td>Rice husk ash/MoS2</td><td>10.95</td><td>0.60</td><td>32</td><td>2.10</td><td>-</td><td>-</td><td>-</td><td>-</td><td>Phthalocitosan electrolyte polymer/DMF/ethylene carbonate/tetrapropylammonium iodide/I2</td><td>TiO2/N3</td><td>[236]</td></tr><tr><td>Coconut shell</td><td>Amorphous activated carbon</td><td>7.60</td><td>0.77</td><td>32</td><td>0.84</td><td>-</td><td>-</td><td>-</td><td>-</td><td>LiI/2/4-tertbutylpyridine in acetonitrile</td><td>TiO2/N719</td><td>[237]</td></tr><tr><td>Coconut shell</td><td>Graphitic carbon</td><td>10.00</td><td>0.77</td><td>36</td><td>1.24</td><td>-</td><td>-</td><td>-</td><td>-</td><td>LiI/2/4-tertbutylpyridine in acetonitrile</td><td>TiO2/N719</td><td>[237]</td></tr><tr><td>Coconut shell</td><td>Activated charcoal</td><td>19.49</td><td>0.65</td><td>62</td><td>7.85</td><td>19.52</td><td>0.69</td><td>70</td><td>9.41</td><td>LiI/2/1,2-dimethyl-3-propyl imidazolium iodide/tert-butylpyridine in acetonitrile</td><td>TiO2/N719</td><td>[170]</td></tr><tr><td>Pumpkin stem</td><td>Activated carbon</td><td>3.84</td><td>0.611</td><td>0.475</td><td>2.79</td><td>4.54</td><td>0.736</td><td>49.3</td><td>4.04</td><td>KI/I2in ethylene glycol</td><td>TiO2/N719</td><td>[183]</td></tr><tr><td>Mangosteen peel</td><td>Carbon material</td><td>5.58</td><td>0.70</td><td>0.51</td><td>1.99</td><td>5.42</td><td>0.62</td><td>52</td><td>1.75</td><td>NaI/2/Li2CO3in acetonitrile</td><td>TiO2/Mangosteen peel extract</td><td>[167]</td></tr><tr><td>Mangosteen peel</td><td>Carbon material</td><td>8.70</td><td>0.60</td><td>50</td><td>2.63</td><td>4.72</td><td>0.57</td><td>54</td><td>1.47</td><td>di-5-(1-methyltetrazole)/5-mercapto-1-methyltetrazole N-tetramethylammonium salt)/4-tert-butylpyridine/LiCO4in acetonitrile</td><td>TiO2/Mangosteen peel extract</td><td>[167]</td></tr><tr><td>Pine cone flower</td><td>honeycomb-like activated porous carbon</td><td>13.51</td><td>0.71</td><td>52</td><td>4.98</td><td>14.29</td><td>0.71</td><td>62</td><td>6.25</td><td>HPE</td><td>TiO2/N719</td><td>[239]</td></tr><tr><td>Fallen leaves</td><td>Honeycomb porous carbon</td><td>14.99</td><td>0.70</td><td>53</td><td>5.52</td><td>15.96</td><td>0.70</td><td>58</td><td>6.56</td><td>HPE</td><td>TiO2/N719</td><td>[240]</td></tr><tr><td>Lotus</td><td>Biochar</td><td>14.33</td><td>0.44</td><td>23</td><td>1.42</td><td>-</td><td>-</td><td>-</td><td>-</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[242]</td></tr><tr><td>Lotus</td><td>Biochar</td><td>1.50</td><td>0.43</td><td>23</td><td>0.15</td><td>1.05</td><td>0.52</td><td>66</td><td>0.36</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/Lotus leaf extract</td><td>[242]</td></tr><tr><td>Weeping willow wood</td><td>Amorphous carbon</td><td>11.31</td><td>0.67</td><td>21</td><td>1.55</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Phoenix wood</td><td>Amorphous carbon</td><td>12.14</td><td>0.65</td><td>24</td><td>1.91</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Camphor wood</td><td>Amorphous carbon</td><td>11.31</td><td>0.64</td><td>22</td><td>1.58</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Chinese fir wood</td><td>Amorphous carbon</td><td>10.79</td><td>0.65</td><td>20</td><td>1.38</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Maple wood</td><td>Amorphous carbon</td><td>11.58</td><td>0.67</td><td>22</td><td>1.68</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Peach wood</td><td>Amorphous carbon</td><td>11.42</td><td>0.67</td><td>19</td><td>1.48</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Poplar wood</td><td>Amorphous carbon</td><td>12.15</td><td>0.62</td><td>24</td><td>1.83</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Cypress wood</td><td>Amorphous carbon</td><td>10.94</td><td>0.67</td><td>17</td><td>1.23</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Tea-oil camellia wood</td><td>Amorphous carbon</td><td>10.54</td><td>0.62</td><td>21</td><td>1.37</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Orange wood</td><td>Amorphous carbon</td><td>12.19</td><td>0.67</td><td>22</td><td>1.81</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Chinaberry wood</td><td>Amorphous carbon</td><td>12.58</td><td>0.64</td><td>21</td><td>1.66</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Oak wood</td><td>Mesoporous carbon</td><td></td><td></td><td></td><td>7.98</td><td></td><td></td><td></td><td>7.93</td><td>LiI/12/1,2-dimethyl-3-propylimidazolium iodide/4-tert-butyl pyridine in acetonitrile</td><td>TiO2/N719</td><td>[243]</td></tr><tr><td>Bamboo</td><td>Mesoporous carbon</td><td></td><td></td><td></td><td>4.53</td><td></td><td></td><td></td><td>7.93</td><td>LiI/12/1,2-dimethyl-3-propylimidazolium iodide/4-tert-butyl pyridine in acetonitrile</td><td>TiO2/N719</td><td>[243]</td></tr><tr><td>Pine needles leaf</td><td>Amorphous carbon</td><td>10.14</td><td>0.62</td><td>17</td><td>1.07</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Camphor leaf</td><td>Amorphous carbon</td><td>11.98</td><td>0.53</td><td>22</td><td>1.37</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Palm leaf</td><td>Amorphous carbon</td><td>11.53</td><td>0.63</td><td>25</td><td>1.85</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Maple leaf</td><td>Amorphous carbon</td><td>9.64</td><td>0.51</td><td>25</td><td>1.20</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Poplar leaf</td><td>Amorphous carbon</td><td>10.96</td><td>0.49</td><td>25</td><td>1.33</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Chinese fir leaf</td><td>Amorphous carbon</td><td>9.07</td><td>0.53</td><td>23</td><td>1.09</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Red after-wood leaf</td><td>Amorphous carbon</td><td>10.07</td><td>0.62</td><td>18</td><td>1.14</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Sunflower stalk</td><td>Layered activated carbon</td><td>15.20</td><td>0.67</td><td>64</td><td>6.56</td><td>15.77</td><td>0.70</td><td>65</td><td>7.19</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[173]</td></tr><tr><td>Aloe peel</td><td>Honeycomb-like porous carbon/acetylene black</td><td>14.15</td><td>0.72</td><td>0.68</td><td>6.92</td><td>15.77</td><td>0.70</td><td>65</td><td>7.19</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[174]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon</td><td>12.46</td><td>0.68</td><td>30</td><td>2.43</td><td>15.38</td><td>0.67</td><td>60</td><td>6.34</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon/FeTa2O6</td><td>15.16</td><td>0.70</td><td>65</td><td>6.85</td><td>15.38</td><td>0.67</td><td>60</td><td>6.34</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon/CoTa2O6</td><td>15.79</td><td>0.70</td><td>62</td><td>6.79</td><td>15.38</td><td>0.67</td><td>60</td><td>6.34</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon/CuTa10O26</td><td>15.19</td><td>0.68</td><td>63</td><td>6.53</td><td>15.38</td><td>0.67</td><td>60</td><td>6.34</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>14.12</td><td>0.71</td><td>65</td><td>6.52</td><td>15.77</td><td>0.70</td><td>65</td><td>7.14</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[176]</td></tr><tr><td>Aloe peel</td><td>Porous carbon/ZnNb2O6</td><td>19.12</td><td>0.71</td><td>65</td><td>8.83</td><td>15.77</td><td>0.70</td><td>65</td><td>7.14</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[176]</td></tr></table>","table_caption":"[\"Table 7. Photovoltaic parameters of DSSCs based on the various counter electrodes in comparison with standard Pt counter electrode. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[60,42,156,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[823,940,937,950]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(continued on next page) ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[492,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"16 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[57,79,937,894]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/","list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":"[\"\"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[823,897,937,910]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(continued on next page) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,42,156,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[492,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"17 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[57,79,937,921]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0707/a0b48b9227420ab533ee9a28baa1e3353e925da8e5709ee8cf821fb3f4d6f630.jpg","list_items":null,"page_idx":"17","sub_type":null,"table_body":"<table><tr><td rowspan=\"2\">Source</td><td rowspan=\"2\">Counter electrode material</td><td colspan=\"4\">Natural product-based counter electrode</td><td colspan=\"4\">Pt counter electrode</td><td rowspan=\"2\">Electrolyte solution</td><td rowspan=\"2\">Photoanode/Dye</td><td rowspan=\"2\">Reference</td></tr><tr><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η (%)</td><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η (%)</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>15.04</td><td>0.72</td><td>59</td><td>6.40</td><td>15.96</td><td>0.70</td><td>63</td><td>7.04</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>Porous carbon/MnWO4</td><td>15.52</td><td>0.69</td><td>68</td><td>7.33</td><td>15.96</td><td>0.70</td><td>63</td><td>7.04</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>Porous carbon/ZnWO4</td><td>17.12</td><td>0.69</td><td>65</td><td>7.61</td><td>15.96</td><td>0.70</td><td>63</td><td>7.04</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>Porous carbon/CuWO4</td><td>13.84</td><td>0.73</td><td>64</td><td>6.52</td><td>15.96</td><td>0.70</td><td>63</td><td>7.04</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>3D network carbon</td><td>14.86</td><td>0.62</td><td>66</td><td>6.07</td><td>15.76</td><td>0.65</td><td>66</td><td>6.74</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>3D network carbon/ZnMoO4</td><td>16.41</td><td>0.69</td><td>67</td><td>7.65</td><td>15.76</td><td>0.65</td><td>66</td><td>6.74</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>3D network carbon/Cu2Mo3O9</td><td>15.71</td><td>0.74</td><td>63</td><td>7.33</td><td>15.76</td><td>0.65</td><td>66</td><td>6.74</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>3D network carbon/MnMoO4</td><td>15.52</td><td>0.65</td><td>68</td><td>6.92</td><td>15.76</td><td>0.65</td><td>66</td><td>6.74</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>Porous carbon/MnO2</td><td>12.81</td><td>0.73</td><td>64</td><td>6.11</td><td>13.32</td><td>0.72</td><td>66</td><td>6.44</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[179]</td></tr><tr><td>Aloe peel</td><td>Porous carbon/Co/MnO2</td><td>15.45</td><td>0.72</td><td>68</td><td>7.01</td><td>13.32</td><td>0.72</td><td>66</td><td>6.44</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[179]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon</td><td>12.12</td><td>0.76</td><td>69</td><td>6.45</td><td>13.44</td><td>0.73</td><td>69</td><td>6.80</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[180]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon/NiTa2O6</td><td>14.61</td><td>0.74</td><td>65</td><td>7.09</td><td>13.44</td><td>0.73</td><td>69</td><td>6.80</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[180]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon/MnTa2O6</td><td>15.41</td><td>0.74</td><td>65</td><td>7.39</td><td>13.44</td><td>0.73</td><td>69</td><td>6.80</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[180]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon/AlTaO4</td><td>15.80</td><td>0.76</td><td>65</td><td>7.86</td><td>13.44</td><td>0.73</td><td>69</td><td>6.80</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[180]</td></tr></table>","table_caption":"[\"Table 7 (continued) \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[823,926,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(continued on next page) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,42,156,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[492,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"18 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[57,79,937,909]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0799/ef613a94039e54b8228aaaf59924d6025d78a3d8e09ce158449e3db08b899d66.jpg","list_items":null,"page_idx":"18","sub_type":null,"table_body":"<table><tr><td rowspan=\"2\">Source</td><td rowspan=\"2\">Counter electrode material</td><td colspan=\"4\">Natural product-based counter electrode</td><td colspan=\"4\">Pt counter electrode</td><td rowspan=\"2\">Electrolyte solution</td><td rowspan=\"2\">Photoanode/Dye</td><td rowspan=\"2\">Reference</td></tr><tr><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η (%)</td><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η (%)</td></tr><tr><td>Pomelo peel</td><td>Carbon material</td><td>14.56</td><td>0.70</td><td>68</td><td>6.94</td><td>14.48</td><td>0.73</td><td>64</td><td>6.72</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[181]</td></tr><tr><td>Kelp</td><td>N, S, P-doped/Co NPs</td><td>14.71</td><td>0.75</td><td>68</td><td>7.48</td><td>14.73</td><td>0.75</td><td>73</td><td>7.64</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[244]</td></tr><tr><td>Orange fiber</td><td>Carbon material/CoS nanoflakes</td><td>11.58</td><td>0.74</td><td>69</td><td>5.94</td><td>12.02</td><td>0.73</td><td>64</td><td>5.57</td><td>DN-OD05</td><td>TiO2/C264 triphenylamine</td><td>[185]</td></tr><tr><td>Anchovy</td><td>N and S co-doped activated porous carbon</td><td>18.78</td><td>0.89</td><td>76</td><td>12.72</td><td>19.17</td><td>0.87</td><td>73</td><td>12.23</td><td>Co(bpy)3+/2+</td><td>TiO2/SM-315 porphyrin</td><td>[166]</td></tr><tr><td>Fish waste</td><td>N, P and S tri-doped activated porous carbon</td><td>15.64</td><td>0.75</td><td>67</td><td>7.83</td><td>15.98</td><td>0.76</td><td>69</td><td>8.34</td><td>LiI/2/1,2-dimethyl-3-propyl imidazolium iodide/tert-butylpyridine in acetonitrile.</td><td>TiO2/N3</td><td>[245]</td></tr><tr><td>Human hair</td><td>Carbon material/PEDOT:PSS</td><td>14.58</td><td>0.76</td><td>58</td><td>6.54</td><td>15.64</td><td>0.74</td><td>63</td><td>7.29</td><td>LiI/2/1-methyl-3-propylimidazolium iodide/tetraethylpyridine/Li2CO3in acetonitrile.</td><td>TiO2/N719</td><td>[246]</td></tr><tr><td>Ground coffee waste</td><td>N-doped porous carbon</td><td>15.09</td><td>0.76</td><td>73</td><td>8.32</td><td>14.73</td><td>0.77</td><td>72</td><td>8.07</td><td>I2/1-butyl-3-methylimidazolium iodide/guanidinium thiocyanate/4-tert-butylpyridine in acetonitrile and valeronitrile mixture (volume ratio 85:15)</td><td>TiO2/N719</td><td>[188]</td></tr><tr><td>Filter paper</td><td>Amorphous carbon</td><td>15.02</td><td>0.70</td><td>45</td><td>4.72</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Facial tissue</td><td>Amorphous carbon</td><td>14.80</td><td>0.69</td><td>64</td><td>4.70</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Waste carton</td><td>Porous carbon</td><td>14.20</td><td>0.77</td><td>62</td><td>6.76</td><td>14.84</td><td>0.76</td><td>66</td><td>7.51</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[182]</td></tr><tr><td>Waste carton</td><td>Porous carbon/WC</td><td>14.56</td><td>0.76</td><td>60</td><td>7.32</td><td>14.84</td><td>0.76</td><td>66</td><td>7.51</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[182]</td></tr><tr><td>Bagasse</td><td>Carbon material</td><td>5.20</td><td>0.72</td><td>8</td><td>0.31</td><td>15.00</td><td>0.72</td><td>57</td><td>6.08</td><td>LiI/2/1,2-Dimethyl-3-propylimidazolium iodide/4-tert-butyl-pyridine in acetonitrile</td><td>TiO2/N719</td><td>[171]</td></tr><tr><td>Bagasse</td><td>Nitrogen-doped bagasse</td><td>10.7</td><td>0.69</td><td>37</td><td>2.48</td><td>15.00</td><td>0.72</td><td>57</td><td>6.08</td><td>LiI/2/1,2-Dimethyl-3-propylimidazolium iodide/4-tert-butyl-pyridine in acetonitrile</td><td>TiO2/N719</td><td>[171]</td></tr><tr><td>Bagasse</td><td>Carbon material/Pt NPs</td><td>12.4</td><td>0.66</td><td>45</td><td>3.69</td><td>15.00</td><td>0.72</td><td>57</td><td>6.08</td><td>LiI/2/1,2-Dimethyl-3-propylimidazolium iodide/4-tert-butyl-pyridine in acetonitrile</td><td>TiO2/N719</td><td>[171]</td></tr><tr><td>Bagasse</td><td>Nitrogen-doped bagasse/Pt NPs</td><td>15.3</td><td>0.73</td><td>62</td><td>6.98</td><td>15.00</td><td>0.72</td><td>57</td><td>6.08</td><td>LiI/2/1,2-Dimethyl-3-propylimidazolium iodide/4-tert-butyl-pyridine in acetonitrile</td><td>TiO2/N719</td><td>[171]</td></tr><tr><td>Table sugar</td><td>Carbon materiala</td><td>-</td><td>-</td><td>-</td><td>3.24</td><td>-</td><td>-</td><td>-</td><td>4.02</td><td>Iodolite</td><td>TiO2/RK-1</td><td>[184]</td></tr><tr><td>Sucrose</td><td>Carbon materiala</td><td>-</td><td>-</td><td>-</td><td>0.04</td><td>-</td><td>-</td><td>-</td><td>4.02</td><td>Iodolite</td><td>TiO2/RK-1</td><td>[184]</td></tr></table>","table_caption":"[\"Table 7 (continued) \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[823,914,937,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(continued on next page) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,42,156,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[492,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"19 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[57,79,937,273]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0151/79d865b183978109cc457e8123383417991188356ce7e252c1ae8a4870bef0c3.jpg","list_items":null,"page_idx":"19","sub_type":null,"table_body":"<table><tr><td rowspan=\"2\">Source</td><td rowspan=\"2\">Counter electrode material</td><td colspan=\"4\">Natural product-based counter electrode</td><td colspan=\"4\">Pt counter electrode</td><td rowspan=\"2\">Electrolyte solution</td><td rowspan=\"2\">Photoanode/Dye</td><td rowspan=\"2\">Reference</td></tr><tr><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η(%)</td><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η(%)</td></tr><tr><td>Humic acid</td><td>Carbon material</td><td>12.55</td><td>0.76</td><td>65</td><td>6.14</td><td>13.85</td><td>0.75</td><td>68</td><td>7.10</td><td>Lil/I2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[247]</td></tr><tr><td>Humic acid</td><td>Carbon material/Ni</td><td>13.51</td><td>0.76</td><td>68</td><td>7.01</td><td>13.85</td><td>0.75</td><td>68</td><td>7.10</td><td>Lil/I2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[247]</td></tr><tr><td>Ovalbumin</td><td>N-doped carbon aerogel</td><td>12.01</td><td>0.70</td><td>56</td><td>4.68</td><td>12.71</td><td>0.71</td><td>59</td><td>5.35</td><td>Iodolyte HI-30</td><td>TiO2/N719</td><td>[248]</td></tr></table>","table_caption":"[\"Table 7 (continued) \"]","table_footnote":"[\"a The $V_{oc}$ from ref. [184] is unreliable. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[161,335,836,750]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 7. Preparation routes of the carbon-based natural product-derived counter electrode materials. The employed carbon-based materials are displayed in the blue dialog box. \"]","image_footnote":"[]","img_path":"images/0792/1dcf65a628e8c5d64d2ae49799516cefcac08a70860a9ede3c5e5e3344ee651c.jpg","list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[57,798,487,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"discussing the performance of each device with the natural product-based counter electrode, DSSC performance with the standard platinum counter electrode used as the benchmark is discussed. The PCE of platinum-based devices varies from 0.36 to $12.23\\%$ . However, there are no consistent compositions of the dyes and electrolytes mentioned in the literature, which results in varied PCE values. This reduces the possibility of making a fair comparison of PCE values obtained from the various literature. The ruthenium-based dye N719 remains the most favorable, followed by ruthenium-based N3 dye. The other dyes mentioned in the literature are Zn-based SM-315, RK-1, C264 porphyrin, and natural ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,798,939,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"product-based (lotus leaf and mangosteen peel extract) dyes. For the electrolytes, almost all the literature studied utilized the $\\mathrm{I}_3 / \\mathrm{I}^-$ redox pair as inorganic iodide and/or various forms of imidazolium iodide salt as a source of $\\Gamma^{-}$ . $\\Gamma^{-}$ was used either as a fresh chemical mixture or a commercially prepared solution mixed with the solvent, forming acetonitrile or an acetonitrile/valeronitrile mixture. In addition to these specimens, electrolyte additives such as 4-tert-butyl pyridine and guanidium thiocyanate are also incorporated into the electrolytes to enhance DSSC performance [13, 16]. Kim et al. incorporated the only $\\mathrm{Co(bpy)_3^{3 + / 2 + }}$ redox pair electrolytes found in the current literature ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,42,157,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"20 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[58,90,937,920]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0401/56a3b02ddf11300fe6974a95be36ddd708dc46bdc0152bd3047ed93fc4da1323.jpg","list_items":null,"page_idx":"20","sub_type":null,"table_body":"<table><tr><td>Source</td><td>Extracted counter electrode material</td><td>Additive and/or modifier</td><td>Binder or Adhesive</td><td>SBET(m2g-1)</td><td>Pore volume (cm3g-1)</td><td>Rt(Ω cm2)</td><td>Rct(Ω cm2)</td><td>Cd(μF cm2)</td><td>Zw(Ω cm2)</td><td>Ip(mA cm-2)</td><td>Epp(V)</td><td>ηrel</td><td>Reference</td></tr><tr><td>Rice husk</td><td>Porous carbon</td><td>-</td><td>Titanium isopropoxide</td><td>1095</td><td>0.61</td><td>21.4</td><td>1.3</td><td>42</td><td>1.3</td><td>-3.5a</td><td>-</td><td>0.94</td><td>[165]</td></tr><tr><td>Coconut shell</td><td>Activated charcoal</td><td>-</td><td>Poly vinyl acetate</td><td>-</td><td>-</td><td>30.0</td><td>1.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.83</td><td>[170]</td></tr><tr><td>Pumpkin stem</td><td>Activated carbon</td><td>-</td><td>-</td><td>793</td><td>0.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-3.0a</td><td>0.60a</td><td>0.69</td><td>[183]</td></tr><tr><td>Weeping willow wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.25</td><td>[241]</td></tr><tr><td>Phoenix wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>273</td><td>-</td><td>31.3</td><td>22.7</td><td>-</td><td>-</td><td>-1.8</td><td>0.588</td><td>0.31</td><td>[241]</td></tr><tr><td>Camphor wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.25</td><td>[241]</td></tr><tr><td>Chinese fir wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.22</td><td>[241]</td></tr><tr><td>Maple wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.27</td><td>[241]</td></tr><tr><td>Peach wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.24</td><td>[241]</td></tr><tr><td>Poplar wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.29</td><td>[241]</td></tr><tr><td>Cypress wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.20</td><td>[241]</td></tr><tr><td>Tea-oil camellia wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.22</td><td>[241]</td></tr><tr><td>Orange wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.29</td><td>[241]</td></tr><tr><td>Chinaberry wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.27</td><td>[241]</td></tr><tr><td>Oak wood</td><td>Mesoporous carbon</td><td>-</td><td>-</td><td>852</td><td>0.6</td><td>15.1</td><td>10.0</td><td>-</td><td>95.3</td><td>-</td><td>-</td><td>1.01</td><td>[243]</td></tr><tr><td>Bamboo</td><td>Mesoporous carbon</td><td>-</td><td>-</td><td>542</td><td>0.3</td><td>14.6</td><td>38.4</td><td>-</td><td>76.0</td><td>-</td><td>-</td><td>0.57</td><td>[243]</td></tr><tr><td>Pine needles leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.17</td><td>[241]</td></tr><tr><td>Camphor leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.22</td><td>[241]</td></tr><tr><td>Palm leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>7.1</td><td>-</td><td>32.1</td><td>22.8</td><td>-</td><td>-</td><td>-1.2</td><td>0.582</td><td>0.30</td><td>[241]</td></tr><tr><td>Maple leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.19</td><td>[241]</td></tr><tr><td>Poplar leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.21</td><td>[241]</td></tr><tr><td>Chinese fir leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.17</td><td>[241]</td></tr><tr><td>Red after-wood leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.18</td><td>[241]</td></tr><tr><td>Lotus</td><td>Biochar</td><td>-</td><td>Carboxymethyl cellulose</td><td>30.9</td><td>-</td><td>-</td><td>40.7</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.42</td><td>[242]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon</td><td>-</td><td>ZrO2</td><td>1286</td><td>0.7</td><td>27.4</td><td>12.4</td><td>-</td><td>-</td><td>-6.0a</td><td>0.4a</td><td>0.96</td><td>[174]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon</td><td>-</td><td>ZrO2</td><td>13b</td><td>0.1b</td><td>7808</td><td>8663</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.38</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>-</td><td>ZrO2</td><td>507</td><td>-</td><td>14.0</td><td>12.2</td><td>-</td><td>11.4</td><td>-4.7</td><td>0.847</td><td>0.91</td><td>[176]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>-</td><td>ZrO2</td><td>-</td><td>-</td><td>15.9</td><td>4.6</td><td>-</td><td>-</td><td>-1.6</td><td>0.770</td><td>0.91</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>3D network carbon</td><td>-</td><td>ZrO2</td><td>-</td><td>-</td><td>11.7</td><td>0.7</td><td>-</td><td>-</td><td>-1.3</td><td>0.442</td><td>0.90</td><td>[178]</td></tr><tr><td>Pomelo peel</td><td>Carbon material</td><td>-</td><td>ZrO2</td><td>1377</td><td>0.7</td><td>15.3</td><td>7.1</td><td>8.5</td><td>-</td><td>-2.8</td><td>0.530</td><td>1.03</td><td>[181]</td></tr><tr><td>Bagasse</td><td>Carbon material</td><td>-</td><td>Polyvinyl pyrrolidone</td><td>19.4</td><td>-</td><td>6.6</td><td>544</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.05</td><td>[171]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon</td><td>-</td><td>ZrO2</td><td>1286b</td><td>0.7b</td><td>12.3</td><td>1.2</td><td>-</td><td>-</td><td>-2.0</td><td>0.760</td><td>0.95</td><td>[180]</td></tr><tr><td>Anchovy</td><td>N and S co-doped</td><td>-</td><td>-</td><td>2622</td><td>1.9</td><td>3.0</td><td>7.56</td><td>-</td><td>-</td><td>-0.3a</td><td>0.075a</td><td>1.04</td><td>[166]</td></tr></table>","table_caption":"[\"Table 8. Electrochemical, electrocatalytic, and structural properties of various counter electrodes. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[823,925,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(continued on next page) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,42,156,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[492,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"21 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[57,79,937,911]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0915/670af4d9c623624a032fdb4878e15e0f40c97fc6349a137d51be361ef7e07dd4.jpg","list_items":null,"page_idx":"21","sub_type":null,"table_body":"<table><tr><td>Source</td><td>Extracted counter electrode material</td><td>Additive and/or modifier</td><td>Binder or Adhesive</td><td>SBET(m2g-1)</td><td>Pore volume (cm3g-1)</td><td>Rt(Ω cm2)</td><td>Rct(Ω cm2)</td><td>Cd(μF cm2)</td><td>Zw(Ω cm2)</td><td>Ip(mA cm-2)</td><td>Epp(V)</td><td>ηrel</td><td>Reference</td></tr><tr><td></td><td>activated porous carbon</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Fish waste</td><td>N, P and S tri-doped activated porous carbon</td><td>-</td><td>Ethyl cellulose/terpineol/titanium isopropoxide</td><td>2933</td><td>0.8</td><td>-</td><td>0.5</td><td>-</td><td>-</td><td>-5.0a</td><td>0.5a</td><td>0.94</td><td>[245]</td></tr><tr><td>Filter paper</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>2.2</td><td>-</td><td>22.6</td><td>8.8</td><td>-</td><td>-</td><td>-1.49</td><td>0.543</td><td>0.76</td><td>[241]</td></tr><tr><td>Facial tissue</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>3.2</td><td>-</td><td>23.4</td><td>8.3</td><td>-</td><td>-</td><td>-1.57</td><td>0.531</td><td>0.75</td><td>[241]</td></tr><tr><td>Waste carton</td><td>Porous carbon</td><td>-</td><td>ZrO2</td><td>824</td><td>0.7</td><td>16.7</td><td>13.1</td><td>-</td><td>-</td><td>-1.9a</td><td>0.660</td><td>0.90</td><td>[182]</td></tr><tr><td>Table sugar</td><td>Carbon materiala</td><td>-</td><td>Polyvinylidene difluoride</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.81</td><td>[184]</td></tr><tr><td>Sucrose</td><td>Carbon materiala</td><td>-</td><td>Polyvinylidene difluoride</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.01</td><td>[184]</td></tr><tr><td>Humic acid</td><td>Carbon material</td><td>-</td><td>Ethyl cellulose/terpineol</td><td>-</td><td>-</td><td>10.1</td><td>11.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.86</td><td>[247]</td></tr><tr><td>Ovalbumin</td><td>N-doped carbon aerogel</td><td>-</td><td>Oleylamine</td><td>158</td><td>-</td><td>17.6</td><td>0.83</td><td>1.4</td><td>-</td><td>-</td><td>-</td><td>0.87</td><td>[248]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon</td><td>FeTa2O6</td><td>ZrO2</td><td>-</td><td>-</td><td>7.0</td><td>12.9</td><td>-</td><td>-</td><td>-4.5a</td><td>0.281</td><td>1.08</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon</td><td>CoTa2O6</td><td>ZrO2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-3.0a</td><td>0.262</td><td>1.07</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon</td><td>ZrO2/CuTa10O26</td><td>ZrO2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-2.5a</td><td>0.351</td><td>1.03</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>ZnNb2O6</td><td>ZrO2</td><td>140</td><td>-</td><td>12.8</td><td>6.5</td><td>-</td><td>4.7</td><td>-3.7</td><td>0.456</td><td>1.24</td><td>[176]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>MnWO4</td><td>ZrO2</td><td>-</td><td>-</td><td>12.8</td><td>2.6</td><td>-</td><td>-</td><td>-2.0</td><td>0.563</td><td>1.04</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>ZnWO4</td><td>ZrO2</td><td>-</td><td>-</td><td>11.6</td><td>1.7</td><td>-</td><td>-</td><td>-2.0</td><td>0.424</td><td>1.08</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>CuWO4</td><td>ZrO2</td><td>-</td><td>-</td><td>16.6</td><td>6.2</td><td>-</td><td>-</td><td>-1.6</td><td>0.581</td><td>0.93</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>3D network carbon</td><td>ZnMoO4</td><td>ZrO2</td><td>-</td><td>-</td><td>11.4</td><td>0.7</td><td>-</td><td>-</td><td>-1.8</td><td>0.435</td><td>1.14</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>3D network carbon</td><td>Cu2Mo3O9</td><td>ZrO2</td><td>-</td><td>-</td><td>10.6</td><td>1.4</td><td>-</td><td>-</td><td>-1.5</td><td>0.706</td><td>1.09</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>3D network carbon</td><td>MnMoO4</td><td>ZrO2</td><td>-</td><td>-</td><td>11.2</td><td>2.2</td><td>-</td><td>-</td><td>-1.0</td><td>0.784</td><td>1.03</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>MnO2</td><td>ZrO2</td><td>632</td><td>0.4</td><td>13.2</td><td>10.1</td><td>-</td><td>-</td><td>-2.2</td><td>0.460</td><td>0.95</td><td>[179]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>Co/MnO2</td><td>ZrO2</td><td>661</td><td>0.4</td><td>19.8</td><td>1.1</td><td>-</td><td>-</td><td>-2.3</td><td>0.480</td><td>1.09</td><td>[179]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon</td><td>NiTa2O6</td><td>ZrO2</td><td>-</td><td>-</td><td>13.4</td><td>1.6</td><td>-</td><td>-</td><td>-2.3</td><td>0.436</td><td>1.04</td><td>[180]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon</td><td>MnTa2O6</td><td>ZrO2</td><td>-</td><td>-</td><td>11.5</td><td>1.2</td><td>-</td><td>-</td><td>-2.5</td><td>0.394</td><td>1.09</td><td>[180]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon</td><td>AlTaO4</td><td>ZrO2</td><td>-</td><td>-</td><td>10.7</td><td>0.7</td><td>-</td><td>-</td><td>-2.8</td><td>0.398</td><td>1.16</td><td>[180]</td></tr><tr><td>Bagasse</td><td>Carbon material</td><td>Nitrogen</td><td>Polyvinyl pyrrolidone</td><td>29.0</td><td>-</td><td>8.8</td><td>28.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.41</td><td>[171]</td></tr><tr><td>Bagasse</td><td>Carbon material</td><td>Pt NPs</td><td>Polyvinyl pyrrolidone</td><td>56.3</td><td>-</td><td>9.6</td><td>7.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.61</td><td>[171]</td></tr><tr><td>Bagasse</td><td>Carbon material</td><td>Nitrogen/Pt NPs</td><td>Polyvinyl pyrrolidone</td><td>90.0</td><td>-</td><td>5.3</td><td>1.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.15</td><td>[171]</td></tr><tr><td>Kelp</td><td>N, S, P-tri-doped carbon</td><td>Co NPs</td><td>-</td><td>142</td><td>0.1</td><td>37.3</td><td>0.9</td><td>96.7</td><td>-</td><td>-0.8a</td><td>0.3a</td><td>0.98</td><td>[244]</td></tr><tr><td>Orange fiber</td><td>Carbon material</td><td>CoS nanoflakes</td><td>Ethylene glycol-terpineol</td><td>9.9</td><td>-</td><td>31.8</td><td>36.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.07</td><td>[185]</td></tr><tr><td>Waste carton</td><td>Porous carbon</td><td>WC</td><td>ZrO2</td><td>-</td><td>-</td><td>17.1</td><td>7.1</td><td>-</td><td>-</td><td>-1.8a</td><td>-</td><td>0.97</td><td>[182]</td></tr><tr><td>Humic acid</td><td>Carbon material</td><td>Ni</td><td>Ethyl cellulose/terpineol</td><td>-</td><td>-</td><td>9.1</td><td>7.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.99</td><td>[247]</td></tr><tr><td>Rice husk</td><td>Activated carbon</td><td>Acetylene black</td><td>Ethyl cellulose</td><td>200</td><td>-</td><td>16.0</td><td>3.4</td><td>-</td><td>30.0</td><td>-2.8</td><td>0.692</td><td>0.91</td><td>[235]</td></tr><tr><td>Rice husk</td><td>Nano-Si@ACs</td><td>Acetylene black</td><td>Ethyl cellulose</td><td>240</td><td>-</td><td>15.9</td><td>2.1</td><td>-</td><td>27.9</td><td>-4.2</td><td>0.426</td><td>1.11</td><td>[235]</td></tr><tr><td>Mangosteen peel</td><td>Carbon material</td><td>PEDOT:PSS</td><td>-</td><td>125</td><td>-</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-</td><td>1.14</td></tr></table>","table_caption":"[\"Table 8 (continued) \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[823,916,936,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(continued on next page) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,44,156,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[816,44,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[492,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"22 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[57,80,937,301]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0941/6a51d28d61368a1e9c99346e8402d434c3f56627e61c4b51d221b712b27ad615.jpg","list_items":null,"page_idx":"22","sub_type":null,"table_body":"<table><tr><td>Source</td><td>Extracted counter electrode material</td><td>Additive and/or modifier</td><td>Binder or Adhesive</td><td>SBET(m2g-1)</td><td>Pore volume (cm3g-1)</td><td>Rs(Ω cm2)</td><td>Rct(Ω cm2)</td><td>Cd(μF cm2)</td><td>Zw(Ω cm2)</td><td>Ip(mA cm-2)</td><td>Epp(V)</td><td>ηrel</td><td>Reference</td></tr><tr><td>Mangosteen peel</td><td>Carbon material</td><td>PEDOT:PSS</td><td>-</td><td>125</td><td>-</td><td></td><td></td><td></td><td></td><td></td><td>-</td><td>1.79</td><td>[167]</td></tr><tr><td>Pine cone flower</td><td>Honeycomb-like activated porous carbon</td><td>Carbon black</td><td>Polyvinylidene fluoride</td><td>1598</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-3.0</td><td>-</td><td>0.80</td><td>[239]</td></tr><tr><td>Fallen leaves</td><td>Honeycomb porous carbon</td><td>Carbon black</td><td>Polyvinylidene fluoride</td><td>2196</td><td>1.7</td><td>-</td><td>25.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.84</td><td>[240]</td></tr><tr><td>Sunflower stalk</td><td>Layered activated carbon</td><td>Acetylene black</td><td>Polytetrafluoroethylene</td><td>1505</td><td>0.9</td><td>18.4</td><td>7.8</td><td>-</td><td>-</td><td>-2.5a</td><td>0.3a</td><td>0.91</td><td>[173]</td></tr><tr><td>Human hair</td><td>Carbon material</td><td>PEDOT:PSS</td><td>-</td><td>188</td><td>-</td><td>16.7</td><td>7.1</td><td>-</td><td>-</td><td>-0.9a</td><td>0.3a</td><td>0.90</td><td>[246]</td></tr><tr><td>Ground coffee waste</td><td>N-doped porous carbon</td><td>Nafion</td><td>-</td><td>1200</td><td>-</td><td>6.1</td><td>0.5</td><td>5174.0</td><td></td><td></td><td></td><td>1.03</td><td>[188]</td></tr></table>","table_caption":"[\"Table 8 (continued) \"]","table_footnote":"[\"a Approximate value taken from the relevant figures in the articles. \",\"b Taken from ref. [174]. \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[57,353,485,445]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"[166]. However, all the other experiments made use of $\\mathrm{TiO_2}$ as a photoanode. The preparation of the photoanode may also contribute to DSSC performance since the prepared photoanode varied commercially-prepared $\\mathrm{TiO_2}$ to the controlled morphology-synthesized $\\mathrm{TiO_2}$ . The effects of $\\mathrm{TiO_2}$ morphology are not included in the current discussion since most research did not include the characterization of the $\\mathrm{TiO_2}$ electrode. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,446,485,538]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The table shows that the poorest PCE is achieved by the devices that used natural dyes as a sensitizer [167, 168], with PCE $< 2\\%$ , regardless of the electrolyte. On the other hand, the highest PCE was obtained using the $\\mathrm{Co(bpy)_3^{3 + / 2 + }}$ redox couple electrolyte and Zn-based SM-315 [166], with $12.23\\%$ which appears to be higher than the average PCE listed in Table 7. The PCE of this DSSC arrangement correlates with the highest PCE for the $\\mathrm{Co(bpy)_3^{3 + / 2 + } / SM - 315}$ electrolyte/dye pair of $13\\%$ [169]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,539,487,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Pt-based devices with standard $\\mathrm{I}_3 / \\mathrm{I}^-$ redox couple electrolytes with inorganic iodide and/or imidazolium iodide, either with or without additive, have PCE ranges of 4.02 and $9.41\\%$ respectively. It is worth reiterating that close comparisons of DSSC performance for studied literature have not been found, even if the devices employ the same set of electrolytes and dyes. For example, the highest PCE of $9.41\\%$ was obtained with $\\mathrm{LiI / I_2 / 1}$ 2-dimethyl-3-propyl imidazolium iodide/4-tert-butylpyridine in acetonitrile electrolyte without both guanidium thiocyanate additive and N719 dye as in Ref. [170]. However, DSSCs with similar electrolytes and dyes performed worse with a PCE of $6.08\\%$ [171]. In contrast, $V_{oc}$ of the two devices are comparable, as $J_{sc}$ and $FF$ differ significantly. This could benefit the $\\mathrm{TiO_2}$ photoanode, which has a larger surface area or porosity, allowing light to scatter. This, in turn, enhances the light-harvesting efficiency compared to top-down $\\mathrm{TiO_2}$ photoanode synthesis from the commercial precursor in [170]. Efficient light harvesting by using light scattering in the photoanode is a way to increase the $J_{sc}$ of the DSSC [172]. Different PCE results may appear from the same research group even if the same photoanode, dye, electrolyte, and counter electrode preparation are used. The Yun research group from Xi'an University of Architecture and Technology published a set of works on DSSCs with similar experimental methodologies [173, 174, 175, 176, 177, 178, 179, 180, 181, 182]. The works consistently utilized a \"complete\" set of electrolytes where inorganic iodide salt (LiI), imidazolium salt (1-butyl-3-methylimidazolium iodide), and additives (4-tert-butyl pyridine and guanidinium thiocyanate) with acetonitrile were used as the solvent, and N719 was used as the dye. This resulted in the PCEs of the Pt-based DSSCs in the range of 6.34 and $7.19\\%$ . These values obtained may be caused by experimental random error due to uncertainties in the measurement. The average value deviation obtained was $6.5\\%$ , which was small enough for the PCE values of the platinum-based DSSC ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,353,937,445]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"devices to be classified as accurate. It is also evident that electrolytes with only inorganic iodide without the imidazolium iodide salt and additives yielded a less satisfactory device performance than the more sophisticated electrolytes. Madhu et al. utilized $\\mathrm{KI} / \\mathrm{I}_2$ in ethylene glycol in conjunction with N719 dye for a DSSC with a Pt-counter electrode. The attained PCE of the Pt-based DSSC was $4.04\\%$ which was lower than the average value [183]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,446,937,588]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The performance of natural product-based counter electrodes can be briefly compared with platinum-based electrodes. From the same sources, it is stated that both the $V_{oc}$ between natural product-based counter electrodes and Pt-based electrodes are generally comparable, with differences of less than $100\\mathrm{mV}$ . The photovoltaic efficiency of the DSSC is mainly affected by $J_{sc}$ and $FF$ values. Improvement in $J_{sc}$ and $FF$ are considered to play a vital role in DSSC performance. Both the $J_{sc}$ and $FF$ values can be improved by enhancing the electrocatalytic activities of the counter electrodes. This can be achieved by modifying the structural and electronic properties of the electrodes, as described in the next section. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,614,929,639]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.3. The relationship between the structure and performance of the counter electrode ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,653,937,693]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To compare the performance of natural product-based electrodes with platinum-based electrodes under the same experimental conditions for each study, let us define the relative DSSC PCE as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,703,937,728]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\eta_ {r e l} = \\frac {\\eta_ {N P}}{\\eta_ {P t}} \\tag {3}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,738,937,896]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\eta_{rel}$ , $\\eta_{NP}$ , and $\\eta_{Pt}$ are the relative frequency, PCE of the natural product-based DSSC, and PCE of the platinum-based DSSC, respectively. If the value is below 1, the natural product-based DSSCs underperform those of the platinum-based DSSCs. In contrast, if the value is equal to or larger than 1, the natural product-based DSSCs perform qualitatively better than the platinum-based DSSCs. However, as previously mentioned, due to experimental uncertainties, $\\eta_{rel}$ between 0.90 and 1.10 may have error uncertainties. Therefore, this range of the $\\eta_{rel}$ values cannot be used to conclude whether the natural product-based DSSCs performed better or worse than the platinum counterpart. Nevertheless, DSSCs with an $\\eta_{rel}$ value below 0.7 suggested that they performed worse than their platinum counterparts since the absolute PCE was below $3\\%$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,896,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The important electrochemical properties of the counter electrode are the series resistance $(R_{s})$ , charge transfer resistance $(R_{ct})$ , double layer capacitance $(C_d)$ , and Nernst diffusion impedance $(Z_w)$ . These values can ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,42,157,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"23 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[57,65,485,264]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"be obtained from the electrochemical impedance spectra (EIS) technique. A smaller $R_{ct}$ value indicates a higher electrocatalytic activity of $\\mathrm{I}_3$ reduction. $C_d$ affects the surface area of the counter electrode, and $Z_w$ influences the diffusion velocity of the redox couple in the electrolyte. A higher surface area contributes to a larger $C_d$ , while a faster diffusion rate causes $Z_w$ to decrease. Other parameters, peak current density $(I_p)$ and peak-to-peak separation $(E_{pp})$ , are used to evaluate the catalytic performance of a counter electrode. Both of these can be determined by using the cyclic voltammetry method. Although the current high-performance DSSC devices use $\\mathrm{Co}^{3+ / 2+}$ as a redox couple, most DSSCs still utilize $\\mathrm{I}_3 / \\mathrm{I}^-$ for their economic benefits. Therefore, the discussion will be focused on the $\\mathrm{I}_3$ reduction ability of the counter electrode. The electrochemical properties of the counter electrode are generally related to the structural properties. These are mainly determined by the BET surface area and the pore size. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,264,485,382]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To fabricate natural product-based electrodes, some additional components are usually incorporated. Since amorphous, disordered, and porous carbon materials are known for their poor adhesion to FTO [62], additional binder or adhesive materials must be incorporated. Additionally, amorphous carbon is also known for its low conductivity; thus, conducting material can also be incorporated into the counter electrode. However, not all of the works in the literature employed additional conducting materials since the extracted materials are not necessarily amorphous carbon materials but rather various morphologies of carbon. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,383,485,527]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Table 8 lists the electrocatalytic properties of natural product-based materials and their available surface area and total pore volume. Since not all electrochemical data are available in the literature, we can take several examples of natural product-based materials and discuss their electrochemical properties. Nevertheless, the main performance concern remains the PCE, which we defined here as the $\\eta_{rel}$ that are available throughout the literature. It is also clear that from the extraction of natural product materials and the optional modifications to the fabrication of counter electrodes, some structural properties can be altered due to treatment methods (i.e., spin coating or doctor blade method). For instance, the material's BET surface and pore size are determined before ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,65,937,117]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"counter electrode fabrication. In contrast, the electrochemical and electrocatalytic properties are determined at the counter electrode stage. Nevertheless, the changes in the structural properties may be neglected. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,118,937,302]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"First, let us discuss the DSSC based on the counter electrode materials without any intended chemical additives and/or modifications. These materials span from amorphous inactivated carbon to N, P, and S tridoped activated porous carbon. In this category, the poorest DSSC performance $\\eta_{rel}$ is 0.01 with an absolute PCE of $0.04\\%$ obtained by the carbon material from sucrose-based DSSC [184] while the best performance is obtained by the N and S codoped activated porous carbon from an anchovy-based DSSC with $\\eta_{rel}$ of 1.04 and absolute PCE of $12.73\\%$ [166]. However, it should be noted that the best DSSC that falls within this category employs the $\\mathrm{Co}^{3 + / 2 + }$ redox couple electrolyte, which indeed gives better DSSC performance than the $\\mathrm{I}_3 / \\mathrm{I}^-$ based electrolyte [169]. The other fish-based DSSCs, namely, N, P, and S tridoped activated porous carbon-based DSSCs also exhibit a remarkably high $\\eta_{rel}$ of 0.94 and absolute PCE of $7.83\\%$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,303,937,500]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The relationship between the structural properties can be discussed in terms of the surface area and total pore volume of the electrode and the electrochemical properties of the electrode. The surface areas of natural product materials span from 2 to ca. $3000\\mathrm{m}^2\\mathrm{g}^{-1}$ . Interestingly, the materials with a relatively high BET surface area, i.e., $>800\\mathrm{m}^2\\mathrm{g}^{-1}$ , exhibit excellent PCE efficiency compared to the materials with lower surface areas. This is due to more $\\mathrm{I}_3$ that can adsorb on the counter electrode surface and pores, as illustrated in Figure 8. The electron transfer efficiency on the electrode/electrolyte interface can be deduced from the $R_{ct}$ values. For the most efficient electron transfer process, the $R_{ct}$ value must be small. As seen from Figure 9, a high electrode surface corresponds to a low $R_{ct}$ , which is below $14\\Omega\\mathrm{cm}^2$ . This leads to the $\\eta_{rel}$ values being larger than 0.9 or absolute PCE values larger than $7.0\\%$ . As expected, the counter electrode material with a low surface exhibits worse DSSC performance than the Pt-based DSSC. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,501,937,527]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The presence of heteroatoms from the biomass source in the final product materials can also enhance the DSSC performance. The perfor ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[188,554,811,914]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 8. Illustration of the interactions between $\\\\mathrm{I}_3$ with porous carbon counter electrode. \"]","image_footnote":"[]","img_path":"images/0128/11f3e21a4ba22d9aedb2db2f230b6115d1ec4830b021970cd09be74df25dc725.jpg","list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[58,42,157,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"24 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[211,68,791,374]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 9. Distribution of $\\\\eta_{\\\\mathrm{rel}}$ and $R_{\\\\mathrm{ct}}$ with correlation to $S_{\\\\mathrm{BET}}$ of the natural product-based counter electrode without additive. \"]","image_footnote":"[]","img_path":"images/0285/24e6511a3652e7f3850285c995590f3750451c61364da30d632560b3b552f8f7.jpg","list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[60,424,484,515]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"mance can be seen by the high $\\eta_{rel}$ of N, P, and S tridoped activated porous carbon from fish and N-doped carbon aerogel from ovalbumin, which is close to 1. The latter possesses a relatively lower BET surface area of $150\\mathrm{m}^2\\mathrm{g}^{-1}$ . The lone pair electrons of the heteroatoms can serve as electron donors to accelerate $\\mathrm{I}_3$ reduction. Additionally, the doped atoms in the carbon structure can induce defects, increasing the ion-accessible surface area. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,517,485,677]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The efficiency of the electrocatalytic activities of the counter electrode can also be determined by the peak current density $(I_{p})$ and peak-to-peak separation $(E_{pp})$ values from the cyclic voltammetry experiment. However, most of the results are presented as qualitative instead of quantitative. The exact values are determined by parameters such as scan rate and electrolyte, among other similar parameters. For instance, the values are always compared to the Pt-based counter electrode. The more negative the $I_{p}$ value is, the smoother the reduction reaction at the electrolyte/electrolyte interface. The same applies to $E_{pp}$ , where a smaller $E_{pp}$ value implies that the electrocatalytic activity is better. In all cases, the natural product-based electrodes have $\\eta_{rel}$ values close to 1, and $I_{p}$ and $E_{pp}$ values close to those of Pt-based electrodes. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,678,485,887]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Next, we discuss the counter electrode with intended modifications. The modifications include the incorporation of conducting materials and/or incorporation of more active catalytic materials. As seen from Table 3, generally, the natural product/composite materials exhibit excellent $\\eta_{rel}$ compared to natural product materials with significantly lower $R_{ct}$ values compared to naturally-produced electrode materials. As an example, carbon material from orange fiber incorporated with CoS nanoparticles exhibits a $\\eta_{rel}$ of 1.07 and PCE of $5.94\\%$ , with a lower BET surface of ca. $10\\mathrm{m}^2\\mathrm{g}^{-1}$ [185]. The PCE value can be explained by the enhanced electrocatalytic activities of $\\mathrm{Co_xS_y}$ compounds. Such is the case, as different phases of cobalt sulfide have been investigated as an excellent oxygen evolution reaction (OER) electrocatalysts due to the overpotential for the OER [186]. For this reason, it can be confirmed that $\\mathrm{Co_xS_y}$ plays a vital role in the enhanced electrocatalytic activity of $\\mathrm{I}_3$ reduction instead of the orange fiber carbonaceous material because the carbonaceous material is able to exhibit a low BET surface. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,889,484,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A similar enhancement of the counter electrode electrocatalytic activity is also achieved by porous carbon/metal oxide composite materials. The Yun research group from Xi'an University of Architecture and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,424,936,609]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Technology published a set of works on natural products and waste-based counter electrodes with various metal oxides and a metal carbide [173, 174, 175, 176, 177, 178, 179, 180, 181, 182]. Most of the works employed aloe peel as the source of biomass. Even without any inorganic materials, the resulting porous materials from aloe peel achieved remarkably excellent DSSC performance. A better DSSC performance can be achieved by incorporating inorganic compounds as inorganic materials can be well dispersed throughout porous carbon materials. As noted by the authors, the oxide enhances the catalytic activities since the band alignment of the inorganic materials matches those of the $\\mathrm{I}_3$ reduction potential. Combining the high surface area of the porous carbon material with the excellent electronic properties of the inorganic materials is proven to decrease the $R_{ct}$ values to below $5\\Omega \\mathrm{cm}^2$ . Therefore, inorganic materials and natural product-based materials have synergistic effects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,610,936,713]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The second class of additives is conducting materials. These additive materials include Nafion, PEDOT:PSS, and acetylene/carbon black. Nafion and PEDOT:PSS are well-known conducting polymers containing sulfonic acid functional groups that can act as proton conductors. The conducting polymer can also serve as the binder of the counter electrode material to the FTO glass. Yeh et al. proposed that the interactions between Nafion and electrode materials are due to their hydrophobic interactions [187]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,718,936,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It may be better to introduce a functional group to the carbonaceous material of the counter electrode material. An alternative would be to extract the chemically functionalized carbonaceous materials, as shown in Ref. [188] for Nafion additives/binders. The incorporation of Nafion into the counter electrode is proven to enhance the PCE of the DSSC, as in the work of Yeh et al. [187]. Yeh et al. compared the performance of graphene with graphene/Nafion-based DSSCs. Incorporating Nafion into the graphene counter electrode is proven to increase the PCE from 4.58 to $7.69\\%$ . Chung et al. extracted N-doped porous carbon from ground coffee waste combined with Nafion for DSSC counter electrodes [188]. Owing to the large surface area of the porous carbon, increasing the ion-accessible surface area due to the doped nitrogen, the PCE reaches as high as $8.32\\%$ with a $\\eta_{rel}$ of 1.03, meaning that the N-doped porous carbon has a comparable efficiency with the Pt electrode, which is also consistent with the electrocatalytic properties of the material with a very low $R_{ct}$ of $0.5\\Omega\\mathrm{cm}^2$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,42,154,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[816,42,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[492,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"25 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[58,66,406,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.4. Remarks on natural carbon for dye-sensitized solar cells ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,92,485,185]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Carbon, as an abundant material, has great potential to be developed and become desirable counter-electrode for DSSC. A replacement for platinum is needed for DSSC production. Research trends on carbon utilization for DSSC counter electrodes are still growing and show impressive performance improvements; for example, the modification of carbon into porous carbon with a large surface area or other modifications to increase the catalytic performance toward the redox couple species. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,197,470,211]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5. Green synthesis metal oxide semiconductor for photoanodes ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,224,485,384]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\mathrm{ZnO}$ and $\\mathrm{TiO_2}$ are the most common semiconductors that are used in DSSCs. Generally, the semiconductor provides the surface for dye adsorption, collecting electrons from the excited dye and conducting the electrons toward the external circuit [1, 2, 3]. The synthesis of metal and metal oxide nanoparticles using green biological methods is a preferred synthesis method compared to physical and chemical methods. Green methods are cost-effective, environmentally friendly, and easily processed. Based on our records, the use of green-synthesized $\\mathrm{ZnO}$ or $\\mathrm{TiO_2}$ for DSSC applications is still limited; however, a recent study shows that green synthesis can facilitate the desired oxide particle structure and shape for DSSC applications [189]. Below we review various methods for the preparation of $\\mathrm{ZnO}$ and $\\mathrm{TiO_2}$ through a green approach. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,395,295,409]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5.1. Synthesis of ZnO using plant extract ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,422,485,566]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Anbuvannan et al. synthesized ZnO nanoparticles using Anisochilus carnosus leaf extract. Zinc nitrate as a precursor was added to the leaf extract at $60^{\\circ}\\mathrm{C}$ . The mixture was subsequently boiled for $20\\mathrm{min}$ until the color became dark yellow. The obtained paste was annealed at $400^{\\circ}\\mathrm{C}$ for two hours to obtain ZnO nanoparticles. The morphology and size of the obtained ZnO were confirmed by TEM. It was revealed that a majority of the ZnO nanoparticles were quasi-spherical with sizes ranging from 30 to $40\\mathrm{nm}$ . The photocatalytic performance showed that it enhanced the degradation of methylene blue under UV irradiation. Green-synthesized ZnO exhibited potential antibacterial properties against several pathogens [190]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,567,485,711]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ZnO nanoparticles may also be synthesized using aqueous Cassia fistula plant extract. The Cassia fistula plant extract was used as a fuel obtained by the solution combustion method. $\\mathrm{Zn(NO_3)_3\\cdot 6H_2O}$ was dissolved in the aqueous plant extract. The mixture was kept in a preheated muffle furnace at $400^{\\circ}\\mathrm{C}$ for approximately five minutes. Based on the TEM image, the particles consisted of many agglomerated particles and sponges in a form similar to irregularly shaped particles with an average crystallite size of $5 - 15\\mathrm{nm}$ . The obtained ZnO nanoparticles showed adequate performance in methylene blue dye under sunlight and UV illumination, in addition to displaying significant antioxidant properties [191]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,712,485,856]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The same solution combustion method was applied to green-synthesized $\\mathrm{ZnO}$ nanoparticles using an aqueous extract of Abutilon indicum. Zinc nitrate hexahydrate $(\\mathrm{Zn(NO_3)_2\\cdot 6H_2O})$ was mixed with the aqueous extract. After constant stirring for $2 - 5\\mathrm{min}$ , the mixture was kept in a preheated muffle furnace at a temperature of $200\\pm 5^{\\circ}\\mathrm{C}$ for $2 - 3\\mathrm{min}$ . After being filtered and rinsed, the $\\mathrm{ZnO}$ nanoparticles were calcined for two hours. The obtained $\\mathrm{ZnO}$ nanoparticles were homogeneous and equally distributed over the surface with a grain size of $16.72\\mathrm{nm}$ and bandgap energy of $3.37\\mathrm{eV}$ . The obtained $\\mathrm{ZnO}$ nanoparticles demonstrated effective performance in degrading Acid Black 234. $\\mathrm{ZnO}$ nanoparticles also display antioxidant and anticancer properties [192]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,857,485,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Another work carried out by Thema et al. was to synthesize ZnO nanoparticles using Agathosma betulina plant extract. Zinc nitrate hexahydrate $(\\mathrm{Zn(NO_3)_2\\cdot 6H_2O})$ , which was used as a zinc precursor, was mixed with the leaf extract and heated at $100^{\\circ}\\mathrm{C}$ for two hours. The obtained precipitate was washed, dried, and annealed at various temperatures from $100 - 500^{\\circ}C$ for two hours. It was found that $500^{\\circ}C$ was ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,65,937,129]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the optimal temperature for obtaining highly crystalline $\\mathrm{ZnO}$ nanocrystals. The HRTEM image shows that the optimized sample consisted of quasi-spherical agglomerated nanoscale particles with diameters ranging from 12 to $26\\mathrm{nm}$ . That nanoparticle exhibited a good varistor response [193]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,131,937,276]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ZnO nanoparticles were successfully synthesized using Carica papaya leaf extract and applied for photocatalytic and photovoltaic applications. The papaya leaf extract was added to a zinc acetate dihydrate solution at $60^{\\circ}\\mathrm{C}$ and $\\mathrm{pH}8$ before being stirred for two hours to synthesize ZnO nanoparticles. The washed precipitate was subsequently dried at $80^{\\circ}\\mathrm{C}$ for $12\\mathrm{h}$ . The synthesized ZnO nanoparticles had a pristine hexagonal wurtzite structure inside spheres with a diameter of approximately 50 nm. The photoactivity results revealed that ZnO nanoparticles completely degraded methylene blue dye within $180\\mathrm{min}$ under UV irradiation while showing an energy conversion efficiency of $1.6\\%$ and a current density of $81\\mathrm{mAcm}^{-2}$ [194]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,276,937,448]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Most research shows that green-synthesized $\\mathrm{ZnO}$ nanoparticles obtained nanoparticles in a spherical shape. However, several researchers reported that $\\mathrm{ZnO}$ nanorods could be successfully prepared using a green synthesis approach. Li Fu and Zhuxian Fu synthesized $\\mathrm{ZnO}$ nanorods mediated by Plectranthus amboinicus leaf extract. Zinc nitrate was mixed with the leaf extract and stirred at $80^{\\circ}\\mathrm{C}$ for four hours. The obtained pale white precipitate was centrifuged, washed, and calcined at $200^{\\circ}\\mathrm{C}$ for one hour. SEM characterization showed that $\\mathrm{ZnO}$ nanoparticles had a rod-shaped structure with an average particle size of 88 nm. The photocatalytic activity study revealed that biosynthesized $\\mathrm{ZnO}$ had an excellent photocatalytic performance in methyl red degradation under UV irradiation compared to chemically-synthesized $\\mathrm{ZnO}$ nanoparticles [195]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,448,937,592]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ZnO nanoparticles with various shapes were successfully synthesized using Phyllanthus niruri leaf extract. Zinc nitrate was added to the boiled leaf extract at $60^{\\circ}\\mathrm{C}$ after the stem turned yellow. The obtained paste was then calcined at $400^{\\circ}\\mathrm{C}$ for two hours to obtain a light white-colored powder. FESEM analysis showed that ZnO nanoparticles had rectangular, triangular, radial hexagonal, rod, and spherical shapes with an average size of $25.61\\mathrm{nm}$ . Biosynthesized ZnO showed excellent photocatalytic activity for methylene blue reduction and has many potential applications as semiconductor, pyroelectric, piezoelectric, catalyst, and optoelectronic, as well for phytochemical, and pharmacological, and medical purposes [196]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,607,757,620]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5.2. Synthesis of ZnO using microorganism ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,633,937,712]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Aspergillus fumigatus JCF fungi successfully mediated green-synthesized $\\mathrm{ZnO}$ nanoparticles. $\\mathrm{ZnSO_4}$ was added as a precursor to the fungal filtrate (pH 6.5) and incubated at $72^{\\circ}C$ for $72\\mathrm{h}$ in an orbital shaker. The obtained white precipitate was centrifuged and lyophilized. SEM images revealed that the prepared $\\mathrm{ZnO}$ nanoparticles were spherical with an average size of $60 - 80\\mathrm{nm}$ [197]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,712,937,804]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Jayaseelan et al. successfully synthesized ZnO nanoparticles using Aeromonas hydrophilic bacteria. ZnO was added to the bacterial culture solution and incubated at $30^{\\circ}\\mathrm{C}$ for $24\\mathrm{h}$ in a shaker incubator. After being cooled and incubated at room temperature for approximately $12 - 48\\mathrm{h}$ , white deposits were collected. The obtained ZnO nanoparticles were smooth and had a spherical shape. This suggests that it has significant antibacterial and antifungal properties [198]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,805,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Another green synthesis method to prepare ZnO nanoparticles is by using the yeast strain Pichia kudriavzevii, a method that was successfully carried out by Moghaddam et al. Zinc acetate dihydrate $(\\mathrm{Zn}(\\mathrm{CH}_3\\mathrm{COO})_2\\cdot 2\\mathrm{H}_2\\mathrm{O})$ was mixed with fungal cell-free filtrate and incubated at $35^{\\circ}\\mathrm{C}$ in a shaking incubator and agitated for 12, 24, and $36\\mathrm{h}$ . The obtained white precipitate was centrifuged and dried at $150^{\\circ}\\mathrm{C}$ for six hours. The results from TEM analysis showed that the average particle sizes were $10\\pm 2.08$ , $32\\pm 4.7$ , and $59\\pm 10.6\\mathrm{nm}$ for incubation times of 12, 24, and $36\\mathrm{h}$ , respectively. It was observed that the ZnO nanoparticles tended to agglomerate due to high surface energy [199]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,42,157,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"26 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[58,65,299,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5.3. Synthesis of $\\mathrm{TiO_2}$ using plant extract ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,90,485,235]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\mathrm{TiO_2}$ nanoparticles were synthesized by Goutam et al. using a leaf extract of Jatropha curcas L [200]. Titanium chloride $(\\mathrm{TiCl}_4)$ was used as a precursor. $80~\\mathrm{mL}$ of $0.5\\mathrm{M}$ $\\mathrm{TiCl_4}$ was added to $80~\\mathrm{mL}$ of filtered leaf extract at a ratio of 1:1 (v/v) with continuous stirring for $20\\mathrm{min}$ at room temperature. After adding an ammonia solution, the precipitates were separated, washed, dried, and calcined at $450^{\\circ}\\mathrm{C}$ for three hours. The obtained $\\mathrm{TiO_2}$ nanoparticles were spherical with a diameter ranging from $10 - 20\\mathrm{nm}$ [200]. The nanoparticles were later applied for the simultaneous removal of chemical oxygen demand (COD) and chromium (Cr) from secondary treated tannery wastewater (TWW). The results gave removals of 82.26 and $76.48\\%$ for COD and Cr, respectively [200]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,237,485,394]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Santhoshkumar et al. synthesized $\\mathrm{TiO_2}$ nanoparticles using Psidium guajava aqueous leaf extract, and before being concluded, $\\mathrm{TiO_2}$ nanoparticles were efficacious as antibacterial and antioxidant agents. $\\mathrm{TiO(OH)_2}$ was used as the precursor. The pure $\\mathrm{TiO(OH)_2}$ and aqueous leaf extract were stirred for several hours until the solution turned light green. The synthesized $\\mathrm{TiO_2}$ nanoparticles showed a spherical shape and clusters with an average size of $32.58\\mathrm{nm}$ $\\mathrm{TiO_2}$ nanoparticles exhibited better antibacterial properties when than the standard antibiotic disk. $\\mathrm{TiO_2}$ nanoparticles were also advantageous in terms of antibacterial properties compared to tetracycline, with a maximum zone of 25 and 23 mm inhibition when faced against Staphylococcus aureus and Escherichia coli, respectively [201]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,395,485,474]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Patidar et al. prepared $\\mathrm{TiO_2}$ nanoparticles using Moringa oleifera leaf extract. Anatase $\\mathrm{TiO_2}$ with an average crystallite size of $12.22\\mathrm{nm}$ was obtained. As the precursor, titanium tetraisoproxide (TTIP) was mixed with the ethanolic leaf extract and stirred for four hours. After centrifugation and washing, the $\\mathrm{TiO_2}$ nanoparticles were dried, ground, and calcined at $500^{\\circ}\\mathrm{C}$ for approximately five hours [202]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,475,485,645]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Another work of synthesizing $\\mathrm{TiO_2}$ using a biosynthesis approach was carried out by Subhapriya S and Gomathipriya P. $\\mathrm{TiO_2}$ nanoparticles were synthesized using Trigonella foenum-graecum extract, and their antibacterial properties were studied. The extract was added to titanium oxysulfate for $15\\mathrm{min}$ before dropping $1\\textrm{M}$ sodium hydroxide into the solution until $\\mathrm{pH}8$ was reached. The washed precipitate was calcined at $700^{\\circ}\\mathrm{C}$ for three hours to obtain crystalline $\\mathrm{TiO_2}$ nanoparticles. The obtained $\\mathrm{TiO_2}$ nanoparticles had a spherical shape with a size ranging between 20 and $90~\\mathrm{nm}$ . It also showed excellent antibacterial properties toward Staphylococcus aureus, Enterococcus faecalis, Klebsiella pneumoniae, Streptococcus faecalis, Pseudomonas aeruginosa, Escherichia coli, Proteus vulgaris, Bacillus subtilis, Yersinia enterocolitica, and the fungus Candida albicans [203]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,646,485,762]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Rajkumari et al. synthesized $\\mathrm{TiO_2}$ nanoparticles by using an aqueous leaf extract of Aloe barbadensis. They also studied the antibiofilm potential against Pseudomonas aeruginosa PAO1. In the synthesis procedure, the leaf extract was added by droplets into titanium chloride $(\\mathrm{TiCl}_4)$ at pH 7 and stirred for three hours. The washed precipitate was then dried at $100^{\\circ}\\mathrm{C}$ for seven hours. The obtained $\\mathrm{TiO_2}$ nanoparticles had a spherical shape with a size ranging from 20 to $50~\\mathrm{nm}$ , as confirmed by SEM and TEM analysis. The biosynthesized $\\mathrm{TiO_2}$ nanoparticles were found to exhibit a high antibiofilm efficacy against P.aeruginosa [204]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,764,485,843]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The most recent research was conducted by Senthamarai et. al., [189]. They prepared $\\mathrm{TiO_2}$ particle using the pineapple, orange, and grape fruit extracts. The grape extract facilitates the formation of the $\\mathrm{TiO_2}$ nanotube structure. As a result, this sample obtained the highest power conversion efficiency (4.33%) in comparison to the other extracts when built as a DSSC device using N4719 as a sensitizer. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,857,294,871]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5.4. Synthesis $\\mathrm{TiO}_2$ using microorganism ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,883,485,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\mathrm{TiO_2}$ nanoparticles were successfully synthesized using Aspergillus flavus TFR 7 fungi. First, mycelia were developed from fungal cultivation. The reaped mycelia were resuspended in demineralized water and incubated for $48\\mathrm{h}$ at $28^{\\circ}\\mathrm{C}$ to obtain a cell-free filtrate containing ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,65,937,118]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"extracellular enzymes. The filtrate was mixed with titanium precursor salt and incubated at $150~\\mathrm{rpm}$ and $28^{\\circ}\\mathrm{C}$ to obtain $\\mathrm{TiO_2}$ nanoparticles. The acquired $\\mathrm{TiO_2}$ nanoparticles had an average particle size of approximately $18~\\mathrm{nm}$ , as observed by DLS analysis [205]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,118,937,263]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Another work from Khan et al. showed that Bacillus amyloliquefaciens cultivation could be used to synthesize $\\mathrm{TiO_2}$ nanoparticles. $\\mathrm{TiOSO_4}$ was used as a titanium precursor. It was added to the prepared medium containing cultivated bacteria and incubated for $24\\mathrm{h}$ at $37^{\\circ}C.$ The gathered white precipitate was centrifuged, washed, and calcined at 500 $^\\circ C$ for three hours. The synthesized $\\mathrm{TiO_2}$ nanoparticles were spherical with a size ranging from 22.11 to $99.28~\\mathrm{nm},$ as observed by TEM analysis. The photocatalytic activity of doped and undoped biosynthesized $\\mathrm{TiO_2}$ nanoparticles to degrade the RR31 dye under UV irradiation at room temperature was tested. The results suggested that all samples were capable of degrading a photocatalytic RR31 dye [206]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,263,937,368]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The synthesis of $\\mathrm{TiO_2}$ nanoparticles was successfully mediated by baker's yeast (Saccharomyces cerevisiae). A $\\mathrm{TiO(OH)_2}$ solution was added to the cultivated yeast solution. Consecutively, it was heated in a steam bath at $60^{\\circ}\\mathrm{C}$ for $10 - 20\\mathrm{min}$ . After being cooled and incubated at room temperature for approximately $12 - 48\\mathrm{h}$ , the $\\mathrm{TiO_2}$ nanoparticles were found as-deposited white clusters at the bottom of the tube. The obtained $\\mathrm{TiO_2}$ nanoparticles were almost spherical at $12.57\\pm 0.22\\mathrm{nm}$ , as confirmed by TEM [207]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,382,810,395]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5.5. $\\mathrm{TiO}_2$ synthesis using aqueous solution approach ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,409,937,525]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Green-synthesized $\\mathrm{TiO_2}$ can be achieved using a modified sol-gel method known as the peroxo sol-gel method. In this method, water is used as a solvent instead of organic solvents, and pH 7 is required as a synthesized condition [208, 209]. Gao et al. successfully synthesized micropatterns of $\\mathrm{TiO_2}$ thin films using this method. $\\mathrm{H}_2\\mathrm{TiO}_3$ was used as a titanium precursor, and it was dissolved in a mixture that contained ammonia and $\\mathrm{H}_2\\mathrm{O}_2$ aqueous solution. The obtained thin film was smooth and crack-free, formed by the coalescence of nanosized particles of 10-20 nm in diameter [208]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,527,937,645]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Thin films of $\\mathrm{TiO_2}$ were successfully prepared using this green sol-gel method carried out by Ge et al. Titanium sulfate $(\\mathrm{TiOSO_4:nH_2O})$ $\\mathrm{H}_2\\mathrm{O}_2,$ and ammonia were used as the starting materials. The obtained yellow and transparent PTA solution was used as a coating solution. The $\\mathrm{TiO_2}$ -coated substrate was successively calcined at $500^{\\circ}\\mathrm{C}$ for $30\\mathrm{min}$ . SEM analysis showed that the $\\mathrm{TiO_2}$ thin film was uniformly comprised of spherical particles with an average particle size of $30 - 40\\mathrm{nm}$ . The thin film showed the best photocatalytic activity, reaching $99\\%$ methyl orange degradation under $160\\mathrm{min}$ of UV irradiation [210]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,646,937,751]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Another green synthesis approach is by using an \"aqueous\" solution. This chemical method was applied successfully in aqueous electrophoretic deposition. Benehkohal et al. used this method to prepare $\\mathrm{TiO_2 - ZnO}$ composite photoanodes for DSSCs. $\\mathrm{Zn(NO_3)_2}$ was added to a suspension of $\\mathrm{TiO_2}$ powder and an isopropanol-water mixture. Subsequently, the suspension was sonicated for one and a half hours before electrophoretic deposition (EPD). Next, the obtained layer was dried at room temperature and could be used for multiple characterizations [211]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,765,766,778]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5.6. Remarks on green synthesis metal oxide ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,791,937,870]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Oxide semiconductor synthesis through the green synthesis approach has the advantage of controlling the particle size and shape. Among the other green synthesis methods, microorganism synthesis assistance has the most difficulty. The synthesis step is tricky and requires time. Green synthesis using plant extracts seems more promising. The scale-up of this process requires the plantation land planning to supply the resources. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,883,605,896]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6. Conclusion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,910,937,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The synthesis, characterization, and performance of natural product-based DSSCs have been reviewed in depth. Overall, there are some ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,42,157,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,54]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"27 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[57,65,485,118]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"inconsistencies in the DSSC performance across the literature, mainly due to the different types of components used. However, the detailed atomic-level understanding of the electronic process that occurs among the components remains poorly understood and needs to be further explored. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,118,485,210]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Natural dyes need to be modified to obtain a better performance. Most modifications were concerned with improving the electronic properties and the other limitation of natural dyes, including dye stability, dye aggregation, and weak interaction with the oxide semiconductor surface. A computational study is among the best methods to investigate the electronic properties at the molecular level and the charge transport process. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,210,485,316]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Natural biopolymers are promising for the development of quasi-solid DSSCs. The quasi-solid DSSC minimizes the decrease in cell performance due to volatilization issues. The major problem with using natural biopolymers is their low conductivity. The low conductivity issue has been overcome by looking for a suitable redox couple, adding the ionic liquid, or adding another additive. Theoretical and computational studies regarding the charge transfer process in polyelectrolyte gel systems are limited and challenging to explore. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,316,485,419]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Natural carbon-based counter electrodes have become promising candidates for replacing more expensive Pt-based counter electrodes. It appears that a DSSC with a porous carbon-based counter electrode with a large surface area gives a comparable performance to the Pt-based electrode. The low-surface area natural product-based electrode can achieve a remarkably good DSSC performance if the extracted material is combined with electrocatalytically active inorganic and/or conductive materials. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,421,485,619]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"There is always a trade-off between the performance, production cost, and environmental aspects of natural product-based DSSC fabrication. Most of the authors cited in this paper argue that natural products are readily available in the surroundings as wastes or byproducts. One issue regarding the utilization of natural products is their inhomogeneous content, which can bring either benefits or drawbacks to the extraction processes of the intended material and DSSC performances. The impurities contained in the source must be removed using harsh chemicals if necessary. On the other hand, impurities can also benefit DSSC performances. Another issue is the reproducibility of the material extracted from the natural product, where the material obtained can have different structures and properties. Additionally, the choice of the other components has to be taken into account. Therefore, to prepare natural-based DSSCs, parameters such as cost, chemical requirements, and environmental aspects must be considered to achieve proper DSSC performance. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,619,485,698]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, we note that it remains plausible to improve DSSC performance by incorporating natural product-derived materials into DSSC components. If the cost and chemical precursors are not taken into account, we can employ naturally-derived porous carbon and green-synthesized semiconductors in DSSC devices. However, the dyes and electrolytes must still come from commercial products. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,712,144,723]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Declarations ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,738,230,750]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Author contribution statement ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,764,485,790]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"All authors listed have significantly contributed to the development and the writing of this article. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,805,164,815]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Funding statement ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[57,829,485,883]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This work was supported by the Ministry of Research and Technology of Republic Indonesia through the PDUPT Scheme (973/PKS/ITS/2021), and by the Faculty of Mathematics and Natural Science (183/J01.1.28/PL.06.02/2021). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,897,213,909]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data availability statement ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[78,923,440,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data included in article/supp. material/referenceed in article. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,66,700,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Declaration of interests statement ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[529,92,784,104]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The authors declare no conflict of interest. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,127,643,139]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Additional information ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[529,153,845,167]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"No additional information is available for this paper. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,180,638,192]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgements ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,206,939,272]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"YK is gratefully to the Ministry of Research and Technology of Republic Indonesia for funding this research through the PDUPT Scheme with contract number 973/PKS/ITS/2021. ASH acknowledges the support from Faculty of Mathematics and Natural Science, University of Gadjah Mada under contract number 183/J01.1.28/PL.06.02/2021. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,288,584,298]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[519,312,934,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[1] A. Hagfeldt, G. Boschloo, L. Sun, L. Kloo, H. Pettersson, Dye-sensitized solar cells, Chem. Rev. 110 (2010) 6595-6663. \",\"[2] J. Gong, J. Liang, K. Sumathy, Review on dye-sensitized solar cells (DSSCs): fundamental concepts and novel materials, Renew. Sustain. Energy Rev. 16 (2012) 5848-5860. \",\"[3] K. Sharma, V. Sharma, S.S. Sharma, Dye-sensitized solar cells: fundamentals and current status, Nanoscale Res. Lett. 13 (2018) 381. \",\"[4] D.F. Watson, G.J. 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Mohamed, Biopolymer electrolytes based on blend of kappa-carrageenan and cellulose derivatives for potential application in dye sensitized solar cell, Electrochim. Acta 175 (2015) 162-168. \",\"[219] S. Che Balian, A. Ahmad, N. Mohamed, The effect of lithium iodide to the properties of carboxymethyl $\\\\kappa$ -carrageenan/carboxymethyl cellulose polymer electrolyte and dye-sensitized solar cell performance, Polymers (Basel) 8 (2016) 163. \",\"[220] T. Sugumaran, D.S. Silvaraj, N.M. Saidu, N.K. Farhana, S. Ramesh, K. Ramesh, S. Ramesh, The conductivity and dielectric studies of polymer electrolytes based on iota-carrageenan with sodium iodide and 1-butyl-3-methylimidazolium iodide for the dye-sensitized solar cells, Ionics (Kiel) 25 (2019) 763-771. \",\"[221] E. Praveen, I.J. Peter, A.M. Kumar, K. Ramachandran, K. Jayakumar, Boosting of power conversion efficiency of 2D ZnO nanostructures-based DSSC by the lorentz force with chitosan polymer electrolyte, J. Inorg. Organomet. Polym. Mater. (2020) 4927-4943. \",\"[222] M. Khalilili, M. Abedi, H.S. Amoli, S.A. Mozaffari, Comparison of chitosan and chitosan nanoparticles on the performance and charge recombination of water-based gel electrolyte in dye sensitized solar cells, Carbohydr. Polym. 175 (2017) 1-6. \",\"[223] F.H. Muhammad, R.H.Y. Subban, T. Winie, Solid solutions of hexanoyl chitosan/ poly(vinyl chloride) blends and NaI for all-solid-state dye-sensitized solar cells, Ionics (Kiel) 25 (2019) 3373-3386. \",\"[224] M. Vasei, F. Tajabadi, A. Jabbari, N. Taghavinia, Stable dye-sensitized solar cells based on a gel electrolyte with ethyl cellulose as the gelator, Appl. Phys. A Mater. Sci. Process 120 (2015) 869-874. \",\"[225] P. Li, Y. Zhang, W. Fa, Y. Zhang, B. Huang, Synthesis of a grafted cellulose gel electrolyte in an ionic liquid ([Bmim]I) for dye-sensitized solar cells, Carbohydr. Polymer 86 (2011) 1216-1220. \",\"[226] G.P. Salvador, D. Pugliese, F. Bella, A. Chiappone, A. Sacco, S. Bianco, M. Quaglio, New insights in long-term photovoltaic performance characterization of cellulose-based gel electrolytes for stable dye-sensitized solar cells, Electrochim. Acta 146 (2014) 44-51. \",\"[227] A. Chiappone, F. Bella, J.R. Nair, G. Meligrana, R. Bongiovanni, C. Gerbaldi, Structure-performance correlation of nanocellulose-based polymer electrolytes for efficient quasi-solid DSSCs, ChemElectroChem 1 (2014), 1241-1241. \",\"[228] M. Willgert, A. Boujemaaoui, E. Malmstrom, E.C. Constable, C.E. Housecroft, Copper-based dye-sensitized solar cells with quasi-solid nano cellulose composite electrolytes, RSC Adv. 6 (2016) 56571-56579. \",\"[229] M.H. Khanimirzaei, S. Ramesh, K. Ramesh, Hydroxypropyl cellulose based nonvolatile gel polymer electrolytes for dye-sensitized solar cell applications using 1-methyl-3-propylimidazolium iodide ionic liquid, Sci. Rep. 5 (2015). \",\"[230] T. Or, K. Miettunen, E.D. Cranston, J.M. Moran-Mirabal, J. Vapaavuori, Cellulose nanocrystal aerogels as electrolyte scaffolds for glass and plastic dye-sensitized solar cells, ACS Appl. Energy Mater. 2 (2019) 5635-5642. \",\"[231] J.W.Y. Liew, K.S. Loh, A. Ahmad, K.L. Lim, W.R. Wan Daud, Synthesis and characterization of modified $\\\\kappa$ -carrageenan for enhanced proton conductivity as polymer electrolyte membrane, PLoS One 12 (2017) 1-15. \",\"[232] N.K. Farhana, F.S. Omar, R. Shanti, Y.K. Mahipal, S. Ramesh, K. Ramesh, Iota-carrageenan-based polymer electrolyte: impact on ionic conductivity with incorporation of AmNTFSI ionic liquid for supercapacitor, Ionics (Kiel). 25 (2019) 3321-3329. \",\"[233] M.I.H. Sohaimy, M.I.N. Isa, Ionic conductivity and conduction mechanism studies on cellulose based solid polymer electrolytes doped with ammonium carbonate, Polym. Bull. 74 (2017) 1371-1386. \",\"[234] M. Latifi, A. Ahmad, H. Kaddami, N.H. Hassan, R. Dieden, Y. Habibi, Chemical modification and processing of chitin for sustainable production of biobased electrolytes, Polymers (Basel) 12 (2020) 1-16. \",\"[235] W. Ahmad, M.R. Al Bahrani, Z. Yang, J. Khan, W. Jing, F. Jiang, L. Chu, N. Liu, L. Li, Y. Gao, Extraction of nano-silicon with activated carbons simultaneously from rice husk and their synergistic catalytic effect in counter electrodes of dyesensitized solar cells, Sci. Rep. 6 (2016) 1-11. \",\"[236] J. Theerthagiri, R.A. Senthil, P. Arunachalam, J. Madhavan, M.H. Buraidah, A. Santhanam, A.K. Arof, Synthesis of various carbon incorporated flower-like $\\\\mathrm{MoS}_2$ microspheres as counter electrode for dye-sensitized solar cells, J. Solid State Electrochem. 21 (2017) 581-590. \",\"[237] V. Loryuenyong, A. Buasri, P. Lerdvilainarit, K. Manachevakulm, S. Sompong, Production of graphitic carbon-based nanocomposites from $\\\\mathrm{K}_2\\\\mathrm{CO}_3$ -activated coconut shells as counter electrodes for dye-sensitized solar-cell applications, J. Kor. Phys. Soc. 68 (2016) 317-322. \"]","page_idx":"31","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[60,42,156,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[490,952,507,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"32 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[60,65,482,267]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[238] K.K. Dasari, V. Gumtapure, Activated carbon-based dye-sensitized solar cell for development of highly sensitive temperature and current sensor, Mater. Res. Express 6 (2019), 085531. \",\"[239] G. Nagaraju, J.H. Lim, S.M. Cha, J.S. Yu, Three-dimensional activated porous carbon with meso/macropore structures derived from fallen pine cone flowers: a low-cost counter electrode material in dye-sensitized solar cells, J. Alloys Compd. 693 (2017) 1297-1304. \",\"[240] S.M. Cha, G. Nagaraju, S.C. Sekhar, L.K. Bharat, J.S. Yu, Fallen leaves derived honeycomb-like porous carbon as a metal-free and low-cost counter electrode for dye-sensitized solar cells with excellent tri-iodide reduction, J. Colloid Interface Sci. 513 (2018) 843–851. \",\"[241] S. Xu, C. Liu, J. Wiezorek, 20 renewable biowastes derived carbon materials as green counter electrodes for dye-sensitized solar cells, Mater. Chem. Phys. 204 (2018) 294-304. \",\"[242] P. Huang, S.J. Xu, M. Zhang, W. Zhong, Z.H. Xiao, Y.P. Luo, Lotus leaf derived natural dye as sensitizer and biochar as counter electrode for dye-sensitized solar cells, Mater. Sci. Forum 993 (2020) 884-892. \",\"[243] Q.W. Jiang, G.R. Li, F. Wang, X.P. Gao, Highly ordered mesoporous carbon arrays from natural wood materials as counter electrode for dye-sensitized solar cells, Electrochem. Commun. 12 (2010) 924-927. \"]","page_idx":"32","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[512,65,934,235]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[244] D. Wu, C. Zhu, Y. Shi, H. Jing, J. Hu, X. Song, D. Si, S. Liang, C. Hao, Biomass-derived multilayer-graphene-encapsulated cobalt nanoparticles as efficient electrocatalyst for versatile renewable energy applications, ACS Sustain. Chem. Eng. 7 (2019) 1137-1145. \",\"[245] P. Ma, W. Lu, X. Yan, W. Li, L. Li, Y. Fang, X. Yin, Z. Liu, Y. Lin, Heteroatom tridoped porous carbon derived from waste biomass as Pt-free counter electrode in dye-sensitized solar cells, RSC Adv. 8 (2018) 18427-18433. \",\"[246] K. Moolsarn, A. Tangtrakarn, A. Pimsawat, K. Duangsa, C. Mongkolkachit, W. Maiaugree, V. Amornkitbamrung, A dye-sensitized solar cell using a composite of PEDOT: PSS and carbon derived from human hair for a counter electrode, Int. J. Photoenergy 2017 (2017). \",\"[247] Y. Di, S. Jia, N. Li, C. Hao, H. Zhang, S. Hu, Ni-incorporated carbon materials derived from humic acid as efficient low-cost electrocatalysts for dye-sensitized solar cells, Org. Electron. 76 (2020) 105395. \",\"[248] M. Butt, K. Preuss, M.-M. Titirici, H. Rehman, J. Briscoe, Biomass-derived nitrogen-doped carbon aerogel counter electrodes for dye sensitized solar cells, Materials (Basel) 11 (2018) 1171. \"]","page_idx":"32","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[60,42,156,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y. Kusumawati et al. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[815,42,937,52]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Heliyon 7 (2021) e08436 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[492,952,505,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"33 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[58,184,174,197]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Review article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,206,529,226]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Natural resources for dye-sensitized solar cells \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[838,208,890,247]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0007/78026f383237e705af19a3e21bedad8fef44412254bdcf1638d2ce62b956972e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,240,640,259]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Yuly Kusumawati a,\\\\*, Aulia S. Hutama b, Diana V. Wellia c, Riki Subagyo a \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,266,801,298]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"$^{a}$ Department of Chemistry, Institut Teknologi Sepuluh Nopember, Sukolilo Campus, Surabaya, 60111, Indonesia \\\",\\\"$^{b}$ Department of Chemistry, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Jalan Sekip Utara, Bulaksumur, Yogyakarta, 55281, Indonesia \\\",\\\"$^{c}$ Department of Chemistry, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Padang, 24516, Indonesia \\\"]\",\n \"page_idx\": \"0\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[58,327,193,339]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ARTICLEINFO \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,353,109,363]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,365,181,374]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dye sensitized solar cells \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,375,146,385]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Natural resources \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,385,117,395]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biopolymer \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,397,184,406]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Natural counter electrode \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,408,137,417]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green synthesis \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[334,327,435,339]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABSTRACT \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[332,353,937,522]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"While the development of dye-sensitized solar cells (DSSCs) has been ongoing for more than 30 years, the currently obtained efficiency is unsatisfactory. However, the study of DSSC development has produced a fundamental understanding of cell performance and inspired other devices, such as perovskite cell solar cells. DSSCs consist of a dye-sensitized photoanode, a counter electrode, and a redox couple in the electrolyte system. Each of the components has an important role and cofunctions with each other to obtain a high power conversion efficiency. Various modifications to each DSSC component have been applied to improve their performance. Additionally, to generate improvements, the effort to reduce production costs has been crucial. The utilization of natural sources for DSSC components is a possible solution to this issue. The utilization of natural resources also aims to increase the value of the natural resource itself. In this review, the applications of various natural sources for DSSC components are described, as well as the modification efforts that have been made to enhance their performance. The discussion covers the utilization of natural dye for sensitizer dyes in liquid DSSC applications: (1) utilization of biopolymers for quasi-solid DSSC electrolytes, (2) green synthesis methods for photoanode semiconductors, and (3) development of natural carbon counter electrodes. The detailed factors that influence improvements in cell performance are also addressed. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,559,163,571]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,585,485,689]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Multiple renewable energy sources must be developed to meet rapidly increasing energy demand and human population growth. Countries around the world should utilize their natural resources as renewable energy to ensure sustainability. Solar energy is an abundant resource available in many countries. It has enabled continuous growth in the development of solar cells in recent decades. Among solar technologies, dye-sensitized solar cells (DSSCs) are photovoltaic devices that have attracted much attention since the 1990s. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,691,485,795]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 1 presents a model of DSSC structure and function. It consists of two electrodes. One electrode is an oxide-semiconductor mesoporous layer deposited onto fluorine-doped tin oxide (FTO) glass and sensitized by a dye, which acts as a photoanode. The other is platinized FTO glass as a cathode, also called a counter electrode. An electrolyte system is placed between these two electrodes. The most common DSSC liquid electrolyte consists of an $\\\\mathrm{I}_3 / \\\\mathrm{T}^-$ redox couple dissolved in an organic solvent such as acetonitrile. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,796,485,823]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Electricity in the DSSC is produced by the electron transfer process displayed in the inset section in Figure 1. When the dye - which acts \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,559,937,742]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"as a sensitizer in DSSC - receives solar radiation, the electron from the highest occupied molecular orbital (HOMO) excites the lowest unoccupied molecular orbital (LUMO). Electrons are subsequently injected into the oxide semiconductor conduction band. After that, the electrons travel to the external circuit through the anode and cathode. Once the electrons arrive at the external circuit, they change the redox couple species state from oxidized to reduced. The electrons obtained from the reversal of the redox couple utilize dye regeneration. This cycle is repeated until electricity is gathered. General article reviews have already been published on the primary or fundamental concepts of DSSCs [1, 2, 3], the electron transfer mechanism in DSSCs [4, 5, 6, 7], and recent progress about DSSC development [8, 9, 10, 11], which will be beneficial for readers who need additional information. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,744,937,822]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The assessed performance for the DSSC is the light-to-electricity conversion efficiency or power conversion efficiency (PCE, $\\\\%$ ). The PCE is contributed by the photoanode, counter electrode, electrolyte, and dye employed in the DSSC device. The PCE is proportional to the short circuit current density $(J_{sc})$ , open-circuit voltage $(V_{oc})$ , and fill factor $(FF)$ as follows. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[428,42,569,55]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[60,74,161,158]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CellPress \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[388,76,628,89]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Contents lists available at ScienceDirect \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[463,105,549,126]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[371,145,643,160]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"journal homepage: www.cell.com/heliyon \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[852,76,936,160]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[67,844,201,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"* Corresponding author. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[80,856,418,867]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"E-mail address: y_kusumawati@chem.its.ac.id (Y. Kusumawati). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[57,876,319,887]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1016/j.heliyon.2021.e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[58,889,598,901]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received 28 August 2021; Received in revised form 14 October 2021; Accepted 16 November 2021 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[58,902,937,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2405-8440/© 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[163,66,836,290]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 1. A model of dye-sensitized solar-cell structure and function. (Red/Ox = the coupled redox species for example $\\\\\\\\mathrm{I}_3\\\\\\\\mathbin{\\\\\\\\text{一}}/\\\\\\\\mathrm{T}$ ; VB = Valence band; CB = Conduction band). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0876/36f9eaf855edc4a9cad11636fc6e3be44459162573027363be8b781f95483561.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,339,485,353]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\eta \\\\sim J _ {s c} \\\\times V _ {o c} \\\\times F F \\\\tag {1}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[57,358,485,490]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The short circuit current $(J_{\\\\mathrm{sc}})$ correlates with both the photoanode and counter electrode performance. The value of $J_{\\\\mathrm{sc}}$ can be increased by improving the efficiency of light harvesting. The improvement can be conducted, for instance, by finding a proper sensitizer that can more strongly attach to $\\\\mathrm{TiO_2}$ surfaces or pores [12]. The counter electrode has a crucial role in catalyzing the redox couple in the electrolyte solution. The reduced species will be transported to the photoanode, reduce the oxidized dye, and continue the light absorption cycle. Therefore, a counter electrode with high electrocatalytic activity, charge transport activity, and low resistance is highly desirable to increase the $J_{\\\\mathrm{sc}}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,490,485,530]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The open-circuit voltage $(V_{oc})$ is the difference in the Fermi level of electrons in $\\\\mathrm{TiO}_2(E_F)$ and the redox potential of the electrolyte $(E_{redox})$ over the charge $(q)$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,539,485,566]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV _ {o c} = \\\\frac {\\\\left(E _ {F} - E _ {r e d o x}\\\\right)}{q} \\\\tag {2}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[57,572,485,668]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theoretically, $V_{oc}$ can reach up to 1.6 V. However, due to the energy mismatches between the $E_{redox}$ and HOMO levels of the dye and between the conduction band level $(E_c)$ of TiO2 and the LUMO of the dye, the maximum voltage is reduced to $\\\\frac{(E_c - E_{redox})}{q}$ [13]. The $V_{oc}$ can be tuned by several means. An example of this is putting additives into the electrolyte to shift the conduction band level of TiO2 and/or proper choice of $\\\\mathrm{I}^{-}$ salt source [14, 15, 16]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,669,485,761]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The $FF$ depends on the serial resistance and shunt resistance of the devices. Serial resistance in DSSCs is the resistance of the electron transfer process in the external circuit to the counter electrode. Shunt resistance is the resistance of the back electron transfer to the photoanode. Therefore, to increase the $FF$ value, the serial resistance must be minimal, while the shunt resistance must be maximal. The DSSCs first published by Grätzel in 1991 gained a cell PCE of $7.1 - 7.9\\\\%$ [17]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,761,485,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For the last three decades, increasing the PCE has remained a challenge in enhancing DSSC performance. Ideally, DSSC improvement requires the optimization of all device components. For example, the oxide semiconductor layer of the photoanode is expected to have a mesoporous structure to immobilize a maximum amount of dye to absorb adequate solar light [18, 19]. To have a mesoporous structure, various methods have been proposed. Surfactants are the most straightforward templating agents to control the surface area of the resulting semiconductors [20, 21, 22]. The use of sodium dodecyl sulfate in the oxide synthesis step can improve the cell performance to $6.08\\\\%$ compared to the $4.06\\\\%$ cell performance when using $\\\\mathrm{TiO_2}$ P25 [20]. The template-free semiconductor synthesis method, with controllable size and surface area, can also be carried out to synthesize the oxide photoanodes. This has been \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,339,937,457]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"demonstrated by Hosni et al., who prepared a zinc oxide nanotubes with a diameter of $35\\\\mathrm{nm}$ [23]. The layer of this particle is highly porous, which is beneficial for DSSC performance. Another method for photoanode improvement is to prepare an oxide semiconductor with a one-dimensional structure. It has been proven that the one-dimensional structure will be beneficial for electron transport within the oxide matrix [23, 24, 25, 26]. Zhang et al. developed a $\\\\mathrm{TiO_2}$ nanotube DSSC, and they obtained a satisfactory PCE of $9.86\\\\%$ . The necks formed between $\\\\mathrm{TiO_2}$ nanotube particles are responsible for charge transport [27]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,457,937,718]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dye sensitizer optimization has been studied to improve cell performance and reduce the cell production cost. Metal-free organic dyes have become an alternative to classical organo-ruthenium complexes due to multiple advantages, such as low cost, tunable properties, and high molar extinction coefficients [28]. Dye design works usually utilize quantum chemical calculations in conjunction with the experimental works. Quantum chemical calculations are pivotal in predicting the electronic properties of dyes to provide a molecular-level explanation of the electronic process. Experimental and theoretical molecular engineering has been carried out to arrange the donor (D), $\\\\pi$ -spacer ( $\\\\pi$ -conjugation section of the dye) and acceptor (A) units to obtain either D- $\\\\pi$ -A [29], D-A- $\\\\pi$ -A [30], or D-D- $\\\\pi$ -A structures [31]. Despite the endeavor, not all results were satisfactory. For example, the D- $\\\\pi$ -A thiophene dyes developed by Babu et al. only achieved a PCE of $4.24\\\\%$ . On the other hand, Wang et al. succeeded in preparing a D-A- $\\\\pi$ -A-based DSSC and produced a PCE value of $9.83\\\\%$ . The study of the binding of dyes onto the oxide surface is also vital to ensure an efficient electron injection process [32, 33]. Additionally, it is important to tune the HOMO and LUMO levels of the dyes to obtain an efficient intramolecular charge transfer process and electron injection into the photoanode. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,721,937,878]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Studies on electrolytes focus on finding alternatives to iodine/triiodide liquid-based electrolyte solution, which presents. This has led to a replacement of the $\\\\mathrm{I}_3 / \\\\mathrm{I}^-$ redox couple by other redox couples, such as $\\\\mathrm{Co}^{2+} / \\\\mathrm{Co}^{3+}$ [34, 35, 36], nitroxide radicals [37, 38], copper complexes [39, 40], thiolate/disulfide [41], and ferrocenium/ferrocene [42, 43]. In addition, to overcome electrolyte leakage, quasi-solid DSSCs, which use a polymer gel as an electrolyte medium, have been considered [44, 45, 46]. Unfortunately, quasi-solid DSSCs have not shown a better PCE value than liquid DSSCs, with PCE values ranging from $4\\\\%$ to $5\\\\%$ [44]. A few have a PEC value of $7\\\\%$ , such as a PAN (polyacrylonitrile)-based DSSC combined with RbI and tetrahexylammonium iodide salt developed by Bandara et al. [47]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,880,937,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For the counter electrode component, research has been focused on finding a platinum substitute. It is evident that platinum-based DSSC show superior performance as catalyst for the reduction of $\\\\Gamma_{3}$ to $\\\\Gamma^{-}$ . However, since it is a noble metal, the production cost of platinum-based \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,42,154,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[494,952,502,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,65,485,223]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"DSSCs are expensive [48, 49]. Various materials have then been proposed to replace platinum, such as carbon-based materials, including allotrope graphene [50, 51, 52, 53] or carbon nanotubes [54, 55], conductive polymers such as PEDOT [56], metal-organic frameworks (MOF) [49, 57], and perovskites [58, 59]. Research on counter electrodes also focuses on flexible counter electrodes to extend DSSC applications [60, 61]. In general, most nonplatinum counter electrode-based DSSCs have a lower PCE than the platinum DSSCs. However, some materials outperform the platinum materials and appear to be promising for further development [48, 62]. For instance, the graphene nanoplate-based counter electrode prepared by Kakiage et al. has a PCE value of $14.7\\\\%$ [53]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,223,485,341]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The best performance of DSSC currently recorded is one that uses copper complex redox couple-based electrolytes developed by Zhang et al. This cell employs a sensitizer constructed by a bulky donor N-(2',4'- bis (dodecyloxy)-[1,1'-biphenyl]-4-yl)-2',4'-bis(dodecyloxy)-N-phenyl[1,1'-biphenyl]-4-amine and an electron acceptor 4-(benzo[c] [1, 2, 5] thiadiazol-4-yl) benzoic acid coupled with the PEDOT (poly(3,4-ethylenedioxythiophene) counter electrode. This cell shows a PCE value of $34.5\\\\%$ under warm white fluorescent light at 1000 lux. Based on these results, the cell is the best cell for ambient light device applications [63]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,343,487,593]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To improve DSSC performance and decrease their cost, the utilization of natural resources has attracted much attention. Natural resources aim to achieve sustainability and reliability and support an eco-friendly environment [64, 65]. In this review, the current progress on natural resource utilization in DSSC development is presented. Although Mariotti et al. [66] recently reviewed the development of eco-friendly and cost-effective materials for DSSCs, the point of view of that work is slightly different from the current review. In the present review, the natural resources as material sources that build DSSCs will be further elaborated on. The purposes of this review are to describe the utilization of natural resources in DSSCs and their shortcomings. The discussion will point out the natural resource utilization in each DSSC component: natural dyes for sensitizers, natural polymers for quasi-solid DSSC electrolytes, and natural carbon for counter electrodes. In most DSSCs, $\\\\mathrm{TiO_2}$ and ZnO photoanode are usually taken from either commercial sources or chemically and physically controlled synthetic procedures. Here, we also present the possibility of preparing photoanodes from the oxides obtained through green synthesis with controllable structures and morphologies. Figure 2 presents the illustration of the scope of this review. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,607,284,620]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. Natural dye for sensitizer DSSC \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,633,487,713]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The sensitizer is one of the vital components in DSSCs. It aids in capturing visible to near-infrared light over a broad spectrum range with high molar extinction coefficients. It must also produce good charge separation to avoid electron recombination and efficient electron injection into oxide semiconductors [67]. Ruthenium-based dyes have shown good performance in fulfilling sensitizer requirements. Due to their rare \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,65,937,211]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"availability and high cost, alternative dyes have been developed to replace ruthenium complex dyes [68]. Natural dyes offer good opportunities. They have been considered due to their high molar extinction coefficient and their abundant availability [68, 69]. Families of natural dyes that have been explored for sensitizers applications in DSSCs include betanin or betalain [70, 71, 72, 73, 74, 75, 76, 77, 78], chlorophyll [72, 73, 74, 75, 76, 77, 78, 79, 80], and anthocyanin [28, 88, 89, 90, 91, 92, 93, 94]. The cosensitization of two dyes is also of high interest to enhance their performance [95, 96]. In the following sections, we present details of the various families of natural dyes and explain multiple research efforts undertaken to overcome their limitations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,225,589,235]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.1. Betanin \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,250,937,369]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Betanins are a category of pigments that belong to the betalain class. The betanin structure is presented in Figure 3. In their chemical structure, betalains contain an N-heterocyclic bearing hydroxyl functional group. Betalain compounds are divided into betacyanins, red-violet pigments, and betaxanthin, yellow pigments. Approximately $75 - 95\\\\%$ of red-violet pigments are composed of betanin. Notably, this pigment can be extracted from Caryophyllales plants [66, 97]. Betanins have inspired researchers to utilize these compounds for sensitizers in DSSCs [70, 71, 72, 73, 74, 75, 76, 77, 78]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,370,937,540]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The betanin sensitizer was first reported in 2005 by a research group from Uppsala University [80]. Unfortunately, the DSSC performance was still considered relatively poor. They conducted the research using an unsealed cell and reported a poor performance with a very low $J_{SC}$ , even with an $FF$ value in the same range of the standard ruthenium dye cell. Among the tested cells, the use of an ethanol solvent for the electrolyte showed the best result [80]. In 2011, Sandquist et al. from Washington State University reported a relatively higher PCE of the betanin-based DSSC than the previous study [71]. They made improvements by using 3-methoxypropionate (MPN) as the electrolyte solvent and employing a blocking layer. Their improvement led to a PCE of $2.7\\\\%$ [71]. This report showed that using MPN as an electrolyte solvent gives a better result than acetonitrile. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,540,937,646]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Table 1 summarizes the results of betanin-based DSSCs. It highlights the efforts and modifications that have been conducted thus far. Based on Table 1, we can conclude that the factors that have to be considered to develop betanin-based DSSCs are (1) the extraction process of the dyes [70, 71, 72]; (2) the immersion system for sensitizing the photoanode [71, 72, 73]; (3) the incorporation of a small amount of metal/cation to tune the electronic properties of the photoanode [73, 74, 77]; and (4) the choice of the electrolyte system [70, 72, 74, 77]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,646,937,712]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Table 1 shows that most PCEs of the betanin-based DSSCs do not exceed $3\\\\%$ . The best result was obtained for cells using medium-pressure liquid chromatography-extracted betanin [71]. Incorporating Ag and Au nanoparticles into the photoanode can also enhance light absorption due to the surface plasmon resonance effect [74, 77]. Moreover, Au \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[166,742,831,914]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 2. The illustration of natural resources for DSSC application. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0856/55e61d7a30d41fd68242b023305b7ee5a1dc4ab967b6082b7fa1f500d6224e71.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[58,42,157,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[494,952,504,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[255,65,480,337]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(a) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0691/093bdf2ad69a4552a940d5ee8a5b5281d78b40333d7a4f69eefbcc7ecf45cd4d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[512,64,736,336]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(b) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0890/753642f648bf614b83ad016bda612cd27d7c3c451fb6c4eddcf51249a4ca473c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[201,424,457,733]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(c) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0392/fd2ffe66b4da2a6485cf5babcaad63e3d6db14ac6164f45f76f3f6fb37f9a9e4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[485,443,789,728]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(d) \\\",\\\"Figure 3. Structure of (a) Betalain and (b) Betanin and structure of the constituent pigment, namely (c) betacyanin and (d) betaxanthin. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0514/611d15fa01fc5fd13f10483b519d3d78c2ef16d18afefef1ba3028c3381d87d0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,795,485,873]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"incorporation provokes a Schottky barrier effect at the Au and $\\\\mathrm{TiO_2}$ interface. This effect can reduce the charge recombination from the oxide conduction band to the LUMO of dyes or electrolyte species [77]. Maintaining the acidic condition of the solvent upon the extraction process or photoanode immersion can also be considered since the structure of betanin is known to be influenced by the solution pH [73]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,875,485,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Multiple experimental and computational studies have also been performed to gain insights into the intramolecular electronic properties of betanin and the charge electron mechanism on the $\\\\mathrm{TiO_2}$ surface. Many findings explain betanin limitations that should help to find solutions for \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,795,937,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"cell improvement. Knorr et al. reported that during the recombination process of electron injection, a radical species is formed. This radical species provokes betanin oxidation [98]. Damayanti et al. revealed that one of the three carboxyl moieties of betanin limits the betanin charge transfer to the oxide semiconductor [99]. Based on these findings, betanin modification can be carried out to develop a betanin-based DSSC. Dye aggregation is also prominent in betanin-based DSSC performance. This phenomenon can either be beneficial or detrimental to cell performance. The absorbed photon energy will be partly lost due to thermal processes and noncharge collection [100]. In contrast, Treat et al. found \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,42,154,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[494,952,502,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[60,63,931,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0841/89d8212cb6250485ca906f892ae96b2d5c5bf1a3c782fdcd9199d7196003909f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>No</td><td>Source</td><td>Pigmen</td><td>Solvent of extraction</td><td>Technique of purification</td><td>Photoanode</td><td>Counter electrode</td><td>Redox couple</td><td>Electrolyte solvent</td><td>JSC(mA/cm2)</td><td>VOC(V)</td><td>FF</td><td>η(%)</td><td>Referen-ce</td></tr><tr><td rowspan=\\\"3\\\">1</td><td rowspan=\\\"3\\\">Red beetroot (Beta vulgaris)</td><td rowspan=\\\"3\\\">Betanin</td><td rowspan=\\\"3\\\">0.1 M HCl in ethanol</td><td rowspan=\\\"3\\\">Collum chromatography (Waters MCX ion-exchange column or Sephadex G25) for purifying</td><td rowspan=\\\"3\\\">P25 TiO2</td><td rowspan=\\\"3\\\">Pt</td><td rowspan=\\\"3\\\">I2, LiI</td><td>acetonitrile (ACN)</td><td>0.52</td><td>0.27</td><td>0.47</td><td>0.07</td><td rowspan=\\\"3\\\">[70]</td></tr><tr><td>3-methoxypropinitrile (MPN)</td><td>0.89</td><td>0.26</td><td>0.47</td><td>0.11</td></tr><tr><td>3-methoxypropinitrile (MPN) with HCl and 4-tert-Butylpyridine (TBP)</td><td>2.42</td><td>0.44</td><td>0.63</td><td>0.67</td></tr><tr><td rowspan=\\\"6\\\">2</td><td rowspan=\\\"6\\\">Red beetroot (Beta vulgaris)</td><td rowspan=\\\"6\\\">Betanin</td><td rowspan=\\\"6\\\">Potassium phosphate buffer</td><td rowspan=\\\"6\\\">Develop the reverse-phase medium pressure liquid chromatography for purifying the extracted betanine</td><td>P25 TiO2 without bloking layer</td><td rowspan=\\\"6\\\">Pt</td><td rowspan=\\\"6\\\">I2, LiI</td><td rowspan=\\\"3\\\">acetonitrile (ACN)</td><td>10.55</td><td>0.35</td><td>0.57</td><td>2.04</td><td rowspan=\\\"6\\\">[71]</td></tr><tr><td>P25 TiO2 with TiCl4post treated</td><td>9.34</td><td>0.44</td><td>0.57</td><td>2.27</td></tr><tr><td>P25 TiO2 with bloking layer</td><td>13.91</td><td>0.36</td><td>0.56</td><td>2.71</td></tr><tr><td>P25 TiO2 without bloking layer</td><td rowspan=\\\"3\\\">3-methoxypropinitrile (MPN)</td><td>7.64</td><td>0.39</td><td>0.51</td><td>1.46</td></tr><tr><td>P25 TiO2 with TiCl4post treated</td><td>10.13</td><td>0.36</td><td>0.55</td><td>1.93</td></tr><tr><td>P25 TiO2 with bloking layer</td><td>8.61</td><td>0.44</td><td>0.61</td><td>2.22</td></tr><tr><td rowspan=\\\"6\\\">3</td><td rowspan=\\\"6\\\">Red beetroot (Beta vulgaris)</td><td rowspan=\\\"6\\\">Betalain</td><td>Water-HCl</td><td rowspan=\\\"3\\\">-</td><td rowspan=\\\"3\\\">The TiO2 porous film electrode was manufactured by using the sol-gel method, starting from the commercial titanium(IV)</td><td rowspan=\\\"6\\\">Pt</td><td rowspan=\\\"6\\\">I2, KI</td><td rowspan=\\\"6\\\">Ethyleneglicole:acetonitrile (4:1, volume ratio)</td><td>0.38</td><td>0.36</td><td>0.69</td><td>0.12</td><td rowspan=\\\"6\\\">[72]</td></tr><tr><td>Water-ascorbic acid</td><td>0.39</td><td>0.35</td><td>0.62</td><td>0.11</td></tr><tr><td>Methanol-HCl</td><td>0.09</td><td>0.36</td><td>0.65</td><td>0.03</td></tr><tr><td>Water-HCl</td><td rowspan=\\\"3\\\">pressure liquid chromatography (MPLC) for purifying</td><td rowspan=\\\"3\\\">oxide, anatase, nanopowder <25 nm, from Sigma-Aldrich, and titanium isopropoxide (Sigma-Aldrich)</td><td>2.95</td><td>0.36</td><td>0.30</td><td>0.40</td></tr><tr><td>Water-ascorbic acid</td><td>0.42</td><td>0.40</td><td>0.56</td><td>0.12</td></tr><tr><td>Methanol-HCl</td><td>0.16</td><td>0.37</td><td>0.65</td><td>0.05</td></tr><tr><td rowspan=\\\"3\\\">4</td><td rowspan=\\\"3\\\">Paper flower (Bougainville glabra)</td><td rowspan=\\\"3\\\">Betaxanthin betacyanine</td><td>Water-HCl pH = 5.70</td><td rowspan=\\\"3\\\">-</td><td rowspan=\\\"3\\\">TiO2film from blending P25 and Triton x-100</td><td rowspan=\\\"3\\\">Pt</td><td rowspan=\\\"3\\\">-</td><td rowspan=\\\"3\\\">-</td><td>2.27</td><td>0.41</td><td>0.61</td><td>0.57</td><td rowspan=\\\"3\\\">[73]</td></tr><tr><td>Water-HCl pH = 3</td><td>3.72</td><td>0.44</td><td>0.59</td><td>0.98</td></tr><tr><td>Water-HCl pH = 1.23</td><td>1.13</td><td>0.44</td><td>0.43</td><td>0.21</td></tr><tr><td rowspan=\\\"2\\\">5</td><td rowspan=\\\"2\\\">Beetroot (Beta vulgaris)</td><td rowspan=\\\"2\\\">Betanin</td><td rowspan=\\\"2\\\">Potassium phosphate buffer</td><td rowspan=\\\"2\\\">Develop the reverse-phase medium pressure liquid chromatography for purifying the extracted betanine</td><td>TiO2</td><td rowspan=\\\"2\\\">Pt</td><td rowspan=\\\"2\\\">I2, LiI</td><td rowspan=\\\"2\\\">N-methyl-2-pyrrolidone (NMP) solvent with 6% by weight polyvinylidene fluoride (PVDF)</td><td>1.47</td><td>0.49</td><td>0.63</td><td>0.58</td><td rowspan=\\\"2\\\">[74]</td></tr><tr><td>AgNPs coated onto TiO2</td><td>1.65</td><td>0.51</td><td>0.64</td><td>0.68</td></tr><tr><td>6</td><td>Bracks of paper flower (Bougainville glabra)</td><td>Betaxanthin betacyanine</td><td>Acetone-water</td><td>-</td><td>TiO2NPs</td><td>Pt</td><td>I2, LiI, TBP</td><td>3-methoxypropinitrile (MPN)</td><td>-</td><td>-</td><td>0.59</td><td>0.25</td><td>[75]</td></tr><tr><td rowspan=\\\"2\\\">7</td><td rowspan=\\\"2\\\">Sicilian prickly pears (Opuntia ficus indica) Blackberry()</td><td rowspan=\\\"2\\\">Betalain (the dominant pigmen is betaxantin)</td><td rowspan=\\\"2\\\">Ethanol and HCl/ carboxylic acid/tartaric acid as acids and co-adsorbers.</td><td rowspan=\\\"2\\\">-</td><td rowspan=\\\"2\\\">TiO2nanocrystalline</td><td rowspan=\\\"2\\\">Pt</td><td rowspan=\\\"2\\\">GuNCS, TBP</td><td rowspan=\\\"2\\\">Acetonitrile:valeronitrile (85:15)</td><td>7.85</td><td>0.38</td><td>0.62</td><td>1.87</td><td rowspan=\\\"2\\\">[76]</td></tr><tr><td>5.85</td><td>0.32</td><td>0.57</td><td>1.07</td></tr><tr><td rowspan=\\\"3\\\">8</td><td rowspan=\\\"3\\\">Red Beetroot (Beta vulgaris)</td><td rowspan=\\\"3\\\">Betanin</td><td rowspan=\\\"3\\\">Water-HCl</td><td rowspan=\\\"3\\\">-</td><td rowspan=\\\"3\\\">ZnO/Au</td><td rowspan=\\\"3\\\">Pt</td><td rowspan=\\\"3\\\">I2, KI</td><td>Water</td><td>0.05</td><td>0.25</td><td>0.33</td><td>0.48</td><td rowspan=\\\"3\\\">[77]</td></tr><tr><td>Asetonitrile</td><td>0.99</td><td>0.15</td><td>0.21</td><td>2.99</td></tr><tr><td>PVA</td><td>0.01</td><td>0.06</td><td>0.29</td><td>0.01</td></tr><tr><td>9</td><td>Red boot (Beta vulgaris L.)</td><td>Betanin</td><td>Ethanol-HCl</td><td>Sephadex DEAE A25 column and Phenomenon Strata C18 SPE Column</td><td>TiO2</td><td>Pt</td><td>I2, LiI</td><td>Acetonitrile</td><td>14</td><td>0.38</td><td>-</td><td>3.00</td><td>[78]</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. The summarized results on betanine-based DSSCs. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[944,60,954,157]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[944,815,954,937]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[37,495,45,504]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,65,487,119]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"that aggregated dye induces a broadened absorbance spectrum, increasing the light-harvesting efficiency [78]. A comprehensive review of the dye aggregation phenomena and their implications for DSSC performance can be found in Ref. [101]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,132,159,145]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2. Chlorophyll \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,158,485,433]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Chlorophylls are a family of pigments classified into chlorin family. They consist of a tetrapyrrole derivative as a chelating ligand and an $\\\\mathrm{Mg}^{2+}$ ion as a central ion. Based on the ligand structure, chlorophyll is divided into chlorophyll-a, chlorophyll-b, chlorophyll-c1, chlorophyll-c2, and chlorophyll-f. The motivation to consider chlorophyll as natural DSSC sensitizers is to mimic the photosynthesis phenomenon. Based on our records, Kay et al. were the first to investigate chlorophyll-based DSSCs in 1993. They also compared the cell performance with a modified chlorophyll in which a $\\\\mathrm{Cu}^{2+}$ ion replaced the $\\\\mathrm{Mg}^{2+}$ ion. They reported the following cell parameters: $J_{SC}$ of $9.4\\\\mathrm{mAcm}^{-2}$ , $V_{OC}$ of $0.52\\\\mathrm{V}$ , and PCE of $2.6\\\\%$ . This best result was obtained with the addition of a coadsorbate using polyhydroxyl compounds such as glucose, glycerol, or sorbitol [79]. Coadsorbates were used to reduce electron recombination from the couple redox species to the photoanode surface. We also noted that even though Kay et al. were the first group to develop chlorophyll-based DSSCs, Cu-chlorophyll $\\\\mathrm{TiO}_2$ sensitization was first observed by Kamat et al. in 1986. They investigated the photoelectrochemical mechanism in a sensitized $\\\\mathrm{TiO}_2$ system using laser flash photolysis, time-resolved microwave absorption, and spectrofluorometry techniques. For these experiments, they measured the sample in dispersion form [102]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,435,485,645]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the next decade, research on chlorophyll-based DSSCs was continued by Amao et al. They used a dye derived from chlorophyll extracted from Spirulina, namely, Chl-e6. The obtained results were not satisfactory since the $J_{SC}$ was only $0.305\\\\mathrm{mAcm}^{-2}$ and the $V_{OC}$ was 0.426 V [80]. Wang and coworkers reported research results on chlorophyll-based DSSCs in Refs. [103, 104, 105, 106]. They developed DSSCs using a modified chlorophyll as a photosensitizer. They added a natural conjugated redox spacer to prevent the recombination of electrons with the oxidized sensitizer. Approximately $30\\\\%$ of the cell performance was improved after performing this modification [82, 103]. They also compared the performance of chlorophyll-based DSSCs using $\\\\mathrm{TiO_2}$ and $\\\\mathrm{ZnO}$ photoanodes. They concluded that the limitation of chlorophyll-ZnO-based DSSCs was caused by far location of the molecular orbital involved in the electron excitation process from the anchoring site [105]. A complete summary of the research on chlorophyll-based DSSCs is summarized in Table 2. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,646,487,791]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Many works have already focused on applying chlorophyll dye in DSSCs due to its role in the photosynthesis process. There have also been many reports on the utilization of synthetic porphyrin-sensitized DSSCs. The first was due to Jasieniak et al. from Flinders University, Australia, in 2004. They did not obtain a satisfactory result at that time, and their best cell efficiency was only $0.69\\\\%$ [107]. Impressively, in 2011, Yella et al. succeeded in preparing DSSCs based on multiple synthetic porphyrin dyes with a cobalt redox couple. The efficiency of their device reached $12\\\\%$ [108]. This promising result suggests the need for further investigation in the utilization of porphyrin dyes as sensitizers in DSSC applications. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,805,171,817]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.3. Anthocyanins \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,831,487,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Research on the application of anthocyanins as natural dyes in DSSCs is relatively abundant. These dyes are present in almost all colorful fruit and flowers and offer a large panel of potentially interesting dyes for DSSC applications. By looking at their chemical structure, anthocyanins have hydroxyl moieties, and some of them possess a catechol group [109]. They can act as anchoring groups to attach the dye onto the semiconductor surface. The catechol group showed better performance as an anchoring group than the carboxylic group because the latter \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,65,937,119]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"presents an electron-withdrawing character [110]. Table 3 summarizes the main published results on anthocyanin utilization as a sensitizer for DSSCs. This table shows that the anthocyanin performance is still lower than that of the chlorophyll derivative dyes. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,132,685,145]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.4. Remarks on natural dyes \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,158,937,316]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the last twenty years, reports from the scientific community on using natural dyes as a sensitizer for DSSCs have given unsatisfactory results in terms of efficiency. Many works have reported efficiencies below $2\\\\%$ [70, 83, 89]. Some of them have succeeded in reaching a PCE of $5\\\\%$ [82]. The motivations to develop natural dyes for sensitizers in DSSCs are their abundant availability, environmental friendliness, cost effectiveness, and biodegradable. Unfortunately, no one reported a PCE higher than $10\\\\%$ for natural dyes based on our record. Most of them have relatively low PCE values of approximately $3 - 4\\\\%$ . The deficiency of natural dyes lies in their stability. They also easily agglomerate, and then the photogenerated charges are not efficiently collected [111]. Almost all of them attach poorly to the oxide semiconductor surface [69, 99]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,317,937,423]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The incorporation of natural dyes in working DSSC devices remains a challenging task. Chlorophyll derivatives display the best performance among the outlined dyes, making chlorophyll derivative dyes the most researched compared to others. The strong performance of chlorophyll inspires synthetic chlorophyll-based dyes, which are no longer natural dyes. However, the lack of research on the other dyes presents the opportunity for further investigations, as the derivatives of the other dyes have not been much explored. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,436,742,448]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. Biopolymer for quasi-solid DSSC \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,462,778,475]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1. Development of biopolymer used in DSSC \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,488,937,593]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The first DSSC employed a liquid electrolyte that contained a redox couple. The utilization of a liquid electrolyte faces various problems, including solvent leakages, desorption of dye attached to the photoanode, and some practical issues of sealing [112, 113]. These reasons encouraged many researchers to develop quasi-solid electrolytes. They notably developed polymers, and among them, biopolymers have attracted much attention in line with sustainability issues and the utilization of natural resources. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,593,937,751]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Research on the utilization of biopolymers for DSSC applications started in 2010. The initial study was carried out by Buraidah et al., who used a chitosan biopolymer for solid electrolytes. The composition of $27.5\\\\%$ chitosan, $22.5\\\\%$ $\\\\mathrm{NH_4I}$ , and $50\\\\%$ BMII $(w\\\\%)$ produced a good conductivity of $3.34\\\\times 10^{-5}\\\\mathrm{Scm}^{-1}$ , which at the time was comparable with other polymer cells [114]. In the following years, Buraidaeh et al. developed copolymer chitosan and poly(vinyl alcohol) (PVA) to improve polymer electrolyte conductivity [115]. Several reports emerged during the same period where agarose had been used for quasi-solid DSSCs [116]. Several biopolymers that have been widely developed for quasi-solid DSSCs in the past were agarose, carrageenan, cellulose, and chitin/chitosan [117]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,752,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A more comprehensive list of the previous research is summarized in Table 4. Figure 4 presents a map of conductivity and cell performance of various biopolymer-based DSSCs. Among natural biopolymers, agarose and cellulose show promising results. Their cell efficiency value ranges from 4.5 to $7\\\\%$ . Table 4 also mentions various modifications that have been carried out to improve cell performance. The presence of an ionic liquid can increase the conductivity and improve the charge transfer. Singh et al. investigated the influence of a 1-ethyl-3-methylimidazolium ionic liquid in an agarose-based electrolyte. This ionic liquid increased the short circuit current from $1\\\\mathrm{mAcm}^{-2}$ to $3.3\\\\mathrm{mAcm}^{-2}$ . Moreover, Huang et al. showed that the presence of a 1-methyl-3-hexylimidazolium iodide (MHII) ionic liquid in cyanoethylated hydroxypropyl cellulose (CN-HPC) reduced the charge recombination between redox couple species and the oxide semiconductor surface due to the bulky structure of \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,42,157,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[494,952,504,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[60,87,931,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0715/e721b707196df13da6dc28664fe3a5c2e48f1e0a0c3fb8e5b249ee52906caf79.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>No</td><td>Sources</td><td>Solvent of extraction</td><td>Modification</td><td>Photoanodes</td><td>Counter electrode</td><td>Redox couple</td><td>Electrolyte Solvent</td><td>JSC(mA/cm2)</td><td>VOC(V)</td><td>FF</td><td>η(%)</td><td>Reference</td></tr><tr><td>1</td><td>Commercial chlorophyll from Sigma</td><td>-</td><td>Replaced Mg2+with Cu2+</td><td>TiO2</td><td>Pt-foil</td><td>KI, I2</td><td>80%ethylene carbonate and 20% propylene carbonate</td><td>0.54</td><td>0.42</td><td>-</td><td>2.6</td><td>[80]</td></tr><tr><td>2</td><td>Commercial chlorine-e6 derived from chlorophyll extracted from Spirulina</td><td>-</td><td>-</td><td>TiO2nanocrystalline</td><td>C-OTE</td><td>KI, I2</td><td>Ethylene glycol/acetonitrile</td><td>0.305</td><td>0.43</td><td>0.45</td><td>0.73</td><td>[79]</td></tr><tr><td rowspan=\\\"6\\\">3</td><td>Spinach leave (Spinacia oleracea L.)</td><td>Ethanol T=50 °C</td><td>-</td><td>TiO2nanofluid</td><td>Plate of lower conductive glass</td><td>I-/I3</td><td>Acetonitrile</td><td>0.467</td><td>0.55</td><td>0.51</td><td>0.13</td><td>[81]</td></tr><tr><td rowspan=\\\"5\\\">Ipomoea (Ipomoea carnea)</td><td>Ethanol T=50 °C</td><td></td><td></td><td></td><td></td><td></td><td>0.914</td><td>0.54</td><td>0.56</td><td>0.28</td><td></td></tr><tr><td>Ethanol T=50 °C</td><td></td><td></td><td></td><td></td><td></td><td>0.915</td><td>0.51</td><td>0.55</td><td>0.25</td><td></td></tr><tr><td>Ethanol T=50 °C</td><td></td><td></td><td></td><td></td><td></td><td>0.982</td><td>0.54</td><td>0.56</td><td>0.29</td><td></td></tr><tr><td>Ethanol T=50 °C</td><td></td><td></td><td></td><td></td><td></td><td>1.120</td><td>0.57</td><td>0.59</td><td>0.32</td><td></td></tr><tr><td>Ethanol T=50 °C</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\\\"5\\\">4</td><td rowspan=\\\"5\\\">Spirulina geileri</td><td rowspan=\\\"5\\\">Methanol Modification function group (hydrocarbon) by transesterification using methyl esther</td><td rowspan=\\\"5\\\">Chlorine-1 (methyl) Chlorine-2 (hexyl) Chlorine-3 (dodecyl) Chlorine-4 (2-butyloctyl) Chlorine-5 (cholesteryl)</td><td rowspan=\\\"5\\\">TiO2NPs</td><td rowspan=\\\"5\\\">Pt wire</td><td rowspan=\\\"5\\\">BMII, I2, Additive: GNCS, TPB</td><td rowspan=\\\"5\\\">Acetonitrile-valeronitrile</td><td>15</td><td>0.60</td><td>0.72</td><td>6.5</td><td>[82]</td></tr><tr><td>15.5</td><td>0.62</td><td>0.73</td><td>7.0</td><td></td></tr><tr><td>17.4</td><td>0.64</td><td>0.72</td><td>8.0</td><td></td></tr><tr><td>13.9</td><td>0.65</td><td>0.74</td><td>6.6</td><td></td></tr><tr><td>13.6</td><td>0.64</td><td>0.70</td><td>6.1</td><td></td></tr><tr><td>5</td><td>Pomegranate leaves (Punica granatum L.)</td><td>Ethanol</td><td>-</td><td>TiO2NPs</td><td>Pt-thin film on FTO</td><td>I2, LiI Additive: TBP</td><td>Acetonitrile</td><td>2.05</td><td>0.56</td><td>0.52</td><td>0.59</td><td>[83]</td></tr><tr><td>6</td><td>Pandan leaves (Pandanus amaryllifolius)</td><td>Ethanol-tartaric acid</td><td>-</td><td>TiO2</td><td>Pt-FTO</td><td>NaI</td><td>PVDF-HFP</td><td>1.91</td><td>0.48</td><td>0.56</td><td>0.51</td><td>[84]</td></tr><tr><td rowspan=\\\"2\\\">7</td><td rowspan=\\\"2\\\">Spinach (Spinacia oleracea L.)</td><td rowspan=\\\"2\\\">Ethanol using ultrasonic technique water using ultrasonic technique</td><td rowspan=\\\"2\\\">-</td><td rowspan=\\\"2\\\">TiO2</td><td rowspan=\\\"2\\\">Graphite-ITO</td><td rowspan=\\\"2\\\">I-/I3</td><td rowspan=\\\"2\\\">Acetonitrile</td><td>0.32</td><td>0.38</td><td>0.36</td><td>1-2</td><td>[85]</td></tr><tr><td>0.35</td><td>0.44</td><td>0.49</td><td></td><td></td></tr><tr><td rowspan=\\\"5\\\">8</td><td rowspan=\\\"5\\\">Marigold leaves (Tagetes patula)</td><td rowspan=\\\"5\\\">Water</td><td rowspan=\\\"5\\\">Effect dipping time of ZnS in dye solution</td><td>ZnS (0 h)</td><td rowspan=\\\"5\\\">Graphite</td><td rowspan=\\\"5\\\">S2/Sn2</td><td rowspan=\\\"5\\\">NaOH-Na2S</td><td>0.297</td><td>0.21</td><td>0.30</td><td>0.05</td><td>[86]</td></tr><tr><td>ZnS (2 h)</td><td>0.400</td><td>0.23</td><td>0.21</td><td>0.05</td><td></td></tr><tr><td>ZnS (4 h)</td><td>0.463</td><td>0.29</td><td>0.28</td><td>0.10</td><td></td></tr><tr><td>ZnS (6 h)</td><td>0.520</td><td>0.24</td><td>0.24</td><td>0.09</td><td></td></tr><tr><td>ZnS (8 h)</td><td>0.533</td><td>0.30</td><td>0.31</td><td>0.12</td><td></td></tr><tr><td rowspan=\\\"6\\\">9</td><td rowspan=\\\"6\\\">Bryophyte</td><td rowspan=\\\"6\\\">Ethanol</td><td rowspan=\\\"6\\\">-</td><td rowspan=\\\"6\\\">TiO2</td><td rowspan=\\\"6\\\">Pt-FTO</td><td>TPAI(2%)-I2(0.17%w/w)</td><td rowspan=\\\"6\\\">PAN-EC-PC</td><td>0.94</td><td>0.63</td><td>0.75</td><td>0.45</td><td>[87]</td></tr><tr><td>TPAI(4%)-I2(0.34%w/w)</td><td>4.08</td><td>0.54</td><td>0.58</td><td>1.27</td><td></td></tr><tr><td>TPAI(6%)-I2(0.51%w/w)</td><td>5.51</td><td>0.53</td><td>0.53</td><td>1.52</td><td></td></tr><tr><td>TPAI(8%)-I2(0.68%w/w)</td><td>6.10</td><td>0.53</td><td>0.51</td><td>1.66</td><td></td></tr><tr><td>TPAI(10%)-I2(0.85%w/w)</td><td>5.78</td><td>0.6</td><td>0.57</td><td>1.97</td><td></td></tr><tr><td>TPAI(12%)-I2(0.97%w/w)</td><td>5.96</td><td>0.62</td><td>0.50</td><td>1.86</td><td></td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2. The summarized research on chlorophyll-based DSSCs. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[944,58,955,157]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[944,815,954,937]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[58,90,937,590]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0221/63928f3a95074ce1941d8c0281f6576edaf41e8e7c625bc3b7facc82c61192e4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>No</td><td>Sources</td><td>Solvent of extraction</td><td>Photoanode</td><td>Counter electrode</td><td>Redox couple</td><td>Solvent of electrolyte</td><td>JSC(mA/cm2)</td><td>VOC(V)</td><td>FF</td><td>η(%)</td><td>Reference</td></tr><tr><td rowspan=\\\"2\\\">1</td><td rowspan=\\\"2\\\">Henna leaves(Lawsonia inermis)</td><td>Ethanol</td><td rowspan=\\\"2\\\">TiO2</td><td rowspan=\\\"2\\\">Pt</td><td rowspan=\\\"2\\\">KI, I2</td><td rowspan=\\\"2\\\">Ethylene glycol-acetonitrile</td><td>1.87</td><td>0.59</td><td>0.58</td><td>0.66</td><td rowspan=\\\"2\\\">[88]</td></tr><tr><td>Ethanol-water</td><td>1.35</td><td>0.59</td><td>0.65</td><td>0.52</td></tr><tr><td rowspan=\\\"4\\\">2</td><td rowspan=\\\"4\\\">Canna indicaSalvia splendensCow berry (Vaccinium vitis-idaea)Solanum nigrum</td><td rowspan=\\\"4\\\">Ethanol-water</td><td rowspan=\\\"4\\\">TiO2</td><td rowspan=\\\"4\\\">Pt</td><td rowspan=\\\"4\\\">Lil, I2,TBP and BMII</td><td rowspan=\\\"4\\\">Acetonitrile-valeronitrile</td><td>0.82</td><td>0.54</td><td>0.59</td><td>0.29</td><td rowspan=\\\"4\\\">[89]</td></tr><tr><td>0.7</td><td>0.56</td><td>0.61</td><td>0.26</td></tr><tr><td>0.4</td><td>0.56</td><td>0.54</td><td>0.13</td></tr><tr><td>1.01</td><td>0.54</td><td>0.51</td><td>0.31</td></tr><tr><td rowspan=\\\"4\\\">3</td><td rowspan=\\\"4\\\">Mulberry Fruits(Morus nigra)</td><td rowspan=\\\"4\\\">Metanol:water:acetic-acid:25:21:4</td><td rowspan=\\\"4\\\">P25 TiO2</td><td>Purified SWCNTs</td><td rowspan=\\\"4\\\">I-/I3-</td><td rowspan=\\\"4\\\">Acetonitrile</td><td>2.65</td><td>0.59</td><td>0.51</td><td>0.67</td><td rowspan=\\\"4\\\">[90]</td></tr><tr><td>SWCNTs</td><td>2.41</td><td>0.47</td><td>0.38</td><td>0.42</td></tr><tr><td>Purified MWCNTs</td><td>3.12</td><td>0.48</td><td>0.39</td><td>0.52</td></tr><tr><td>MWCNTs</td><td>1.71</td><td>0.51</td><td>0.44</td><td>0.39</td></tr><tr><td rowspan=\\\"4\\\">4</td><td rowspan=\\\"4\\\">Roselle (Hibiscus sabdariffa)</td><td rowspan=\\\"4\\\">Citric acid</td><td>TiO2</td><td rowspan=\\\"4\\\">Pt</td><td rowspan=\\\"4\\\">I-/I3-</td><td rowspan=\\\"4\\\">Acetonitrile</td><td>4.8</td><td>0.45</td><td>0.43</td><td>0.92</td><td rowspan=\\\"4\\\">[28]</td></tr><tr><td>Na-TiO2(6%)</td><td>5.5</td><td>0.55</td><td>0.55</td><td>1.65</td></tr><tr><td>Na(6%)-Yeast (4%)-TiO2</td><td>6.2</td><td>0.58</td><td>0.60</td><td>2.17</td></tr><tr><td>Na(6%)-Yeast (6%)-TiO2</td><td>6.9</td><td>0.62</td><td>0.56</td><td>2.40</td></tr><tr><td rowspan=\\\"4\\\">5</td><td rowspan=\\\"4\\\">Mangosteen pericarp(Garcinia mangostanaL.)</td><td>Methanol:HCl (99:1) + add benzoic acid (1:0)</td><td rowspan=\\\"4\\\">TiO2NTs</td><td rowspan=\\\"4\\\">Pt</td><td rowspan=\\\"4\\\">I-/I3-</td><td rowspan=\\\"4\\\">Acetonitrile</td><td>0.0069</td><td>0.26</td><td>0.39</td><td>0.23</td><td rowspan=\\\"4\\\">[91]</td></tr><tr><td>Methanol:HCl (99:1) + add benzoic acid (1:0.5)</td><td>0.0125</td><td>0.16</td><td>0.36</td><td>0.23</td></tr><tr><td>Methanol:HCl (99:1) + add benzoic acid (1:0.8)</td><td>0.0043</td><td>0.31</td><td>0.66</td><td>0.29</td></tr><tr><td>Methanol:HCl (99:1) + add benzoic acid (1:1)</td><td>0.0065</td><td>0.36</td><td>0.48</td><td>0.37</td></tr><tr><td rowspan=\\\"2\\\">6</td><td rowspan=\\\"2\\\">Seduduk fruit(Malabrichum MelastomaL)</td><td>Ethanol-HCl</td><td rowspan=\\\"2\\\">P25 TiO2</td><td rowspan=\\\"2\\\">C</td><td rowspan=\\\"2\\\">NaI2</td><td rowspan=\\\"2\\\">PEG</td><td rowspan=\\\"2\\\">-</td><td rowspan=\\\"2\\\">-</td><td rowspan=\\\"2\\\">-</td><td>0.62</td><td rowspan=\\\"2\\\">[92]</td></tr><tr><td>Ethanol-HCl with salicylic acid</td><td>1.32</td></tr><tr><td>7</td><td>Vaccinium meridionale</td><td>Ethanol-water bu proculation method</td><td>P25 TiO2</td><td>Pt</td><td>KI, I2,KClO4</td><td>Acetonitrile</td><td>-</td><td>-</td><td>-</td><td>-</td><td>[93]</td></tr><tr><td rowspan=\\\"2\\\">8</td><td rowspan=\\\"2\\\">Jabuticaba fruits(Plinia cauliflora)</td><td rowspan=\\\"2\\\">Absolute ethanol</td><td>TiO2(doctorblade)</td><td rowspan=\\\"2\\\">C</td><td rowspan=\\\"2\\\">I2, KI</td><td rowspan=\\\"2\\\">PVP</td><td>0.23</td><td>0.35</td><td>0.23</td><td>0.08</td><td rowspan=\\\"2\\\">[94]</td></tr><tr><td>TiO2(spin coating)</td><td>0.38</td><td>0.41</td><td>0.29</td><td>0.13</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 3. The summarized research on anthocyanin based DSSCs. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[57,614,487,694]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MHII compared to $\\\\mathrm{I}^{-}$ [118]. The addition of $\\\\mathrm{Co}_3\\\\mathrm{O}_4$ , NiO, and $\\\\mathrm{TiO}_2$ nanoparticles can also improve conductivity [119]. The presence of cross-linking networks between nanoparticles and polymers facilitates ion transport within the polymer matrix. The addition of nanoparticles can also be detrimental due to the formation of nanoparticle aggregates [120]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,712,391,725]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2. Structural aspects of biopolymer for quasi-solid DSSC \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,738,485,829]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"All of the biopolymers mentioned previously, which are widely applied to polymer gel electrolytes, are polysaccharides. These biopolymers consist of the hexa-pyranose building block of D-glucose as a monomer with various glycosidic linkages, either $\\\\alpha$ -1,3 or $\\\\beta$ -1,4. In chitin or chitosan, D-glucose is substituted by amine or acetyl amine groups. Table 5 presents the chemical structure information and conductivity of these biopolymers. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,829,485,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The hydroxyl groups in polymer chains are responsible for establishing the bond with the ionic species in the electrolyte, which subsequently contributes to the ionic conductivity [121, 122, 123]. Furthermore, the functional groups on the polymer chain play an essential role in creating the bond with the liquid as a dispersed phase in the gelation process [124]. The gel polymer electrolyte system in a DSSC consists of the polymer matrix and liquid. The polymer matrix acts as the immobilizer or dispersion medium, while the liquid functions as a \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,614,937,718]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"dispersed phase. Liquid can also function as a solvent for ionic species or redox couples. The interaction of these three components is vital for charges to be transferred to ensure good cell performance. One of the studies on this topic was conducted by Shih et al., where the interfacial interaction of iodide as a redox couple and agarose as a polymer matrix was investigated. The XPS study confirmed the formation of polyiodide in the electrolyte, which benefited the charge transfer channels after adding $\\\\mathrm{TiO_2}$ nanoparticles into the electrolyte gel system [119]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,720,937,851]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Molecular-level studies concerning this background are necessary. Unfortunately, only a small number of previous studies that are relevant to natural polymer systems were found. Yoon et al. theoretically observed the interaction between the ionic liquid 1-propyl-3-methyl imidazolium iodide (PMII) and the synthetic polymer poly(styrene-block-ethylene oxide-block-styrene) (SEOS) to investigate the complex structure of PMII and SEOS during the interaction stages. This experiment will then be used to explain the typical bonding and charge transfer [125]. Thus, to do so, further studies in natural polymer systems are still needed. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,870,781,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.3. Remarks on biopolymer quasi solid DSSCs \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,897,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Biopolymer electrolytes for DSSCs have been chosen as a solution to overcome the shortcomings of liquid electrolytes, such as solvent volatilization, poor stability due to leakage or counter electrode corrosion, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,42,154,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[494,952,502,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[63,92,931,860]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0437/5b3d1cd864c5a9637fd944185079ed2def2d4b6301c0e77a48b581e0c13912f7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>No</td><td>Biopolymer as Gel electrolyte</td><td>Modification biopolymer</td><td>Electrolyte solvent</td><td>Redox couple</td><td>Photoanode</td><td>Counter electrode</td><td>Dye</td><td>Conductivity (mS/cm)</td><td>JSC(mA/cm2)</td><td>VOC(V)</td><td>FF</td><td>η(%)</td><td>Reference</td></tr><tr><td rowspan=\\\"39\\\">1</td><td rowspan=\\\"39\\\">Agarose</td><td>Ratio agarose (%)</td><td rowspan=\\\"14\\\">1-methyl-2-pyrrolidinone (NMP)</td><td rowspan=\\\"14\\\">I2,LiI</td><td rowspan=\\\"14\\\">P25 TiO2</td><td rowspan=\\\"14\\\">Pt</td><td rowspan=\\\"14\\\">-</td><td></td><td></td><td></td><td></td><td></td><td rowspan=\\\"14\\\">[116]</td></tr><tr><td>1</td><td>0.28</td><td>6.16</td><td>0.58</td><td>0.67</td><td>3.20</td></tr><tr><td>1.5</td><td>0.39</td><td>7.56</td><td>0.62</td><td>0.63</td><td>3.97</td></tr><tr><td>2</td><td>0.36</td><td>8.24</td><td>0.60</td><td>0.62</td><td>4.14</td></tr><tr><td>2.5</td><td>0.32</td><td>5.16</td><td>0.63</td><td>0.69</td><td>3.01</td></tr><tr><td>3</td><td>0.65</td><td>5.32</td><td>0.62</td><td>0.64</td><td>2.83</td></tr><tr><td>4</td><td>-</td><td>4.44</td><td>0.63</td><td>0.72</td><td>2.73</td></tr><tr><td>5</td><td>0.66</td><td>2.12</td><td>0.68</td><td>0.78</td><td>1.49</td></tr><tr><td>Ratio TiO2 in agarose (%)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0</td><td>0.30</td><td>7.76</td><td>0.66</td><td>0.53</td><td>3.77</td></tr><tr><td>2.5</td><td>0.44</td><td>10.96</td><td>0.55</td><td>0.57</td><td>4.74</td></tr><tr><td>5</td><td>0.51</td><td>8.84</td><td>0.55</td><td>0.56</td><td>4.45</td></tr><tr><td>7.5</td><td>0.33</td><td>9.20</td><td>0.55</td><td>0.52</td><td>3.64</td></tr><tr><td>10</td><td>0.34</td><td>9.04</td><td>0.57</td><td>0.48</td><td>3.42</td></tr><tr><td rowspan=\\\"8\\\">-</td><td rowspan=\\\"8\\\">NMP</td><td>10%LiI, I2</td><td rowspan=\\\"8\\\">P25 TiO2</td><td rowspan=\\\"8\\\">Pt</td><td rowspan=\\\"8\\\">N719</td><td>1.99</td><td rowspan=\\\"8\\\" colspan=\\\"4\\\">Not measured</td><td rowspan=\\\"8\\\">[212]</td></tr><tr><td>15%LiI, I2</td><td>3.16</td></tr><tr><td>20%LiI, I2</td><td>3.98</td></tr><tr><td>25%LiI, I2</td><td>2.39</td></tr><tr><td>30%LiI, I2</td><td>3.31</td></tr><tr><td>35%LiI, I2</td><td>3.89</td></tr><tr><td>65%LiI, I2</td><td>5.62</td></tr><tr><td>85%LiI, I2</td><td>5.62</td></tr><tr><td rowspan=\\\"5\\\">-</td><td>DMSO/PC</td><td rowspan=\\\"5\\\">GuSCN, NMBI, I2</td><td rowspan=\\\"5\\\">P25 TiO2</td><td rowspan=\\\"5\\\">Pt</td><td rowspan=\\\"5\\\">N719</td><td>14.2</td><td>4.65</td><td>0.73</td><td>0.58</td><td>1.97</td><td rowspan=\\\"5\\\">[213]</td></tr><tr><td>DMSO/4EG</td><td>4.4</td><td>3.69</td><td>0.65</td><td>0.57</td><td>1.38</td></tr><tr><td>DMSO/3EG</td><td>4.6</td><td>4.01</td><td>0.61</td><td>0.57</td><td>1.39</td></tr><tr><td>DMSO/PEG</td><td>6.2</td><td>3.21</td><td>0.58</td><td>0.57</td><td>1.06</td></tr><tr><td>DMSO (20v%)</td><td>5.0</td><td>3.69</td><td>0.58</td><td>0.54</td><td>1.15</td></tr><tr><td rowspan=\\\"4\\\">0.5% agarose</td><td rowspan=\\\"9\\\">PC/DMSO (8:2)</td><td>MPII</td><td rowspan=\\\"9\\\">Double-layer TiO2</td><td rowspan=\\\"9\\\">Pt</td><td rowspan=\\\"9\\\">N719</td><td rowspan=\\\"9\\\">-</td><td>11.73</td><td>0.70</td><td>0.64</td><td>5.25</td><td rowspan=\\\"9\\\">[214]</td></tr><tr><td>AEII</td><td>11.71</td><td>0.72</td><td>0.65</td><td>5.45</td></tr><tr><td>APII</td><td>11.53</td><td>0.70</td><td>0.62</td><td>4.97</td></tr><tr><td>DAIII</td><td>11.84</td><td>0.70</td><td>0.60</td><td>4.96</td></tr><tr><td>0wt% agarose</td><td rowspan=\\\"5\\\">AEII</td><td>12.26</td><td>0.66</td><td>0.60</td><td>4.97</td></tr><tr><td>0.5wt% agarose</td><td>11.71</td><td>0.72</td><td>0.65</td><td>5.45</td></tr><tr><td>0.65wt% agarose</td><td>11.45</td><td>0.76</td><td>0.68</td><td>5.89</td></tr><tr><td>0.8wt% agarose</td><td>11.82</td><td>0.75</td><td>0.64</td><td>5.68</td></tr><tr><td>1.0wt% agarose</td><td>11.96</td><td>0.70</td><td>0.63</td><td>5.31</td></tr><tr><td>0 mT NiO-agarose</td><td rowspan=\\\"3\\\">NMP</td><td rowspan=\\\"3\\\">LiI, I2</td><td rowspan=\\\"3\\\">P25 TiO2</td><td rowspan=\\\"3\\\">Pt</td><td rowspan=\\\"3\\\">N719</td><td rowspan=\\\"3\\\">-</td><td>4.5</td><td>0.77</td><td>0.45</td><td>1.61</td><td rowspan=\\\"3\\\">[215]</td></tr><tr><td>14 mT NiO-agarose</td><td>4.7</td><td>0.80</td><td>0.56</td><td>2.32</td></tr><tr><td>25 mT NiO-agarose</td><td>5.9</td><td>0.74</td><td>0.64</td><td>2.95</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 4. The summary of various researches reported on the biopolymer-based quasi solid DSSC. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[846,868,930,882]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(continued on next page) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[944,58,955,157]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[944,815,954,937]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[60,90,931,915]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0844/17fa711c1f4b12dbd4721bf760e41118a3b4760bbf2c5bcd72a562e23f97348e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>No</td><td>Biopolymer as Gel electrolyte</td><td>Modification biopolymer</td><td>Electrolyte solvent</td><td>Redox couple</td><td>Photoanode</td><td>Counter electrode</td><td>Dye</td><td>Conductivity (mS/cm)</td><td>JSC(mA/cm2)</td><td>VOC(V)</td><td>FF</td><td>η(%)</td><td>Reference</td></tr><tr><td></td><td></td><td>35 mT NiO-agarose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6.0</td><td>0.77</td><td>0.62</td><td>2.94</td><td></td></tr><tr><td></td><td></td><td>45 mT NiO-agarose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4.2</td><td>0.76</td><td>0.61</td><td>2.24</td><td></td></tr><tr><td></td><td></td><td>55 mT NiO-agarose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.5</td><td>0.78</td><td>0.70</td><td>1.37</td><td></td></tr><tr><td></td><td></td><td>-</td><td>PC/DMSO</td><td>AEII, GuSCN, NMBI, I2</td><td>a-TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>10.39</td><td>0.80</td><td>0.71</td><td>5.89</td><td>[216]</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>a-TiO2+30% PEG (0 min)</td><td></td><td></td><td></td><td>13.29</td><td>0.74</td><td>0.66</td><td>6.54</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>a-TiO2+30% PEG (30 min)</td><td></td><td></td><td></td><td>14.18</td><td>0.74</td><td>0.69</td><td>7.18</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>a-TiO2+30% PEG (60 min)</td><td></td><td></td><td></td><td>14.32</td><td>0.75</td><td>0.69</td><td>7.43</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>a-TiO2+30% PEG (90 min)</td><td></td><td></td><td></td><td>14.57</td><td>0.73</td><td>0.68</td><td>7.28</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>a-TiO2+30% PEG (120 min)</td><td></td><td></td><td></td><td>13.89</td><td>0.74</td><td>0.68</td><td>7.04</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>a-TiO2+30% PEG (150 min)</td><td></td><td></td><td></td><td>11.36</td><td>0.68</td><td>0.65</td><td>4.98</td><td></td></tr><tr><td></td><td></td><td>TiO2-agarose</td><td>NMP</td><td>LiI, I2</td><td>TiO2 NPs</td><td>Pt</td><td>N719</td><td>2.66</td><td>5.28</td><td>0.61</td><td>0.55</td><td>1.71</td><td>[120]</td></tr><tr><td></td><td></td><td>Co3O4-agarose</td><td></td><td></td><td></td><td></td><td></td><td>4.37</td><td>7.24</td><td>0.64</td><td>0.46</td><td>2.11</td><td></td></tr><tr><td></td><td></td><td>NiO-agarose</td><td></td><td></td><td></td><td></td><td></td><td>3.33</td><td>6.20</td><td>0.63</td><td>0.52</td><td>2.02</td><td></td></tr><tr><td></td><td></td><td>-</td><td>NMP/MPN</td><td>LiI, I2, PMI, NMBI</td><td>TiO2 NPs</td><td>Pt</td><td>Ruthenizer 520-DN</td><td>14.09</td><td>10.7</td><td>0.82</td><td>-</td><td>4.9</td><td>[119]</td></tr><tr><td></td><td></td><td>Agarose</td><td></td><td></td><td></td><td></td><td></td><td>8.31</td><td>10.7</td><td>0.78</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td></td><td>TiO2-agarose</td><td></td><td></td><td></td><td></td><td></td><td>12.12</td><td>11.8</td><td>0.80</td><td>-</td><td>5.1</td><td></td></tr><tr><td></td><td></td><td>-</td><td>DMSO</td><td>KI, I2</td><td>TiO2</td><td>Pt</td><td>N3 dye</td><td>-</td><td>1.00</td><td>0.57</td><td>0.56</td><td>0.33</td><td>[217]</td></tr><tr><td></td><td></td><td></td><td></td><td>KI, I2, IL</td><td></td><td></td><td></td><td></td><td>1.90</td><td>0.75</td><td>0.77</td><td>0.47</td><td></td></tr><tr><td></td><td></td><td></td><td>DMF</td><td>KI, I2</td><td></td><td></td><td></td><td></td><td>1.00</td><td>0.63</td><td>0.60</td><td>0.72</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>KI, I2, IL</td><td></td><td></td><td></td><td></td><td>3.30</td><td>0.62</td><td>0.66</td><td>1.36</td><td></td></tr><tr><td>2</td><td>Kappa-Carrageenan</td><td>Carboxymethyl kappa-carrageenan/wt-carboxymethyl cellulose:NH4(I (30% wt)</td><td>Acetic acid</td><td>NH4I, I2</td><td>TiO2</td><td>Pt</td><td>N719</td><td>2.41</td><td>0.42</td><td>0.50</td><td>0.64</td><td>0.13</td><td>[218]</td></tr><tr><td></td><td></td><td>Carboxymethyl kappa-carrageenan/wt-carboxymethyl cellulose:LiI (10% wt)</td><td>Acetic acid</td><td>LiI, I2</td><td>TiO2</td><td>Pt</td><td>N719</td><td>1.66</td><td>0.05</td><td>0.50</td><td>0.90</td><td>0.02</td><td>[219]</td></tr><tr><td></td><td></td><td>Carboxymethyl kappa-carrageenan/wt-carboxymethyl cellulose:LiI (20% wt)</td><td></td><td></td><td></td><td></td><td></td><td>2.73</td><td>0.12</td><td>0.49</td><td>0.80</td><td>0.05</td><td></td></tr><tr><td></td><td></td><td>Carboxymethyl kappa-carrageenan/wt-carboxymethyl cellulose:LiI (30% wt)</td><td></td><td></td><td></td><td></td><td></td><td>3.89</td><td>0.40</td><td>0.49</td><td>0.57</td><td>0.11</td><td></td></tr><tr><td>3</td><td>Iota Carrageenan</td><td>-</td><td>Water</td><td>NaI, I2</td><td>TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>2.58</td><td>0.41</td><td>0.60</td><td>0.63</td><td>[220]</td></tr><tr><td></td><td></td><td>Iota carrageenan +10%wt ionic liquid</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3.63</td><td>0.43</td><td>0.42</td><td>0.64</td><td></td></tr><tr><td></td><td></td><td>Iota carrageenan +20%wt ionic liquid</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.71</td><td>0.45</td><td>0.54</td><td>0.65</td><td></td></tr><tr><td></td><td></td><td>Iota carrageenan +30%wt ionic liquid</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3.38</td><td>0.46</td><td>0.47</td><td>0.72</td><td></td></tr><tr><td></td><td></td><td>Iota carrageenan +40%wt ionic liquid</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1.74</td><td>0.43</td><td>0.54</td><td>0.40</td><td></td></tr><tr><td>4</td><td>Chitosan</td><td>27.5%wt chitosan</td><td>DMF</td><td>22.5% wt NH4I - 50%wt I2</td><td>TiO2</td><td>Pt</td><td>Anthocyanin</td><td>1.51</td><td>0.76</td><td>0.38</td><td>0.48</td><td>0.14</td><td>[114]</td></tr><tr><td></td><td></td><td>11%wt chitosan</td><td></td><td>9% wt NH4I - 80%wt I2</td><td></td><td></td><td></td><td>3.02</td><td>0.90</td><td>0.37</td><td>0.45</td><td>0.15</td><td></td></tr><tr><td></td><td></td><td>11%wt of chitosan-PEO (ratio 30:70)</td><td></td><td>9% wt NH4I - 80%wt I2</td><td></td><td></td><td></td><td>5.52</td><td>1.21</td><td>0.40</td><td>0.47</td><td>0.23</td><td></td></tr><tr><td></td><td></td><td>adding PEG as plasticizer</td><td>Formic acid</td><td>KI, I2</td><td>Bi2Ti2O7</td><td>Pt</td><td>N719</td><td>-</td><td>2.72</td><td>0.63</td><td>0.36</td><td>0.73</td><td>[221]</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Bi2Ti2O7: 2% Sm</td><td></td><td></td><td></td><td>3.65</td><td>0.69</td><td>0.49</td><td>1.45</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Bi2Ti2O7: 2% Eu</td><td></td><td></td><td></td><td>8.42</td><td>0.72</td><td>0.39</td><td>2.77</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Bi2Ti2O7: 2% Gd</td><td></td><td></td><td></td><td>8.36</td><td>0.72</td><td>0.55</td><td>3.88</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Bi2Ti2O7: 2% Dy</td><td></td><td></td><td></td><td>8.83</td><td>0.74</td><td>0.50</td><td>3.86</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Bi2Ti2O7: 2% Ho</td><td></td><td></td><td></td><td>5.90</td><td>0.72</td><td>0.52</td><td>2.58</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Bi2Ti2O7: 2% Er</td><td></td><td></td><td></td><td>6.36</td><td>0.67</td><td>0.43</td><td>2.18</td><td></td></tr><tr><td></td><td></td><td>Chitosan</td><td>Acetic acid</td><td>KI, I2</td><td>TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>1.29</td><td>0.62</td><td>0.82</td><td>0.66</td><td>[222]</td></tr><tr><td></td><td></td><td>Chitosan NPs by ultrasonication methods</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.18</td><td>0.58</td><td>0.78</td><td>0.99</td><td></td></tr><tr><td></td><td></td><td>Chitosan NPs by ionic gelatin methods</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3.66</td><td>0.55</td><td>0.61</td><td>1.23</td><td></td></tr><tr><td></td><td></td><td>Hexanoyl chitosan/PVC</td><td>THF</td><td>20%NaI, I2</td><td>TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>5.31</td><td>0.63</td><td>0.54</td><td>1.80</td><td>[223]</td></tr><tr><td></td><td></td><td></td><td></td><td>30%NaI, I2</td><td></td><td></td><td></td><td></td><td>8.62</td><td>0.58</td><td>0.59</td><td>2.93</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>40%NaI, I2</td><td></td><td></td><td></td><td></td><td>6.32</td><td>0.67</td><td>0.62</td><td>2.59</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>30%NaI, I2, GuSCN, TBP</td><td></td><td></td><td></td><td></td><td>17.69</td><td>0.65</td><td>0.46</td><td>5.31</td><td></td></tr><tr><td></td><td></td><td>Cellulose</td><td>-</td><td>Acetonitrile</td><td>LII, I2, TBP, TBAI</td><td>TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>17.05</td><td>0.67</td><td>0.57</td><td>[224]</td></tr><tr><td></td><td></td><td>Adding 3.5 wt% ethyl cellulose as gelator</td><td></td><td></td><td></td><td></td><td></td><td></td><td>14.94</td><td>0.70</td><td>0.61</td><td>6.37</td><td></td></tr><tr><td></td><td></td><td>Adding 5.8 wt% ethyl cellulose as gelator</td><td></td><td></td><td></td><td></td><td></td><td></td><td>14.91</td><td>0.68</td><td>0.59</td><td>5.98</td><td></td></tr><tr><td></td><td></td><td>Adding 8.8 wt% ethyl cellulose as gelator</td><td></td><td></td><td></td><td></td><td></td><td></td><td>14.23</td><td>0.68</td><td>0.57</td><td>5.51</td><td></td></tr><tr><td></td><td></td><td>Grafted cellulose</td><td>-</td><td>KI, I2</td><td>TiO2</td><td>Pt</td><td>Ru dye</td><td></td><td>12.65</td><td>0.71</td><td>0.61</td><td>5.51</td><td>[225]</td></tr><tr><td></td><td></td><td>CN-HPC (cyanoethylated hydroxypropyl cellulose)</td><td>MPN</td><td>MHII, LII, I2, TBP</td><td>TiO2 adding MgO</td><td>Pt</td><td>N719</td><td>-</td><td>13.67</td><td>0.74</td><td>0.69</td><td>7.02</td><td>[118]</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>SD2</td><td></td><td>12.17</td><td>0.74</td><td>0.75</td><td>6.76</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>MHII, LII, I2, TBP</td><td></td><td></td><td>N719</td><td></td><td>14.40</td><td>0.76</td><td>0.70</td><td>7.55</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>SD2</td><td></td><td>12.65</td><td>0.78</td><td>0.75</td><td>7.40</td><td></td></tr><tr><td></td><td></td><td>3% micro-cellulose</td><td>-</td><td>LII, I2, MPI, EMISCN, TBP</td><td>TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>5.45</td><td>0.54</td><td>0.60</td><td>1.75</td><td>[226]</td></tr><tr><td></td><td></td><td>4% micro-cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5.42</td><td>0.53</td><td>0.57</td><td>1.64</td><td></td></tr><tr><td></td><td></td><td>5% micro-cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7.37</td><td>0.61</td><td>0.58</td><td>2.69</td><td></td></tr><tr><td></td><td></td><td>6% micro-cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7.47</td><td>0.58</td><td>0.61</td><td>2.62</td><td></td></tr><tr><td></td><td></td><td>0%-Nanoscale microfibrillated cellulose</td><td>Acetonitrile</td><td>NaI, I2, TBP</td><td>TiO2</td><td>Pt</td><td>N719</td><td>-</td><td>11.7</td><td>0.65</td><td>0.59</td><td>4.42</td><td>[227]</td></tr><tr><td></td><td></td><td>5%-Nanoscale microfibrillated cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>11.9</td><td>0.68</td><td>0.58</td><td>4.71</td><td></td></tr><tr><td></td><td></td><td>10%-Nanoscale microfibrillated cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12.3</td><td>0.71</td><td>0.59</td><td>5.11</td><td></td></tr><tr><td></td><td></td><td>20%-Nanoscale microfibrillated cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>13.2</td><td>0.73</td><td>0.60</td><td>5.84</td><td></td></tr><tr><td></td><td></td><td>30%-Nanoscale microfibrillated cellulose</td><td></td><td></td><td></td><td></td><td></td><td></td><td>15.2</td><td>0.76</td><td>0.61</td><td>7.03</td><td></td></tr><tr><td></td><td></td><td>0%-cellulose nanocrystall</td><td>water</td><td>NaI, I2, TBP</td><td>TiO2</td><td>Pt</td><td>Cu based dye</td><td>-</td><td>0.3</td><td>0.63</td><td>0.48</td><td>0.08</td><td>[228]</td></tr><tr><td></td><td></td><td>5%-cellulose nanocrystal</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1.9</td><td>0.49</td><td>0.27</td><td>0.26</td><td></td></tr><tr><td></td><td></td><td>10%-cellulose nanocrystal</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.5</td><td>0.51</td><td>0.30</td><td>0.39</td><td></td></tr><tr><td></td><td></td><td>20%-cellulose nanocrystal</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.6</td><td>0.53</td><td>0.39</td><td>0.54</td><td></td></tr><tr><td></td><td></td><td>40%-cellulose nanocrystall</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.3</td><td>0.57</td><td>0.67</td><td>0.89</td><td></td></tr><tr><td></td><td></td><td>60%-cellulose nanocrystal</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.8</td><td>0.57</td><td>0.60</td><td>0.96</td><td></td></tr><tr><td></td><td></td><td>80%-cellulose nanocrystal</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.8</td><td>0.58</td><td>0.66</td><td>1.09</td><td></td></tr><tr><td></td><td></td><td>100%-cellulose nanocrystall</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.0</td><td>0.60</td><td>0.50</td><td>0.61</td><td></td></tr><tr><td></td><td></td><td>Hydroxylpropyl cellulose (HPC) and EC/PC as plasticizer</td><td>-</td><td>NaI</td><td>P25 TiO2</td><td>Pt</td><td>N719</td><td>4.94</td><td>13.65</td><td>0.49</td><td>0.58</td><td>3.94</td><td>[229]</td></tr><tr><td></td><td></td><td></td><td></td><td>NaI-40%wtMPII</td><td></td><td></td><td></td><td>5.85</td><td>11.69</td><td>0.58</td><td>0.62</td><td>4.23</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>NaI-60%wtMPII</td><td></td><td></td><td></td><td>5.79</td><td>12.72</td><td>0.55</td><td>0.61</td><td>4.27</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>NaI-80%wtMPII</td><td></td><td></td><td></td><td>5.93</td><td>13.20</td><td>0.58</td><td>0.63</td><td>4.80</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>NaI-100%wtMPII</td><td></td><td></td><td></td><td>6.49</td><td>14.71</td><td>0.57</td><td>0.63</td><td>5.19</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>NaI-100%wtMPII</td><td></td><td></td><td></td><td>7.37</td><td>13.73</td><td>0.61</td><td>0.69</td><td>5.79</td><td></td></tr><tr><td></td><td></td><td>Cellulose nanocrystal blend with POEGMA</td><td>Sulfuric acid</td><td>HSE-EL, MPN</td><td>TiO2</td><td>Pt</td><td>Dyesol (Ru dye)</td><td>-</td><td>13.6</td><td>0.69</td><td>0.53</td><td>4.98</td><td>[230]</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 4 (continued) \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[944,60,954,156]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[37,492,45,505]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[944,816,954,937]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[846,922,929,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(continued on next page) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[60,78,931,899]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": \"[\\\"\\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[944,60,954,156]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[944,816,954,937]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[846,905,929,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(continued on next page) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[60,90,931,544]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": \"[\\\"\\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[944,60,954,156]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[944,816,954,937]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[161,66,505,428]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0305/91c4fe4f9063462a12d6bc989291ce08b0800bbb2d4078a97b21b694a1955800.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[509,68,836,428]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 4. The map of conductivity towards the cell performance various biopolymer based DSSC. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/1016/9c6e2a869f43026e37d928e85e26e0d61e19f0044d606d068a5e63b1dbf02c99.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[58,491,937,825]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0126/eb8f909c9be215cf52fa98a18fe2b935d33133fca157b6425ee3832dc82448b8.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Biopolymer</td><td>Monomer unit</td><td>Linkage</td><td>Dimer</td><td>Electrolyte</td><td>Conductivity value (S/cm)</td><td>Referen-ce</td></tr><tr><td>Agarose</td><td>[HOH]</td><td>α-1,3 β-1,4</td><td>[HOH]</td><td>LiI/I2(2.5 wt%)</td><td>3.94 × 10-4</td><td>[116]</td></tr><tr><td rowspan=\\\"3\\\">Carrageenan</td><td rowspan=\\\"2\\\">[OSSO]</td><td rowspan=\\\"2\\\">α-1,3 β-1,4</td><td>[O3SO]</td><td>-</td><td>2.79 × 10-6</td><td>[231]</td></tr><tr><td>[O3SO]</td><td>NH4I/I2</td><td>2.41 × 10-3</td><td>[218]</td></tr><tr><td>[OSO]</td><td>β-1,4</td><td>[O3SO]</td><td>MgTf2: AmNTFSI (27:10 wt%)</td><td>9.25 × 10-5</td><td>[232]</td></tr><tr><td rowspan=\\\"2\\\">Cellulose</td><td rowspan=\\\"2\\\">[HOH]</td><td rowspan=\\\"2\\\">β-1,4</td><td>[HOH]</td><td>-</td><td>9.33 × 10-9</td><td rowspan=\\\"2\\\">[233]</td></tr><tr><td>[HOH]</td><td>(NH4)2CO3(11 wt%)</td><td>2.28 × 10-6</td></tr><tr><td>Chitin</td><td>[HOH]</td><td>β-1,4</td><td>[HOH]</td><td>-</td><td>1.55 × 10-9</td><td>[234]</td></tr><tr><td>Chitosan</td><td>[HOH]</td><td>β-1,4</td><td>[HOH]</td><td>NH4I/I2</td><td>5.52 × 10-3</td><td>[114]</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 5. The most used biopolymers as electrolyte in quasi-solid DSSC. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[57,858,487,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and dye photodegradation. The improvement of biopolymers for quasisolid DSSCs is focused on increasing ionic transport through the polymer matrix. As mentioned in the previous section, the modeling or computational studies will be a good choice to study the interaction of responsible species involved in charge transfer. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,858,808,871]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. Natural carbon for DSSC counter electrode \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,883,937,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The high cost and rarity of platinum as the counter electrode in DSSCs prompts one to replace the noble metal with an alternative conducting material with a relative or similar efficiency. However, platinum-based \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,42,154,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[492,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"13 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,65,485,145]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"DSSCs remain the benchmark for assessing the performance of DSSCs [48, 62]. Thus far, several materials have been employed as alternative replacements of platinum as the counter electrode. These include carbonaceous materials [62, 126], conducting polymers [127, 128], transition metal carbides, nitrides, oxides, sulfides [129], and alloys [130]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,143,485,288]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Among the proposed materials for the platinum replacement of the DSSC counter electrode, carbonaceous or carbon-based materials remain one of the most studied platinum-replacement counter electrode candidates for DSSCs [62] due to their remarkable intrinsic chemical and physical characteristics, such as a high surface area, high catalytic activity, high electrical conductivity, excellent thermal stability, and good corrosion resistance, accompanied by their beneficial economic and environmental aspects. Due to the versatility of carbon-based materials, they are employed not only as counter electrodes in DSSCs but also as electrodes in electrochemical capacitors (supercapacitors) [131], and Li-ion batteries [132]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,288,485,486]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The usage of carbon-based materials dates back to the original formulation of the DSSC by the Grätzel research group [133]. Grätzel and coworkers employed a graphite powder/carbon black composite attached to a $\\\\mathrm{SnO}_2$ (TO) substrate as a counter electrode with a standard DSSC arrangement of $\\\\mathrm{I}_2 / \\\\mathrm{I}_3$ electrolyte and $\\\\mathrm{TiO}_2$ (anatase) photoelectrode, achieving a power conversion efficiency (PCE) of $6.7\\\\%$ . The encouraging results on the PCE of the low-cost carbon-based counter electrode prompted researchers to further develop the carbon-based counter electrodes by employing new microstructures of carbon materials such as porous carbon, carbon nanotube, graphene, and carbon nanofiber [61, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157], modifying of the existing phases such as doping or functionalizing with heteroatoms [158, 159, 160, 161] or incorporating with other materials like silica [162]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,486,485,645]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the context of the current review, natural products such as biomass have become essential sources of carbon-based materials. Biomasses are undoubtedly rich in carbonaceous materials, yet their low retrieval cost and high availability make them promising candidates for the mass production of carbon-based materials and waste valorization. There are at least 60 different biomass sources for carbon-based electrodes employed in supercapacitors, Li-ion batteries, and fuel cells, as summarized in a recent review [163]. In environmental applications, biomass-derived carbon materials have become routinely employed as adsorbents for dyes, heavy metals, and so on [164, 165] in water and wastewater, owing to their large surface area and active adsorption sites. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,646,485,815]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This section will discuss natural product-derived counter electrodes to gain insight into the relationship between the synthetic method, structure, and performance in DSSC cells. Figure 5 and Table 6 show the available literature on counter electrodes from various biomasses, wastes, and commercial biomasses, which will be included in the discussion. Interestingly, most of, if not all, the literature comes from authors who reside in Asia, more specifically, East and Southeast Asian countries. Due to the high diversity of primary natural resources from these regions, the current review results may benefit researchers from these countries to valorize natural products as more functional materials. It is worth mentioning that the natural products discussed here are not necessarily waste but also commercially produced biomass such as humic acid and ovalbumin. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,831,453,844]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.1. Preparation of counter electrode materials from natural products \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,857,485,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As listed in Table 6, a wealth of natural product resources is available for counter electrodes. Describing detailed procedures of the material extraction and counter electrode fabrication for each study would be too exhaustive. Nevertheless, this subsection will present the general trend of the resulting products with each of the preparation routes of counter electrode materials. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,66,934,380]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 5. Typical sources for counter electrode materials from natural products based on the number of available articles. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/1007/8120a52346fb46f8096e15e079c603809b59c0858273fe7ef52c99f2f02436ef.jpg\",\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[510,466,936,802]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0193/691ae89198394b180278721972a793080f78747dac81fff84d2be1737fb842a5.jpg\",\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Type</td><td>Source</td><td>References</td></tr><tr><td rowspan=\\\"12\\\">Agricultural biomass</td><td>Rice husk</td><td>[165, 235, 236]</td></tr><tr><td>Coconut shell</td><td>[170, 237, 238]</td></tr><tr><td>Pumpkin stem</td><td>[183]</td></tr><tr><td>Mangosteen peel</td><td>[167]</td></tr><tr><td>Pine cone flower</td><td>[239]</td></tr><tr><td>Various leaves</td><td>[240, 241, 242]</td></tr><tr><td>Various woods</td><td>[241, 243]</td></tr><tr><td>Sunflower stalk</td><td>[173]</td></tr><tr><td>Aloe peel</td><td>[174, 175, 176, 177, 178, 179, 180]</td></tr><tr><td>Kelp</td><td>[244]</td></tr><tr><td>Orange fiber</td><td>[185]</td></tr><tr><td>Pomelo peel</td><td>[181]</td></tr><tr><td rowspan=\\\"2\\\">Animal biomass</td><td>Fish</td><td>[166, 245]</td></tr><tr><td>Human hair</td><td>[246]</td></tr><tr><td rowspan=\\\"4\\\">Post-consumer waste</td><td>Ground coffee</td><td>[188]</td></tr><tr><td>Facial tissue</td><td>[241]</td></tr><tr><td>Paper</td><td>[241]</td></tr><tr><td>Carton</td><td>[182]</td></tr><tr><td rowspan=\\\"5\\\">Commercial biomass</td><td>Bagasse</td><td>[171]</td></tr><tr><td>Table sugar</td><td>[184]</td></tr><tr><td>Sucrose</td><td>[184]</td></tr><tr><td>Humic acid</td><td>[247]</td></tr><tr><td>Ovalbumin</td><td>[248]</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 6. Various available sources for carbon electrode derived from natural products. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[507,815,937,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It seems evident that natural product resources mostly contain carbon obtained from macromolecule constituents. As seen from Figure 6, the extracted materials for counter electrodes from the literature are primarily carbon-based materials, with several types ranging from porous carbon to biochar, depending on the preparation route and sources. They can be categorized based on different chemical compositions, porous sizes, and surface areas. Other extracted materials include silicon or silica-based materials, such as rice husk ash, which seem to gain less attention due to more unsatisfactory DSSC performance than carbon-based materials. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,42,157,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[492,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"14 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[184,66,811,534]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 6. Typical counter electrode materials extracted from natural products and from literature. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0939/c29951f23caa91be1e1251b5f9f710d3540007353763659ff6e45fb859537215.jpg\",\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,578,485,788]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The types of extracted carbon-based materials based on morphology are explained in greater detail in this section. These materials can be divided into two groups: inactivate carbon material and porous carbon material. However, the naming for the former is somehow quite ambiguous across the literature. Inactivate carbon material in this review refers to carbon material that is mainly prepared by carbonization techniques, such as heat treatment (pyrolysis), without any further treatment apart from washing and/or drying. By this definition, the simple \\\"carbon material,\\\" amorphous carbon material, and biochar listed in Table 7 belong to this group. Spherical carbon materials can also be categorized into this group. The second group seems to have a more obvious definition. The carbon-based materials in this group have porous structures, as revealed mostly by SEM images, and quantitatively, the total porous size. More specifically, the materials usually have a mesoporous structure. According to the morphology, activated carbon and porous carbon belong to the second group of carbon-based materials. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,789,485,934]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Generally, the preparation of carbon-based counter electrode materials usually involves several procedures, including pretreatment, carbonization, and activation. Figure 7 summarizes the general procedure for preparing carbon-based counter electrode materials. The pretreatment step is conducted to remove impurities and water, which can be achieved by washing, drying, and mechanical treatments such as cutting, grinding, and sieving. The second procedure is carbonization, which occurs through high-temperature annealing under an inert atmosphere (pyrolysis) and hydrothermal carbonization. The former carbonization technique will yield amorphous carbon, charcoal, and biochar, while the latter gives the spherical carbon morphology. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,578,937,697]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Depending on the intended final target material, further activation and carbonization may be conducted to enhance the surface area and develop the pores, carried out by either physical or chemical activation to prepare \\\"porous carbon\\\". The resulting \\\"inactivate carbon material\\\" is usually mixed with chemical activators such as KOH and $\\\\mathrm{ZnCl}_2$ , followed by further heating at high temperatures. The base can react with the carbon to develop pores within the carbon structure. Simultaneous physical activation and carbonization, along with chemical activation, can be carried out by microwave treatment. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,697,937,868]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"One issue regarding the utilization of natural products is their inhomogeneous content, which can bring either benefits or drawback to the extraction processes of the intended counter electrode material and DSSC performance. The impurities contained in the source have to be removed using harsh chemicals if necessary. On the other hand, impurities can also benefit DSSC performance due to the introduction of defective sites into the counter electrode structure, enhancing the electrocatalytic activities. Another issue is the reproducibility of the material extracted from the natural product, where the material obtained can have a different structure, morphology, and surface area. However, there seems to be a consistent preparation route for porous carbon. While the resulting materials have a quantitatively different surface area, the characterization reveals that they belong to a similar class of porous carbon. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,883,833,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.2. The performance of the natural carbon-based DSSC \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,910,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Table 7 lists the photovoltaic performances of DSSC devices that used counter electrodes derived from natural products. Before further \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,42,154,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[492,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"15 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[58,85,937,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0992/fce8ed385b57e05c757558c3a39e9116722b9ecf4febc5e06dc25d99544c403d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=\\\"2\\\">Source</td><td rowspan=\\\"2\\\">Counter electrode material</td><td colspan=\\\"4\\\">Natural product-based counter electrode</td><td colspan=\\\"4\\\">Pt counter electrode</td><td rowspan=\\\"2\\\">Electrolyte solution</td><td rowspan=\\\"2\\\">Photoanode/Dye</td><td rowspan=\\\"2\\\">Reference</td></tr><tr><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η(%)</td><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η(%)</td></tr><tr><td>Rice husk</td><td>Porous carbon</td><td>14.53</td><td>0.680</td><td>64</td><td>6.32</td><td>14.61</td><td>0.69</td><td>66</td><td>6.69</td><td>LiI/2/1-methyl-3-hexylimidazolium iodide/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N3</td><td>[165]</td></tr><tr><td>Rice husk</td><td>ACs/Acetylene Black</td><td>15.01</td><td>0.73</td><td>60</td><td>6.57</td><td>15.20</td><td>0.74</td><td>64</td><td>7.20</td><td>LiI/2/1-methyl-3-propyl imidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile and valeronitrile (85:15)</td><td>TiO2/N719</td><td>[235]</td></tr><tr><td>Rice husk</td><td>Nano-Si@ACs/Acetylene Black</td><td>15.50</td><td>0.76</td><td>67</td><td>8.01</td><td>15.20</td><td>0.74</td><td>64</td><td>7.20</td><td>LiI/2/1-methyl-3-propyl imidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile and valeronitrile (85:15)</td><td>TiO2/N719</td><td>[235]</td></tr><tr><td>Rice husk</td><td>Rice husk ash/MoS2</td><td>10.95</td><td>0.60</td><td>32</td><td>2.10</td><td>-</td><td>-</td><td>-</td><td>-</td><td>Phthalocitosan electrolyte polymer/DMF/ethylene carbonate/tetrapropylammonium iodide/I2</td><td>TiO2/N3</td><td>[236]</td></tr><tr><td>Coconut shell</td><td>Amorphous activated carbon</td><td>7.60</td><td>0.77</td><td>32</td><td>0.84</td><td>-</td><td>-</td><td>-</td><td>-</td><td>LiI/2/4-tertbutylpyridine in acetonitrile</td><td>TiO2/N719</td><td>[237]</td></tr><tr><td>Coconut shell</td><td>Graphitic carbon</td><td>10.00</td><td>0.77</td><td>36</td><td>1.24</td><td>-</td><td>-</td><td>-</td><td>-</td><td>LiI/2/4-tertbutylpyridine in acetonitrile</td><td>TiO2/N719</td><td>[237]</td></tr><tr><td>Coconut shell</td><td>Activated charcoal</td><td>19.49</td><td>0.65</td><td>62</td><td>7.85</td><td>19.52</td><td>0.69</td><td>70</td><td>9.41</td><td>LiI/2/1,2-dimethyl-3-propyl imidazolium iodide/tert-butylpyridine in acetonitrile</td><td>TiO2/N719</td><td>[170]</td></tr><tr><td>Pumpkin stem</td><td>Activated carbon</td><td>3.84</td><td>0.611</td><td>0.475</td><td>2.79</td><td>4.54</td><td>0.736</td><td>49.3</td><td>4.04</td><td>KI/I2in ethylene glycol</td><td>TiO2/N719</td><td>[183]</td></tr><tr><td>Mangosteen peel</td><td>Carbon material</td><td>5.58</td><td>0.70</td><td>0.51</td><td>1.99</td><td>5.42</td><td>0.62</td><td>52</td><td>1.75</td><td>NaI/2/Li2CO3in acetonitrile</td><td>TiO2/Mangosteen peel extract</td><td>[167]</td></tr><tr><td>Mangosteen peel</td><td>Carbon material</td><td>8.70</td><td>0.60</td><td>50</td><td>2.63</td><td>4.72</td><td>0.57</td><td>54</td><td>1.47</td><td>di-5-(1-methyltetrazole)/5-mercapto-1-methyltetrazole N-tetramethylammonium salt)/4-tert-butylpyridine/LiCO4in acetonitrile</td><td>TiO2/Mangosteen peel extract</td><td>[167]</td></tr><tr><td>Pine cone flower</td><td>honeycomb-like activated porous carbon</td><td>13.51</td><td>0.71</td><td>52</td><td>4.98</td><td>14.29</td><td>0.71</td><td>62</td><td>6.25</td><td>HPE</td><td>TiO2/N719</td><td>[239]</td></tr><tr><td>Fallen leaves</td><td>Honeycomb porous carbon</td><td>14.99</td><td>0.70</td><td>53</td><td>5.52</td><td>15.96</td><td>0.70</td><td>58</td><td>6.56</td><td>HPE</td><td>TiO2/N719</td><td>[240]</td></tr><tr><td>Lotus</td><td>Biochar</td><td>14.33</td><td>0.44</td><td>23</td><td>1.42</td><td>-</td><td>-</td><td>-</td><td>-</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[242]</td></tr><tr><td>Lotus</td><td>Biochar</td><td>1.50</td><td>0.43</td><td>23</td><td>0.15</td><td>1.05</td><td>0.52</td><td>66</td><td>0.36</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/Lotus leaf extract</td><td>[242]</td></tr><tr><td>Weeping willow wood</td><td>Amorphous carbon</td><td>11.31</td><td>0.67</td><td>21</td><td>1.55</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Phoenix wood</td><td>Amorphous carbon</td><td>12.14</td><td>0.65</td><td>24</td><td>1.91</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Camphor wood</td><td>Amorphous carbon</td><td>11.31</td><td>0.64</td><td>22</td><td>1.58</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Chinese fir wood</td><td>Amorphous carbon</td><td>10.79</td><td>0.65</td><td>20</td><td>1.38</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Maple wood</td><td>Amorphous carbon</td><td>11.58</td><td>0.67</td><td>22</td><td>1.68</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Peach wood</td><td>Amorphous carbon</td><td>11.42</td><td>0.67</td><td>19</td><td>1.48</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Poplar wood</td><td>Amorphous carbon</td><td>12.15</td><td>0.62</td><td>24</td><td>1.83</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Cypress wood</td><td>Amorphous carbon</td><td>10.94</td><td>0.67</td><td>17</td><td>1.23</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Tea-oil camellia wood</td><td>Amorphous carbon</td><td>10.54</td><td>0.62</td><td>21</td><td>1.37</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/I2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Orange wood</td><td>Amorphous carbon</td><td>12.19</td><td>0.67</td><td>22</td><td>1.81</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Chinaberry wood</td><td>Amorphous carbon</td><td>12.58</td><td>0.64</td><td>21</td><td>1.66</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Oak wood</td><td>Mesoporous carbon</td><td></td><td></td><td></td><td>7.98</td><td></td><td></td><td></td><td>7.93</td><td>LiI/12/1,2-dimethyl-3-propylimidazolium iodide/4-tert-butyl pyridine in acetonitrile</td><td>TiO2/N719</td><td>[243]</td></tr><tr><td>Bamboo</td><td>Mesoporous carbon</td><td></td><td></td><td></td><td>4.53</td><td></td><td></td><td></td><td>7.93</td><td>LiI/12/1,2-dimethyl-3-propylimidazolium iodide/4-tert-butyl pyridine in acetonitrile</td><td>TiO2/N719</td><td>[243]</td></tr><tr><td>Pine needles leaf</td><td>Amorphous carbon</td><td>10.14</td><td>0.62</td><td>17</td><td>1.07</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Camphor leaf</td><td>Amorphous carbon</td><td>11.98</td><td>0.53</td><td>22</td><td>1.37</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Palm leaf</td><td>Amorphous carbon</td><td>11.53</td><td>0.63</td><td>25</td><td>1.85</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Maple leaf</td><td>Amorphous carbon</td><td>9.64</td><td>0.51</td><td>25</td><td>1.20</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Poplar leaf</td><td>Amorphous carbon</td><td>10.96</td><td>0.49</td><td>25</td><td>1.33</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Chinese fir leaf</td><td>Amorphous carbon</td><td>9.07</td><td>0.53</td><td>23</td><td>1.09</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Red after-wood leaf</td><td>Amorphous carbon</td><td>10.07</td><td>0.62</td><td>18</td><td>1.14</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/12/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Sunflower stalk</td><td>Layered activated carbon</td><td>15.20</td><td>0.67</td><td>64</td><td>6.56</td><td>15.77</td><td>0.70</td><td>65</td><td>7.19</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[173]</td></tr><tr><td>Aloe peel</td><td>Honeycomb-like porous carbon/acetylene black</td><td>14.15</td><td>0.72</td><td>0.68</td><td>6.92</td><td>15.77</td><td>0.70</td><td>65</td><td>7.19</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[174]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon</td><td>12.46</td><td>0.68</td><td>30</td><td>2.43</td><td>15.38</td><td>0.67</td><td>60</td><td>6.34</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon/FeTa2O6</td><td>15.16</td><td>0.70</td><td>65</td><td>6.85</td><td>15.38</td><td>0.67</td><td>60</td><td>6.34</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon/CoTa2O6</td><td>15.79</td><td>0.70</td><td>62</td><td>6.79</td><td>15.38</td><td>0.67</td><td>60</td><td>6.34</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon/CuTa10O26</td><td>15.19</td><td>0.68</td><td>63</td><td>6.53</td><td>15.38</td><td>0.67</td><td>60</td><td>6.34</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>14.12</td><td>0.71</td><td>65</td><td>6.52</td><td>15.77</td><td>0.70</td><td>65</td><td>7.14</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[176]</td></tr><tr><td>Aloe peel</td><td>Porous carbon/ZnNb2O6</td><td>19.12</td><td>0.71</td><td>65</td><td>8.83</td><td>15.77</td><td>0.70</td><td>65</td><td>7.14</td><td>LiI/12/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[176]</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 7. Photovoltaic parameters of DSSCs based on the various counter electrodes in comparison with standard Pt counter electrode. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[60,42,156,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[823,940,937,950]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(continued on next page) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[492,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"16 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,79,937,894]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/\",\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": \"[\\\"\\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[823,897,937,910]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(continued on next page) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,42,156,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[492,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"17 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,79,937,921]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0707/a0b48b9227420ab533ee9a28baa1e3353e925da8e5709ee8cf821fb3f4d6f630.jpg\",\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=\\\"2\\\">Source</td><td rowspan=\\\"2\\\">Counter electrode material</td><td colspan=\\\"4\\\">Natural product-based counter electrode</td><td colspan=\\\"4\\\">Pt counter electrode</td><td rowspan=\\\"2\\\">Electrolyte solution</td><td rowspan=\\\"2\\\">Photoanode/Dye</td><td rowspan=\\\"2\\\">Reference</td></tr><tr><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η (%)</td><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η (%)</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>15.04</td><td>0.72</td><td>59</td><td>6.40</td><td>15.96</td><td>0.70</td><td>63</td><td>7.04</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>Porous carbon/MnWO4</td><td>15.52</td><td>0.69</td><td>68</td><td>7.33</td><td>15.96</td><td>0.70</td><td>63</td><td>7.04</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>Porous carbon/ZnWO4</td><td>17.12</td><td>0.69</td><td>65</td><td>7.61</td><td>15.96</td><td>0.70</td><td>63</td><td>7.04</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>Porous carbon/CuWO4</td><td>13.84</td><td>0.73</td><td>64</td><td>6.52</td><td>15.96</td><td>0.70</td><td>63</td><td>7.04</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>3D network carbon</td><td>14.86</td><td>0.62</td><td>66</td><td>6.07</td><td>15.76</td><td>0.65</td><td>66</td><td>6.74</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>3D network carbon/ZnMoO4</td><td>16.41</td><td>0.69</td><td>67</td><td>7.65</td><td>15.76</td><td>0.65</td><td>66</td><td>6.74</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>3D network carbon/Cu2Mo3O9</td><td>15.71</td><td>0.74</td><td>63</td><td>7.33</td><td>15.76</td><td>0.65</td><td>66</td><td>6.74</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>3D network carbon/MnMoO4</td><td>15.52</td><td>0.65</td><td>68</td><td>6.92</td><td>15.76</td><td>0.65</td><td>66</td><td>6.74</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>Porous carbon/MnO2</td><td>12.81</td><td>0.73</td><td>64</td><td>6.11</td><td>13.32</td><td>0.72</td><td>66</td><td>6.44</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[179]</td></tr><tr><td>Aloe peel</td><td>Porous carbon/Co/MnO2</td><td>15.45</td><td>0.72</td><td>68</td><td>7.01</td><td>13.32</td><td>0.72</td><td>66</td><td>6.44</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[179]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon</td><td>12.12</td><td>0.76</td><td>69</td><td>6.45</td><td>13.44</td><td>0.73</td><td>69</td><td>6.80</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[180]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon/NiTa2O6</td><td>14.61</td><td>0.74</td><td>65</td><td>7.09</td><td>13.44</td><td>0.73</td><td>69</td><td>6.80</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[180]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon/MnTa2O6</td><td>15.41</td><td>0.74</td><td>65</td><td>7.39</td><td>13.44</td><td>0.73</td><td>69</td><td>6.80</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[180]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon/AlTaO4</td><td>15.80</td><td>0.76</td><td>65</td><td>7.86</td><td>13.44</td><td>0.73</td><td>69</td><td>6.80</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[180]</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 7 (continued) \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[823,926,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(continued on next page) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,42,156,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[492,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,79,937,909]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0799/ef613a94039e54b8228aaaf59924d6025d78a3d8e09ce158449e3db08b899d66.jpg\",\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=\\\"2\\\">Source</td><td rowspan=\\\"2\\\">Counter electrode material</td><td colspan=\\\"4\\\">Natural product-based counter electrode</td><td colspan=\\\"4\\\">Pt counter electrode</td><td rowspan=\\\"2\\\">Electrolyte solution</td><td rowspan=\\\"2\\\">Photoanode/Dye</td><td rowspan=\\\"2\\\">Reference</td></tr><tr><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η (%)</td><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η (%)</td></tr><tr><td>Pomelo peel</td><td>Carbon material</td><td>14.56</td><td>0.70</td><td>68</td><td>6.94</td><td>14.48</td><td>0.73</td><td>64</td><td>6.72</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[181]</td></tr><tr><td>Kelp</td><td>N, S, P-doped/Co NPs</td><td>14.71</td><td>0.75</td><td>68</td><td>7.48</td><td>14.73</td><td>0.75</td><td>73</td><td>7.64</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[244]</td></tr><tr><td>Orange fiber</td><td>Carbon material/CoS nanoflakes</td><td>11.58</td><td>0.74</td><td>69</td><td>5.94</td><td>12.02</td><td>0.73</td><td>64</td><td>5.57</td><td>DN-OD05</td><td>TiO2/C264 triphenylamine</td><td>[185]</td></tr><tr><td>Anchovy</td><td>N and S co-doped activated porous carbon</td><td>18.78</td><td>0.89</td><td>76</td><td>12.72</td><td>19.17</td><td>0.87</td><td>73</td><td>12.23</td><td>Co(bpy)3+/2+</td><td>TiO2/SM-315 porphyrin</td><td>[166]</td></tr><tr><td>Fish waste</td><td>N, P and S tri-doped activated porous carbon</td><td>15.64</td><td>0.75</td><td>67</td><td>7.83</td><td>15.98</td><td>0.76</td><td>69</td><td>8.34</td><td>LiI/2/1,2-dimethyl-3-propyl imidazolium iodide/tert-butylpyridine in acetonitrile.</td><td>TiO2/N3</td><td>[245]</td></tr><tr><td>Human hair</td><td>Carbon material/PEDOT:PSS</td><td>14.58</td><td>0.76</td><td>58</td><td>6.54</td><td>15.64</td><td>0.74</td><td>63</td><td>7.29</td><td>LiI/2/1-methyl-3-propylimidazolium iodide/tetraethylpyridine/Li2CO3in acetonitrile.</td><td>TiO2/N719</td><td>[246]</td></tr><tr><td>Ground coffee waste</td><td>N-doped porous carbon</td><td>15.09</td><td>0.76</td><td>73</td><td>8.32</td><td>14.73</td><td>0.77</td><td>72</td><td>8.07</td><td>I2/1-butyl-3-methylimidazolium iodide/guanidinium thiocyanate/4-tert-butylpyridine in acetonitrile and valeronitrile mixture (volume ratio 85:15)</td><td>TiO2/N719</td><td>[188]</td></tr><tr><td>Filter paper</td><td>Amorphous carbon</td><td>15.02</td><td>0.70</td><td>45</td><td>4.72</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Facial tissue</td><td>Amorphous carbon</td><td>14.80</td><td>0.69</td><td>64</td><td>4.70</td><td>15.81</td><td>0.64</td><td>62</td><td>6.23</td><td>LiI/2/4-tert-butylpyridine in 3-methoxypropionitrile</td><td>TiO2/N719</td><td>[241]</td></tr><tr><td>Waste carton</td><td>Porous carbon</td><td>14.20</td><td>0.77</td><td>62</td><td>6.76</td><td>14.84</td><td>0.76</td><td>66</td><td>7.51</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[182]</td></tr><tr><td>Waste carton</td><td>Porous carbon/WC</td><td>14.56</td><td>0.76</td><td>60</td><td>7.32</td><td>14.84</td><td>0.76</td><td>66</td><td>7.51</td><td>LiI/2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[182]</td></tr><tr><td>Bagasse</td><td>Carbon material</td><td>5.20</td><td>0.72</td><td>8</td><td>0.31</td><td>15.00</td><td>0.72</td><td>57</td><td>6.08</td><td>LiI/2/1,2-Dimethyl-3-propylimidazolium iodide/4-tert-butyl-pyridine in acetonitrile</td><td>TiO2/N719</td><td>[171]</td></tr><tr><td>Bagasse</td><td>Nitrogen-doped bagasse</td><td>10.7</td><td>0.69</td><td>37</td><td>2.48</td><td>15.00</td><td>0.72</td><td>57</td><td>6.08</td><td>LiI/2/1,2-Dimethyl-3-propylimidazolium iodide/4-tert-butyl-pyridine in acetonitrile</td><td>TiO2/N719</td><td>[171]</td></tr><tr><td>Bagasse</td><td>Carbon material/Pt NPs</td><td>12.4</td><td>0.66</td><td>45</td><td>3.69</td><td>15.00</td><td>0.72</td><td>57</td><td>6.08</td><td>LiI/2/1,2-Dimethyl-3-propylimidazolium iodide/4-tert-butyl-pyridine in acetonitrile</td><td>TiO2/N719</td><td>[171]</td></tr><tr><td>Bagasse</td><td>Nitrogen-doped bagasse/Pt NPs</td><td>15.3</td><td>0.73</td><td>62</td><td>6.98</td><td>15.00</td><td>0.72</td><td>57</td><td>6.08</td><td>LiI/2/1,2-Dimethyl-3-propylimidazolium iodide/4-tert-butyl-pyridine in acetonitrile</td><td>TiO2/N719</td><td>[171]</td></tr><tr><td>Table sugar</td><td>Carbon materiala</td><td>-</td><td>-</td><td>-</td><td>3.24</td><td>-</td><td>-</td><td>-</td><td>4.02</td><td>Iodolite</td><td>TiO2/RK-1</td><td>[184]</td></tr><tr><td>Sucrose</td><td>Carbon materiala</td><td>-</td><td>-</td><td>-</td><td>0.04</td><td>-</td><td>-</td><td>-</td><td>4.02</td><td>Iodolite</td><td>TiO2/RK-1</td><td>[184]</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 7 (continued) \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[823,914,937,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(continued on next page) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,42,156,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[492,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"19 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,79,937,273]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0151/79d865b183978109cc457e8123383417991188356ce7e252c1ae8a4870bef0c3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=\\\"2\\\">Source</td><td rowspan=\\\"2\\\">Counter electrode material</td><td colspan=\\\"4\\\">Natural product-based counter electrode</td><td colspan=\\\"4\\\">Pt counter electrode</td><td rowspan=\\\"2\\\">Electrolyte solution</td><td rowspan=\\\"2\\\">Photoanode/Dye</td><td rowspan=\\\"2\\\">Reference</td></tr><tr><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η(%)</td><td>Jsc(mA·cm-2)</td><td>Voc(V)</td><td>FF(%)</td><td>η(%)</td></tr><tr><td>Humic acid</td><td>Carbon material</td><td>12.55</td><td>0.76</td><td>65</td><td>6.14</td><td>13.85</td><td>0.75</td><td>68</td><td>7.10</td><td>Lil/I2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[247]</td></tr><tr><td>Humic acid</td><td>Carbon material/Ni</td><td>13.51</td><td>0.76</td><td>68</td><td>7.01</td><td>13.85</td><td>0.75</td><td>68</td><td>7.10</td><td>Lil/I2/1-butyl-3-methylimidazolium iodide/4-tert-butyl pyridine/guanidinium thiocyanate in acetonitrile</td><td>TiO2/N719</td><td>[247]</td></tr><tr><td>Ovalbumin</td><td>N-doped carbon aerogel</td><td>12.01</td><td>0.70</td><td>56</td><td>4.68</td><td>12.71</td><td>0.71</td><td>59</td><td>5.35</td><td>Iodolyte HI-30</td><td>TiO2/N719</td><td>[248]</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 7 (continued) \\\"]\",\n \"table_footnote\": \"[\\\"a The $V_{oc}$ from ref. [184] is unreliable. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[161,335,836,750]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 7. Preparation routes of the carbon-based natural product-derived counter electrode materials. The employed carbon-based materials are displayed in the blue dialog box. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0792/1dcf65a628e8c5d64d2ae49799516cefcac08a70860a9ede3c5e5e3344ee651c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[57,798,487,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"discussing the performance of each device with the natural product-based counter electrode, DSSC performance with the standard platinum counter electrode used as the benchmark is discussed. The PCE of platinum-based devices varies from 0.36 to $12.23\\\\%$ . However, there are no consistent compositions of the dyes and electrolytes mentioned in the literature, which results in varied PCE values. This reduces the possibility of making a fair comparison of PCE values obtained from the various literature. The ruthenium-based dye N719 remains the most favorable, followed by ruthenium-based N3 dye. The other dyes mentioned in the literature are Zn-based SM-315, RK-1, C264 porphyrin, and natural \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,798,939,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"product-based (lotus leaf and mangosteen peel extract) dyes. For the electrolytes, almost all the literature studied utilized the $\\\\mathrm{I}_3 / \\\\mathrm{I}^-$ redox pair as inorganic iodide and/or various forms of imidazolium iodide salt as a source of $\\\\Gamma^{-}$ . $\\\\Gamma^{-}$ was used either as a fresh chemical mixture or a commercially prepared solution mixed with the solvent, forming acetonitrile or an acetonitrile/valeronitrile mixture. In addition to these specimens, electrolyte additives such as 4-tert-butyl pyridine and guanidium thiocyanate are also incorporated into the electrolytes to enhance DSSC performance [13, 16]. Kim et al. incorporated the only $\\\\mathrm{Co(bpy)_3^{3 + / 2 + }}$ redox pair electrolytes found in the current literature \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,42,157,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"20 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[58,90,937,920]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0401/56a3b02ddf11300fe6974a95be36ddd708dc46bdc0152bd3047ed93fc4da1323.jpg\",\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Source</td><td>Extracted counter electrode material</td><td>Additive and/or modifier</td><td>Binder or Adhesive</td><td>SBET(m2g-1)</td><td>Pore volume (cm3g-1)</td><td>Rt(Ω cm2)</td><td>Rct(Ω cm2)</td><td>Cd(μF cm2)</td><td>Zw(Ω cm2)</td><td>Ip(mA cm-2)</td><td>Epp(V)</td><td>ηrel</td><td>Reference</td></tr><tr><td>Rice husk</td><td>Porous carbon</td><td>-</td><td>Titanium isopropoxide</td><td>1095</td><td>0.61</td><td>21.4</td><td>1.3</td><td>42</td><td>1.3</td><td>-3.5a</td><td>-</td><td>0.94</td><td>[165]</td></tr><tr><td>Coconut shell</td><td>Activated charcoal</td><td>-</td><td>Poly vinyl acetate</td><td>-</td><td>-</td><td>30.0</td><td>1.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.83</td><td>[170]</td></tr><tr><td>Pumpkin stem</td><td>Activated carbon</td><td>-</td><td>-</td><td>793</td><td>0.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-3.0a</td><td>0.60a</td><td>0.69</td><td>[183]</td></tr><tr><td>Weeping willow wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.25</td><td>[241]</td></tr><tr><td>Phoenix wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>273</td><td>-</td><td>31.3</td><td>22.7</td><td>-</td><td>-</td><td>-1.8</td><td>0.588</td><td>0.31</td><td>[241]</td></tr><tr><td>Camphor wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.25</td><td>[241]</td></tr><tr><td>Chinese fir wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.22</td><td>[241]</td></tr><tr><td>Maple wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.27</td><td>[241]</td></tr><tr><td>Peach wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.24</td><td>[241]</td></tr><tr><td>Poplar wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.29</td><td>[241]</td></tr><tr><td>Cypress wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.20</td><td>[241]</td></tr><tr><td>Tea-oil camellia wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.22</td><td>[241]</td></tr><tr><td>Orange wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.29</td><td>[241]</td></tr><tr><td>Chinaberry wood</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.27</td><td>[241]</td></tr><tr><td>Oak wood</td><td>Mesoporous carbon</td><td>-</td><td>-</td><td>852</td><td>0.6</td><td>15.1</td><td>10.0</td><td>-</td><td>95.3</td><td>-</td><td>-</td><td>1.01</td><td>[243]</td></tr><tr><td>Bamboo</td><td>Mesoporous carbon</td><td>-</td><td>-</td><td>542</td><td>0.3</td><td>14.6</td><td>38.4</td><td>-</td><td>76.0</td><td>-</td><td>-</td><td>0.57</td><td>[243]</td></tr><tr><td>Pine needles leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.17</td><td>[241]</td></tr><tr><td>Camphor leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.22</td><td>[241]</td></tr><tr><td>Palm leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>7.1</td><td>-</td><td>32.1</td><td>22.8</td><td>-</td><td>-</td><td>-1.2</td><td>0.582</td><td>0.30</td><td>[241]</td></tr><tr><td>Maple leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.19</td><td>[241]</td></tr><tr><td>Poplar leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.21</td><td>[241]</td></tr><tr><td>Chinese fir leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.17</td><td>[241]</td></tr><tr><td>Red after-wood leaf</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.18</td><td>[241]</td></tr><tr><td>Lotus</td><td>Biochar</td><td>-</td><td>Carboxymethyl cellulose</td><td>30.9</td><td>-</td><td>-</td><td>40.7</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.42</td><td>[242]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon</td><td>-</td><td>ZrO2</td><td>1286</td><td>0.7</td><td>27.4</td><td>12.4</td><td>-</td><td>-</td><td>-6.0a</td><td>0.4a</td><td>0.96</td><td>[174]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon</td><td>-</td><td>ZrO2</td><td>13b</td><td>0.1b</td><td>7808</td><td>8663</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.38</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>-</td><td>ZrO2</td><td>507</td><td>-</td><td>14.0</td><td>12.2</td><td>-</td><td>11.4</td><td>-4.7</td><td>0.847</td><td>0.91</td><td>[176]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>-</td><td>ZrO2</td><td>-</td><td>-</td><td>15.9</td><td>4.6</td><td>-</td><td>-</td><td>-1.6</td><td>0.770</td><td>0.91</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>3D network carbon</td><td>-</td><td>ZrO2</td><td>-</td><td>-</td><td>11.7</td><td>0.7</td><td>-</td><td>-</td><td>-1.3</td><td>0.442</td><td>0.90</td><td>[178]</td></tr><tr><td>Pomelo peel</td><td>Carbon material</td><td>-</td><td>ZrO2</td><td>1377</td><td>0.7</td><td>15.3</td><td>7.1</td><td>8.5</td><td>-</td><td>-2.8</td><td>0.530</td><td>1.03</td><td>[181]</td></tr><tr><td>Bagasse</td><td>Carbon material</td><td>-</td><td>Polyvinyl pyrrolidone</td><td>19.4</td><td>-</td><td>6.6</td><td>544</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.05</td><td>[171]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon</td><td>-</td><td>ZrO2</td><td>1286b</td><td>0.7b</td><td>12.3</td><td>1.2</td><td>-</td><td>-</td><td>-2.0</td><td>0.760</td><td>0.95</td><td>[180]</td></tr><tr><td>Anchovy</td><td>N and S co-doped</td><td>-</td><td>-</td><td>2622</td><td>1.9</td><td>3.0</td><td>7.56</td><td>-</td><td>-</td><td>-0.3a</td><td>0.075a</td><td>1.04</td><td>[166]</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 8. Electrochemical, electrocatalytic, and structural properties of various counter electrodes. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[823,925,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(continued on next page) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,42,156,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[492,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"21 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,79,937,911]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0915/670af4d9c623624a032fdb4878e15e0f40c97fc6349a137d51be361ef7e07dd4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Source</td><td>Extracted counter electrode material</td><td>Additive and/or modifier</td><td>Binder or Adhesive</td><td>SBET(m2g-1)</td><td>Pore volume (cm3g-1)</td><td>Rt(Ω cm2)</td><td>Rct(Ω cm2)</td><td>Cd(μF cm2)</td><td>Zw(Ω cm2)</td><td>Ip(mA cm-2)</td><td>Epp(V)</td><td>ηrel</td><td>Reference</td></tr><tr><td></td><td>activated porous carbon</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Fish waste</td><td>N, P and S tri-doped activated porous carbon</td><td>-</td><td>Ethyl cellulose/terpineol/titanium isopropoxide</td><td>2933</td><td>0.8</td><td>-</td><td>0.5</td><td>-</td><td>-</td><td>-5.0a</td><td>0.5a</td><td>0.94</td><td>[245]</td></tr><tr><td>Filter paper</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>2.2</td><td>-</td><td>22.6</td><td>8.8</td><td>-</td><td>-</td><td>-1.49</td><td>0.543</td><td>0.76</td><td>[241]</td></tr><tr><td>Facial tissue</td><td>Amorphous carbon</td><td>-</td><td>Carboxymethyl cellulose</td><td>3.2</td><td>-</td><td>23.4</td><td>8.3</td><td>-</td><td>-</td><td>-1.57</td><td>0.531</td><td>0.75</td><td>[241]</td></tr><tr><td>Waste carton</td><td>Porous carbon</td><td>-</td><td>ZrO2</td><td>824</td><td>0.7</td><td>16.7</td><td>13.1</td><td>-</td><td>-</td><td>-1.9a</td><td>0.660</td><td>0.90</td><td>[182]</td></tr><tr><td>Table sugar</td><td>Carbon materiala</td><td>-</td><td>Polyvinylidene difluoride</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.81</td><td>[184]</td></tr><tr><td>Sucrose</td><td>Carbon materiala</td><td>-</td><td>Polyvinylidene difluoride</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.01</td><td>[184]</td></tr><tr><td>Humic acid</td><td>Carbon material</td><td>-</td><td>Ethyl cellulose/terpineol</td><td>-</td><td>-</td><td>10.1</td><td>11.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.86</td><td>[247]</td></tr><tr><td>Ovalbumin</td><td>N-doped carbon aerogel</td><td>-</td><td>Oleylamine</td><td>158</td><td>-</td><td>17.6</td><td>0.83</td><td>1.4</td><td>-</td><td>-</td><td>-</td><td>0.87</td><td>[248]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon</td><td>FeTa2O6</td><td>ZrO2</td><td>-</td><td>-</td><td>7.0</td><td>12.9</td><td>-</td><td>-</td><td>-4.5a</td><td>0.281</td><td>1.08</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon</td><td>CoTa2O6</td><td>ZrO2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-3.0a</td><td>0.262</td><td>1.07</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Spherical carbon</td><td>ZrO2/CuTa10O26</td><td>ZrO2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-2.5a</td><td>0.351</td><td>1.03</td><td>[175]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>ZnNb2O6</td><td>ZrO2</td><td>140</td><td>-</td><td>12.8</td><td>6.5</td><td>-</td><td>4.7</td><td>-3.7</td><td>0.456</td><td>1.24</td><td>[176]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>MnWO4</td><td>ZrO2</td><td>-</td><td>-</td><td>12.8</td><td>2.6</td><td>-</td><td>-</td><td>-2.0</td><td>0.563</td><td>1.04</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>ZnWO4</td><td>ZrO2</td><td>-</td><td>-</td><td>11.6</td><td>1.7</td><td>-</td><td>-</td><td>-2.0</td><td>0.424</td><td>1.08</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>CuWO4</td><td>ZrO2</td><td>-</td><td>-</td><td>16.6</td><td>6.2</td><td>-</td><td>-</td><td>-1.6</td><td>0.581</td><td>0.93</td><td>[177]</td></tr><tr><td>Aloe peel</td><td>3D network carbon</td><td>ZnMoO4</td><td>ZrO2</td><td>-</td><td>-</td><td>11.4</td><td>0.7</td><td>-</td><td>-</td><td>-1.8</td><td>0.435</td><td>1.14</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>3D network carbon</td><td>Cu2Mo3O9</td><td>ZrO2</td><td>-</td><td>-</td><td>10.6</td><td>1.4</td><td>-</td><td>-</td><td>-1.5</td><td>0.706</td><td>1.09</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>3D network carbon</td><td>MnMoO4</td><td>ZrO2</td><td>-</td><td>-</td><td>11.2</td><td>2.2</td><td>-</td><td>-</td><td>-1.0</td><td>0.784</td><td>1.03</td><td>[178]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>MnO2</td><td>ZrO2</td><td>632</td><td>0.4</td><td>13.2</td><td>10.1</td><td>-</td><td>-</td><td>-2.2</td><td>0.460</td><td>0.95</td><td>[179]</td></tr><tr><td>Aloe peel</td><td>Porous carbon</td><td>Co/MnO2</td><td>ZrO2</td><td>661</td><td>0.4</td><td>19.8</td><td>1.1</td><td>-</td><td>-</td><td>-2.3</td><td>0.480</td><td>1.09</td><td>[179]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon</td><td>NiTa2O6</td><td>ZrO2</td><td>-</td><td>-</td><td>13.4</td><td>1.6</td><td>-</td><td>-</td><td>-2.3</td><td>0.436</td><td>1.04</td><td>[180]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon</td><td>MnTa2O6</td><td>ZrO2</td><td>-</td><td>-</td><td>11.5</td><td>1.2</td><td>-</td><td>-</td><td>-2.5</td><td>0.394</td><td>1.09</td><td>[180]</td></tr><tr><td>Aloe peel</td><td>Honeycomb porous carbon</td><td>AlTaO4</td><td>ZrO2</td><td>-</td><td>-</td><td>10.7</td><td>0.7</td><td>-</td><td>-</td><td>-2.8</td><td>0.398</td><td>1.16</td><td>[180]</td></tr><tr><td>Bagasse</td><td>Carbon material</td><td>Nitrogen</td><td>Polyvinyl pyrrolidone</td><td>29.0</td><td>-</td><td>8.8</td><td>28.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.41</td><td>[171]</td></tr><tr><td>Bagasse</td><td>Carbon material</td><td>Pt NPs</td><td>Polyvinyl pyrrolidone</td><td>56.3</td><td>-</td><td>9.6</td><td>7.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.61</td><td>[171]</td></tr><tr><td>Bagasse</td><td>Carbon material</td><td>Nitrogen/Pt NPs</td><td>Polyvinyl pyrrolidone</td><td>90.0</td><td>-</td><td>5.3</td><td>1.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.15</td><td>[171]</td></tr><tr><td>Kelp</td><td>N, S, P-tri-doped carbon</td><td>Co NPs</td><td>-</td><td>142</td><td>0.1</td><td>37.3</td><td>0.9</td><td>96.7</td><td>-</td><td>-0.8a</td><td>0.3a</td><td>0.98</td><td>[244]</td></tr><tr><td>Orange fiber</td><td>Carbon material</td><td>CoS nanoflakes</td><td>Ethylene glycol-terpineol</td><td>9.9</td><td>-</td><td>31.8</td><td>36.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.07</td><td>[185]</td></tr><tr><td>Waste carton</td><td>Porous carbon</td><td>WC</td><td>ZrO2</td><td>-</td><td>-</td><td>17.1</td><td>7.1</td><td>-</td><td>-</td><td>-1.8a</td><td>-</td><td>0.97</td><td>[182]</td></tr><tr><td>Humic acid</td><td>Carbon material</td><td>Ni</td><td>Ethyl cellulose/terpineol</td><td>-</td><td>-</td><td>9.1</td><td>7.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.99</td><td>[247]</td></tr><tr><td>Rice husk</td><td>Activated carbon</td><td>Acetylene black</td><td>Ethyl cellulose</td><td>200</td><td>-</td><td>16.0</td><td>3.4</td><td>-</td><td>30.0</td><td>-2.8</td><td>0.692</td><td>0.91</td><td>[235]</td></tr><tr><td>Rice husk</td><td>Nano-Si@ACs</td><td>Acetylene black</td><td>Ethyl cellulose</td><td>240</td><td>-</td><td>15.9</td><td>2.1</td><td>-</td><td>27.9</td><td>-4.2</td><td>0.426</td><td>1.11</td><td>[235]</td></tr><tr><td>Mangosteen peel</td><td>Carbon material</td><td>PEDOT:PSS</td><td>-</td><td>125</td><td>-</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-</td><td>1.14</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 8 (continued) \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[823,916,936,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(continued on next page) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,44,156,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[816,44,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[492,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"22 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,80,937,301]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0941/6a51d28d61368a1e9c99346e8402d434c3f56627e61c4b51d221b712b27ad615.jpg\",\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Source</td><td>Extracted counter electrode material</td><td>Additive and/or modifier</td><td>Binder or Adhesive</td><td>SBET(m2g-1)</td><td>Pore volume (cm3g-1)</td><td>Rs(Ω cm2)</td><td>Rct(Ω cm2)</td><td>Cd(μF cm2)</td><td>Zw(Ω cm2)</td><td>Ip(mA cm-2)</td><td>Epp(V)</td><td>ηrel</td><td>Reference</td></tr><tr><td>Mangosteen peel</td><td>Carbon material</td><td>PEDOT:PSS</td><td>-</td><td>125</td><td>-</td><td></td><td></td><td></td><td></td><td></td><td>-</td><td>1.79</td><td>[167]</td></tr><tr><td>Pine cone flower</td><td>Honeycomb-like activated porous carbon</td><td>Carbon black</td><td>Polyvinylidene fluoride</td><td>1598</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-3.0</td><td>-</td><td>0.80</td><td>[239]</td></tr><tr><td>Fallen leaves</td><td>Honeycomb porous carbon</td><td>Carbon black</td><td>Polyvinylidene fluoride</td><td>2196</td><td>1.7</td><td>-</td><td>25.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.84</td><td>[240]</td></tr><tr><td>Sunflower stalk</td><td>Layered activated carbon</td><td>Acetylene black</td><td>Polytetrafluoroethylene</td><td>1505</td><td>0.9</td><td>18.4</td><td>7.8</td><td>-</td><td>-</td><td>-2.5a</td><td>0.3a</td><td>0.91</td><td>[173]</td></tr><tr><td>Human hair</td><td>Carbon material</td><td>PEDOT:PSS</td><td>-</td><td>188</td><td>-</td><td>16.7</td><td>7.1</td><td>-</td><td>-</td><td>-0.9a</td><td>0.3a</td><td>0.90</td><td>[246]</td></tr><tr><td>Ground coffee waste</td><td>N-doped porous carbon</td><td>Nafion</td><td>-</td><td>1200</td><td>-</td><td>6.1</td><td>0.5</td><td>5174.0</td><td></td><td></td><td></td><td>1.03</td><td>[188]</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 8 (continued) \\\"]\",\n \"table_footnote\": \"[\\\"a Approximate value taken from the relevant figures in the articles. \\\",\\\"b Taken from ref. [174]. \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[57,353,485,445]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"[166]. However, all the other experiments made use of $\\\\mathrm{TiO_2}$ as a photoanode. The preparation of the photoanode may also contribute to DSSC performance since the prepared photoanode varied commercially-prepared $\\\\mathrm{TiO_2}$ to the controlled morphology-synthesized $\\\\mathrm{TiO_2}$ . The effects of $\\\\mathrm{TiO_2}$ morphology are not included in the current discussion since most research did not include the characterization of the $\\\\mathrm{TiO_2}$ electrode. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,446,485,538]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The table shows that the poorest PCE is achieved by the devices that used natural dyes as a sensitizer [167, 168], with PCE $< 2\\\\%$ , regardless of the electrolyte. On the other hand, the highest PCE was obtained using the $\\\\mathrm{Co(bpy)_3^{3 + / 2 + }}$ redox couple electrolyte and Zn-based SM-315 [166], with $12.23\\\\%$ which appears to be higher than the average PCE listed in Table 7. The PCE of this DSSC arrangement correlates with the highest PCE for the $\\\\mathrm{Co(bpy)_3^{3 + / 2 + } / SM - 315}$ electrolyte/dye pair of $13\\\\%$ [169]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,539,487,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Pt-based devices with standard $\\\\mathrm{I}_3 / \\\\mathrm{I}^-$ redox couple electrolytes with inorganic iodide and/or imidazolium iodide, either with or without additive, have PCE ranges of 4.02 and $9.41\\\\%$ respectively. It is worth reiterating that close comparisons of DSSC performance for studied literature have not been found, even if the devices employ the same set of electrolytes and dyes. For example, the highest PCE of $9.41\\\\%$ was obtained with $\\\\mathrm{LiI / I_2 / 1}$ 2-dimethyl-3-propyl imidazolium iodide/4-tert-butylpyridine in acetonitrile electrolyte without both guanidium thiocyanate additive and N719 dye as in Ref. [170]. However, DSSCs with similar electrolytes and dyes performed worse with a PCE of $6.08\\\\%$ [171]. In contrast, $V_{oc}$ of the two devices are comparable, as $J_{sc}$ and $FF$ differ significantly. This could benefit the $\\\\mathrm{TiO_2}$ photoanode, which has a larger surface area or porosity, allowing light to scatter. This, in turn, enhances the light-harvesting efficiency compared to top-down $\\\\mathrm{TiO_2}$ photoanode synthesis from the commercial precursor in [170]. Efficient light harvesting by using light scattering in the photoanode is a way to increase the $J_{sc}$ of the DSSC [172]. Different PCE results may appear from the same research group even if the same photoanode, dye, electrolyte, and counter electrode preparation are used. The Yun research group from Xi'an University of Architecture and Technology published a set of works on DSSCs with similar experimental methodologies [173, 174, 175, 176, 177, 178, 179, 180, 181, 182]. The works consistently utilized a \\\"complete\\\" set of electrolytes where inorganic iodide salt (LiI), imidazolium salt (1-butyl-3-methylimidazolium iodide), and additives (4-tert-butyl pyridine and guanidinium thiocyanate) with acetonitrile were used as the solvent, and N719 was used as the dye. This resulted in the PCEs of the Pt-based DSSCs in the range of 6.34 and $7.19\\\\%$ . These values obtained may be caused by experimental random error due to uncertainties in the measurement. The average value deviation obtained was $6.5\\\\%$ , which was small enough for the PCE values of the platinum-based DSSC \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,353,937,445]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"devices to be classified as accurate. It is also evident that electrolytes with only inorganic iodide without the imidazolium iodide salt and additives yielded a less satisfactory device performance than the more sophisticated electrolytes. Madhu et al. utilized $\\\\mathrm{KI} / \\\\mathrm{I}_2$ in ethylene glycol in conjunction with N719 dye for a DSSC with a Pt-counter electrode. The attained PCE of the Pt-based DSSC was $4.04\\\\%$ which was lower than the average value [183]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,446,937,588]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The performance of natural product-based counter electrodes can be briefly compared with platinum-based electrodes. From the same sources, it is stated that both the $V_{oc}$ between natural product-based counter electrodes and Pt-based electrodes are generally comparable, with differences of less than $100\\\\mathrm{mV}$ . The photovoltaic efficiency of the DSSC is mainly affected by $J_{sc}$ and $FF$ values. Improvement in $J_{sc}$ and $FF$ are considered to play a vital role in DSSC performance. Both the $J_{sc}$ and $FF$ values can be improved by enhancing the electrocatalytic activities of the counter electrodes. This can be achieved by modifying the structural and electronic properties of the electrodes, as described in the next section. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,614,929,639]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.3. The relationship between the structure and performance of the counter electrode \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,653,937,693]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To compare the performance of natural product-based electrodes with platinum-based electrodes under the same experimental conditions for each study, let us define the relative DSSC PCE as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,703,937,728]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\eta_ {r e l} = \\\\frac {\\\\eta_ {N P}}{\\\\eta_ {P t}} \\\\tag {3}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,738,937,896]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\eta_{rel}$ , $\\\\eta_{NP}$ , and $\\\\eta_{Pt}$ are the relative frequency, PCE of the natural product-based DSSC, and PCE of the platinum-based DSSC, respectively. If the value is below 1, the natural product-based DSSCs underperform those of the platinum-based DSSCs. In contrast, if the value is equal to or larger than 1, the natural product-based DSSCs perform qualitatively better than the platinum-based DSSCs. However, as previously mentioned, due to experimental uncertainties, $\\\\eta_{rel}$ between 0.90 and 1.10 may have error uncertainties. Therefore, this range of the $\\\\eta_{rel}$ values cannot be used to conclude whether the natural product-based DSSCs performed better or worse than the platinum counterpart. Nevertheless, DSSCs with an $\\\\eta_{rel}$ value below 0.7 suggested that they performed worse than their platinum counterparts since the absolute PCE was below $3\\\\%$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,896,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The important electrochemical properties of the counter electrode are the series resistance $(R_{s})$ , charge transfer resistance $(R_{ct})$ , double layer capacitance $(C_d)$ , and Nernst diffusion impedance $(Z_w)$ . These values can \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,42,157,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,65,485,264]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"be obtained from the electrochemical impedance spectra (EIS) technique. A smaller $R_{ct}$ value indicates a higher electrocatalytic activity of $\\\\mathrm{I}_3$ reduction. $C_d$ affects the surface area of the counter electrode, and $Z_w$ influences the diffusion velocity of the redox couple in the electrolyte. A higher surface area contributes to a larger $C_d$ , while a faster diffusion rate causes $Z_w$ to decrease. Other parameters, peak current density $(I_p)$ and peak-to-peak separation $(E_{pp})$ , are used to evaluate the catalytic performance of a counter electrode. Both of these can be determined by using the cyclic voltammetry method. Although the current high-performance DSSC devices use $\\\\mathrm{Co}^{3+ / 2+}$ as a redox couple, most DSSCs still utilize $\\\\mathrm{I}_3 / \\\\mathrm{I}^-$ for their economic benefits. Therefore, the discussion will be focused on the $\\\\mathrm{I}_3$ reduction ability of the counter electrode. The electrochemical properties of the counter electrode are generally related to the structural properties. These are mainly determined by the BET surface area and the pore size. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,264,485,382]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To fabricate natural product-based electrodes, some additional components are usually incorporated. Since amorphous, disordered, and porous carbon materials are known for their poor adhesion to FTO [62], additional binder or adhesive materials must be incorporated. Additionally, amorphous carbon is also known for its low conductivity; thus, conducting material can also be incorporated into the counter electrode. However, not all of the works in the literature employed additional conducting materials since the extracted materials are not necessarily amorphous carbon materials but rather various morphologies of carbon. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,383,485,527]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Table 8 lists the electrocatalytic properties of natural product-based materials and their available surface area and total pore volume. Since not all electrochemical data are available in the literature, we can take several examples of natural product-based materials and discuss their electrochemical properties. Nevertheless, the main performance concern remains the PCE, which we defined here as the $\\\\eta_{rel}$ that are available throughout the literature. It is also clear that from the extraction of natural product materials and the optional modifications to the fabrication of counter electrodes, some structural properties can be altered due to treatment methods (i.e., spin coating or doctor blade method). For instance, the material's BET surface and pore size are determined before \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,65,937,117]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"counter electrode fabrication. In contrast, the electrochemical and electrocatalytic properties are determined at the counter electrode stage. Nevertheless, the changes in the structural properties may be neglected. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,118,937,302]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"First, let us discuss the DSSC based on the counter electrode materials without any intended chemical additives and/or modifications. These materials span from amorphous inactivated carbon to N, P, and S tridoped activated porous carbon. In this category, the poorest DSSC performance $\\\\eta_{rel}$ is 0.01 with an absolute PCE of $0.04\\\\%$ obtained by the carbon material from sucrose-based DSSC [184] while the best performance is obtained by the N and S codoped activated porous carbon from an anchovy-based DSSC with $\\\\eta_{rel}$ of 1.04 and absolute PCE of $12.73\\\\%$ [166]. However, it should be noted that the best DSSC that falls within this category employs the $\\\\mathrm{Co}^{3 + / 2 + }$ redox couple electrolyte, which indeed gives better DSSC performance than the $\\\\mathrm{I}_3 / \\\\mathrm{I}^-$ based electrolyte [169]. The other fish-based DSSCs, namely, N, P, and S tridoped activated porous carbon-based DSSCs also exhibit a remarkably high $\\\\eta_{rel}$ of 0.94 and absolute PCE of $7.83\\\\%$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,303,937,500]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The relationship between the structural properties can be discussed in terms of the surface area and total pore volume of the electrode and the electrochemical properties of the electrode. The surface areas of natural product materials span from 2 to ca. $3000\\\\mathrm{m}^2\\\\mathrm{g}^{-1}$ . Interestingly, the materials with a relatively high BET surface area, i.e., $>800\\\\mathrm{m}^2\\\\mathrm{g}^{-1}$ , exhibit excellent PCE efficiency compared to the materials with lower surface areas. This is due to more $\\\\mathrm{I}_3$ that can adsorb on the counter electrode surface and pores, as illustrated in Figure 8. The electron transfer efficiency on the electrode/electrolyte interface can be deduced from the $R_{ct}$ values. For the most efficient electron transfer process, the $R_{ct}$ value must be small. As seen from Figure 9, a high electrode surface corresponds to a low $R_{ct}$ , which is below $14\\\\Omega\\\\mathrm{cm}^2$ . This leads to the $\\\\eta_{rel}$ values being larger than 0.9 or absolute PCE values larger than $7.0\\\\%$ . As expected, the counter electrode material with a low surface exhibits worse DSSC performance than the Pt-based DSSC. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,501,937,527]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The presence of heteroatoms from the biomass source in the final product materials can also enhance the DSSC performance. The perfor \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[188,554,811,914]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 8. Illustration of the interactions between $\\\\\\\\mathrm{I}_3$ with porous carbon counter electrode. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0128/11f3e21a4ba22d9aedb2db2f230b6115d1ec4830b021970cd09be74df25dc725.jpg\",\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[58,42,157,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"24 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[211,68,791,374]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 9. Distribution of $\\\\\\\\eta_{\\\\\\\\mathrm{rel}}$ and $R_{\\\\\\\\mathrm{ct}}$ with correlation to $S_{\\\\\\\\mathrm{BET}}$ of the natural product-based counter electrode without additive. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0285/24e6511a3652e7f3850285c995590f3750451c61364da30d632560b3b552f8f7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[60,424,484,515]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"mance can be seen by the high $\\\\eta_{rel}$ of N, P, and S tridoped activated porous carbon from fish and N-doped carbon aerogel from ovalbumin, which is close to 1. The latter possesses a relatively lower BET surface area of $150\\\\mathrm{m}^2\\\\mathrm{g}^{-1}$ . The lone pair electrons of the heteroatoms can serve as electron donors to accelerate $\\\\mathrm{I}_3$ reduction. Additionally, the doped atoms in the carbon structure can induce defects, increasing the ion-accessible surface area. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,517,485,677]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The efficiency of the electrocatalytic activities of the counter electrode can also be determined by the peak current density $(I_{p})$ and peak-to-peak separation $(E_{pp})$ values from the cyclic voltammetry experiment. However, most of the results are presented as qualitative instead of quantitative. The exact values are determined by parameters such as scan rate and electrolyte, among other similar parameters. For instance, the values are always compared to the Pt-based counter electrode. The more negative the $I_{p}$ value is, the smoother the reduction reaction at the electrolyte/electrolyte interface. The same applies to $E_{pp}$ , where a smaller $E_{pp}$ value implies that the electrocatalytic activity is better. In all cases, the natural product-based electrodes have $\\\\eta_{rel}$ values close to 1, and $I_{p}$ and $E_{pp}$ values close to those of Pt-based electrodes. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,678,485,887]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Next, we discuss the counter electrode with intended modifications. The modifications include the incorporation of conducting materials and/or incorporation of more active catalytic materials. As seen from Table 3, generally, the natural product/composite materials exhibit excellent $\\\\eta_{rel}$ compared to natural product materials with significantly lower $R_{ct}$ values compared to naturally-produced electrode materials. As an example, carbon material from orange fiber incorporated with CoS nanoparticles exhibits a $\\\\eta_{rel}$ of 1.07 and PCE of $5.94\\\\%$ , with a lower BET surface of ca. $10\\\\mathrm{m}^2\\\\mathrm{g}^{-1}$ [185]. The PCE value can be explained by the enhanced electrocatalytic activities of $\\\\mathrm{Co_xS_y}$ compounds. Such is the case, as different phases of cobalt sulfide have been investigated as an excellent oxygen evolution reaction (OER) electrocatalysts due to the overpotential for the OER [186]. For this reason, it can be confirmed that $\\\\mathrm{Co_xS_y}$ plays a vital role in the enhanced electrocatalytic activity of $\\\\mathrm{I}_3$ reduction instead of the orange fiber carbonaceous material because the carbonaceous material is able to exhibit a low BET surface. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,889,484,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A similar enhancement of the counter electrode electrocatalytic activity is also achieved by porous carbon/metal oxide composite materials. The Yun research group from Xi'an University of Architecture and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,424,936,609]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Technology published a set of works on natural products and waste-based counter electrodes with various metal oxides and a metal carbide [173, 174, 175, 176, 177, 178, 179, 180, 181, 182]. Most of the works employed aloe peel as the source of biomass. Even without any inorganic materials, the resulting porous materials from aloe peel achieved remarkably excellent DSSC performance. A better DSSC performance can be achieved by incorporating inorganic compounds as inorganic materials can be well dispersed throughout porous carbon materials. As noted by the authors, the oxide enhances the catalytic activities since the band alignment of the inorganic materials matches those of the $\\\\mathrm{I}_3$ reduction potential. Combining the high surface area of the porous carbon material with the excellent electronic properties of the inorganic materials is proven to decrease the $R_{ct}$ values to below $5\\\\Omega \\\\mathrm{cm}^2$ . Therefore, inorganic materials and natural product-based materials have synergistic effects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,610,936,713]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The second class of additives is conducting materials. These additive materials include Nafion, PEDOT:PSS, and acetylene/carbon black. Nafion and PEDOT:PSS are well-known conducting polymers containing sulfonic acid functional groups that can act as proton conductors. The conducting polymer can also serve as the binder of the counter electrode material to the FTO glass. Yeh et al. proposed that the interactions between Nafion and electrode materials are due to their hydrophobic interactions [187]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,718,936,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It may be better to introduce a functional group to the carbonaceous material of the counter electrode material. An alternative would be to extract the chemically functionalized carbonaceous materials, as shown in Ref. [188] for Nafion additives/binders. The incorporation of Nafion into the counter electrode is proven to enhance the PCE of the DSSC, as in the work of Yeh et al. [187]. Yeh et al. compared the performance of graphene with graphene/Nafion-based DSSCs. Incorporating Nafion into the graphene counter electrode is proven to increase the PCE from 4.58 to $7.69\\\\%$ . Chung et al. extracted N-doped porous carbon from ground coffee waste combined with Nafion for DSSC counter electrodes [188]. Owing to the large surface area of the porous carbon, increasing the ion-accessible surface area due to the doped nitrogen, the PCE reaches as high as $8.32\\\\%$ with a $\\\\eta_{rel}$ of 1.03, meaning that the N-doped porous carbon has a comparable efficiency with the Pt electrode, which is also consistent with the electrocatalytic properties of the material with a very low $R_{ct}$ of $0.5\\\\Omega\\\\mathrm{cm}^2$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,42,154,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[816,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[492,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"25 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[58,66,406,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.4. Remarks on natural carbon for dye-sensitized solar cells \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,92,485,185]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Carbon, as an abundant material, has great potential to be developed and become desirable counter-electrode for DSSC. A replacement for platinum is needed for DSSC production. Research trends on carbon utilization for DSSC counter electrodes are still growing and show impressive performance improvements; for example, the modification of carbon into porous carbon with a large surface area or other modifications to increase the catalytic performance toward the redox couple species. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,197,470,211]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5. Green synthesis metal oxide semiconductor for photoanodes \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,224,485,384]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\mathrm{ZnO}$ and $\\\\mathrm{TiO_2}$ are the most common semiconductors that are used in DSSCs. Generally, the semiconductor provides the surface for dye adsorption, collecting electrons from the excited dye and conducting the electrons toward the external circuit [1, 2, 3]. The synthesis of metal and metal oxide nanoparticles using green biological methods is a preferred synthesis method compared to physical and chemical methods. Green methods are cost-effective, environmentally friendly, and easily processed. Based on our records, the use of green-synthesized $\\\\mathrm{ZnO}$ or $\\\\mathrm{TiO_2}$ for DSSC applications is still limited; however, a recent study shows that green synthesis can facilitate the desired oxide particle structure and shape for DSSC applications [189]. Below we review various methods for the preparation of $\\\\mathrm{ZnO}$ and $\\\\mathrm{TiO_2}$ through a green approach. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,395,295,409]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5.1. Synthesis of ZnO using plant extract \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,422,485,566]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Anbuvannan et al. synthesized ZnO nanoparticles using Anisochilus carnosus leaf extract. Zinc nitrate as a precursor was added to the leaf extract at $60^{\\\\circ}\\\\mathrm{C}$ . The mixture was subsequently boiled for $20\\\\mathrm{min}$ until the color became dark yellow. The obtained paste was annealed at $400^{\\\\circ}\\\\mathrm{C}$ for two hours to obtain ZnO nanoparticles. The morphology and size of the obtained ZnO were confirmed by TEM. It was revealed that a majority of the ZnO nanoparticles were quasi-spherical with sizes ranging from 30 to $40\\\\mathrm{nm}$ . The photocatalytic performance showed that it enhanced the degradation of methylene blue under UV irradiation. Green-synthesized ZnO exhibited potential antibacterial properties against several pathogens [190]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,567,485,711]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ZnO nanoparticles may also be synthesized using aqueous Cassia fistula plant extract. The Cassia fistula plant extract was used as a fuel obtained by the solution combustion method. $\\\\mathrm{Zn(NO_3)_3\\\\cdot 6H_2O}$ was dissolved in the aqueous plant extract. The mixture was kept in a preheated muffle furnace at $400^{\\\\circ}\\\\mathrm{C}$ for approximately five minutes. Based on the TEM image, the particles consisted of many agglomerated particles and sponges in a form similar to irregularly shaped particles with an average crystallite size of $5 - 15\\\\mathrm{nm}$ . The obtained ZnO nanoparticles showed adequate performance in methylene blue dye under sunlight and UV illumination, in addition to displaying significant antioxidant properties [191]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,712,485,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The same solution combustion method was applied to green-synthesized $\\\\mathrm{ZnO}$ nanoparticles using an aqueous extract of Abutilon indicum. Zinc nitrate hexahydrate $(\\\\mathrm{Zn(NO_3)_2\\\\cdot 6H_2O})$ was mixed with the aqueous extract. After constant stirring for $2 - 5\\\\mathrm{min}$ , the mixture was kept in a preheated muffle furnace at a temperature of $200\\\\pm 5^{\\\\circ}\\\\mathrm{C}$ for $2 - 3\\\\mathrm{min}$ . After being filtered and rinsed, the $\\\\mathrm{ZnO}$ nanoparticles were calcined for two hours. The obtained $\\\\mathrm{ZnO}$ nanoparticles were homogeneous and equally distributed over the surface with a grain size of $16.72\\\\mathrm{nm}$ and bandgap energy of $3.37\\\\mathrm{eV}$ . The obtained $\\\\mathrm{ZnO}$ nanoparticles demonstrated effective performance in degrading Acid Black 234. $\\\\mathrm{ZnO}$ nanoparticles also display antioxidant and anticancer properties [192]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,857,485,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Another work carried out by Thema et al. was to synthesize ZnO nanoparticles using Agathosma betulina plant extract. Zinc nitrate hexahydrate $(\\\\mathrm{Zn(NO_3)_2\\\\cdot 6H_2O})$ , which was used as a zinc precursor, was mixed with the leaf extract and heated at $100^{\\\\circ}\\\\mathrm{C}$ for two hours. The obtained precipitate was washed, dried, and annealed at various temperatures from $100 - 500^{\\\\circ}C$ for two hours. It was found that $500^{\\\\circ}C$ was \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,65,937,129]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the optimal temperature for obtaining highly crystalline $\\\\mathrm{ZnO}$ nanocrystals. The HRTEM image shows that the optimized sample consisted of quasi-spherical agglomerated nanoscale particles with diameters ranging from 12 to $26\\\\mathrm{nm}$ . That nanoparticle exhibited a good varistor response [193]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,131,937,276]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ZnO nanoparticles were successfully synthesized using Carica papaya leaf extract and applied for photocatalytic and photovoltaic applications. The papaya leaf extract was added to a zinc acetate dihydrate solution at $60^{\\\\circ}\\\\mathrm{C}$ and $\\\\mathrm{pH}8$ before being stirred for two hours to synthesize ZnO nanoparticles. The washed precipitate was subsequently dried at $80^{\\\\circ}\\\\mathrm{C}$ for $12\\\\mathrm{h}$ . The synthesized ZnO nanoparticles had a pristine hexagonal wurtzite structure inside spheres with a diameter of approximately 50 nm. The photoactivity results revealed that ZnO nanoparticles completely degraded methylene blue dye within $180\\\\mathrm{min}$ under UV irradiation while showing an energy conversion efficiency of $1.6\\\\%$ and a current density of $81\\\\mathrm{mAcm}^{-2}$ [194]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,276,937,448]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Most research shows that green-synthesized $\\\\mathrm{ZnO}$ nanoparticles obtained nanoparticles in a spherical shape. However, several researchers reported that $\\\\mathrm{ZnO}$ nanorods could be successfully prepared using a green synthesis approach. Li Fu and Zhuxian Fu synthesized $\\\\mathrm{ZnO}$ nanorods mediated by Plectranthus amboinicus leaf extract. Zinc nitrate was mixed with the leaf extract and stirred at $80^{\\\\circ}\\\\mathrm{C}$ for four hours. The obtained pale white precipitate was centrifuged, washed, and calcined at $200^{\\\\circ}\\\\mathrm{C}$ for one hour. SEM characterization showed that $\\\\mathrm{ZnO}$ nanoparticles had a rod-shaped structure with an average particle size of 88 nm. The photocatalytic activity study revealed that biosynthesized $\\\\mathrm{ZnO}$ had an excellent photocatalytic performance in methyl red degradation under UV irradiation compared to chemically-synthesized $\\\\mathrm{ZnO}$ nanoparticles [195]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,448,937,592]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ZnO nanoparticles with various shapes were successfully synthesized using Phyllanthus niruri leaf extract. Zinc nitrate was added to the boiled leaf extract at $60^{\\\\circ}\\\\mathrm{C}$ after the stem turned yellow. The obtained paste was then calcined at $400^{\\\\circ}\\\\mathrm{C}$ for two hours to obtain a light white-colored powder. FESEM analysis showed that ZnO nanoparticles had rectangular, triangular, radial hexagonal, rod, and spherical shapes with an average size of $25.61\\\\mathrm{nm}$ . Biosynthesized ZnO showed excellent photocatalytic activity for methylene blue reduction and has many potential applications as semiconductor, pyroelectric, piezoelectric, catalyst, and optoelectronic, as well for phytochemical, and pharmacological, and medical purposes [196]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,607,757,620]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5.2. Synthesis of ZnO using microorganism \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,633,937,712]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Aspergillus fumigatus JCF fungi successfully mediated green-synthesized $\\\\mathrm{ZnO}$ nanoparticles. $\\\\mathrm{ZnSO_4}$ was added as a precursor to the fungal filtrate (pH 6.5) and incubated at $72^{\\\\circ}C$ for $72\\\\mathrm{h}$ in an orbital shaker. The obtained white precipitate was centrifuged and lyophilized. SEM images revealed that the prepared $\\\\mathrm{ZnO}$ nanoparticles were spherical with an average size of $60 - 80\\\\mathrm{nm}$ [197]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,712,937,804]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Jayaseelan et al. successfully synthesized ZnO nanoparticles using Aeromonas hydrophilic bacteria. ZnO was added to the bacterial culture solution and incubated at $30^{\\\\circ}\\\\mathrm{C}$ for $24\\\\mathrm{h}$ in a shaker incubator. After being cooled and incubated at room temperature for approximately $12 - 48\\\\mathrm{h}$ , white deposits were collected. The obtained ZnO nanoparticles were smooth and had a spherical shape. This suggests that it has significant antibacterial and antifungal properties [198]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,805,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Another green synthesis method to prepare ZnO nanoparticles is by using the yeast strain Pichia kudriavzevii, a method that was successfully carried out by Moghaddam et al. Zinc acetate dihydrate $(\\\\mathrm{Zn}(\\\\mathrm{CH}_3\\\\mathrm{COO})_2\\\\cdot 2\\\\mathrm{H}_2\\\\mathrm{O})$ was mixed with fungal cell-free filtrate and incubated at $35^{\\\\circ}\\\\mathrm{C}$ in a shaking incubator and agitated for 12, 24, and $36\\\\mathrm{h}$ . The obtained white precipitate was centrifuged and dried at $150^{\\\\circ}\\\\mathrm{C}$ for six hours. The results from TEM analysis showed that the average particle sizes were $10\\\\pm 2.08$ , $32\\\\pm 4.7$ , and $59\\\\pm 10.6\\\\mathrm{nm}$ for incubation times of 12, 24, and $36\\\\mathrm{h}$ , respectively. It was observed that the ZnO nanoparticles tended to agglomerate due to high surface energy [199]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,42,157,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"26 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[58,65,299,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5.3. Synthesis of $\\\\mathrm{TiO_2}$ using plant extract \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,90,485,235]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\mathrm{TiO_2}$ nanoparticles were synthesized by Goutam et al. using a leaf extract of Jatropha curcas L [200]. Titanium chloride $(\\\\mathrm{TiCl}_4)$ was used as a precursor. $80~\\\\mathrm{mL}$ of $0.5\\\\mathrm{M}$ $\\\\mathrm{TiCl_4}$ was added to $80~\\\\mathrm{mL}$ of filtered leaf extract at a ratio of 1:1 (v/v) with continuous stirring for $20\\\\mathrm{min}$ at room temperature. After adding an ammonia solution, the precipitates were separated, washed, dried, and calcined at $450^{\\\\circ}\\\\mathrm{C}$ for three hours. The obtained $\\\\mathrm{TiO_2}$ nanoparticles were spherical with a diameter ranging from $10 - 20\\\\mathrm{nm}$ [200]. The nanoparticles were later applied for the simultaneous removal of chemical oxygen demand (COD) and chromium (Cr) from secondary treated tannery wastewater (TWW). The results gave removals of 82.26 and $76.48\\\\%$ for COD and Cr, respectively [200]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,237,485,394]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Santhoshkumar et al. synthesized $\\\\mathrm{TiO_2}$ nanoparticles using Psidium guajava aqueous leaf extract, and before being concluded, $\\\\mathrm{TiO_2}$ nanoparticles were efficacious as antibacterial and antioxidant agents. $\\\\mathrm{TiO(OH)_2}$ was used as the precursor. The pure $\\\\mathrm{TiO(OH)_2}$ and aqueous leaf extract were stirred for several hours until the solution turned light green. The synthesized $\\\\mathrm{TiO_2}$ nanoparticles showed a spherical shape and clusters with an average size of $32.58\\\\mathrm{nm}$ $\\\\mathrm{TiO_2}$ nanoparticles exhibited better antibacterial properties when than the standard antibiotic disk. $\\\\mathrm{TiO_2}$ nanoparticles were also advantageous in terms of antibacterial properties compared to tetracycline, with a maximum zone of 25 and 23 mm inhibition when faced against Staphylococcus aureus and Escherichia coli, respectively [201]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,395,485,474]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Patidar et al. prepared $\\\\mathrm{TiO_2}$ nanoparticles using Moringa oleifera leaf extract. Anatase $\\\\mathrm{TiO_2}$ with an average crystallite size of $12.22\\\\mathrm{nm}$ was obtained. As the precursor, titanium tetraisoproxide (TTIP) was mixed with the ethanolic leaf extract and stirred for four hours. After centrifugation and washing, the $\\\\mathrm{TiO_2}$ nanoparticles were dried, ground, and calcined at $500^{\\\\circ}\\\\mathrm{C}$ for approximately five hours [202]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,475,485,645]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Another work of synthesizing $\\\\mathrm{TiO_2}$ using a biosynthesis approach was carried out by Subhapriya S and Gomathipriya P. $\\\\mathrm{TiO_2}$ nanoparticles were synthesized using Trigonella foenum-graecum extract, and their antibacterial properties were studied. The extract was added to titanium oxysulfate for $15\\\\mathrm{min}$ before dropping $1\\\\textrm{M}$ sodium hydroxide into the solution until $\\\\mathrm{pH}8$ was reached. The washed precipitate was calcined at $700^{\\\\circ}\\\\mathrm{C}$ for three hours to obtain crystalline $\\\\mathrm{TiO_2}$ nanoparticles. The obtained $\\\\mathrm{TiO_2}$ nanoparticles had a spherical shape with a size ranging between 20 and $90~\\\\mathrm{nm}$ . It also showed excellent antibacterial properties toward Staphylococcus aureus, Enterococcus faecalis, Klebsiella pneumoniae, Streptococcus faecalis, Pseudomonas aeruginosa, Escherichia coli, Proteus vulgaris, Bacillus subtilis, Yersinia enterocolitica, and the fungus Candida albicans [203]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,646,485,762]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Rajkumari et al. synthesized $\\\\mathrm{TiO_2}$ nanoparticles by using an aqueous leaf extract of Aloe barbadensis. They also studied the antibiofilm potential against Pseudomonas aeruginosa PAO1. In the synthesis procedure, the leaf extract was added by droplets into titanium chloride $(\\\\mathrm{TiCl}_4)$ at pH 7 and stirred for three hours. The washed precipitate was then dried at $100^{\\\\circ}\\\\mathrm{C}$ for seven hours. The obtained $\\\\mathrm{TiO_2}$ nanoparticles had a spherical shape with a size ranging from 20 to $50~\\\\mathrm{nm}$ , as confirmed by SEM and TEM analysis. The biosynthesized $\\\\mathrm{TiO_2}$ nanoparticles were found to exhibit a high antibiofilm efficacy against P.aeruginosa [204]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,764,485,843]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The most recent research was conducted by Senthamarai et. al., [189]. They prepared $\\\\mathrm{TiO_2}$ particle using the pineapple, orange, and grape fruit extracts. The grape extract facilitates the formation of the $\\\\mathrm{TiO_2}$ nanotube structure. As a result, this sample obtained the highest power conversion efficiency (4.33%) in comparison to the other extracts when built as a DSSC device using N4719 as a sensitizer. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,857,294,871]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5.4. Synthesis $\\\\mathrm{TiO}_2$ using microorganism \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,883,485,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\mathrm{TiO_2}$ nanoparticles were successfully synthesized using Aspergillus flavus TFR 7 fungi. First, mycelia were developed from fungal cultivation. The reaped mycelia were resuspended in demineralized water and incubated for $48\\\\mathrm{h}$ at $28^{\\\\circ}\\\\mathrm{C}$ to obtain a cell-free filtrate containing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,65,937,118]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"extracellular enzymes. The filtrate was mixed with titanium precursor salt and incubated at $150~\\\\mathrm{rpm}$ and $28^{\\\\circ}\\\\mathrm{C}$ to obtain $\\\\mathrm{TiO_2}$ nanoparticles. The acquired $\\\\mathrm{TiO_2}$ nanoparticles had an average particle size of approximately $18~\\\\mathrm{nm}$ , as observed by DLS analysis [205]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,118,937,263]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Another work from Khan et al. showed that Bacillus amyloliquefaciens cultivation could be used to synthesize $\\\\mathrm{TiO_2}$ nanoparticles. $\\\\mathrm{TiOSO_4}$ was used as a titanium precursor. It was added to the prepared medium containing cultivated bacteria and incubated for $24\\\\mathrm{h}$ at $37^{\\\\circ}C.$ The gathered white precipitate was centrifuged, washed, and calcined at 500 $^\\\\circ C$ for three hours. The synthesized $\\\\mathrm{TiO_2}$ nanoparticles were spherical with a size ranging from 22.11 to $99.28~\\\\mathrm{nm},$ as observed by TEM analysis. The photocatalytic activity of doped and undoped biosynthesized $\\\\mathrm{TiO_2}$ nanoparticles to degrade the RR31 dye under UV irradiation at room temperature was tested. The results suggested that all samples were capable of degrading a photocatalytic RR31 dye [206]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,263,937,368]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The synthesis of $\\\\mathrm{TiO_2}$ nanoparticles was successfully mediated by baker's yeast (Saccharomyces cerevisiae). A $\\\\mathrm{TiO(OH)_2}$ solution was added to the cultivated yeast solution. Consecutively, it was heated in a steam bath at $60^{\\\\circ}\\\\mathrm{C}$ for $10 - 20\\\\mathrm{min}$ . After being cooled and incubated at room temperature for approximately $12 - 48\\\\mathrm{h}$ , the $\\\\mathrm{TiO_2}$ nanoparticles were found as-deposited white clusters at the bottom of the tube. The obtained $\\\\mathrm{TiO_2}$ nanoparticles were almost spherical at $12.57\\\\pm 0.22\\\\mathrm{nm}$ , as confirmed by TEM [207]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,382,810,395]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5.5. $\\\\mathrm{TiO}_2$ synthesis using aqueous solution approach \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,409,937,525]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Green-synthesized $\\\\mathrm{TiO_2}$ can be achieved using a modified sol-gel method known as the peroxo sol-gel method. In this method, water is used as a solvent instead of organic solvents, and pH 7 is required as a synthesized condition [208, 209]. Gao et al. successfully synthesized micropatterns of $\\\\mathrm{TiO_2}$ thin films using this method. $\\\\mathrm{H}_2\\\\mathrm{TiO}_3$ was used as a titanium precursor, and it was dissolved in a mixture that contained ammonia and $\\\\mathrm{H}_2\\\\mathrm{O}_2$ aqueous solution. The obtained thin film was smooth and crack-free, formed by the coalescence of nanosized particles of 10-20 nm in diameter [208]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,527,937,645]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Thin films of $\\\\mathrm{TiO_2}$ were successfully prepared using this green sol-gel method carried out by Ge et al. Titanium sulfate $(\\\\mathrm{TiOSO_4:nH_2O})$ $\\\\mathrm{H}_2\\\\mathrm{O}_2,$ and ammonia were used as the starting materials. The obtained yellow and transparent PTA solution was used as a coating solution. The $\\\\mathrm{TiO_2}$ -coated substrate was successively calcined at $500^{\\\\circ}\\\\mathrm{C}$ for $30\\\\mathrm{min}$ . SEM analysis showed that the $\\\\mathrm{TiO_2}$ thin film was uniformly comprised of spherical particles with an average particle size of $30 - 40\\\\mathrm{nm}$ . The thin film showed the best photocatalytic activity, reaching $99\\\\%$ methyl orange degradation under $160\\\\mathrm{min}$ of UV irradiation [210]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,646,937,751]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Another green synthesis approach is by using an \\\"aqueous\\\" solution. This chemical method was applied successfully in aqueous electrophoretic deposition. Benehkohal et al. used this method to prepare $\\\\mathrm{TiO_2 - ZnO}$ composite photoanodes for DSSCs. $\\\\mathrm{Zn(NO_3)_2}$ was added to a suspension of $\\\\mathrm{TiO_2}$ powder and an isopropanol-water mixture. Subsequently, the suspension was sonicated for one and a half hours before electrophoretic deposition (EPD). Next, the obtained layer was dried at room temperature and could be used for multiple characterizations [211]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,765,766,778]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5.6. Remarks on green synthesis metal oxide \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,791,937,870]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Oxide semiconductor synthesis through the green synthesis approach has the advantage of controlling the particle size and shape. Among the other green synthesis methods, microorganism synthesis assistance has the most difficulty. The synthesis step is tricky and requires time. Green synthesis using plant extracts seems more promising. The scale-up of this process requires the plantation land planning to supply the resources. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,883,605,896]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6. Conclusion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,910,937,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The synthesis, characterization, and performance of natural product-based DSSCs have been reviewed in depth. Overall, there are some \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,42,157,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,54]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"27 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[57,65,485,118]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"inconsistencies in the DSSC performance across the literature, mainly due to the different types of components used. However, the detailed atomic-level understanding of the electronic process that occurs among the components remains poorly understood and needs to be further explored. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,118,485,210]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Natural dyes need to be modified to obtain a better performance. Most modifications were concerned with improving the electronic properties and the other limitation of natural dyes, including dye stability, dye aggregation, and weak interaction with the oxide semiconductor surface. A computational study is among the best methods to investigate the electronic properties at the molecular level and the charge transport process. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,210,485,316]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Natural biopolymers are promising for the development of quasi-solid DSSCs. The quasi-solid DSSC minimizes the decrease in cell performance due to volatilization issues. The major problem with using natural biopolymers is their low conductivity. The low conductivity issue has been overcome by looking for a suitable redox couple, adding the ionic liquid, or adding another additive. Theoretical and computational studies regarding the charge transfer process in polyelectrolyte gel systems are limited and challenging to explore. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,316,485,419]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Natural carbon-based counter electrodes have become promising candidates for replacing more expensive Pt-based counter electrodes. It appears that a DSSC with a porous carbon-based counter electrode with a large surface area gives a comparable performance to the Pt-based electrode. The low-surface area natural product-based electrode can achieve a remarkably good DSSC performance if the extracted material is combined with electrocatalytically active inorganic and/or conductive materials. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,421,485,619]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"There is always a trade-off between the performance, production cost, and environmental aspects of natural product-based DSSC fabrication. Most of the authors cited in this paper argue that natural products are readily available in the surroundings as wastes or byproducts. One issue regarding the utilization of natural products is their inhomogeneous content, which can bring either benefits or drawbacks to the extraction processes of the intended material and DSSC performances. The impurities contained in the source must be removed using harsh chemicals if necessary. On the other hand, impurities can also benefit DSSC performances. Another issue is the reproducibility of the material extracted from the natural product, where the material obtained can have different structures and properties. Additionally, the choice of the other components has to be taken into account. Therefore, to prepare natural-based DSSCs, parameters such as cost, chemical requirements, and environmental aspects must be considered to achieve proper DSSC performance. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,619,485,698]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, we note that it remains plausible to improve DSSC performance by incorporating natural product-derived materials into DSSC components. If the cost and chemical precursors are not taken into account, we can employ naturally-derived porous carbon and green-synthesized semiconductors in DSSC devices. However, the dyes and electrolytes must still come from commercial products. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,712,144,723]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Declarations \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,738,230,750]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Author contribution statement \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,764,485,790]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"All authors listed have significantly contributed to the development and the writing of this article. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,805,164,815]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Funding statement \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,829,485,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This work was supported by the Ministry of Research and Technology of Republic Indonesia through the PDUPT Scheme (973/PKS/ITS/2021), and by the Faculty of Mathematics and Natural Science (183/J01.1.28/PL.06.02/2021). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,897,213,909]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data availability statement \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[78,923,440,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data included in article/supp. material/referenceed in article. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,66,700,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Declaration of interests statement \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[529,92,784,104]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The authors declare no conflict of interest. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,127,643,139]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Additional information \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[529,153,845,167]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"No additional information is available for this paper. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,180,638,192]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgements \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,206,939,272]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"YK is gratefully to the Ministry of Research and Technology of Republic Indonesia for funding this research through the PDUPT Scheme with contract number 973/PKS/ITS/2021. ASH acknowledges the support from Faculty of Mathematics and Natural Science, University of Gadjah Mada under contract number 183/J01.1.28/PL.06.02/2021. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,288,584,298]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,312,934,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[1] A. Hagfeldt, G. Boschloo, L. Sun, L. Kloo, H. Pettersson, Dye-sensitized solar cells, Chem. Rev. 110 (2010) 6595-6663. \\\",\\\"[2] J. Gong, J. Liang, K. 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Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,507,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"29 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[60,66,482,920]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[76] G. 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Acta 56 (2011) 7347-7351. \\\",\\\"[213] H.L. Hsu, W.T. Hsu, J. Leu, Effects of environmentally benign solvents in the agarose gel electrolytes on dye-sensitized solar cells, Electrochim. Acta 56 (2011) 5904-5909. \\\",\\\"[214] H.L. Hsu, C.F. Tien, Y.T. Yang, J. Leu, Dye-sensitized solar cells based on agarose gel electrolytes using allylimidazolium iodides and environmentally benign solvents, Electrochim. Acta 91 (2013) 208-213. \\\",\\\"[215] Y. Yang, P. Yi, C. Zhou, J. Cui, X. Zheng, S. Xiao, X. Guo, W. Wang, Magnetic field processed solid-state dye-sensitized solar cells with nickel oxide modified agarose electrolyte, J. Power Sources 243 (2013) 919–924. \\\",\\\"[216] H.L. Hsu, C.F. Tien, J. Leu, Effect of pore size/distribution in $\\\\\\\\mathrm{TiO_2}$ films on agarose gel electrolyte-based dye-sensitized solar cells, J. Solid State Electrochem. 18 (2014) 1665-1671. \\\",\\\"[217] R. Singh, B. Bhattacharya, S.K. Tomar, V. Singh, P.K. Singh, Electrical, optical and electrophotochemical studies on agarose based biopolymer electrolyte towards dye sensitized solar cell application, Meas. J. Int. Meas. Confed. 102 (2017) 214-219. \\\",\\\"[218] S. Rudzhiah, A. Ahmad, I. Ahmad, N.S. Mohamed, Biopolymer electrolytes based on blend of kappa-carrageenan and cellulose derivatives for potential application in dye sensitized solar cell, Electrochim. Acta 175 (2015) 162-168. \\\",\\\"[219] S. Che Balian, A. Ahmad, N. Mohamed, The effect of lithium iodide to the properties of carboxymethyl $\\\\\\\\kappa$ -carrageenan/carboxymethyl cellulose polymer electrolyte and dye-sensitized solar cell performance, Polymers (Basel) 8 (2016) 163. \\\",\\\"[220] T. Sugumaran, D.S. Silvaraj, N.M. Saidu, N.K. Farhana, S. Ramesh, K. Ramesh, S. 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Ramesh, Iota-carrageenan-based polymer electrolyte: impact on ionic conductivity with incorporation of AmNTFSI ionic liquid for supercapacitor, Ionics (Kiel). 25 (2019) 3321-3329. \\\",\\\"[233] M.I.H. Sohaimy, M.I.N. Isa, Ionic conductivity and conduction mechanism studies on cellulose based solid polymer electrolytes doped with ammonium carbonate, Polym. Bull. 74 (2017) 1371-1386. \\\",\\\"[234] M. Latifi, A. Ahmad, H. Kaddami, N.H. Hassan, R. Dieden, Y. Habibi, Chemical modification and processing of chitin for sustainable production of biobased electrolytes, Polymers (Basel) 12 (2020) 1-16. \\\",\\\"[235] W. Ahmad, M.R. Al Bahrani, Z. Yang, J. Khan, W. Jing, F. Jiang, L. Chu, N. Liu, L. Li, Y. Gao, Extraction of nano-silicon with activated carbons simultaneously from rice husk and their synergistic catalytic effect in counter electrodes of dyesensitized solar cells, Sci. Rep. 6 (2016) 1-11. \\\",\\\"[236] J. Theerthagiri, R.A. Senthil, P. Arunachalam, J. Madhavan, M.H. Buraidah, A. Santhanam, A.K. Arof, Synthesis of various carbon incorporated flower-like $\\\\\\\\mathrm{MoS}_2$ microspheres as counter electrode for dye-sensitized solar cells, J. Solid State Electrochem. 21 (2017) 581-590. \\\",\\\"[237] V. Loryuenyong, A. Buasri, P. Lerdvilainarit, K. Manachevakulm, S. Sompong, Production of graphitic carbon-based nanocomposites from $\\\\\\\\mathrm{K}_2\\\\\\\\mathrm{CO}_3$ -activated coconut shells as counter electrodes for dye-sensitized solar-cell applications, J. Kor. Phys. Soc. 68 (2016) 317-322. \\\"]\",\n \"page_idx\": \"31\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[60,42,156,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[490,952,507,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"32 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[60,65,482,267]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[238] K.K. Dasari, V. Gumtapure, Activated carbon-based dye-sensitized solar cell for development of highly sensitive temperature and current sensor, Mater. Res. Express 6 (2019), 085531. \\\",\\\"[239] G. Nagaraju, J.H. Lim, S.M. Cha, J.S. Yu, Three-dimensional activated porous carbon with meso/macropore structures derived from fallen pine cone flowers: a low-cost counter electrode material in dye-sensitized solar cells, J. Alloys Compd. 693 (2017) 1297-1304. \\\",\\\"[240] S.M. Cha, G. Nagaraju, S.C. Sekhar, L.K. Bharat, J.S. Yu, Fallen leaves derived honeycomb-like porous carbon as a metal-free and low-cost counter electrode for dye-sensitized solar cells with excellent tri-iodide reduction, J. Colloid Interface Sci. 513 (2018) 843–851. \\\",\\\"[241] S. Xu, C. Liu, J. Wiezorek, 20 renewable biowastes derived carbon materials as green counter electrodes for dye-sensitized solar cells, Mater. Chem. Phys. 204 (2018) 294-304. \\\",\\\"[242] P. Huang, S.J. Xu, M. Zhang, W. Zhong, Z.H. Xiao, Y.P. Luo, Lotus leaf derived natural dye as sensitizer and biochar as counter electrode for dye-sensitized solar cells, Mater. Sci. Forum 993 (2020) 884-892. \\\",\\\"[243] Q.W. Jiang, G.R. Li, F. Wang, X.P. Gao, Highly ordered mesoporous carbon arrays from natural wood materials as counter electrode for dye-sensitized solar cells, Electrochem. Commun. 12 (2010) 924-927. \\\"]\",\n \"page_idx\": \"32\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[512,65,934,235]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[244] D. Wu, C. Zhu, Y. Shi, H. Jing, J. Hu, X. Song, D. Si, S. Liang, C. Hao, Biomass-derived multilayer-graphene-encapsulated cobalt nanoparticles as efficient electrocatalyst for versatile renewable energy applications, ACS Sustain. Chem. Eng. 7 (2019) 1137-1145. \\\",\\\"[245] P. Ma, W. Lu, X. Yan, W. Li, L. Li, Y. Fang, X. Yin, Z. Liu, Y. Lin, Heteroatom tridoped porous carbon derived from waste biomass as Pt-free counter electrode in dye-sensitized solar cells, RSC Adv. 8 (2018) 18427-18433. \\\",\\\"[246] K. Moolsarn, A. Tangtrakarn, A. Pimsawat, K. Duangsa, C. Mongkolkachit, W. Maiaugree, V. Amornkitbamrung, A dye-sensitized solar cell using a composite of PEDOT: PSS and carbon derived from human hair for a counter electrode, Int. J. Photoenergy 2017 (2017). \\\",\\\"[247] Y. Di, S. Jia, N. Li, C. Hao, H. Zhang, S. Hu, Ni-incorporated carbon materials derived from humic acid as efficient low-cost electrocatalysts for dye-sensitized solar cells, Org. Electron. 76 (2020) 105395. \\\",\\\"[248] M. Butt, K. Preuss, M.-M. Titirici, H. Rehman, J. Briscoe, Biomass-derived nitrogen-doped carbon aerogel counter electrodes for dye sensitized solar cells, Materials (Basel) 11 (2018) 1171. \\\"]\",\n \"page_idx\": \"32\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[60,42,156,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y. Kusumawati et al. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[815,42,937,52]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Heliyon 7 (2021) e08436 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[492,952,505,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"33 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1016/j.heliyon.2021.e08436"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Energy and Power Science"},"sha256":{"kind":"string","value":"69a13db1bcc3d2605b6b811dae5809a8e277153d97d333ab1ea37d07161e0825"},"title":{"kind":"string","value":"Natural resources for dye-sensitized solar cells"}}},{"rowIdx":263,"cells":{"abstract":{"kind":"string","value":"\n \nWe accomplish for the first time the next-to-leading-order computation of the weak annihilation contribution to the exclusive electroweak penguin decays $B \\to \\left \\{K, \\pi \\right \\} \\ell^{+} \\ell^{-}$ with an energetic light-flavour meson, which is an essential missing piece of the complete QCD correction to the matrix elements of hadronic operators in the weak effective Hamiltonian. Both the hard functions and the jet functions in the perturbative factorization formulae from the short-distance fluctuations at the two distinct scales $m_b$ and $\\sqrt{m_b \\, \\Lambda}$ are determined at ${\\cal O}(\\alpha_s)$ with the soft-collinear factorization technique. We then demonstrate that the one-loop weak annihilation correction can bring about the noticeable impacts on theory predictions for the CP asymmetries and the isospin asymmetry in the $B \\to \\pi \\ell^{+} \\ell^{-}$ decays.\n "},"author":{"kind":"string","value":"Yue-Long Shen|Yong-Kang Huang|Yu-Ming Wang|Chao Wang"},"content_list":{"kind":"list like","value":[{"bbox":"[84,61,916,83]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Next-to-Leading-Order Weak Annihilation Correction to Rare $B \\to \\{K, \\pi\\} \\ell^{+} \\ell^{-}$ Decays ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[212,95,792,191]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Yong-Kang Huang $^{a}$ , * Yue-Long Shen $^{b,\\dagger}$ , Chao Wang $^{c,\\ddagger}$ and Yu-Ming Wang $^{a\\S}$ $^{a}$ School of Physics, Nankai University, Weijin Road 94, Tianjin 300071, P.R. China $^{b}$ College of Information Science and Engineering, Ocean University of China, Qingdao 266100, Shandong, China $^{c}$ Department of Mathematics and Physics, Huaiyin Institute of Technology, Meicheng East Road 1, Huaian, Jiangsu 223200, P.R. China \n(Dated: March 19, 2024) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[169,210,831,332]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We accomplish for the first time the next-to-leading-order computation of the weak annihilation contribution to the exclusive electroweak penguin decays $B \\to \\{K, \\pi\\} \\ell^{+} \\ell^{-}$ with an energetic light-flavour meson, which is an essential missing piece of the complete QCD correction to the matrix elements of hadronic operators in the weak effective Hamiltonian. Both the hard functions and the jet functions in the perturbative factorization formulae from the short-distance fluctuations at the two distinct scales $m_{b}$ and $\\sqrt{m_b \\Lambda}$ are determined at $\\mathcal{O}(\\alpha_s)$ with the soft-collinear factorization technique. We then demonstrate that the one-loop weak annihilation correction can bring about the noticeable impacts on theory predictions for the CP asymmetries and the isospin asymmetry in the $B \\to \\pi \\ell^{+} \\ell^{-}$ decays. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[212,373,361,386]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"INTRODUCTION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[84,417,488,917]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It is widely recognized that the exclusive electroweak penguin $B$ -meson decays are of extraordinary importance to explore the intricate dynamics of the quark and lepton sectors in the Standard Model (SM) and to probe sensitively the nonstandard effects with clean experimental signatures. The prominent flavour anomalies observed in the flagship semileptonic $b \\rightarrow s\\ell^{+}\\ell^{-}$ decays include the $\\mathcal{O}(4\\sigma)$ deviations of the measured $\\mathcal{BR}(B^{+} \\rightarrow K^{+}\\mu^{+}\\mu^{-})$ in the low- $q^{2}$ bins with respect to the SM predictions and the $\\mathcal{O}(2\\sigma)$ tensions between the LHCb measurements of the angular observable $P_{5}^{\\prime}(B^{0} \\rightarrow K^{0*}\\mu^{+}\\mu^{-})$ and the state-of-the-art SM computations in the two anomalous bins (see [1] for an overview). In addition, the first LHCb measurement of the integrated isospin asymmetry $A_{\\mathrm{I}}(B \\rightarrow K\\mu^{+}\\mu^{-})$ in the entire $q^{2}$ -spectrum deviates from zero at the level of $4\\sigma$ [2], while the updated LHCb measurement of this asymmetry favours the lower significance of $1.5\\sigma$ [3], due to the inclusion of the 2012 data set and the improved analysis of the 2011 data sample. Precision measurements of the isospin asymmetries in the exclusive $b \\rightarrow \\{d,s\\}\\ell^{+}\\ell^{-}$ decays will be highly beneficial for constraining the Wilson coefficients of the $\\Delta B = 1$ four-quark operators and for unraveling the ultimate nature of the spectator-scattering mechanism in hard exclusive reactions generally [4-8] (see [9, 10] for discussions in the context of the radiative $B$ -meson decays). As a consequence, the in-depth exploitation of the flavour structure of the weak effective theory from the exclusive electroweak penguin $B$ -meson decay constitutes one of the primary physics goals of the LHCb and Belle II experiments, thus triggering the intense theoretical activities towards controlling better hadronic uncertainties of the SM predictions for more than one decade (see for ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[511,372,640,388]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"instance [11-20]).","text_format":null,"text_level":null,"type":"text"},{"bbox":"[511,388,919,917]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The field-theoretical framework to systematically address the hadronic matrix elements of the electroweak penguin $B$ -meson decays at large recoil has been constructed in the heavy quark mass limit with the perturbative factorization formalism [21, 22] (see also [23, 24] for an equivalent formulation in soft-collinear effective theory (SCET)). The resulting factorization formulae of the exclusive $b \\rightarrow \\{d, s\\} \\ell^{+} \\ell^{-}$ decay amplitudes can be expressed in terms of heavy-to-light form factors, lightcone distribution amplitudes (LCDAs), and perturbatively calculable short-distance coefficient functions, in analogy to the factorized expressions for the charmless hadronic $B$ -meson decays [25, 26]. In particular, both the weak annihilation and spectator-scattering topologies due to the hard-collinear photon radiation off the light spectator quark yield vanishing contributions to the transverse amplitude of $B \\rightarrow V \\ell^{+} \\ell^{-}$ at leading power in the $\\Lambda / m_{b}$ expansion [21, 27]. This interesting observation motivates further factorization analysis of the particular subleading power corrections to the transverse amplitude dependent of the electric charge of the spectator quark [4, 9, 22], which are fortunately determined by the soft-collinear convolution integrals without the disturbing end-pointed divergences (with the exception of the matrix element of the chromomagnetic dipole operator). However, the factorization-scale invariance of both the transverse and longitudinal amplitudes of $B \\rightarrow V \\ell^{+} \\ell^{-}$ was not completely achieved at the next-to-leading order (NLO) in QCD even in the leading-power approximation, owing to the unknown two-loop matrix elements of QCD penguin operators and the absence of the one-loop weak annihilation contribution in the longitudinal amplitude. Moreover, extending the QCD computation of the leading-power weak annihilation effect in $B \\rightarrow \\{V_{\\parallel}, P\\} \\ell^{+} \\ell^{-}$ to the NLO accuracy is in high de ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[22,257,60,713]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"arXiv:2403.11258v1 [hep-ph] 17 Mar 2024 ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[81,65,490,125]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"mand for unraveling factorization properties of the exclusive heavy-hadron decay amplitudes and for deepening our understanding towards model-independent properties of the $B$ -meson distribution amplitudes. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,126,490,459]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In order to probe the weak annihilation mechanism of the electroweak penguin bottom-meson decays in a theoretically clean fashion, we will concentrate on the rigorous NLO QCD computation of the weak annihilation contribution to $B \\rightarrow \\{K,\\pi\\} \\ell^{+}\\ell^{-}$ at leading power in the heavy quark expansion in this Letter, by employing the modern SCET technique. It is apparent that such higher-order corrections to the exclusive $B \\rightarrow \\pi \\ell^{+}\\ell^{-}$ decay amplitudes become more pronounced than the counterpart $B \\rightarrow K\\ell^{+}\\ell^{-}$ decays, thanks to the unsuppressed contributions from the current-current operators in the weak effective Hamiltonian. Subsequently, we report on a distinctive feature of the obtained soft-collinear factorization formula at $\\mathcal{O}(\\alpha_s)$ , in contrast with the analytical structure of the available leading-order (LO) expression. Phenomenological implications of the newly computed NLO weak annihilation contributions to the semileptonic $B \\rightarrow \\{K,\\pi\\} \\ell^{+}\\ell^{-}$ decay observables will be further explored with the improved lattice determinations of the leading-twist pion and kaon LCDAs as well as one sample model for the two-particle $B$ -meson LCDAs in heavy quark effective theory (HQET). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[194,484,379,498]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"GENERAL ANALYSIS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[81,517,488,563]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The effective weak Hamiltonian for the semileptonic $b \\to D\\ell^{+}\\ell^{-}$ (with $D = d$ , $s$ ) transitions in the SM can be written as [22] ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[101,569,488,601]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {H} _ {\\text {e f f}} = - \\frac {G _ {F}}{\\sqrt {2}} \\left[ V _ {t b} V _ {t D} ^ {*} \\mathcal {H} _ {\\text {e f f}} ^ {(t)} + V _ {u b} V _ {u D} ^ {*} \\mathcal {H} _ {\\text {e f f}} ^ {(u)} \\right] + \\text {h . c .}, (1)\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,607,488,638]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"by employing the unitarity relations of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[138,645,434,678]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {H} _ {\\mathrm {e f f}} ^ {(t)} = C _ {1} \\mathcal {Q} _ {1} ^ {c} + C _ {2} \\mathcal {Q} _ {2} ^ {c} + \\sum_ {i = 3, \\dots , 1 0} C _ {i} \\mathcal {Q} _ {i},\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[137,681,488,703]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {H} _ {\\mathrm {e f f}} ^ {(u)} = C _ {1} \\left(\\mathcal {Q} _ {1} ^ {c} - \\mathcal {Q} _ {1} ^ {u}\\right) + C _ {2} \\left(\\mathcal {Q} _ {2} ^ {c} - \\mathcal {Q} _ {2} ^ {u}\\right). \\qquad (2)\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,708,490,814]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The hadronic matrix elements of the two semileptonic operators $\\mathcal{Q}_{9,10}$ can be readily expressed in terms of the heavy-to-light $B$ -meson decay form factors [28]. The remaining contribution to the electroweak penguin decay amplitude can be determined by the contraction of the exclusive $B \\to \\{K,\\pi\\}\\gamma^{*}$ matrix element with the vector lepton current $\\gamma^{*} \\to \\ell^{+}\\ell^{-}$ . We are then led to introduce ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[83,821,488,878]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\langle P (p ^ {\\prime}) \\gamma^ {*} (q, \\mu) | \\mathcal {H} _ {\\mathrm {e f f}} ^ {(t, u)} | \\bar {B} (p) \\rangle = - \\frac {g _ {\\mathrm {e m}} m _ {b}}{4 \\pi^ {2}} \\frac {\\mathcal {T} _ {P} ^ {(t , u)} (q ^ {2})}{m _ {B}} \\\\ \\times \\left[ q ^ {2} \\left(p _ {\\mu} + p _ {\\mu} ^ {\\prime}\\right) - \\left(m _ {B} ^ {2} - m _ {P} ^ {2}\\right) q _ {\\mu} \\right], \\quad (3) \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,883,491,915]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $|P\\rangle$ represents $|K^{-}\\rangle$ ( $|\\pi^{-}\\rangle$ ) for the charged $B^{-}$ decay, and $|\\bar{K}^0\\rangle$ ( $-\\sqrt{2}\\pi^0$ ) for the neutral $\\bar{B}_d^0$ decay. The ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[524,64,629,127]","code_body":null,"code_caption":null,"image_caption":"[\"(a) \"]","image_footnote":"[]","img_path":"images/0536/8870b33cbcffb3f02673bc150d715f64190be0ba55a2531111747264b585ab0e.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[663,63,769,127]","code_body":null,"code_caption":null,"image_caption":"[\"(b) \"]","image_footnote":"[]","img_path":"images/0754/e63570ae1b69bc6a44c0148bfaaf166149c1e2a7373ff78b6f712d1516c7c3df.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[803,63,906,127]","code_body":null,"code_caption":null,"image_caption":"[\"(c) \",\"FIG. 1. Sample Feynman diagrams for the NLO weak annihilation contribution to $B \\\\rightarrow \\\\{K, \\\\pi\\\\} \\\\ell^{+} \\\\ell^{-}$ , where the circled cross indicates the hard-collinear photon radiation. Note that only the virtual photon emission from the soft spectator quark yields the leading-power contribution in the $\\\\Lambda / m_{b}$ expansion. \"]","image_footnote":"[]","img_path":"images/0863/ea08a7ad8368272f06dfe23af413f4675b1a64ebfc40be1a8af62a2ea371c916.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[511,267,918,300]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"resulting factorization formulae for the hadronic quantities $\\mathcal{T}_P^{(t,u)}$ at leading power can be cast in the form ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[537,308,870,345]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {T} _ {P} ^ {(t, u)} = C _ {P} ^ {(t, u)} (q ^ {2}) f _ {B P} ^ {+} (q ^ {2}) - \\frac {\\pi^ {2}}{N _ {c}} \\frac {\\mathcal {F} _ {B} f _ {P}}{m _ {B}} \\sum_ {m = \\pm}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[537,348,919,385]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\int_ {0} ^ {\\infty} \\frac {d \\omega}{\\omega} \\int_ {0} ^ {1} d u T _ {P, m} ^ {(t, u)} (\\omega , u, \\mu) \\phi_ {B, m} (\\omega , \\mu) \\phi_ {P} (u, \\mu), (4)\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[511,392,919,551]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $f_{BP}^{+}(q^{2})$ denotes the vector form factor defined by the local QCD matrix element $\\langle P(p')|\\bar{D}\\gamma_{\\mu}b|\\bar{B} (p)\\rangle$ . $\\mathcal{F}_B$ corresponds to the HQET $B$ -meson decay constant and $f_{P}$ is the scale-independent decay constant of the energetic pseudoscalar meson. Furthermore $\\phi_{B,\\pm}(\\omega ,\\mu)$ and $\\phi_P(u,\\mu)$ refer to the $B$ -meson and light-meson LCDAs [29-32]. The short-distance coefficient functions $C_P^{(i)}(q^2)$ and $T_{P,m}^{(i)}(\\omega ,u,\\mu)$ $(i = u,t)$ can be expanded perturbatively as follows (similarly for any other partonic quantity) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[511,558,929,594]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nC _ {P} ^ {(i)} = \\sum_ {\\ell} \\left(\\frac {\\alpha_ {s}}{4 \\pi}\\right) ^ {\\ell} C _ {P} ^ {(\\ell , i)}, \\quad T _ {P, m} ^ {(i)} = \\sum_ {\\ell} \\left(\\frac {\\alpha_ {s}}{4 \\pi}\\right) ^ {\\ell} T _ {P, m} ^ {(\\ell , i)}. \\tag {5}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[511,603,919,768]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The analytical expressions of the known perturbative kernels at $\\mathcal{O}(\\alpha_s)$ can be extracted from [21, 22]. In particular, only the subleading twist HQET distribution amplitude $\\phi_{B, - }(\\omega ,\\mu)$ appears in the tree-level factorization formula for the spectator-scattering contribution of $B\\rightarrow P\\ell^{+}\\ell^{-}$ , in sharp contrast with the radiative leponic decays $B\\to \\gamma \\ell \\bar{\\nu}_{\\ell}$ , $B\\to \\gamma \\ell^{+}\\ell^{-}$ [33-36], and the double radiative decay $B_{d,s}\\rightarrow \\gamma \\gamma$ [34, 37-39]. As discussed in [21, 22], it turns out to be advantageous to introduce two effective Wilson coefficients independent of the renormalization conventions for the weak effective Hamiltonian ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[580,775,919,814]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {C} _ {9, P} ^ {(i)} (q ^ {2}) = C _ {9} \\delta^ {i t} + \\frac {2 m _ {b}}{m _ {B}} \\frac {\\mathcal {T} _ {P} ^ {(i)} (q ^ {2})}{f _ {B P} ^ {+} (q ^ {2})}. \\tag {6}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[544,838,885,864]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"QCD FACTORIZATION FOR THE WEAK ANNIHILATION CONTRIBUTION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[511,883,919,915]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We are now in a position to compute the NLO weak annihilation contribution to $B \\to \\{K, \\pi\\} \\ell^{+} \\ell^{-}$ with the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[906,34,919,45]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[81,65,488,261]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"soft-collinear factorization technique. Inspecting the one-loop partonic diagrams displayed in Figure 1 indicates that the four distinct classes of field modes (hard, hard-collinear, anti-hard-collinear, and soft) carrying the four-momenta $P_{\\mathrm{h},\\mu} \\sim \\mathcal{O}(1,1,1)$ , $P_{\\mathrm{hc},\\mu} \\sim \\mathcal{O}(1,\\lambda,\\lambda^{1/2})$ , $P_{\\overline{\\mathrm{hc}},\\mu} \\sim \\mathcal{O}(\\lambda,1,\\lambda^{1/2})$ and $P_{\\mathrm{s},\\mu} \\sim \\mathcal{O}(\\lambda,\\lambda,\\lambda)$ appear in the problem under consideration, where the individual momentum components correspond to $n \\cdot P$ , $\\bar{n} \\cdot P$ and $P_{\\perp}$ for an arbitrary momentum $P_{\\mu}$ . The two light-cone vectors $n_{\\mu}$ and $\\bar{n}_{\\mu}$ satisfying $n^2 = \\bar{n}^2 = 0$ and $n \\cdot \\bar{n} = 2$ are chosen such that $n \\cdot q \\sim \\bar{n} \\cdot p' \\sim \\mathcal{O}(m_b)$ . Additionally, the heavy-quark expansion parameter $\\lambda$ scales as $\\Lambda_{\\mathrm{QCD}} / m_b$ in our power-counting analysis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,261,490,429]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A systematic decoupling of the hard and (anti)-hard-collinear fluctuations can be achieved by taking advantage of the two-step matching strategy $\\mathrm{QCD} \\rightarrow \\mathrm{SCET}_{\\mathrm{I}} \\rightarrow \\mathrm{SCET}_{\\mathrm{II}}$ . In accordance with the power-counting argument developed in the position-space formalism [40-42], both the A0-type and B1-type $\\mathrm{SCET}_{\\mathrm{I}}$ operators can generate the leading-power contribution to the weak annihilation amplitude. It is then straightforward to write down the $\\mathrm{SCET}_{\\mathrm{I}}$ representation of the current-current and QCD penguin operators $\\mathcal{Q}_i \\in \\{\\mathcal{Q}_1^u, \\mathcal{Q}_2^u, \\mathcal{Q}_{3-6}\\}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[165,435,488,454]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {Q} _ {i} = H _ {i} ^ {\\mathrm {I}} \\star \\mathcal {O} ^ {(\\mathrm {A} 0)} + H _ {i} ^ {\\mathrm {I I}} \\star \\mathcal {O} ^ {(\\mathrm {B} 1)}, \\tag {7}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,462,488,522]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"for the \"right-insertion\" topology where the spinor indices are contracted along the quark lines of the bottom meson and the light meson. We have employed here the customary asterisk notation in SCET ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[135,531,392,561]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nH _ {i} ^ {\\mathrm {I}} \\star \\mathcal {O} ^ {(\\mathrm {A 0})} = \\int d \\hat {t} H _ {i} ^ {\\mathrm {I}} (\\hat {t}) \\mathcal {O} ^ {(\\mathrm {A 0})} (t),\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[132,565,488,594]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nH _ {i} ^ {\\mathrm {I I}} \\star \\mathcal {O} ^ {(\\mathrm {B 1})} = \\int d \\hat {t} d \\hat {s} H _ {i} ^ {\\mathrm {I I}} (\\hat {t}, \\hat {s}) \\mathcal {O} ^ {(\\mathrm {B 1})} (t, s), \\tag {8}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,603,488,650]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"with the dimensionless convolution variables $\\hat{t} = (\\bar{n}\\cdot p')t$ and $\\hat{s} = (n\\cdot q)s$ . The explicit expressions of the two SCET $_{\\mathrm{I}}$ operators of our interest are given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[86,657,503,710]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\mathcal {O} ^ {(\\mathrm {A} 0)} = \\left[ (\\bar {\\chi} W _ {\\bar {c}}) (t \\bar {n}) \\frac {\\vec {\\eta}}{2} (1 - \\gamma_ {5}) \\left(W _ {\\bar {c}} ^ {\\dagger} \\chi\\right) (0) \\right] \\\\ \\left[ \\left(\\bar {\\xi} W _ {c}\\right) (0) \\not \\exists (1 - \\gamma_ {5}) h _ {v} (0) \\right], \\tag {9} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[86,714,503,781]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\mathcal {O} ^ {(B 1)} = \\frac {1}{m _ {b}} \\left[ (\\bar {\\chi} W _ {\\bar {c}}) (t \\bar {n}) \\frac {\\not {p h}}{2} (1 - \\gamma_ {5}) \\left(W _ {\\bar {c}} ^ {\\dagger} \\chi\\right) (0) \\right] \\\\ \\left[ \\left(\\bar {\\xi} W _ {c}\\right) (0) \\frac {\\not {h}}{2} \\left[ W _ {c} ^ {\\dagger} i \\not {D} _ {\\perp c} W _ {c} \\right] (s n) \\left(1 + \\gamma_ {5}\\right) h _ {v} (0) \\right], \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,787,488,849]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where the collinear Wilson lines $W_{c}$ and $W_{\\bar{c}}$ are introduced to ensure gauge invariance [40]. Along the same vein, the matching equation for the \"wrong-insertion\" topology takes the form ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[165,856,488,875]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {Q} _ {i} = \\tilde {H} _ {i} ^ {\\mathrm {I}} \\star \\mathcal {O} ^ {(\\mathrm {A} 0)} + \\tilde {H} _ {i} ^ {\\mathrm {I I}} \\star \\mathcal {O} ^ {(\\mathrm {B} 1)}, \\tag {10}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,883,488,914]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where both the bottom and light mesons are made up of the quark-antiquark pair from two different bilinears ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[511,65,919,126]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"in the QCD operators (see [41] for further discussions). Performing the Fourier transformation with respect to the light-cone variables $\\hat{t}$ and $\\hat{s}$ defines the momentum-space short-distance functions ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,135,936,196]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\left\\{\\mathbb {H} _ {i} ^ {\\mathrm {I}}, \\tilde {\\mathbb {H}} _ {i} ^ {\\mathrm {I}} \\right\\} (u) = \\int d \\hat {t} e ^ {i u \\hat {t}} \\left\\{H _ {i} ^ {\\mathrm {I}}, \\tilde {H} _ {i} ^ {\\mathrm {I}} \\right\\} (\\hat {t}), \\\\ \\left\\{\\mathbb {H} _ {i} ^ {\\mathrm {I I}}, \\tilde {\\mathbb {H}} _ {i} ^ {\\mathrm {I I}} \\right\\} (u, \\tau) = \\int d \\hat {t} e ^ {i (u \\hat {t} + \\tau \\hat {s})} \\left\\{H _ {i} ^ {\\mathrm {I I}}, \\tilde {H} _ {i} ^ {\\mathrm {I I}} \\right\\} (\\hat {t}, \\hat {s}). \\tag {11} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[511,203,919,325]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It becomes apparent that we are required to derive both the \"right-insertion\" and the \"wrong-insertion\" matching coefficients for the current-current operators $\\mathcal{Q}_{1,2}^{u}$ , but merely the \"wrong-insertion\" kernels for the QCD penguin operators $\\mathcal{Q}_{3-6}$ . Applying the technical framework of determining the renormalized hard-scattering kernels with the inclusion of the evanescent operators detailed in [43, 44] leads to the desired results at the $\\mathcal{O}(\\alpha_s)$ accuracy ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[516,333,926,484]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\mathbb {H} _ {1} ^ {\\mathrm {I} (0)} = 0, \\quad \\mathbb {H} _ {2} ^ {\\mathrm {I} (0)} = 1, \\quad \\tilde {\\mathbb {H}} _ {1, 4} ^ {\\mathrm {I} (0)} = \\frac {C _ {F}}{N _ {c}}, \\quad \\tilde {\\mathbb {H}} _ {2, 3} ^ {\\mathrm {I} (0)} = \\frac {1}{N _ {c}}, \\\\ \\tilde {\\mathbb {H}} _ {5} ^ {\\mathbf {I} (0)} = \\frac {1 6}{N _ {c}}, \\quad \\tilde {\\mathbb {H}} _ {6} ^ {\\mathbf {I} (0)} = 1 6 \\frac {C _ {F}}{N _ {c}}, \\\\ \\mathbb {H} _ {1} ^ {\\mathrm {I I} (0)} = \\frac {1}{N _ {c}} \\frac {1}{\\bar {u}}, \\quad \\mathbb {H} _ {2} ^ {\\mathrm {I I} (0)} = 2, \\tag {12} \\\\ \\tilde {\\mathbb {H}} _ {1, 4} ^ {\\mathrm {I I} (0)} = \\frac {1}{N _ {c}} \\left[ 2 C _ {F} - \\frac {1}{N _ {c}} \\frac {1}{\\bar {u}} \\right], \\quad \\tilde {\\mathbb {H}} _ {2, 3} ^ {\\mathrm {I I} (0)} = \\frac {2}{N _ {c}} \\left[ 1 + \\frac {1}{\\bar {u}} \\right], \\\\ \\tilde {\\mathbb {H}} _ {5} ^ {\\mathrm {I I} (0)} = 1 6 \\tilde {\\mathbb {H}} _ {2} ^ {\\mathrm {I I} (0)}, \\qquad \\qquad \\tilde {\\mathbb {H}} _ {6} ^ {\\mathrm {I I} (0)} = 1 6 \\tilde {\\mathbb {H}} _ {1} ^ {\\mathrm {I I} (0)}, \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[513,493,544,505]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[521,513,916,744]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\mathbb {H} _ {1} ^ {\\mathrm {I} (1)} = \\frac {C _ {F}}{2 N _ {c}} \\left[ - 6 \\mathcal {L} + \\mathfrak {h} (u) \\right], \\\\ \\mathbb {H} _ {2} ^ {\\mathrm {I} (1)} = - \\frac {C _ {F}}{2} \\left[ \\mathcal {L} ^ {2} + 5 \\mathcal {L} + \\frac {\\pi^ {2}}{6} + 1 2 \\right], \\\\ \\tilde {\\mathbb {H}} _ {1} ^ {\\mathrm {I} (1)} = \\frac {1}{N _ {c}} \\left[ C _ {F} \\mathbb {H} _ {2} ^ {\\mathrm {I} (1)} - \\mathbb {H} _ {1} ^ {\\mathrm {I} (1)} \\right] - C _ {F}, \\\\ \\tilde {\\mathbb {H}} _ {2} ^ {\\mathrm {I} (1)} = \\tilde {\\mathbb {H}} _ {3} ^ {\\mathrm {I} (1)} = \\frac {1}{N _ {c}} \\mathbb {H} _ {2} ^ {\\mathrm {I} (1)} + 2 \\mathbb {H} _ {1} ^ {\\mathrm {I} (1)}, \\tag {13} \\\\ \\tilde {\\mathbb {H}} _ {4} ^ {\\mathrm {I} (1)} = \\frac {1}{N _ {c}} \\left[ C _ {F} \\mathbb {H} _ {2} ^ {\\mathrm {I} (1)} - \\mathbb {H} _ {1} ^ {\\mathrm {I} (1)} \\right] + \\frac {C _ {F}}{N _ {c}} \\left[ \\frac {2}{3} n _ {f} - N _ {c} \\right], \\\\ \\tilde {\\mathbb {H}} _ {5} ^ {\\mathrm {I} (1)} = \\frac {1 6}{N _ {c}} \\mathbb {H} _ {2} ^ {\\mathrm {I} (1)} + 3 2 \\mathbb {H} _ {1} ^ {\\mathrm {I} (1)}, \\\\ \\tilde {\\mathbb {H}} _ {6} ^ {\\mathrm {I} (1)} = \\frac {1 6}{N _ {c}} \\left[ C _ {F} \\mathbb {H} _ {2} ^ {\\mathrm {I} (1)} - \\mathbb {H} _ {1} ^ {\\mathrm {I} (1)} \\right] + \\frac {1 0 C _ {F}}{N _ {c}} \\left[ \\frac {2}{3} n _ {f} - 4 N _ {c} \\right]. \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[511,752,918,768]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For brevity we have introduced the following conventions ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,775,934,840]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\mathfrak {h} (u) = \\ln^ {2} (u \\bar {u}) + \\left(3 - \\frac {2}{u}\\right) \\ln \\bar {u} - 2 \\ln^ {2} u + \\left(3 - \\frac {1}{\\bar {u}}\\right) \\ln u \\\\ + 4 \\operatorname {L i} _ {2} (u) - \\frac {\\pi^ {2}}{3} - 2 2 + i \\pi (2 \\ln \\bar {u} - 2 \\ln u - 3), \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[535,842,933,876]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathcal {L} \\equiv \\ln \\left(\\frac {\\mu^ {2}}{m _ {b} ^ {2}}\\right), \\quad \\bar {u} \\equiv 1 - u, \\quad n _ {f} = 5. \\tag {14}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[511,883,919,914]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As demonstrated in [41, 45, 46], the hard-collinear and aniti-hard-collinear fields decouple already at the hard ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[906,34,919,46]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[81,65,490,127]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"scale of $\\mathcal{O}(m_b)$ . This essential observation can be attributed to the disappearing leading-power interactions between the (hard)-collinear fields with different directions in the SCET Lagrangian after the field redefini ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[511,65,919,126]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tion [47] (see also [48, 49] for an overview). The obtained $\\mathrm{SCET_I}$ matrix elements of $\\mathcal{O}^{(\\mathrm{A0})}$ and $\\mathcal{O}^{(\\mathrm{B1})}$ then fall apart into two distinct sectors each, thus generating the non-local effective matrix elements below ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[107,162,687,196]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\langle P (p ^ {\\prime}) | (\\bar {\\chi} W _ {\\bar {c}}) (t \\bar {n}) \\frac {\\vec {n}}{2} (1 - \\gamma_ {5}) (W _ {\\bar {c}} ^ {\\dagger} \\chi) (0) | 0 \\rangle = i f _ {P} \\frac {\\bar {n} \\cdot p ^ {\\prime}}{2} \\int_ {0} ^ {1} d u e ^ {i (\\bar {n} \\cdot p ^ {\\prime}) u t} \\phi_ {P} (u, \\mu),\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[106,198,928,228]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\int d ^ {4} x e ^ {i q \\cdot x} \\langle 0 | \\mathrm {T} \\left\\{j _ {\\mathrm {e m}, \\mu} ^ {\\parallel} (x), (\\bar {\\xi} W _ {c}) (0) \\gamma_ {5} h _ {v} (0) \\right\\} | \\bar {B} (p) \\rangle = \\mathcal {J} _ {P} ^ {(\\mathrm {A} 0)} (n \\cdot q, \\bar {n} \\cdot q) \\bar {n} _ {\\mu}, \\tag {15}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[106,231,928,261]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\frac{n\\cdot q}{2\\pi}\\int d^{4}x e^{iq\\cdot x}\\int ds e^{i(n\\cdot q)\\tau s}\\langle 0|\\mathrm{T}\\left\\{j_{\\mathrm{em},\\mu}^{\\parallel}(x),\\left(\\bar{\\xi} W_{c}\\right)(0)\\gamma_{5}\\left[W_{c}^{\\dagger}i\\not D_{\\perp c}W_{c}\\right](sn)h_{v}(0)\\right\\} |\\bar{B} (p)\\rangle = \\mathcal{J}_{P}^{\\mathrm{(B1)}}(n\\cdot q,\\bar{n}\\cdot q,\\tau)\\bar{n}_{\\mu}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,301,488,330]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The $\\mathrm{SCET_I}$ representation of the electromagnetic current relevant here is given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,342,495,396]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} j _ {\\mathrm {e m}, \\mu} ^ {\\parallel} \\supset j _ {\\mathrm {e m}, \\mu} ^ {\\parallel , (0)} + j _ {\\mathrm {e m}, \\mu} ^ {\\parallel , (2)} \\tag {16} \\\\ = \\bar {\\xi} \\frac {\\eta \\hbar}{2} \\xi \\bar {n} _ {\\mu} + \\left[ (\\bar {\\xi} W _ {c}) \\frac {\\eta \\hbar}{2} (Y _ {s} ^ {\\dagger} q _ {s}) + (\\bar {q} _ {s} Y _ {s}) \\frac {\\eta \\hbar}{2} (W _ {c} ^ {\\dagger} \\xi) \\right] \\bar {n} _ {\\mu}, \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,406,490,625]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where the second term on the right-hand side converts the soft spectator quark into a hard-collinear quark and counts as $\\mathcal{O}(\\lambda^2)$ . The leading-power current $j_{\\mathrm{em},\\mu}^{\\parallel,(0)}$ can contribute to $\\mathcal{J}_P^{(\\mathrm{A0})}\\left(\\mathcal{J}_P^{(\\mathrm{B1})}\\right)$ only through time-ordered products with an additional SCET Lagrangian $\\mathcal{L}_{\\xi q_s}^{(2)}$ $(\\mathcal{L}_{\\xi q_s}^{(1)})$ [50]. By contrast, the subleading-power current $j_{\\mathrm{em},\\mu}^{\\parallel,(2)}$ can bring about the non-vanishing contribution to $\\mathcal{J}_P^{(\\mathrm{A0})}$ already at tree level (and certainly at higher orders in $\\alpha_s$ with insertions of the unsuppressed SCET Lagrangian $\\mathcal{L}_{\\xi}^{(0)})$ ). Integrating out the hard-collinear fluctuations in the $\\mathrm{SCET_I}$ correlation functions by virtue of the second-step matching $\\mathrm{SCET_I}\\rightarrow \\mathrm{SCET_{II}}$ enables us to derive the soft-collinear factorization formulae [15, 51] ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[86,637,496,720]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\mathcal {J} _ {P} ^ {(A 0)} = \\frac {\\mathcal {F} _ {B} m _ {B}}{2} \\int_ {0} ^ {\\infty} d \\omega \\frac {\\mathbb {J} _ {\\parallel , -} (n \\cdot q , \\bar {n} \\cdot q , \\omega)}{\\bar {n} \\cdot q - \\omega + i 0} \\phi_ {B, -} (\\omega , \\mu), \\\\ \\mathcal {J} _ {P} ^ {\\left(\\mathrm {B} 1\\right)} = \\frac {\\mathcal {F} _ {B} m _ {B}}{2} \\int_ {0} ^ {\\infty} d \\omega \\mathbb {J} _ {\\|, +} (n \\cdot q, \\bar {n} \\cdot q, \\omega , \\tau) \\phi_ {B, +} (\\omega , \\mu). \\tag {17} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[81,732,488,780]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Employing the SCET Feynman rules collected in [52], we can readily determine the renormalized jet functions $\\mathbb{J}_{\\parallel, -}$ and $\\mathbb{J}_{\\parallel, +}$ up to the order $\\alpha_{s}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,792,279,816]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left\\{\\mathbb {J} _ {\\parallel , -} ^ {(0)}, \\mathbb {J} _ {\\parallel , +} ^ {(0)} \\right\\} = \\{1, 0 \\},\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[112,820,478,888]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\mathbb {J} _ {\\parallel , -} ^ {(1)} = C _ {F} \\left[ \\ln^ {2} \\frac {\\hat {\\mu} ^ {2}}{\\omega - \\bar {n} \\cdot q} - 2 \\ln \\frac {\\hat {\\mu} ^ {2}}{\\omega - \\bar {n} \\cdot q} \\ln (1 + \\eta) \\right. \\\\ \\left. - \\ln^ {2} (1 + \\eta) + \\left(\\frac {2}{\\eta} - 1\\right) \\ln (1 + \\eta) - \\frac {\\pi^ {2}}{6} - 1 \\right], \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[112,891,486,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathbb {J} _ {\\parallel , +} ^ {(1)} = 2 C _ {F} \\frac {n \\cdot q}{\\omega} \\ln (1 + \\eta) (1 - \\tau) \\theta (\\tau) \\theta (1 - \\tau), \\tag {18}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[511,300,919,515]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where we have defined two variables $\\hat{\\mu}^2 = \\mu^2 /n\\cdot q$ and $\\eta = -\\omega /\\bar{n}\\cdot q$ . Interestingly, the leading-twist bottommeson distribution amplitude $\\phi_{B, + }(\\omega ,\\mu)$ now enters the perturbative factorization formula (17) of the weak annihilation amplitude at $\\mathcal{O}(\\alpha_s)$ , in contrast with the factorized expression for the tree-level annihilation amplitude. On the basis of the asymptotic behaviours of $\\phi_{B,\\pm}(\\omega ,\\mu)$ [29, 53-59], we can further verify that the soft-collinear convolution integrals in (17) converge at $q^{2}\\sim \\mathcal{O}(m_{b}\\Lambda_{\\mathrm{QCD}})$ and the complex-valued invariant functions $\\mathcal{J}_P^{(\\mathrm{A0})}$ and $\\mathcal{J}_P^{(\\mathrm{B1})}$ cannot be entirely described by the two particular moments $\\lambda_{B, + }^{-1}$ and $\\lambda_{B, - }^{-1}(q^2)$ of the bottom-meson distribution amplitudes as previously introduced in [21]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[511,515,919,575]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We now summarize the explicit expressions of the NLO weak annihilation corrections to the short-distance matching functions $T_{P,m}^{(t,u)}$ appearing in the QCD factorization formulae (4) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,585,933,705]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\left\\{T _ {P, +} ^ {(u)}, T _ {P, +} ^ {(t)} \\right\\} \\supset - Q _ {q} N _ {c} \\frac {2 m _ {B}}{m _ {b}} \\int_ {0} ^ {1} d \\tau \\mathbb {J} _ {| |, +} (n \\cdot q, \\bar {n} \\cdot q, \\omega , \\tau) \\\\ \\left\\{- \\sum_ {i = 1} ^ {2} C _ {i} \\left[ \\mathbb {H} _ {i} ^ {\\mathrm {I I}} (u, \\tau) \\delta_ {q u} - \\tilde {\\mathbb {H}} _ {i} ^ {\\mathrm {I I}} (u, \\tau) \\delta_ {q d} \\delta_ {P \\pi} \\right], \\right. \\\\ \\left. \\sum_ {i = 3} ^ {6} C _ {i} \\tilde {\\mathbb {H}} _ {i} ^ {\\mathrm {I I}} (u, \\tau) \\right\\}, \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[517,709,934,827]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\left\\{T _ {P, -} ^ {(u)}, T _ {P, -} ^ {(t)} \\right\\} \\supset Q _ {q} N _ {c} \\frac {4 m _ {B}}{m _ {b}} \\frac {\\mathbb {J} _ {\\| , -} (n \\cdot q , \\bar {n} \\cdot q , \\omega)}{\\hat {q} ^ {2} - 1 + i 0} \\\\ \\left\\{- \\sum_ {i = 1} ^ {2} C _ {i} \\left[ \\mathbb {H} _ {i} ^ {\\mathrm {I}} (u) \\delta_ {q u} - \\tilde {\\mathbb {H}} _ {i} ^ {\\mathrm {I}} (u) \\delta_ {q d} \\delta_ {P \\pi} \\right], \\right. \\\\ \\left. \\sum_ {i = 3} ^ {6} C _ {i} \\tilde {\\mathbb {H}} _ {i} ^ {\\mathrm {I}} (u) \\right\\}, \\tag {19} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[511,835,919,914]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $Q_{q}$ denotes the electric charge of the soft spectator quark in the $B$ -meson. Furthermore, $\\hat{q}^2 = q^2 / (m_B\\omega)$ , $\\delta_{P\\pi} = 1$ , 0 for $\\pi$ and $K$ mesons, respectively. We remark in passing that the hard coefficient functions $\\mathbb{H}_{1,2}^{\\mathrm{II}}$ and $\\tilde{\\mathbb{H}}_{1-6}^{\\mathrm{II}}$ of the B1-type SCETI operators are independent ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[906,34,919,45]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[81,64,491,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"of the variable $\\tau$ at $\\mathcal{O}(\\alpha_s^0)$ and the jet function $\\mathbb{J}_{\\parallel , + }$ starts from $\\mathcal{O}(\\alpha_s)$ , thus allowing us to perform the integration over $\\tau$ in the obtained $T_{P, + }^{(u,t)}$ straightforwardly in the NLO approximation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[181,156,392,169]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"NUMERICAL ANALYSIS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[81,188,491,595]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We continue to explore phenomenological implications of the NLO weak annihilation contributions to the exclusive rare decays $B \\rightarrow \\{K, \\pi\\} \\ell^{+} \\ell^{-}$ at large hadronic recoil. The Wilson coefficients $C_i$ in the weak effective Hamiltonian (1) will be evaluated at the initial scale $\\mu_W = m_W$ [60, 61] and then evolved to the hard scale $\\mu_{\\mathrm{h}} = m_b$ with the required accuracy (following [62, 63]). We further adopt the three-parameter ansatz for the HQET $B$ -meson LCDAs as proposed in [64] (see [65-68] for additional discussions), which can be analytically evolved into the hard-collinear scale with the renormalization-group (RG) formalism at the leading-logarithmic accuracy. The leptonic decay constants of the $B$ -meson, pion and kaon are taken from the averages of the lattice QCD simulations [69]. Moreover, we will truncate the Gegenbauer expansion of the leading-twist pion and kaon LCDAs by including only the two lowest moments whose intervals have been determined from lattice QCD at the $\\overline{\\mathrm{MS}}$ scale $\\mu_0 = 2.0\\mathrm{GeV}$ with full control of all systematic uncertainties [70]. The two-loop RG evolution of these Gegenbauer moments [71, 72] (see also [73, 74]) will be then implemented for the sake of describing their scale dependence. In particular, we employ the improved QCD predictions of the semileptonic form factors $f_{B\\pi}^{+}(q^{2})$ and $f_{BK}^{+}(q^{2})$ displayed in [18]. The choices for the remaining parameters in numerical studies are identical to the ones summarized in [36]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[81,595,490,914]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Inspecting the numerical features of the effective Wilson coefficient $\\mathcal{C}_{9,P}^{(u)}$ for $B^{-}\\rightarrow \\pi^{-}\\ell^{+}\\ell^{-}$ displayed in Figure 2 indicates that the newly computed NLO weak annihilation contribution can bring about $\\mathcal{O}(35\\%)$ $(\\mathcal{O}(15\\%))$ reduction of the tree-level prediction for the real (imaginary) part of $\\mathcal{C}_{9,P}^{(u)}$ in the kinematic range $1.5\\mathrm{GeV}^2\\leq q^2\\leq 4.0\\mathrm{GeV}^2$ . By contrast, the previously determined NLO QCD correction to the invariant amplitude $\\mathcal{T}_P^{(u)}$ (shown in Figure 2 of [21]) generates, on the one hand, an impact on $\\mathrm{Re}[\\mathcal{C}_{9,P}^{(u)}]$ no more than $10\\%$ numerically in the same kinematic region and, on the other hand, approximately $(15 - 30)\\%$ reduction of the LO prediction of $\\mathrm{Im}[\\mathcal{C}_{9,P}^{(u)}]$ . In consequence, the higher-order weak annihilation effect under discussion provides an intriguing source of the strong phases of the exclusive $b\\to d\\ell^{+}\\ell^{-}$ decay amplitudes. In addition, the NLO weak annihilation correction to the invariant amplitude $\\mathcal{T}_P^{(t)}$ appears to be merely $\\mathcal{O}(3\\%)$ of the previously computed NLO contribution [21, 22] in magnitude at $q^2\\in [1.5,4.0]\\mathrm{GeV}^2$ due to the absence of an important contribution from ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[527,68,906,272]","code_body":null,"code_caption":null,"image_caption":"[\"FIG. 2. Theory prediction for the $q^2$ dependence of the effective Wilson coefficient $\\\\mathcal{C}_{9,P}^{(u)}$ dictating the exclusive $B^{-}\\\\rightarrow \\\\pi^{-}\\\\ell^{+}\\\\ell^{-}$ decay amplitude at LO (black curves), at NLO $_{\\\\mathrm{BFS}}$ (blue curves) and at NLO (pink bands), where the notation \\\"NLO $_{\\\\mathrm{BFS}}$ represents the available NLO computation accomplished in [21, 22], and the uncertainties are obtained from varying the hard and hard-collinear matching scales. \"]","image_footnote":"[]","img_path":"images/0123/0314f6f2963c97ebf3e99bb7d5adce717dd1e54d4aa89f9a7ef67c93c5c087cd.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[511,428,918,457]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the current-current operators $\\mathcal{Q}_{1,2}^{c}$ with the large Wilson coefficients. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[511,458,919,550]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We proceed to explore phenomenological impacts of the determined NLO weak annihilation correction on the CP-averaged branching fraction $(\\mathcal{B}\\mathcal{R})$ , the direct CP asymmetry $(\\mathcal{A}_{\\mathrm{CP}})$ and the CP-averaged isospin asymmetry $(\\mathcal{A}_{\\mathrm{I}})$ for $B \\to P\\ell^{+}\\ell^{-}$ , the latter two of which are explicitly defined by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[511,559,926,631]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} \\mathcal {A} _ {\\mathrm {C P}} = \\frac {\\Gamma (\\bar {B} \\rightarrow \\bar {P} \\ell^ {+} \\ell^ {-}) - \\Gamma (B \\rightarrow P \\ell^ {+} \\ell^ {-})}{\\Gamma (\\bar {B} \\rightarrow \\bar {P} \\ell^ {+} \\ell^ {-}) + \\Gamma (B \\rightarrow P \\ell^ {+} \\ell^ {-})}, \\\\ \\mathcal {A} _ {\\mathrm {I}} = \\frac {\\kappa \\Gamma (\\bar {B} ^ {0} \\rightarrow \\bar {P} ^ {0} \\ell^ {+} \\ell^ {-}) - \\Gamma (B ^ {-} \\rightarrow P ^ {-} \\ell^ {+} \\ell^ {-})}{\\kappa \\Gamma (\\bar {B} ^ {0} \\rightarrow \\bar {P} ^ {0} \\ell^ {+} \\ell^ {-}) + \\Gamma (B ^ {-} \\rightarrow P ^ {-} \\ell^ {+} \\ell^ {-})}, \\tag {20} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[511,641,921,915]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"with the factor $\\kappa = 2,1$ for $P = \\pi^0,K^0$ . Unsurprisingly, including the NLO weak annihilation correction in the improved theory predictions can lead to the negligible impacts on $\\mathcal{BR}(B\\to K\\ell^{+}\\ell^{-})$ and $\\mathcal{BR}(B\\rightarrow \\pi \\ell^{+}\\ell^{-})$ . In virtue of the smallness of the direct CP asymmetries for the exclusive $b\\rightarrow s\\ell^{+}\\ell^{-}$ decay processes in the SM, we collect here only our predictions for the binned asymmetries $\\mathcal{A}_{\\mathrm{CP}}[q_{\\mathrm{min}}^2,q_{\\mathrm{max}}^2] =$ $\\{1.02_{-0.22}^{+0.05},0.64_{-0.24}^{+0.06},0.42_{-0.17}^{+0.10},0.31_{-0.13}^{+0.10},0.26_{-0.10}^{+0.09}\\} \\%$ for $B^{-}\\rightarrow K^{-}\\ell^{+}\\ell^{-}$ and $\\mathcal{A}_{\\mathrm{CP}}[q_{\\mathrm{min}}^2,q_{\\mathrm{max}}^2] =$ $\\{0.01_{-0.12}^{+0.08},0.04_{-0.11}^{+0.07},0.06_{-0.10}^{+0.07},0.08_{-0.10}^{+0.07},0.09_{-0.09}^{+0.07}\\} \\%$ for $\\bar{B}^0\\rightarrow \\bar{K}^0\\ell^+\\ell^-$ , with the choices of the five sample $q^{2}$ bins (following [75]) $[q_{\\mathrm{min}}^2,q_{\\mathrm{max}}^2] =$ $\\{[1.1,2.0],[2.0,3.0],[3.0,4.0],[4.0,5.0],[5.0,6.0]\\}\\mathrm{GeV}^2.$ Moreover, the yielding results for the isospin asymmetry of $B\\rightarrow K\\ell^{+}\\ell^{-}$ in the kinematic ranges $q^{2}\\in [2.0,4.0]\\mathrm{GeV}^{2}$ and $q^{2}\\in [4.0,6.0]\\mathrm{GeV}^{2}$ are given by $(-0.74)_{-0.12}^{+0.21}\\%$ and $(-0.44)_{-0.06}^{+0.08}\\%$ respectively, whose ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[906,34,918,45]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[98,66,475,261]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0522/fb98e650579d96bc4a2c24eabf55da1cf238b393c314f2206260ef25993bb993.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[94,277,473,479]","code_body":null,"code_caption":null,"image_caption":"[\"FIG. 3. Theory predictions for the $q^2$ dependence of the direct CP asymmetries [top] and the isospin asymmetry [down] for the exclusive $B \\\\rightarrow \\\\pi \\\\ell^{+} \\\\ell^{-}$ decays at LO (grey bands), at NLO $_{\\\\mathrm{BFS}}$ (blue bands) and at NLO (pink bands), where the uncertainties are obtained by adding the separate errors due to the variations of all input parameters in quadrature. \"]","image_footnote":"[]","img_path":"images/0598/774f2af7c84959dfee06c7a31d81fafd1ba86161de3c0872f1744c1642cac793.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[86,625,488,914]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"magnitudes and signs are both compatible with the updated LHCb measurements [3]. We now present the comparative predictions for the direct CP asymmetries and the isopsin asymmetry of $B \\to \\pi \\ell^{+} \\ell^{-}$ in Figure 3. It is then evident that the inclusion of the NLO weak annihilation contribution can result in the noticeable shifts of the theory predictions for these asymmetries in the NLO $_{\\mathrm{BFS}}$ approximation: numerically $\\mathcal{O}(15\\%)$ and $\\mathcal{O}(25\\%)$ corrections to $\\mathcal{A}_{\\mathrm{CP}}(B^{-} \\to \\pi^{-} \\ell^{+} \\ell^{-})$ and $\\mathcal{A}_{\\mathrm{I}}(B \\to \\pi \\ell^{+} \\ell^{-})$ . It is perhaps worth mentioning that the predicted CP asymmetry for $\\bar{B}^{0} \\to \\pi^{0} \\ell^{+} \\ell^{-}$ turns out to be significantly smaller than the counterpart result for the charged $B$ -meson decay channel, on account of the hierarchy structure of the LO annihilation amplitudes $[T_{P, -}^{(0,u)}(\\bar{B}^{0} \\to \\pi^{0} \\ell^{+} \\ell^{-})] : [T_{P, -}^{(0,u)}(B^{-} \\to \\pi^{-} \\ell^{+} \\ell^{-})] = [-Q_{d}(C_{F} C_{1} + C_{2})] : [Q_{u} N_{c} C_{2}] \\approx 1:10$ . Importantly, the obtained prediction of the isopsin breaking effect in $B \\to \\pi \\ell^{+} \\ell^{-}$ is approximately 3-6 times larger than that in $B \\to K \\ell^{+} \\ell^{-}$ for $q^{2} \\in [1.5, 4.0]\\mathrm{GeV}^{2}$ , thus enabling ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[511,65,919,111]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"this asymmetry observable to become the sensitive probe of the Wilson coefficients of the current-current operators in the weak effective Hamiltonian. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[650,148,782,161]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CONCLUSIONS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[511,181,919,544]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In conclusion, we have presented the first computation of the NLO weak annihilation contribution to the rare $B \\to \\{K,\\pi\\} \\ell^{+}\\ell^{-}$ decays at leading power in the heavy quark expansion by employing the soft-collinear factorization framework, thus providing the last missing piece in evaluating the QCD correction to the isospin asymmetry $\\mathcal{A}_{\\mathrm{I}}(B \\to \\pi \\ell^{+}\\ell^{-})$ . In contrast with the tree-level annihilation amplitude, we have demonstrated that both the twist-two and twist-three HQET LCDAs of the bottom-meson are in demand to capture the soft QCD dynamics in the established factorization formula of the weak annihilation effect at $\\mathcal{O}(\\alpha_{s})$ . Taking into account such higher-order corrections in the matrix elements of the four-quark operators can result in the notable impacts on our theory predictions for the direct CP asymmetry $\\mathcal{A}_{\\mathrm{CP}}(B^{-} \\to \\pi^{-}\\ell^{+}\\ell^{-})$ as well as the CP-averaged isospin asymmetry $\\mathcal{A}_{\\mathrm{I}}(B \\to \\pi \\ell^{+}\\ell^{-})$ . In addition, the achieved NLO factorization formula of the annihilation amplitude can be straightforwardly extended to the electroweak penguin decays $B \\to \\{K^{*},\\rho ,\\omega \\} \\ell^{+}\\ell^{-}$ with the longitudinally polarized vector mesons (by implementing the appropriate replacements), which are generally accepted as the benchmark channels for exploring the quark flavour-changing dynamics. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[611,580,821,594]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ACKNOWLEDGEMENTS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[511,614,919,750]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Y.K.H. and Y.M.W. acknowledge support from the National Natural Science Foundation of China with Grant No. 12075125. The research of Y.L.S. is supported by the National Natural Science Foundation of China with Grant No. 12175218. C.W. is supported in part by the National Natural Science Foundation of China with Grant No. 12105112 and the Natural Science Foundation of Jiangsu Education Committee with Grant No. 21KJB140027. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[532,806,883,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"* huangyongkang@mail.nankai.edu.cn \",\"† corresponding author: shenylmeteoror@ouc.edu.cn \",\"$\\\\ddagger$ corresponding author: chaowang@nankai.edu.cn \",\"$\\\\S$ corresponding author: wangyuming@nankai.edu.cn \"]","page_idx":"5","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[522,861,916,914]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[1] B. Capdevila, A. Crivellin, and J. Matias, Eur. Phys. J. 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Wein (RQCD), JHEP 08, 065 (2019), [Addendum: JHEP 11, 037 (2020)], arXiv:1903.08038 [hep-lat]. \",\"[71] D. Mueller, Phys. Rev. D 49, 2525 (1994). \",\"[72] D. Mueller, Phys. Rev. D 51, 3855 (1995), arXiv:hep-ph/9411338. \",\"[73] S. S. Agaev, V. M. Braun, N. Offen, and F. A. Porkert, Phys. Rev. D 83, 054020 (2011), arXiv:1012.4671 [hep-ph]. \",\"[74] Y.-M. Wang and Y.-L. Shen, JHEP 12, 037 (2017), arXiv:1706.05680 [hep-ph]. \",\"[75] R. Aaij et al. (LHCb), JHEP 09, 177 (2014), arXiv:1408.0978 [hep-ex]. \"]","page_idx":"7","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[906,34,918,46]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[84,61,916,83]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Next-to-Leading-Order Weak Annihilation Correction to Rare $B \\\\to \\\\{K, \\\\pi\\\\} \\\\ell^{+} \\\\ell^{-}$ Decays \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[212,95,792,191]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Yong-Kang Huang $^{a}$ , * Yue-Long Shen $^{b,\\\\dagger}$ , Chao Wang $^{c,\\\\ddagger}$ and Yu-Ming Wang $^{a\\\\S}$ $^{a}$ School of Physics, Nankai University, Weijin Road 94, Tianjin 300071, P.R. China $^{b}$ College of Information Science and Engineering, Ocean University of China, Qingdao 266100, Shandong, China $^{c}$ Department of Mathematics and Physics, Huaiyin Institute of Technology, Meicheng East Road 1, Huaian, Jiangsu 223200, P.R. China \\n(Dated: March 19, 2024) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[169,210,831,332]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We accomplish for the first time the next-to-leading-order computation of the weak annihilation contribution to the exclusive electroweak penguin decays $B \\\\to \\\\{K, \\\\pi\\\\} \\\\ell^{+} \\\\ell^{-}$ with an energetic light-flavour meson, which is an essential missing piece of the complete QCD correction to the matrix elements of hadronic operators in the weak effective Hamiltonian. Both the hard functions and the jet functions in the perturbative factorization formulae from the short-distance fluctuations at the two distinct scales $m_{b}$ and $\\\\sqrt{m_b \\\\Lambda}$ are determined at $\\\\mathcal{O}(\\\\alpha_s)$ with the soft-collinear factorization technique. We then demonstrate that the one-loop weak annihilation correction can bring about the noticeable impacts on theory predictions for the CP asymmetries and the isospin asymmetry in the $B \\\\to \\\\pi \\\\ell^{+} \\\\ell^{-}$ decays. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[212,373,361,386]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"INTRODUCTION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,417,488,917]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It is widely recognized that the exclusive electroweak penguin $B$ -meson decays are of extraordinary importance to explore the intricate dynamics of the quark and lepton sectors in the Standard Model (SM) and to probe sensitively the nonstandard effects with clean experimental signatures. The prominent flavour anomalies observed in the flagship semileptonic $b \\\\rightarrow s\\\\ell^{+}\\\\ell^{-}$ decays include the $\\\\mathcal{O}(4\\\\sigma)$ deviations of the measured $\\\\mathcal{BR}(B^{+} \\\\rightarrow K^{+}\\\\mu^{+}\\\\mu^{-})$ in the low- $q^{2}$ bins with respect to the SM predictions and the $\\\\mathcal{O}(2\\\\sigma)$ tensions between the LHCb measurements of the angular observable $P_{5}^{\\\\prime}(B^{0} \\\\rightarrow K^{0*}\\\\mu^{+}\\\\mu^{-})$ and the state-of-the-art SM computations in the two anomalous bins (see [1] for an overview). In addition, the first LHCb measurement of the integrated isospin asymmetry $A_{\\\\mathrm{I}}(B \\\\rightarrow K\\\\mu^{+}\\\\mu^{-})$ in the entire $q^{2}$ -spectrum deviates from zero at the level of $4\\\\sigma$ [2], while the updated LHCb measurement of this asymmetry favours the lower significance of $1.5\\\\sigma$ [3], due to the inclusion of the 2012 data set and the improved analysis of the 2011 data sample. Precision measurements of the isospin asymmetries in the exclusive $b \\\\rightarrow \\\\{d,s\\\\}\\\\ell^{+}\\\\ell^{-}$ decays will be highly beneficial for constraining the Wilson coefficients of the $\\\\Delta B = 1$ four-quark operators and for unraveling the ultimate nature of the spectator-scattering mechanism in hard exclusive reactions generally [4-8] (see [9, 10] for discussions in the context of the radiative $B$ -meson decays). As a consequence, the in-depth exploitation of the flavour structure of the weak effective theory from the exclusive electroweak penguin $B$ -meson decay constitutes one of the primary physics goals of the LHCb and Belle II experiments, thus triggering the intense theoretical activities towards controlling better hadronic uncertainties of the SM predictions for more than one decade (see for \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[511,372,640,388]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"instance [11-20]).\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[511,388,919,917]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The field-theoretical framework to systematically address the hadronic matrix elements of the electroweak penguin $B$ -meson decays at large recoil has been constructed in the heavy quark mass limit with the perturbative factorization formalism [21, 22] (see also [23, 24] for an equivalent formulation in soft-collinear effective theory (SCET)). The resulting factorization formulae of the exclusive $b \\\\rightarrow \\\\{d, s\\\\} \\\\ell^{+} \\\\ell^{-}$ decay amplitudes can be expressed in terms of heavy-to-light form factors, lightcone distribution amplitudes (LCDAs), and perturbatively calculable short-distance coefficient functions, in analogy to the factorized expressions for the charmless hadronic $B$ -meson decays [25, 26]. In particular, both the weak annihilation and spectator-scattering topologies due to the hard-collinear photon radiation off the light spectator quark yield vanishing contributions to the transverse amplitude of $B \\\\rightarrow V \\\\ell^{+} \\\\ell^{-}$ at leading power in the $\\\\Lambda / m_{b}$ expansion [21, 27]. This interesting observation motivates further factorization analysis of the particular subleading power corrections to the transverse amplitude dependent of the electric charge of the spectator quark [4, 9, 22], which are fortunately determined by the soft-collinear convolution integrals without the disturbing end-pointed divergences (with the exception of the matrix element of the chromomagnetic dipole operator). However, the factorization-scale invariance of both the transverse and longitudinal amplitudes of $B \\\\rightarrow V \\\\ell^{+} \\\\ell^{-}$ was not completely achieved at the next-to-leading order (NLO) in QCD even in the leading-power approximation, owing to the unknown two-loop matrix elements of QCD penguin operators and the absence of the one-loop weak annihilation contribution in the longitudinal amplitude. Moreover, extending the QCD computation of the leading-power weak annihilation effect in $B \\\\rightarrow \\\\{V_{\\\\parallel}, P\\\\} \\\\ell^{+} \\\\ell^{-}$ to the NLO accuracy is in high de \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[22,257,60,713]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"arXiv:2403.11258v1 [hep-ph] 17 Mar 2024 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[81,65,490,125]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"mand for unraveling factorization properties of the exclusive heavy-hadron decay amplitudes and for deepening our understanding towards model-independent properties of the $B$ -meson distribution amplitudes. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,126,490,459]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In order to probe the weak annihilation mechanism of the electroweak penguin bottom-meson decays in a theoretically clean fashion, we will concentrate on the rigorous NLO QCD computation of the weak annihilation contribution to $B \\\\rightarrow \\\\{K,\\\\pi\\\\} \\\\ell^{+}\\\\ell^{-}$ at leading power in the heavy quark expansion in this Letter, by employing the modern SCET technique. It is apparent that such higher-order corrections to the exclusive $B \\\\rightarrow \\\\pi \\\\ell^{+}\\\\ell^{-}$ decay amplitudes become more pronounced than the counterpart $B \\\\rightarrow K\\\\ell^{+}\\\\ell^{-}$ decays, thanks to the unsuppressed contributions from the current-current operators in the weak effective Hamiltonian. Subsequently, we report on a distinctive feature of the obtained soft-collinear factorization formula at $\\\\mathcal{O}(\\\\alpha_s)$ , in contrast with the analytical structure of the available leading-order (LO) expression. Phenomenological implications of the newly computed NLO weak annihilation contributions to the semileptonic $B \\\\rightarrow \\\\{K,\\\\pi\\\\} \\\\ell^{+}\\\\ell^{-}$ decay observables will be further explored with the improved lattice determinations of the leading-twist pion and kaon LCDAs as well as one sample model for the two-particle $B$ -meson LCDAs in heavy quark effective theory (HQET). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[194,484,379,498]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"GENERAL ANALYSIS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,517,488,563]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The effective weak Hamiltonian for the semileptonic $b \\\\to D\\\\ell^{+}\\\\ell^{-}$ (with $D = d$ , $s$ ) transitions in the SM can be written as [22] \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[101,569,488,601]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {H} _ {\\\\text {e f f}} = - \\\\frac {G _ {F}}{\\\\sqrt {2}} \\\\left[ V _ {t b} V _ {t D} ^ {*} \\\\mathcal {H} _ {\\\\text {e f f}} ^ {(t)} + V _ {u b} V _ {u D} ^ {*} \\\\mathcal {H} _ {\\\\text {e f f}} ^ {(u)} \\\\right] + \\\\text {h . c .}, (1)\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,607,488,638]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"by employing the unitarity relations of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[138,645,434,678]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {H} _ {\\\\mathrm {e f f}} ^ {(t)} = C _ {1} \\\\mathcal {Q} _ {1} ^ {c} + C _ {2} \\\\mathcal {Q} _ {2} ^ {c} + \\\\sum_ {i = 3, \\\\dots , 1 0} C _ {i} \\\\mathcal {Q} _ {i},\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[137,681,488,703]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {H} _ {\\\\mathrm {e f f}} ^ {(u)} = C _ {1} \\\\left(\\\\mathcal {Q} _ {1} ^ {c} - \\\\mathcal {Q} _ {1} ^ {u}\\\\right) + C _ {2} \\\\left(\\\\mathcal {Q} _ {2} ^ {c} - \\\\mathcal {Q} _ {2} ^ {u}\\\\right). \\\\qquad (2)\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,708,490,814]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The hadronic matrix elements of the two semileptonic operators $\\\\mathcal{Q}_{9,10}$ can be readily expressed in terms of the heavy-to-light $B$ -meson decay form factors [28]. The remaining contribution to the electroweak penguin decay amplitude can be determined by the contraction of the exclusive $B \\\\to \\\\{K,\\\\pi\\\\}\\\\gamma^{*}$ matrix element with the vector lepton current $\\\\gamma^{*} \\\\to \\\\ell^{+}\\\\ell^{-}$ . We are then led to introduce \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[83,821,488,878]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\langle P (p ^ {\\\\prime}) \\\\gamma^ {*} (q, \\\\mu) | \\\\mathcal {H} _ {\\\\mathrm {e f f}} ^ {(t, u)} | \\\\bar {B} (p) \\\\rangle = - \\\\frac {g _ {\\\\mathrm {e m}} m _ {b}}{4 \\\\pi^ {2}} \\\\frac {\\\\mathcal {T} _ {P} ^ {(t , u)} (q ^ {2})}{m _ {B}} \\\\\\\\ \\\\times \\\\left[ q ^ {2} \\\\left(p _ {\\\\mu} + p _ {\\\\mu} ^ {\\\\prime}\\\\right) - \\\\left(m _ {B} ^ {2} - m _ {P} ^ {2}\\\\right) q _ {\\\\mu} \\\\right], \\\\quad (3) \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,883,491,915]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $|P\\\\rangle$ represents $|K^{-}\\\\rangle$ ( $|\\\\pi^{-}\\\\rangle$ ) for the charged $B^{-}$ decay, and $|\\\\bar{K}^0\\\\rangle$ ( $-\\\\sqrt{2}\\\\pi^0$ ) for the neutral $\\\\bar{B}_d^0$ decay. The \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[524,64,629,127]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(a) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0536/8870b33cbcffb3f02673bc150d715f64190be0ba55a2531111747264b585ab0e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[663,63,769,127]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(b) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0754/e63570ae1b69bc6a44c0148bfaaf166149c1e2a7373ff78b6f712d1516c7c3df.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[803,63,906,127]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(c) \\\",\\\"FIG. 1. Sample Feynman diagrams for the NLO weak annihilation contribution to $B \\\\\\\\rightarrow \\\\\\\\{K, \\\\\\\\pi\\\\\\\\} \\\\\\\\ell^{+} \\\\\\\\ell^{-}$ , where the circled cross indicates the hard-collinear photon radiation. Note that only the virtual photon emission from the soft spectator quark yields the leading-power contribution in the $\\\\\\\\Lambda / m_{b}$ expansion. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0863/ea08a7ad8368272f06dfe23af413f4675b1a64ebfc40be1a8af62a2ea371c916.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[511,267,918,300]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"resulting factorization formulae for the hadronic quantities $\\\\mathcal{T}_P^{(t,u)}$ at leading power can be cast in the form \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[537,308,870,345]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {T} _ {P} ^ {(t, u)} = C _ {P} ^ {(t, u)} (q ^ {2}) f _ {B P} ^ {+} (q ^ {2}) - \\\\frac {\\\\pi^ {2}}{N _ {c}} \\\\frac {\\\\mathcal {F} _ {B} f _ {P}}{m _ {B}} \\\\sum_ {m = \\\\pm}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[537,348,919,385]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\int_ {0} ^ {\\\\infty} \\\\frac {d \\\\omega}{\\\\omega} \\\\int_ {0} ^ {1} d u T _ {P, m} ^ {(t, u)} (\\\\omega , u, \\\\mu) \\\\phi_ {B, m} (\\\\omega , \\\\mu) \\\\phi_ {P} (u, \\\\mu), (4)\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[511,392,919,551]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $f_{BP}^{+}(q^{2})$ denotes the vector form factor defined by the local QCD matrix element $\\\\langle P(p')|\\\\bar{D}\\\\gamma_{\\\\mu}b|\\\\bar{B} (p)\\\\rangle$ . $\\\\mathcal{F}_B$ corresponds to the HQET $B$ -meson decay constant and $f_{P}$ is the scale-independent decay constant of the energetic pseudoscalar meson. Furthermore $\\\\phi_{B,\\\\pm}(\\\\omega ,\\\\mu)$ and $\\\\phi_P(u,\\\\mu)$ refer to the $B$ -meson and light-meson LCDAs [29-32]. The short-distance coefficient functions $C_P^{(i)}(q^2)$ and $T_{P,m}^{(i)}(\\\\omega ,u,\\\\mu)$ $(i = u,t)$ can be expanded perturbatively as follows (similarly for any other partonic quantity) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[511,558,929,594]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nC _ {P} ^ {(i)} = \\\\sum_ {\\\\ell} \\\\left(\\\\frac {\\\\alpha_ {s}}{4 \\\\pi}\\\\right) ^ {\\\\ell} C _ {P} ^ {(\\\\ell , i)}, \\\\quad T _ {P, m} ^ {(i)} = \\\\sum_ {\\\\ell} \\\\left(\\\\frac {\\\\alpha_ {s}}{4 \\\\pi}\\\\right) ^ {\\\\ell} T _ {P, m} ^ {(\\\\ell , i)}. \\\\tag {5}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[511,603,919,768]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The analytical expressions of the known perturbative kernels at $\\\\mathcal{O}(\\\\alpha_s)$ can be extracted from [21, 22]. In particular, only the subleading twist HQET distribution amplitude $\\\\phi_{B, - }(\\\\omega ,\\\\mu)$ appears in the tree-level factorization formula for the spectator-scattering contribution of $B\\\\rightarrow P\\\\ell^{+}\\\\ell^{-}$ , in sharp contrast with the radiative leponic decays $B\\\\to \\\\gamma \\\\ell \\\\bar{\\\\nu}_{\\\\ell}$ , $B\\\\to \\\\gamma \\\\ell^{+}\\\\ell^{-}$ [33-36], and the double radiative decay $B_{d,s}\\\\rightarrow \\\\gamma \\\\gamma$ [34, 37-39]. As discussed in [21, 22], it turns out to be advantageous to introduce two effective Wilson coefficients independent of the renormalization conventions for the weak effective Hamiltonian \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[580,775,919,814]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {C} _ {9, P} ^ {(i)} (q ^ {2}) = C _ {9} \\\\delta^ {i t} + \\\\frac {2 m _ {b}}{m _ {B}} \\\\frac {\\\\mathcal {T} _ {P} ^ {(i)} (q ^ {2})}{f _ {B P} ^ {+} (q ^ {2})}. \\\\tag {6}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[544,838,885,864]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"QCD FACTORIZATION FOR THE WEAK ANNIHILATION CONTRIBUTION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[511,883,919,915]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We are now in a position to compute the NLO weak annihilation contribution to $B \\\\to \\\\{K, \\\\pi\\\\} \\\\ell^{+} \\\\ell^{-}$ with the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[906,34,919,45]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[81,65,488,261]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"soft-collinear factorization technique. Inspecting the one-loop partonic diagrams displayed in Figure 1 indicates that the four distinct classes of field modes (hard, hard-collinear, anti-hard-collinear, and soft) carrying the four-momenta $P_{\\\\mathrm{h},\\\\mu} \\\\sim \\\\mathcal{O}(1,1,1)$ , $P_{\\\\mathrm{hc},\\\\mu} \\\\sim \\\\mathcal{O}(1,\\\\lambda,\\\\lambda^{1/2})$ , $P_{\\\\overline{\\\\mathrm{hc}},\\\\mu} \\\\sim \\\\mathcal{O}(\\\\lambda,1,\\\\lambda^{1/2})$ and $P_{\\\\mathrm{s},\\\\mu} \\\\sim \\\\mathcal{O}(\\\\lambda,\\\\lambda,\\\\lambda)$ appear in the problem under consideration, where the individual momentum components correspond to $n \\\\cdot P$ , $\\\\bar{n} \\\\cdot P$ and $P_{\\\\perp}$ for an arbitrary momentum $P_{\\\\mu}$ . The two light-cone vectors $n_{\\\\mu}$ and $\\\\bar{n}_{\\\\mu}$ satisfying $n^2 = \\\\bar{n}^2 = 0$ and $n \\\\cdot \\\\bar{n} = 2$ are chosen such that $n \\\\cdot q \\\\sim \\\\bar{n} \\\\cdot p' \\\\sim \\\\mathcal{O}(m_b)$ . Additionally, the heavy-quark expansion parameter $\\\\lambda$ scales as $\\\\Lambda_{\\\\mathrm{QCD}} / m_b$ in our power-counting analysis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,261,490,429]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A systematic decoupling of the hard and (anti)-hard-collinear fluctuations can be achieved by taking advantage of the two-step matching strategy $\\\\mathrm{QCD} \\\\rightarrow \\\\mathrm{SCET}_{\\\\mathrm{I}} \\\\rightarrow \\\\mathrm{SCET}_{\\\\mathrm{II}}$ . In accordance with the power-counting argument developed in the position-space formalism [40-42], both the A0-type and B1-type $\\\\mathrm{SCET}_{\\\\mathrm{I}}$ operators can generate the leading-power contribution to the weak annihilation amplitude. It is then straightforward to write down the $\\\\mathrm{SCET}_{\\\\mathrm{I}}$ representation of the current-current and QCD penguin operators $\\\\mathcal{Q}_i \\\\in \\\\{\\\\mathcal{Q}_1^u, \\\\mathcal{Q}_2^u, \\\\mathcal{Q}_{3-6}\\\\}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[165,435,488,454]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {Q} _ {i} = H _ {i} ^ {\\\\mathrm {I}} \\\\star \\\\mathcal {O} ^ {(\\\\mathrm {A} 0)} + H _ {i} ^ {\\\\mathrm {I I}} \\\\star \\\\mathcal {O} ^ {(\\\\mathrm {B} 1)}, \\\\tag {7}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,462,488,522]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"for the \\\"right-insertion\\\" topology where the spinor indices are contracted along the quark lines of the bottom meson and the light meson. We have employed here the customary asterisk notation in SCET \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[135,531,392,561]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nH _ {i} ^ {\\\\mathrm {I}} \\\\star \\\\mathcal {O} ^ {(\\\\mathrm {A 0})} = \\\\int d \\\\hat {t} H _ {i} ^ {\\\\mathrm {I}} (\\\\hat {t}) \\\\mathcal {O} ^ {(\\\\mathrm {A 0})} (t),\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[132,565,488,594]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nH _ {i} ^ {\\\\mathrm {I I}} \\\\star \\\\mathcal {O} ^ {(\\\\mathrm {B 1})} = \\\\int d \\\\hat {t} d \\\\hat {s} H _ {i} ^ {\\\\mathrm {I I}} (\\\\hat {t}, \\\\hat {s}) \\\\mathcal {O} ^ {(\\\\mathrm {B 1})} (t, s), \\\\tag {8}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,603,488,650]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"with the dimensionless convolution variables $\\\\hat{t} = (\\\\bar{n}\\\\cdot p')t$ and $\\\\hat{s} = (n\\\\cdot q)s$ . The explicit expressions of the two SCET $_{\\\\mathrm{I}}$ operators of our interest are given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[86,657,503,710]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\mathcal {O} ^ {(\\\\mathrm {A} 0)} = \\\\left[ (\\\\bar {\\\\chi} W _ {\\\\bar {c}}) (t \\\\bar {n}) \\\\frac {\\\\vec {\\\\eta}}{2} (1 - \\\\gamma_ {5}) \\\\left(W _ {\\\\bar {c}} ^ {\\\\dagger} \\\\chi\\\\right) (0) \\\\right] \\\\\\\\ \\\\left[ \\\\left(\\\\bar {\\\\xi} W _ {c}\\\\right) (0) \\\\not \\\\exists (1 - \\\\gamma_ {5}) h _ {v} (0) \\\\right], \\\\tag {9} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[86,714,503,781]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\mathcal {O} ^ {(B 1)} = \\\\frac {1}{m _ {b}} \\\\left[ (\\\\bar {\\\\chi} W _ {\\\\bar {c}}) (t \\\\bar {n}) \\\\frac {\\\\not {p h}}{2} (1 - \\\\gamma_ {5}) \\\\left(W _ {\\\\bar {c}} ^ {\\\\dagger} \\\\chi\\\\right) (0) \\\\right] \\\\\\\\ \\\\left[ \\\\left(\\\\bar {\\\\xi} W _ {c}\\\\right) (0) \\\\frac {\\\\not {h}}{2} \\\\left[ W _ {c} ^ {\\\\dagger} i \\\\not {D} _ {\\\\perp c} W _ {c} \\\\right] (s n) \\\\left(1 + \\\\gamma_ {5}\\\\right) h _ {v} (0) \\\\right], \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,787,488,849]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where the collinear Wilson lines $W_{c}$ and $W_{\\\\bar{c}}$ are introduced to ensure gauge invariance [40]. Along the same vein, the matching equation for the \\\"wrong-insertion\\\" topology takes the form \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[165,856,488,875]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {Q} _ {i} = \\\\tilde {H} _ {i} ^ {\\\\mathrm {I}} \\\\star \\\\mathcal {O} ^ {(\\\\mathrm {A} 0)} + \\\\tilde {H} _ {i} ^ {\\\\mathrm {I I}} \\\\star \\\\mathcal {O} ^ {(\\\\mathrm {B} 1)}, \\\\tag {10}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,883,488,914]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where both the bottom and light mesons are made up of the quark-antiquark pair from two different bilinears \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[511,65,919,126]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"in the QCD operators (see [41] for further discussions). Performing the Fourier transformation with respect to the light-cone variables $\\\\hat{t}$ and $\\\\hat{s}$ defines the momentum-space short-distance functions \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,135,936,196]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\left\\\\{\\\\mathbb {H} _ {i} ^ {\\\\mathrm {I}}, \\\\tilde {\\\\mathbb {H}} _ {i} ^ {\\\\mathrm {I}} \\\\right\\\\} (u) = \\\\int d \\\\hat {t} e ^ {i u \\\\hat {t}} \\\\left\\\\{H _ {i} ^ {\\\\mathrm {I}}, \\\\tilde {H} _ {i} ^ {\\\\mathrm {I}} \\\\right\\\\} (\\\\hat {t}), \\\\\\\\ \\\\left\\\\{\\\\mathbb {H} _ {i} ^ {\\\\mathrm {I I}}, \\\\tilde {\\\\mathbb {H}} _ {i} ^ {\\\\mathrm {I I}} \\\\right\\\\} (u, \\\\tau) = \\\\int d \\\\hat {t} e ^ {i (u \\\\hat {t} + \\\\tau \\\\hat {s})} \\\\left\\\\{H _ {i} ^ {\\\\mathrm {I I}}, \\\\tilde {H} _ {i} ^ {\\\\mathrm {I I}} \\\\right\\\\} (\\\\hat {t}, \\\\hat {s}). \\\\tag {11} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[511,203,919,325]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It becomes apparent that we are required to derive both the \\\"right-insertion\\\" and the \\\"wrong-insertion\\\" matching coefficients for the current-current operators $\\\\mathcal{Q}_{1,2}^{u}$ , but merely the \\\"wrong-insertion\\\" kernels for the QCD penguin operators $\\\\mathcal{Q}_{3-6}$ . Applying the technical framework of determining the renormalized hard-scattering kernels with the inclusion of the evanescent operators detailed in [43, 44] leads to the desired results at the $\\\\mathcal{O}(\\\\alpha_s)$ accuracy \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[516,333,926,484]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\mathbb {H} _ {1} ^ {\\\\mathrm {I} (0)} = 0, \\\\quad \\\\mathbb {H} _ {2} ^ {\\\\mathrm {I} (0)} = 1, \\\\quad \\\\tilde {\\\\mathbb {H}} _ {1, 4} ^ {\\\\mathrm {I} (0)} = \\\\frac {C _ {F}}{N _ {c}}, \\\\quad \\\\tilde {\\\\mathbb {H}} _ {2, 3} ^ {\\\\mathrm {I} (0)} = \\\\frac {1}{N _ {c}}, \\\\\\\\ \\\\tilde {\\\\mathbb {H}} _ {5} ^ {\\\\mathbf {I} (0)} = \\\\frac {1 6}{N _ {c}}, \\\\quad \\\\tilde {\\\\mathbb {H}} _ {6} ^ {\\\\mathbf {I} (0)} = 1 6 \\\\frac {C _ {F}}{N _ {c}}, \\\\\\\\ \\\\mathbb {H} _ {1} ^ {\\\\mathrm {I I} (0)} = \\\\frac {1}{N _ {c}} \\\\frac {1}{\\\\bar {u}}, \\\\quad \\\\mathbb {H} _ {2} ^ {\\\\mathrm {I I} (0)} = 2, \\\\tag {12} \\\\\\\\ \\\\tilde {\\\\mathbb {H}} _ {1, 4} ^ {\\\\mathrm {I I} (0)} = \\\\frac {1}{N _ {c}} \\\\left[ 2 C _ {F} - \\\\frac {1}{N _ {c}} \\\\frac {1}{\\\\bar {u}} \\\\right], \\\\quad \\\\tilde {\\\\mathbb {H}} _ {2, 3} ^ {\\\\mathrm {I I} (0)} = \\\\frac {2}{N _ {c}} \\\\left[ 1 + \\\\frac {1}{\\\\bar {u}} \\\\right], \\\\\\\\ \\\\tilde {\\\\mathbb {H}} _ {5} ^ {\\\\mathrm {I I} (0)} = 1 6 \\\\tilde {\\\\mathbb {H}} _ {2} ^ {\\\\mathrm {I I} (0)}, \\\\qquad \\\\qquad \\\\tilde {\\\\mathbb {H}} _ {6} ^ {\\\\mathrm {I I} (0)} = 1 6 \\\\tilde {\\\\mathbb {H}} _ {1} ^ {\\\\mathrm {I I} (0)}, \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[513,493,544,505]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[521,513,916,744]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\mathbb {H} _ {1} ^ {\\\\mathrm {I} (1)} = \\\\frac {C _ {F}}{2 N _ {c}} \\\\left[ - 6 \\\\mathcal {L} + \\\\mathfrak {h} (u) \\\\right], \\\\\\\\ \\\\mathbb {H} _ {2} ^ {\\\\mathrm {I} (1)} = - \\\\frac {C _ {F}}{2} \\\\left[ \\\\mathcal {L} ^ {2} + 5 \\\\mathcal {L} + \\\\frac {\\\\pi^ {2}}{6} + 1 2 \\\\right], \\\\\\\\ \\\\tilde {\\\\mathbb {H}} _ {1} ^ {\\\\mathrm {I} (1)} = \\\\frac {1}{N _ {c}} \\\\left[ C _ {F} \\\\mathbb {H} _ {2} ^ {\\\\mathrm {I} (1)} - \\\\mathbb {H} _ {1} ^ {\\\\mathrm {I} (1)} \\\\right] - C _ {F}, \\\\\\\\ \\\\tilde {\\\\mathbb {H}} _ {2} ^ {\\\\mathrm {I} (1)} = \\\\tilde {\\\\mathbb {H}} _ {3} ^ {\\\\mathrm {I} (1)} = \\\\frac {1}{N _ {c}} \\\\mathbb {H} _ {2} ^ {\\\\mathrm {I} (1)} + 2 \\\\mathbb {H} _ {1} ^ {\\\\mathrm {I} (1)}, \\\\tag {13} \\\\\\\\ \\\\tilde {\\\\mathbb {H}} _ {4} ^ {\\\\mathrm {I} (1)} = \\\\frac {1}{N _ {c}} \\\\left[ C _ {F} \\\\mathbb {H} _ {2} ^ {\\\\mathrm {I} (1)} - \\\\mathbb {H} _ {1} ^ {\\\\mathrm {I} (1)} \\\\right] + \\\\frac {C _ {F}}{N _ {c}} \\\\left[ \\\\frac {2}{3} n _ {f} - N _ {c} \\\\right], \\\\\\\\ \\\\tilde {\\\\mathbb {H}} _ {5} ^ {\\\\mathrm {I} (1)} = \\\\frac {1 6}{N _ {c}} \\\\mathbb {H} _ {2} ^ {\\\\mathrm {I} (1)} + 3 2 \\\\mathbb {H} _ {1} ^ {\\\\mathrm {I} (1)}, \\\\\\\\ \\\\tilde {\\\\mathbb {H}} _ {6} ^ {\\\\mathrm {I} (1)} = \\\\frac {1 6}{N _ {c}} \\\\left[ C _ {F} \\\\mathbb {H} _ {2} ^ {\\\\mathrm {I} (1)} - \\\\mathbb {H} _ {1} ^ {\\\\mathrm {I} (1)} \\\\right] + \\\\frac {1 0 C _ {F}}{N _ {c}} \\\\left[ \\\\frac {2}{3} n _ {f} - 4 N _ {c} \\\\right]. \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[511,752,918,768]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For brevity we have introduced the following conventions \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,775,934,840]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\mathfrak {h} (u) = \\\\ln^ {2} (u \\\\bar {u}) + \\\\left(3 - \\\\frac {2}{u}\\\\right) \\\\ln \\\\bar {u} - 2 \\\\ln^ {2} u + \\\\left(3 - \\\\frac {1}{\\\\bar {u}}\\\\right) \\\\ln u \\\\\\\\ + 4 \\\\operatorname {L i} _ {2} (u) - \\\\frac {\\\\pi^ {2}}{3} - 2 2 + i \\\\pi (2 \\\\ln \\\\bar {u} - 2 \\\\ln u - 3), \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[535,842,933,876]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathcal {L} \\\\equiv \\\\ln \\\\left(\\\\frac {\\\\mu^ {2}}{m _ {b} ^ {2}}\\\\right), \\\\quad \\\\bar {u} \\\\equiv 1 - u, \\\\quad n _ {f} = 5. \\\\tag {14}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[511,883,919,914]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As demonstrated in [41, 45, 46], the hard-collinear and aniti-hard-collinear fields decouple already at the hard \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[906,34,919,46]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[81,65,490,127]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"scale of $\\\\mathcal{O}(m_b)$ . This essential observation can be attributed to the disappearing leading-power interactions between the (hard)-collinear fields with different directions in the SCET Lagrangian after the field redefini \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[511,65,919,126]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tion [47] (see also [48, 49] for an overview). The obtained $\\\\mathrm{SCET_I}$ matrix elements of $\\\\mathcal{O}^{(\\\\mathrm{A0})}$ and $\\\\mathcal{O}^{(\\\\mathrm{B1})}$ then fall apart into two distinct sectors each, thus generating the non-local effective matrix elements below \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[107,162,687,196]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\langle P (p ^ {\\\\prime}) | (\\\\bar {\\\\chi} W _ {\\\\bar {c}}) (t \\\\bar {n}) \\\\frac {\\\\vec {n}}{2} (1 - \\\\gamma_ {5}) (W _ {\\\\bar {c}} ^ {\\\\dagger} \\\\chi) (0) | 0 \\\\rangle = i f _ {P} \\\\frac {\\\\bar {n} \\\\cdot p ^ {\\\\prime}}{2} \\\\int_ {0} ^ {1} d u e ^ {i (\\\\bar {n} \\\\cdot p ^ {\\\\prime}) u t} \\\\phi_ {P} (u, \\\\mu),\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[106,198,928,228]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\int d ^ {4} x e ^ {i q \\\\cdot x} \\\\langle 0 | \\\\mathrm {T} \\\\left\\\\{j _ {\\\\mathrm {e m}, \\\\mu} ^ {\\\\parallel} (x), (\\\\bar {\\\\xi} W _ {c}) (0) \\\\gamma_ {5} h _ {v} (0) \\\\right\\\\} | \\\\bar {B} (p) \\\\rangle = \\\\mathcal {J} _ {P} ^ {(\\\\mathrm {A} 0)} (n \\\\cdot q, \\\\bar {n} \\\\cdot q) \\\\bar {n} _ {\\\\mu}, \\\\tag {15}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[106,231,928,261]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\frac{n\\\\cdot q}{2\\\\pi}\\\\int d^{4}x e^{iq\\\\cdot x}\\\\int ds e^{i(n\\\\cdot q)\\\\tau s}\\\\langle 0|\\\\mathrm{T}\\\\left\\\\{j_{\\\\mathrm{em},\\\\mu}^{\\\\parallel}(x),\\\\left(\\\\bar{\\\\xi} W_{c}\\\\right)(0)\\\\gamma_{5}\\\\left[W_{c}^{\\\\dagger}i\\\\not D_{\\\\perp c}W_{c}\\\\right](sn)h_{v}(0)\\\\right\\\\} |\\\\bar{B} (p)\\\\rangle = \\\\mathcal{J}_{P}^{\\\\mathrm{(B1)}}(n\\\\cdot q,\\\\bar{n}\\\\cdot q,\\\\tau)\\\\bar{n}_{\\\\mu}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,301,488,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The $\\\\mathrm{SCET_I}$ representation of the electromagnetic current relevant here is given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,342,495,396]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} j _ {\\\\mathrm {e m}, \\\\mu} ^ {\\\\parallel} \\\\supset j _ {\\\\mathrm {e m}, \\\\mu} ^ {\\\\parallel , (0)} + j _ {\\\\mathrm {e m}, \\\\mu} ^ {\\\\parallel , (2)} \\\\tag {16} \\\\\\\\ = \\\\bar {\\\\xi} \\\\frac {\\\\eta \\\\hbar}{2} \\\\xi \\\\bar {n} _ {\\\\mu} + \\\\left[ (\\\\bar {\\\\xi} W _ {c}) \\\\frac {\\\\eta \\\\hbar}{2} (Y _ {s} ^ {\\\\dagger} q _ {s}) + (\\\\bar {q} _ {s} Y _ {s}) \\\\frac {\\\\eta \\\\hbar}{2} (W _ {c} ^ {\\\\dagger} \\\\xi) \\\\right] \\\\bar {n} _ {\\\\mu}, \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,406,490,625]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where the second term on the right-hand side converts the soft spectator quark into a hard-collinear quark and counts as $\\\\mathcal{O}(\\\\lambda^2)$ . The leading-power current $j_{\\\\mathrm{em},\\\\mu}^{\\\\parallel,(0)}$ can contribute to $\\\\mathcal{J}_P^{(\\\\mathrm{A0})}\\\\left(\\\\mathcal{J}_P^{(\\\\mathrm{B1})}\\\\right)$ only through time-ordered products with an additional SCET Lagrangian $\\\\mathcal{L}_{\\\\xi q_s}^{(2)}$ $(\\\\mathcal{L}_{\\\\xi q_s}^{(1)})$ [50]. By contrast, the subleading-power current $j_{\\\\mathrm{em},\\\\mu}^{\\\\parallel,(2)}$ can bring about the non-vanishing contribution to $\\\\mathcal{J}_P^{(\\\\mathrm{A0})}$ already at tree level (and certainly at higher orders in $\\\\alpha_s$ with insertions of the unsuppressed SCET Lagrangian $\\\\mathcal{L}_{\\\\xi}^{(0)})$ ). Integrating out the hard-collinear fluctuations in the $\\\\mathrm{SCET_I}$ correlation functions by virtue of the second-step matching $\\\\mathrm{SCET_I}\\\\rightarrow \\\\mathrm{SCET_{II}}$ enables us to derive the soft-collinear factorization formulae [15, 51] \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[86,637,496,720]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\mathcal {J} _ {P} ^ {(A 0)} = \\\\frac {\\\\mathcal {F} _ {B} m _ {B}}{2} \\\\int_ {0} ^ {\\\\infty} d \\\\omega \\\\frac {\\\\mathbb {J} _ {\\\\parallel , -} (n \\\\cdot q , \\\\bar {n} \\\\cdot q , \\\\omega)}{\\\\bar {n} \\\\cdot q - \\\\omega + i 0} \\\\phi_ {B, -} (\\\\omega , \\\\mu), \\\\\\\\ \\\\mathcal {J} _ {P} ^ {\\\\left(\\\\mathrm {B} 1\\\\right)} = \\\\frac {\\\\mathcal {F} _ {B} m _ {B}}{2} \\\\int_ {0} ^ {\\\\infty} d \\\\omega \\\\mathbb {J} _ {\\\\|, +} (n \\\\cdot q, \\\\bar {n} \\\\cdot q, \\\\omega , \\\\tau) \\\\phi_ {B, +} (\\\\omega , \\\\mu). \\\\tag {17} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[81,732,488,780]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Employing the SCET Feynman rules collected in [52], we can readily determine the renormalized jet functions $\\\\mathbb{J}_{\\\\parallel, -}$ and $\\\\mathbb{J}_{\\\\parallel, +}$ up to the order $\\\\alpha_{s}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,792,279,816]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left\\\\{\\\\mathbb {J} _ {\\\\parallel , -} ^ {(0)}, \\\\mathbb {J} _ {\\\\parallel , +} ^ {(0)} \\\\right\\\\} = \\\\{1, 0 \\\\},\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[112,820,478,888]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\mathbb {J} _ {\\\\parallel , -} ^ {(1)} = C _ {F} \\\\left[ \\\\ln^ {2} \\\\frac {\\\\hat {\\\\mu} ^ {2}}{\\\\omega - \\\\bar {n} \\\\cdot q} - 2 \\\\ln \\\\frac {\\\\hat {\\\\mu} ^ {2}}{\\\\omega - \\\\bar {n} \\\\cdot q} \\\\ln (1 + \\\\eta) \\\\right. \\\\\\\\ \\\\left. - \\\\ln^ {2} (1 + \\\\eta) + \\\\left(\\\\frac {2}{\\\\eta} - 1\\\\right) \\\\ln (1 + \\\\eta) - \\\\frac {\\\\pi^ {2}}{6} - 1 \\\\right], \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[112,891,486,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathbb {J} _ {\\\\parallel , +} ^ {(1)} = 2 C _ {F} \\\\frac {n \\\\cdot q}{\\\\omega} \\\\ln (1 + \\\\eta) (1 - \\\\tau) \\\\theta (\\\\tau) \\\\theta (1 - \\\\tau), \\\\tag {18}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[511,300,919,515]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where we have defined two variables $\\\\hat{\\\\mu}^2 = \\\\mu^2 /n\\\\cdot q$ and $\\\\eta = -\\\\omega /\\\\bar{n}\\\\cdot q$ . Interestingly, the leading-twist bottommeson distribution amplitude $\\\\phi_{B, + }(\\\\omega ,\\\\mu)$ now enters the perturbative factorization formula (17) of the weak annihilation amplitude at $\\\\mathcal{O}(\\\\alpha_s)$ , in contrast with the factorized expression for the tree-level annihilation amplitude. On the basis of the asymptotic behaviours of $\\\\phi_{B,\\\\pm}(\\\\omega ,\\\\mu)$ [29, 53-59], we can further verify that the soft-collinear convolution integrals in (17) converge at $q^{2}\\\\sim \\\\mathcal{O}(m_{b}\\\\Lambda_{\\\\mathrm{QCD}})$ and the complex-valued invariant functions $\\\\mathcal{J}_P^{(\\\\mathrm{A0})}$ and $\\\\mathcal{J}_P^{(\\\\mathrm{B1})}$ cannot be entirely described by the two particular moments $\\\\lambda_{B, + }^{-1}$ and $\\\\lambda_{B, - }^{-1}(q^2)$ of the bottom-meson distribution amplitudes as previously introduced in [21]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[511,515,919,575]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We now summarize the explicit expressions of the NLO weak annihilation corrections to the short-distance matching functions $T_{P,m}^{(t,u)}$ appearing in the QCD factorization formulae (4) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,585,933,705]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\left\\\\{T _ {P, +} ^ {(u)}, T _ {P, +} ^ {(t)} \\\\right\\\\} \\\\supset - Q _ {q} N _ {c} \\\\frac {2 m _ {B}}{m _ {b}} \\\\int_ {0} ^ {1} d \\\\tau \\\\mathbb {J} _ {| |, +} (n \\\\cdot q, \\\\bar {n} \\\\cdot q, \\\\omega , \\\\tau) \\\\\\\\ \\\\left\\\\{- \\\\sum_ {i = 1} ^ {2} C _ {i} \\\\left[ \\\\mathbb {H} _ {i} ^ {\\\\mathrm {I I}} (u, \\\\tau) \\\\delta_ {q u} - \\\\tilde {\\\\mathbb {H}} _ {i} ^ {\\\\mathrm {I I}} (u, \\\\tau) \\\\delta_ {q d} \\\\delta_ {P \\\\pi} \\\\right], \\\\right. \\\\\\\\ \\\\left. \\\\sum_ {i = 3} ^ {6} C _ {i} \\\\tilde {\\\\mathbb {H}} _ {i} ^ {\\\\mathrm {I I}} (u, \\\\tau) \\\\right\\\\}, \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[517,709,934,827]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\left\\\\{T _ {P, -} ^ {(u)}, T _ {P, -} ^ {(t)} \\\\right\\\\} \\\\supset Q _ {q} N _ {c} \\\\frac {4 m _ {B}}{m _ {b}} \\\\frac {\\\\mathbb {J} _ {\\\\| , -} (n \\\\cdot q , \\\\bar {n} \\\\cdot q , \\\\omega)}{\\\\hat {q} ^ {2} - 1 + i 0} \\\\\\\\ \\\\left\\\\{- \\\\sum_ {i = 1} ^ {2} C _ {i} \\\\left[ \\\\mathbb {H} _ {i} ^ {\\\\mathrm {I}} (u) \\\\delta_ {q u} - \\\\tilde {\\\\mathbb {H}} _ {i} ^ {\\\\mathrm {I}} (u) \\\\delta_ {q d} \\\\delta_ {P \\\\pi} \\\\right], \\\\right. \\\\\\\\ \\\\left. \\\\sum_ {i = 3} ^ {6} C _ {i} \\\\tilde {\\\\mathbb {H}} _ {i} ^ {\\\\mathrm {I}} (u) \\\\right\\\\}, \\\\tag {19} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[511,835,919,914]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $Q_{q}$ denotes the electric charge of the soft spectator quark in the $B$ -meson. Furthermore, $\\\\hat{q}^2 = q^2 / (m_B\\\\omega)$ , $\\\\delta_{P\\\\pi} = 1$ , 0 for $\\\\pi$ and $K$ mesons, respectively. We remark in passing that the hard coefficient functions $\\\\mathbb{H}_{1,2}^{\\\\mathrm{II}}$ and $\\\\tilde{\\\\mathbb{H}}_{1-6}^{\\\\mathrm{II}}$ of the B1-type SCETI operators are independent \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[906,34,919,45]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[81,64,491,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"of the variable $\\\\tau$ at $\\\\mathcal{O}(\\\\alpha_s^0)$ and the jet function $\\\\mathbb{J}_{\\\\parallel , + }$ starts from $\\\\mathcal{O}(\\\\alpha_s)$ , thus allowing us to perform the integration over $\\\\tau$ in the obtained $T_{P, + }^{(u,t)}$ straightforwardly in the NLO approximation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[181,156,392,169]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"NUMERICAL ANALYSIS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,188,491,595]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We continue to explore phenomenological implications of the NLO weak annihilation contributions to the exclusive rare decays $B \\\\rightarrow \\\\{K, \\\\pi\\\\} \\\\ell^{+} \\\\ell^{-}$ at large hadronic recoil. The Wilson coefficients $C_i$ in the weak effective Hamiltonian (1) will be evaluated at the initial scale $\\\\mu_W = m_W$ [60, 61] and then evolved to the hard scale $\\\\mu_{\\\\mathrm{h}} = m_b$ with the required accuracy (following [62, 63]). We further adopt the three-parameter ansatz for the HQET $B$ -meson LCDAs as proposed in [64] (see [65-68] for additional discussions), which can be analytically evolved into the hard-collinear scale with the renormalization-group (RG) formalism at the leading-logarithmic accuracy. The leptonic decay constants of the $B$ -meson, pion and kaon are taken from the averages of the lattice QCD simulations [69]. Moreover, we will truncate the Gegenbauer expansion of the leading-twist pion and kaon LCDAs by including only the two lowest moments whose intervals have been determined from lattice QCD at the $\\\\overline{\\\\mathrm{MS}}$ scale $\\\\mu_0 = 2.0\\\\mathrm{GeV}$ with full control of all systematic uncertainties [70]. The two-loop RG evolution of these Gegenbauer moments [71, 72] (see also [73, 74]) will be then implemented for the sake of describing their scale dependence. In particular, we employ the improved QCD predictions of the semileptonic form factors $f_{B\\\\pi}^{+}(q^{2})$ and $f_{BK}^{+}(q^{2})$ displayed in [18]. The choices for the remaining parameters in numerical studies are identical to the ones summarized in [36]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[81,595,490,914]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Inspecting the numerical features of the effective Wilson coefficient $\\\\mathcal{C}_{9,P}^{(u)}$ for $B^{-}\\\\rightarrow \\\\pi^{-}\\\\ell^{+}\\\\ell^{-}$ displayed in Figure 2 indicates that the newly computed NLO weak annihilation contribution can bring about $\\\\mathcal{O}(35\\\\%)$ $(\\\\mathcal{O}(15\\\\%))$ reduction of the tree-level prediction for the real (imaginary) part of $\\\\mathcal{C}_{9,P}^{(u)}$ in the kinematic range $1.5\\\\mathrm{GeV}^2\\\\leq q^2\\\\leq 4.0\\\\mathrm{GeV}^2$ . By contrast, the previously determined NLO QCD correction to the invariant amplitude $\\\\mathcal{T}_P^{(u)}$ (shown in Figure 2 of [21]) generates, on the one hand, an impact on $\\\\mathrm{Re}[\\\\mathcal{C}_{9,P}^{(u)}]$ no more than $10\\\\%$ numerically in the same kinematic region and, on the other hand, approximately $(15 - 30)\\\\%$ reduction of the LO prediction of $\\\\mathrm{Im}[\\\\mathcal{C}_{9,P}^{(u)}]$ . In consequence, the higher-order weak annihilation effect under discussion provides an intriguing source of the strong phases of the exclusive $b\\\\to d\\\\ell^{+}\\\\ell^{-}$ decay amplitudes. In addition, the NLO weak annihilation correction to the invariant amplitude $\\\\mathcal{T}_P^{(t)}$ appears to be merely $\\\\mathcal{O}(3\\\\%)$ of the previously computed NLO contribution [21, 22] in magnitude at $q^2\\\\in [1.5,4.0]\\\\mathrm{GeV}^2$ due to the absence of an important contribution from \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[527,68,906,272]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"FIG. 2. Theory prediction for the $q^2$ dependence of the effective Wilson coefficient $\\\\\\\\mathcal{C}_{9,P}^{(u)}$ dictating the exclusive $B^{-}\\\\\\\\rightarrow \\\\\\\\pi^{-}\\\\\\\\ell^{+}\\\\\\\\ell^{-}$ decay amplitude at LO (black curves), at NLO $_{\\\\\\\\mathrm{BFS}}$ (blue curves) and at NLO (pink bands), where the notation \\\\\\\"NLO $_{\\\\\\\\mathrm{BFS}}$ represents the available NLO computation accomplished in [21, 22], and the uncertainties are obtained from varying the hard and hard-collinear matching scales. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0123/0314f6f2963c97ebf3e99bb7d5adce717dd1e54d4aa89f9a7ef67c93c5c087cd.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[511,428,918,457]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the current-current operators $\\\\mathcal{Q}_{1,2}^{c}$ with the large Wilson coefficients. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[511,458,919,550]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We proceed to explore phenomenological impacts of the determined NLO weak annihilation correction on the CP-averaged branching fraction $(\\\\mathcal{B}\\\\mathcal{R})$ , the direct CP asymmetry $(\\\\mathcal{A}_{\\\\mathrm{CP}})$ and the CP-averaged isospin asymmetry $(\\\\mathcal{A}_{\\\\mathrm{I}})$ for $B \\\\to P\\\\ell^{+}\\\\ell^{-}$ , the latter two of which are explicitly defined by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[511,559,926,631]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} \\\\mathcal {A} _ {\\\\mathrm {C P}} = \\\\frac {\\\\Gamma (\\\\bar {B} \\\\rightarrow \\\\bar {P} \\\\ell^ {+} \\\\ell^ {-}) - \\\\Gamma (B \\\\rightarrow P \\\\ell^ {+} \\\\ell^ {-})}{\\\\Gamma (\\\\bar {B} \\\\rightarrow \\\\bar {P} \\\\ell^ {+} \\\\ell^ {-}) + \\\\Gamma (B \\\\rightarrow P \\\\ell^ {+} \\\\ell^ {-})}, \\\\\\\\ \\\\mathcal {A} _ {\\\\mathrm {I}} = \\\\frac {\\\\kappa \\\\Gamma (\\\\bar {B} ^ {0} \\\\rightarrow \\\\bar {P} ^ {0} \\\\ell^ {+} \\\\ell^ {-}) - \\\\Gamma (B ^ {-} \\\\rightarrow P ^ {-} \\\\ell^ {+} \\\\ell^ {-})}{\\\\kappa \\\\Gamma (\\\\bar {B} ^ {0} \\\\rightarrow \\\\bar {P} ^ {0} \\\\ell^ {+} \\\\ell^ {-}) + \\\\Gamma (B ^ {-} \\\\rightarrow P ^ {-} \\\\ell^ {+} \\\\ell^ {-})}, \\\\tag {20} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[511,641,921,915]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"with the factor $\\\\kappa = 2,1$ for $P = \\\\pi^0,K^0$ . Unsurprisingly, including the NLO weak annihilation correction in the improved theory predictions can lead to the negligible impacts on $\\\\mathcal{BR}(B\\\\to K\\\\ell^{+}\\\\ell^{-})$ and $\\\\mathcal{BR}(B\\\\rightarrow \\\\pi \\\\ell^{+}\\\\ell^{-})$ . In virtue of the smallness of the direct CP asymmetries for the exclusive $b\\\\rightarrow s\\\\ell^{+}\\\\ell^{-}$ decay processes in the SM, we collect here only our predictions for the binned asymmetries $\\\\mathcal{A}_{\\\\mathrm{CP}}[q_{\\\\mathrm{min}}^2,q_{\\\\mathrm{max}}^2] =$ $\\\\{1.02_{-0.22}^{+0.05},0.64_{-0.24}^{+0.06},0.42_{-0.17}^{+0.10},0.31_{-0.13}^{+0.10},0.26_{-0.10}^{+0.09}\\\\} \\\\%$ for $B^{-}\\\\rightarrow K^{-}\\\\ell^{+}\\\\ell^{-}$ and $\\\\mathcal{A}_{\\\\mathrm{CP}}[q_{\\\\mathrm{min}}^2,q_{\\\\mathrm{max}}^2] =$ $\\\\{0.01_{-0.12}^{+0.08},0.04_{-0.11}^{+0.07},0.06_{-0.10}^{+0.07},0.08_{-0.10}^{+0.07},0.09_{-0.09}^{+0.07}\\\\} \\\\%$ for $\\\\bar{B}^0\\\\rightarrow \\\\bar{K}^0\\\\ell^+\\\\ell^-$ , with the choices of the five sample $q^{2}$ bins (following [75]) $[q_{\\\\mathrm{min}}^2,q_{\\\\mathrm{max}}^2] =$ $\\\\{[1.1,2.0],[2.0,3.0],[3.0,4.0],[4.0,5.0],[5.0,6.0]\\\\}\\\\mathrm{GeV}^2.$ Moreover, the yielding results for the isospin asymmetry of $B\\\\rightarrow K\\\\ell^{+}\\\\ell^{-}$ in the kinematic ranges $q^{2}\\\\in [2.0,4.0]\\\\mathrm{GeV}^{2}$ and $q^{2}\\\\in [4.0,6.0]\\\\mathrm{GeV}^{2}$ are given by $(-0.74)_{-0.12}^{+0.21}\\\\%$ and $(-0.44)_{-0.06}^{+0.08}\\\\%$ respectively, whose \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[906,34,918,45]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[98,66,475,261]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0522/fb98e650579d96bc4a2c24eabf55da1cf238b393c314f2206260ef25993bb993.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[94,277,473,479]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"FIG. 3. Theory predictions for the $q^2$ dependence of the direct CP asymmetries [top] and the isospin asymmetry [down] for the exclusive $B \\\\\\\\rightarrow \\\\\\\\pi \\\\\\\\ell^{+} \\\\\\\\ell^{-}$ decays at LO (grey bands), at NLO $_{\\\\\\\\mathrm{BFS}}$ (blue bands) and at NLO (pink bands), where the uncertainties are obtained by adding the separate errors due to the variations of all input parameters in quadrature. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0598/774f2af7c84959dfee06c7a31d81fafd1ba86161de3c0872f1744c1642cac793.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[86,625,488,914]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"magnitudes and signs are both compatible with the updated LHCb measurements [3]. We now present the comparative predictions for the direct CP asymmetries and the isopsin asymmetry of $B \\\\to \\\\pi \\\\ell^{+} \\\\ell^{-}$ in Figure 3. It is then evident that the inclusion of the NLO weak annihilation contribution can result in the noticeable shifts of the theory predictions for these asymmetries in the NLO $_{\\\\mathrm{BFS}}$ approximation: numerically $\\\\mathcal{O}(15\\\\%)$ and $\\\\mathcal{O}(25\\\\%)$ corrections to $\\\\mathcal{A}_{\\\\mathrm{CP}}(B^{-} \\\\to \\\\pi^{-} \\\\ell^{+} \\\\ell^{-})$ and $\\\\mathcal{A}_{\\\\mathrm{I}}(B \\\\to \\\\pi \\\\ell^{+} \\\\ell^{-})$ . It is perhaps worth mentioning that the predicted CP asymmetry for $\\\\bar{B}^{0} \\\\to \\\\pi^{0} \\\\ell^{+} \\\\ell^{-}$ turns out to be significantly smaller than the counterpart result for the charged $B$ -meson decay channel, on account of the hierarchy structure of the LO annihilation amplitudes $[T_{P, -}^{(0,u)}(\\\\bar{B}^{0} \\\\to \\\\pi^{0} \\\\ell^{+} \\\\ell^{-})] : [T_{P, -}^{(0,u)}(B^{-} \\\\to \\\\pi^{-} \\\\ell^{+} \\\\ell^{-})] = [-Q_{d}(C_{F} C_{1} + C_{2})] : [Q_{u} N_{c} C_{2}] \\\\approx 1:10$ . Importantly, the obtained prediction of the isopsin breaking effect in $B \\\\to \\\\pi \\\\ell^{+} \\\\ell^{-}$ is approximately 3-6 times larger than that in $B \\\\to K \\\\ell^{+} \\\\ell^{-}$ for $q^{2} \\\\in [1.5, 4.0]\\\\mathrm{GeV}^{2}$ , thus enabling \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[511,65,919,111]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"this asymmetry observable to become the sensitive probe of the Wilson coefficients of the current-current operators in the weak effective Hamiltonian. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[650,148,782,161]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CONCLUSIONS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[511,181,919,544]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In conclusion, we have presented the first computation of the NLO weak annihilation contribution to the rare $B \\\\to \\\\{K,\\\\pi\\\\} \\\\ell^{+}\\\\ell^{-}$ decays at leading power in the heavy quark expansion by employing the soft-collinear factorization framework, thus providing the last missing piece in evaluating the QCD correction to the isospin asymmetry $\\\\mathcal{A}_{\\\\mathrm{I}}(B \\\\to \\\\pi \\\\ell^{+}\\\\ell^{-})$ . In contrast with the tree-level annihilation amplitude, we have demonstrated that both the twist-two and twist-three HQET LCDAs of the bottom-meson are in demand to capture the soft QCD dynamics in the established factorization formula of the weak annihilation effect at $\\\\mathcal{O}(\\\\alpha_{s})$ . Taking into account such higher-order corrections in the matrix elements of the four-quark operators can result in the notable impacts on our theory predictions for the direct CP asymmetry $\\\\mathcal{A}_{\\\\mathrm{CP}}(B^{-} \\\\to \\\\pi^{-}\\\\ell^{+}\\\\ell^{-})$ as well as the CP-averaged isospin asymmetry $\\\\mathcal{A}_{\\\\mathrm{I}}(B \\\\to \\\\pi \\\\ell^{+}\\\\ell^{-})$ . In addition, the achieved NLO factorization formula of the annihilation amplitude can be straightforwardly extended to the electroweak penguin decays $B \\\\to \\\\{K^{*},\\\\rho ,\\\\omega \\\\} \\\\ell^{+}\\\\ell^{-}$ with the longitudinally polarized vector mesons (by implementing the appropriate replacements), which are generally accepted as the benchmark channels for exploring the quark flavour-changing dynamics. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[611,580,821,594]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ACKNOWLEDGEMENTS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[511,614,919,750]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Y.K.H. and Y.M.W. acknowledge support from the National Natural Science Foundation of China with Grant No. 12075125. The research of Y.L.S. is supported by the National Natural Science Foundation of China with Grant No. 12175218. C.W. is supported in part by the National Natural Science Foundation of China with Grant No. 12105112 and the Natural Science Foundation of Jiangsu Education Committee with Grant No. 21KJB140027. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[532,806,883,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"* huangyongkang@mail.nankai.edu.cn \\\",\\\"† corresponding author: shenylmeteoror@ouc.edu.cn \\\",\\\"$\\\\\\\\ddagger$ corresponding author: chaowang@nankai.edu.cn \\\",\\\"$\\\\\\\\S$ corresponding author: wangyuming@nankai.edu.cn \\\"]\",\n \"page_idx\": \"5\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[522,861,916,914]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[1] B. 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(LHCb), JHEP 09, 177 (2014), arXiv:1408.0978 [hep-ex]. \\\"]\",\n \"page_idx\": \"7\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[906,34,918,46]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.48550/arxiv.2403.11258"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Physics"},"sha256":{"kind":"string","value":"7c896148b06987667d68c4435ccead20c3ad6584d609c89c3dcab90082889a43"},"title":{"kind":"string","value":"Next-to-Leading-Order Weak Annihilation Correction to Rare $B \\to \\left \\{K, π\\right \\} \\ell^{+} \\ell^{-}$ Decays"}}},{"rowIdx":264,"cells":{"abstract":{"kind":"string","value":""},"author":{"kind":"string","value":"N A Dalisova|T A Martinova|S E Rozhkov"},"content_list":{"kind":"list like","value":[{"bbox":"[60,131,243,144]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PAPER $\\cdot$ OPEN ACCESS ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,157,655,226]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable development strategy of the dairy agro-industrial complex through the use of waste-free technologies ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,241,611,254]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To cite this article: N A Dalisova et al 2022 IOP Conf. Ser.: Earth Environ. Sci. 1076 012016 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,296,389,309]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"View the article online for updates and enhancements. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[673,131,836,149]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"You may also like ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[699,157,932,318]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- More Efficient Daily Industry in the Face of Market Volatility and Risks \\nI N Vasilenko, I V Cheremushkin and Yu I Slepokurov \",\"Investigation of the process of molding, pressing and salting hard and soft cheeses Q A Mukhiddinov, A M Rakhimov, Dj E Saparov et al. \",\"- Improving Low-Fat Soft Cheese Quality Properties Made From Reconstituted Skim Milk By Using Whey Protein Concentrate as A fat Replacement Dhma Ibrahim Jerro Ai-Bedrani, Sakena Taha Hasan, Abdali Alwan Altaee et al. \"]","page_idx":"0","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[60,771,413,939]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0685/c7544de3c064186ef4105a29a0cb998f1cb0024e187beb6962967c8b9175b74b.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[421,779,489,814]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0531/146336f9932219e3266a1ce0dc968c0f0627a4831af33e47603d0836710211a3.jpg","list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[492,786,734,811]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Electrochemical Society\nAdvancing solid state & electrochemical science & technology ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[494,813,759,828]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"243rd ECS Meeting with SOFC-XVIII ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[494,834,815,849]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"More than 50 symposia are available! ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[494,855,873,871]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Present your research and accelerate science ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[494,878,737,893]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Boston, MA • May 28 - June 2, 2023 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[727,908,914,921]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Learn more and submit! ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,42,584,58]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conference Series: Earth and Environmental Science ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[114,204,870,252]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable development strategy of the dairy agro-industrial complex through the use of waste-free technologies ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[231,282,640,299]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"N A Dalisova $^{1,4}$ , T A Martinova $^{2}$ and S E Rozhkov $^{3}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[231,305,695,320]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{1}$ Krasnoyarsk State Agrarian University, Krasnoyarsk, Russia ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[231,320,823,350]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{2}$ Siberian State University of Science and Technology named after Reshetneva, Krasnoyarsk, Russia ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[233,350,610,366]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{3}$ Siberian Federal University, Krasnoyarsk, Russia ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[231,394,430,410]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{4}$ E-mail: dalnata@mail.ru ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[231,423,882,562]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract. Currently, waste-free technologies in the food industry play an important role in the sustainable development of dairy enterprises, as well as in solving food, economic, environmental and energy problems. One of the ways to strengthen the food industry is the introduction of new food processing technologies. This, in turn, requires more carefulness processing of agricultural raw materials and more rational use of useful ingredients. In this regard, the goal is to develop a technology for the production of cottage cheese with certain qualitative and physico-chemical properties. The research results show that albumin cottage cheese (or albumin) obtained with the help of whey protein meets quality standards, and the economic efficiency of this production product is very high which increases the production development and sustainability of agricultural enterprises. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,589,243,602]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[112,603,882,707]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The sustainable development strategy of the company is to gain, maintain and strengthen the competitive position of the company in the market for a long period of time. The formulation of development strategies is of great importance for companies of all sizes and for various specific activities. The problem and the relevance of its solution lies in the fact that for any organization there are problems of survival and continuity of its development. The formation of an enterprise development strategy is a necessary tool for the economic prosperity of an enterprise in unstable economic conditions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,709,880,769]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sustainable development strategy is very important for companies of any size and with different business characteristics. Companies should allocate and use resources wisely. In market conditions, a business can improve its efficiency, correctly define goals and objectives and analyze the objectivity of the external and internal environment [1-3]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,769,880,844]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Strengthening the company's capacity in the field of sustainable strategic development has a beneficial effect on risk management skills. In such a situation, the available capabilities consider the existence of certain organizational capabilities that can minimize the damage caused by dangerous situations. Due to the specific conditions of their activities, internal and external conditions of development, the potential of each company is unique. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,844,880,874]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The problems faced by agricultural production and its distinctive features have led to delays in the use of modern management tools on farms. Most farms have not yet implemented their strategic plans. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,66,198,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"AEGIS-2022 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[784,66,882,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Publishing ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,81,431,95]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conf. Series: Earth and Environmental Science ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[463,81,589,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1076 (2022) 012016 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[640,81,882,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"doi:10.1088/1755-1315/1076/1/012016 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,913,198,934]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CC BY ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[198,913,880,935]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[112,938,371,950]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Published under licence by IOP Publishing Ltd ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[497,940,507,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[112,133,884,180]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, in the absence of a scientific strategy for industrial development at each stage of management, it is impossible to get out of the crisis and lay the foundations for the gradual sustainable development strategy of the agricultural economy. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,193,326,207]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. Materials and methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[110,207,882,283]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The dairy market in Russia is an integral part of the Russian food industry. The food industry plays a huge role in the economy of any country. Currently, there are 25,000 enterprises in the Russian food industry, and its share in Russian production exceeds $10\\%$ . In quantitative terms, the market share of whole milk is about $84\\%$ . The most important dairy product consumed is cheese with a market share of about $8\\%$ , followed by butter with a market share of $5\\%$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,283,880,344]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Milk and dairy products are traditionally an important part of the diet of Russians. Experts believe that the Russian \"dairy\" business will always be profitable, according to StepbyStep, only $1.8\\%$ of the population does not consume dairy products. Most of the produced milk is used for processing and production of dairy products [4-6]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,344,880,387]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dairy products are very popular among almost all categories of the country's population. It is bought at the same price by representatives of all age groups, regardless of residence place and income level. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,388,880,418]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The most famous producers of dairy products are: \"Wimm Bill Dan\", \"Danon\", \"Unimilk\", \"Korenovsky Dairy Canning Plant\", \"Iskra\", \"Alekseevsky Dairy Canning Plant\". ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,419,880,448]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"One of the main diversified agricultural enterprises of the Yemelyanovsky district in the Krasnoyarsk Region is LLC \"Yemelyanovo\". ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,448,880,494]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The main goal of the organization is to sell agricultural products in local natural and environmental conditions, market conditions, effectively use land and production materials and achieve benefits for its members and employees. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,522,882,678]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0175/b1bfbfd8d30d3265012eb2194a5ca314b4235fc8b4a4a740e3bbfcba4bab0bd6.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":"<table><tr><td>Indicator</td><td>2019</td><td>2020</td><td>2021</td><td>Deviation from 2019</td><td>2021</td></tr><tr><td>1. The cost of commercial products in current prices, thousand rubles</td><td>209402</td><td>234188</td><td>267777</td><td>58375</td><td></td></tr><tr><td>2. The average annual number of employees, people</td><td>176</td><td>175</td><td>174</td><td>-2</td><td></td></tr><tr><td>3. The average annual cost of fixed assets, thousand rubles</td><td>100181</td><td>96585</td><td>108818</td><td>8637</td><td></td></tr><tr><td>4. Agricultural land area, ha</td><td>11200</td><td>11200</td><td>11200</td><td>-</td><td></td></tr><tr><td>5. Livestock, conditional head</td><td>1598</td><td>1389</td><td>1568</td><td>-30</td><td></td></tr></table>","table_caption":"[\"Table 1. Production sizes \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[112,690,880,720]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The main activity of the enterprise is the production of agricultural products. Cultivation of food crops and production of milk and beef. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,720,880,766]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A particular specialization of the farm is the cultivation of Hereford-a valuable breed of beef cattle. Marbled meat is obtained from it. Using optimal feeding conditions, walking areas and balanced feed - Hereford bulls of LLC \"Yemelyanovo\" weigh up to 1.3-1.5 tons. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,766,880,811]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The farm was organized in 1956. In 1991, the state farm \"Yemelyanovsky\" was reorganized into an agricultural joint-stock company. In 2001, the form of ownership changed, and the company was transformed into a closed joint stock company. In 2003, LLC \"Yemelyanovo\" was established [7-9]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,811,880,856]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The farm is constantly updating equipment, acquiring new equipment and introducing modern technologies in crop production and animal husbandry. Within walking distance from \"Pure field\", the chain store presents the entire range of meat, dairy and bakery products of the company. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[134,857,626,871]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Strategic analysis is considered one of the main types of analysis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,871,880,902]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This analysis can help identify the strengths and weaknesses of the company, as well as threats related to the external environment, thereby helping to understand how to solve these problems. First, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,66,198,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"AEGIS-2022 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[784,66,882,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Publishing ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,81,431,95]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conf. Series: Earth and Environmental Science ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[463,81,589,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1076 (2022) 012016 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[640,81,882,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"doi:10.1088/1755-1315/1076/1/012016 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[497,939,507,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[110,134,880,163]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"analyze the external environment of the company through the environmental factors it faces: competitors, suppliers and consumers [10-12]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,163,880,194]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"By analyzing competitors, it was found that there are several agricultural companies in the region, the main of which are the \"Chernogorov\" farm and the \"Andronovo Agricultural\" company. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,194,880,223]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The activities of LLC \"Yemelyanovo\" and its competitors are aimed at the production, processing and sale of crop and livestock products. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,223,880,268]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"LLC \"Yemelyanovo\" is not inferior to its competitor farm \"Chernygorov\" in price, quality and distribution channels, but its market share is small, and product promotion lags behind. The \"Chernygorov\" farm also uses discounts and promotions for wholesalers and ordinary buyers. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,269,882,330]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If we compare LLC \"Yemelyanovo\" and SEC \"Andronovsky\", we can say that the products of these companies are on the same level in price, quality and promotion. In comparison with the SEC \"Andronovsky\", LLC \"Yemelyanovo\" has a significant market share, and LLC \"Yemelyanovo\" has certain advantages in the sales channels of its products (table 2). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,358,882,593]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0226/c9600402734f8044075f2ff607407d239e87639ac1851752240c71faff84d1cc.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":"<table><tr><td rowspan=\"2\">Competitors</td><td rowspan=\"2\">Product Features</td><td>Advantages</td><td>Disadvantages</td></tr><tr><td colspan=\"2\">In relation to LLC "Yemelyanovo"</td></tr><tr><td rowspan=\"5\">LLC\n"Chernogorov"</td><td>1 Price</td><td>On the same level</td><td></td></tr><tr><td>2. Quality</td><td>On the same level</td><td></td></tr><tr><td>3. Market share</td><td>More</td><td></td></tr><tr><td>4. Promotion</td><td>Discount system</td><td>Limited set of promotion tools</td></tr><tr><td>5. Implementation channels</td><td>A wide range of implementation channels</td><td></td></tr><tr><td rowspan=\"5\">SEC\n"Andronovsky"</td><td>1 Price</td><td>On the same level</td><td></td></tr><tr><td>2. Quality</td><td>On the same level</td><td></td></tr><tr><td>3. Market share</td><td></td><td>Less</td></tr><tr><td>4. Promotion</td><td>On the same level</td><td></td></tr><tr><td>5. Implementation channels</td><td>Wholesale only</td><td></td></tr></table>","table_caption":"[\"Table 2. Analysis of competitors of LLC \\\"Yemelyanovo\\\" \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[112,606,880,637]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The activities of LLC \"Yemelyanovo\" and its competitors are aimed at the production, processing and sale of crop and livestock products. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,637,880,682]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"LLC \"Yemelyanovo\" is not inferior to its competitor LLC \"Chernogorov\" in price, quality and distribution channels, but its market share is small, and product promotion lags behind. The LLC \"Chernogorov\" also uses discounts and promotions for wholesalers and ordinary buyers [13-15]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,682,880,742]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If we compare LLC \"Yemelyanovo\" and SEC \"Andronovsky\", we can say that the products of these companies are on the same level in price, quality and promotion. In comparison with the SEC \"Andronovsky\", LLC \"Yemelyanovo\" has a significant market share, and LLC \"Yemelyanovo\" has certain advantages in the sales channels of its products (table 5). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,742,880,773]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The most optimal direction of sustainable development strategy at present is the introduction of a new product to the regional market and its further promotion, including the international market. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,787,200,801]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. Results ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[112,801,880,846]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"According to the segmentation of the market by types of milk products - milk occupies $60\\%$ of the market share, fermented milk products $25\\%$ , sour cream $6\\%$ , cottage cheese $7\\%$ , other products $2\\%$ . The main initiator of the purchase of cottage cheese are women, mostly 25-55 years old. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,847,880,891]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Currently, LLC \"Yemelyanovo\" follows the strategy of \"deeper penetration into the market\" (\"improvement of activities\"), which assumes an increase in the volume of products to the existing group of consumers without making any changes [16-19]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,66,198,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"AEGIS-2022 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[784,66,880,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Publishing ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,81,431,95]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conf. Series: Earth and Environmental Science ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[463,81,589,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1076 (2022) 012016 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[640,81,882,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"doi:10.1088/1755-1315/1076/1/012016 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[497,939,507,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[112,133,880,192]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The main activity of the enterprise remains the same. The principles of successful business development for the company LLC \"Yemelyanovskoe\" are high quality, reasonable prices, exact terms. High quality is ensured by the appropriate level of technology, professional training and quality control. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,193,880,254]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As a result of the strategic analysis of LLC \"Yemelyanovo\", it is certain that the company has sufficient capacity to start producing albumin cottage cheese. This product is unique for the region, which creates a significant competitive advantage, increases the production development and sustainability of the strategic development of the enterprise [20-22]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,254,880,299]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Albumin cottage cheese is a cottage cheese made from whey. The sweet whey that remains after cheese production is a by-product of cheese production. It contains a valuable protein albumin, which is perfectly absorbed by the human body and is very useful. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,299,880,344]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Cottage cheese containing albumin does not contain salt. It is recommended for people with diseases of the liver and biliary tract. For healthy people, this is an excellent protein food that is almost completely absorbed, improves metabolic processes in the body and improves metabolism in the body. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,344,880,419]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The value of protein cottage cheese lies in the fact that this type of fermented milk contains whey, which positively affects the function of the digestive system and does not lead to excess fat in the body. This product is rich in vitamin complexes. The product on the market is a novelty, and competitors have not yet mastered this type of product, which is due to the availability of prices for these products [23-25]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,419,880,480]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This product is unique for the region, which creates a significant competitive advantage. Such a project in the Krasnoyarsk Region will be launched for the first time, and the company LLC \"Yemelyanovo\" will successfully outstrip competitors and increase work efficiency, increase production development and sustainable development strategy of agricultural enterprises. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[137,480,640,495]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The implementation of the project is pursued by a number of tasks: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[137,510,880,603]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"to release albumin cottage cheese; \",\"to launch an advertising campaign among consumers in the Krasnoyarsk Region to increase demand; \",\"- to offer goods to kindergartens and schools as wholesale consumers. The products on the market are new, competitors have not mastered this type of cottage cheese, which is due to the price availability of these products. \"]","page_idx":"4","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[112,617,880,676]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"During the study, several options were studied, and it was concluded that this product replaced the usual and grain cottage cheese. In the production of this type of cottage cheese, consumers' interest in the product will be caused by a high concentration of protein molecules with a low-fat content and an affordable price [26-28]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,676,880,752]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Milk albumin was produced according to GOST R 53493-2009 \"Milk albumin. Technical conditions. The technology of food-grade milk albumin includes preparation for albumin deposition, albumin milk aging, neutralization, albumin filtration, cooling and packaging. Consider the technological cycle used for the production of albumin cottage cheese and the corresponding operations: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,752,880,888]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1) the whey is heated in the pasteurizer tank to $75^{\\\\circ}\\\\mathrm{C}$ , after which it is fed into the curd maker's container, where the whey is rolled into a curd mass, exposed to the temperature factor $(+95^{\\\\circ}\\\\mathrm{C})$ , which provides direct steam supply through the barbuter. This stage lasts 1.5-2.0 hours; \",\"2) for whey, the acid content is adjusted to a value of $24 - 26^{\\\\circ}\\\\mathrm{t}$ by adding a solution of citric acid. \",\"3) at 30 minutes from the formation of the curd mass, the product is decanted into a container, from where the whey is pumped into a buffer vessel. In the tank, the whey is settled before the recovery procedure, then fed into the tank for heat exchange; \",\"4) for exactly 12 hours, the cottage cheese is in the refrigerator, where it is self-pressed, after which it is ready for sale. \"]","page_idx":"4","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[114,66,198,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"AEGIS-2022 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[784,66,880,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Publishing ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,81,431,95]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conf. Series: Earth and Environmental Science ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[463,81,589,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1076 (2022) 012016 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[640,81,882,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"doi:10.1088/1755-1315/1076/1/012016 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[497,939,507,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[141,148,855,212]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0428/640b6c7ef44fdc94dc4c343028f0624480f412125914d09e12c804531c03b13d.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td>Indicators</td><td>Characteristic</td></tr><tr><td>Taste, smell</td><td>Clean, without foreign odors and tastes</td></tr><tr><td>Colour</td><td>White, uniform throughout the mass</td></tr><tr><td>Appearance, consistency</td><td>Homogeneous, gentle, smearing</td></tr></table>","table_caption":"[\"Table 3. Organoleptic indicators \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[139,239,857,305]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0050/3ad5d17ce5d037af9a0a5f32db79b7b739d44267a1593b41d6455b9b5cb18c7c.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td>Indicators</td><td>Fact</td><td>Norm</td></tr><tr><td>Protein content, %</td><td>12</td><td>12</td></tr><tr><td>Acidity, T</td><td>67±0,5</td><td>65-70</td></tr><tr><td>Mass fraction of dry substances, %</td><td>20</td><td>20</td></tr></table>","table_caption":"[\"Table 4. Basic physical and chemical indicators \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[110,317,882,498]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The cooking technology is very simple: the whey circulates when heated by steam, passes through the filter, settles on it, and the output is whey without protein. Thus, a fine-grained cottage cheese containing valuable albumin milk proteins is obtained. The continuation of the process may be different. Cottage cheese can be sweet, salty and flavored with mint, vanilla, etc., in combination with fruits or berries. The fat content in protein yogurt depends on the fat content in the original whey and the filler used to give the yogurt certain properties. Cottage cheese with albumin is not sour at all, it is delicious and healthy. There is also one advantage: homemade protein cottage cheese is much cheaper than fermented milk. Albumin from cottage cheese is an excellent protein product for a healthy diet. After the conducted research at the company LLC \"Yemelyanovo\" LLC, it was decided that it was necessary to produce $7,875\\mathrm{kg}$ of albumin cottage cheese per month. To produce this amount of product, 175 tons of whey will be required. The distribution channels will be supermarkets such as \"Alley\", \"Commander\", \"Krasny Yar\", \"OK\". ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,513,231,526]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. Conclusion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[110,527,882,663]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Only the application of a number of methods from various sectors of the economy can give today's economic and production effect, and bring Russian enterprises to a new level of sustainable strategic development. This has led to the practical necessity of writing this work, which is devoted to the generalization of theoretical research and practical developments of sustainable strategic development in modern economic conditions through the use of waste-free technologies. Industrial processing of milk into cottage cheese based on the principles of waste-free technology is an important reserve for reducing the consumption of raw materials, increasing production efficiency and sustainable development of dairy agricultural enterprises. Due to the use of whey, it is possible to partially solve the problems of shortage of raw materials at agricultural enterprises. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[115,678,206,691]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[115,693,882,903]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[1] Hetmanets V N 2013 Bulletin of ASAU 4 (102) \",\"[2] Fedorova M A and Gorodov A A 2020 IOP Conference Series: Earth and Environmental Science 548(2) 022013 \",\"[3] Ozerova M G, Filimonova N G and Ermakova I N 2021 IOP Conference Series: Earth and Environmental Science 677(2) 022070 \",\"[4] Stepanova E V 2020 IOP Conference Series: Earth and Environmental Science 548(2) 022098 \",\"[5] Rozhkova A V and Rozhkov S E 2022 IOP Conference Series: Earth and Environmental Science 981(3) 032013 \",\"[6] Rozhkova A V and Dalisova N A 2021 IOP Conference Series: Earth and Environmental Science 677(2) 022048 \",\"[7] Nezamova O A and Olentsova J A 2021 IOP Conference Series: Earth and Environmental Science 839(2) 022060 \",\"[8] Stepanova EV 2021 IOP Conference Series: Earth and Environmental Science 848(1) 012181 \",\"[9] Rozhkova A 2021 IOP Conference Series: Earth and Environmental Science 677(2) 022045 \"]","page_idx":"5","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[114,66,198,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"AEGIS-2022 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[784,66,880,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Publishing ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,81,431,95]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conf. Series: Earth and Environmental Science ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[463,81,589,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1076 (2022) 012016 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[640,81,880,95]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"doi:10.1088/1755-1315/1076/1/012016 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[497,939,507,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[115,131,884,660]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[10] Stupina, A.A., Zhukov, E.A., Ezhemanskaya, S.N., Karaseva, M.V., Korpacheva, L.N. 2016 IOP Conference Series: Materials Science and Engineering 155(1) 012024 \",\"[11] Ozerova M G, Pyzhikova N I and Filimonova N G 2020 IOP Conference Series: Earth and Environmental Science 421(3) 032058 \",\"[12] Ruiga I R, Stupina A A, Kovzunova E S, Chayka A A and Shkradyuk I A 2019 Journal of Physics: Conference Series 1399(3) 033118 \",\"[13] Gvozkova V.S., Bubin M.N. Modern approach to strategic planning // Modern research. - 2018. - № 1 (05). - Pp. 10-12 \",\"[14] Kuzmina V.A. Codex Alimentarius. Milk and dairy products / Translated from English. Codex Alimentarius. Milk and milk products - Moscow: Publishing house \\\"The Whole World\\\", 2007 118 p. \",\"[15] Stepanova E 2020 ACM International Conference Proceeding Series 3444479 \",\"[16] Belyakova G Y, Zabuga E V and Stepanova E V 2021 IOP Conference Series: Earth and Environmental Science 839(2) 022088 \",\"[17] Stupina A A, Antamoshkina O I, Ruiga I R, Korpacheva L N and Kovzunova E S 2021 IOP Conference Series: Materials Science and Engineering 1047(1) 012039 \",\"[18] Nezamova O A and Olentsova J A 2022 IOP Conference Series: Earth and Environmental Science 981(3) 032018 \",\"[19] Stepanova E V and Rozhkova A V 2020 E3S Web of Conferences 161 01075 \",\"[20] Rozhkova A V and Stepanova E V 2022 IOP Conference Series: Earth and Environmental Science 981(2) 022087 \",\"[21] Nezamova O and Olentsova J 2020 ACM International Conference Proceeding Series 3444481 \",\"[22] Filimonova N G, Ozerova M G, Ermakova I N and Miheeva N B 2019 IOP Conference Series: Earth and Environmental Science 315(2) 022098 \",\"[23] Gorodov, A A, Fedorova M A, Gavrilova O Yu 2019 IOP Conference Series: Earth and Environmental Science 315(2) 022041 \",\"[24] Gavrilova O Yu and Fedorova M A 2020 IOP Conference Series: Earth and Environmental Science 548(2) 022025 \",\"[25] Stupina A A, Rozhkova A V, Olentsova J A and Rozhkov S E 2021 r IOP Conference Series: Earth and Environmental Science 839(2) 022092 \",\"[26] Fedorova M A 2021 IOP Conference Series: Earth and Environmental Science 839(2) 022047 \",\"[27] Khramtsov A.G., Vasilisin S.V. Handbook of dairy production technologist. Vol. 5: Products from skimmed milk, buttermilk and whey. - St. Petersburg: GIORD, 2004. \",\"[28] Stupina A A, Shigina A A, Shigin A O, Karaseva M V, Korpacheva L N 2016 IOP Conference Series: Materials Science and Engineering 155(1) 012025 \"]","page_idx":"6","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[114,66,198,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"AEGIS-2022 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[784,66,880,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Publishing ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,81,431,95]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conf. Series: Earth and Environmental Science ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[463,81,589,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1076 (2022) 012016 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[640,81,882,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"doi:10.1088/1755-1315/1076/1/012016 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[497,939,507,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[60,131,243,144]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PAPER $\\\\cdot$ OPEN ACCESS \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,157,655,226]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable development strategy of the dairy agro-industrial complex through the use of waste-free technologies \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,241,611,254]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To cite this article: N A Dalisova et al 2022 IOP Conf. Ser.: Earth Environ. Sci. 1076 012016 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,296,389,309]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"View the article online for updates and enhancements. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[673,131,836,149]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"You may also like \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[699,157,932,318]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- More Efficient Daily Industry in the Face of Market Volatility and Risks \\\\nI N Vasilenko, I V Cheremushkin and Yu I Slepokurov \\\",\\\"Investigation of the process of molding, pressing and salting hard and soft cheeses Q A Mukhiddinov, A M Rakhimov, Dj E Saparov et al. \\\",\\\"- Improving Low-Fat Soft Cheese Quality Properties Made From Reconstituted Skim Milk By Using Whey Protein Concentrate as A fat Replacement Dhma Ibrahim Jerro Ai-Bedrani, Sakena Taha Hasan, Abdali Alwan Altaee et al. \\\"]\",\n \"page_idx\": \"0\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[60,771,413,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0685/c7544de3c064186ef4105a29a0cb998f1cb0024e187beb6962967c8b9175b74b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[421,779,489,814]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0531/146336f9932219e3266a1ce0dc968c0f0627a4831af33e47603d0836710211a3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[492,786,734,811]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Electrochemical Society\\nAdvancing solid state & electrochemical science & technology \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[494,813,759,828]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"243rd ECS Meeting with SOFC-XVIII \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[494,834,815,849]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"More than 50 symposia are available! \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[494,855,873,871]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Present your research and accelerate science \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[494,878,737,893]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Boston, MA • May 28 - June 2, 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[727,908,914,921]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Learn more and submit! \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,42,584,58]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Conference Series: Earth and Environmental Science \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[114,204,870,252]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable development strategy of the dairy agro-industrial complex through the use of waste-free technologies \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[231,282,640,299]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"N A Dalisova $^{1,4}$ , T A Martinova $^{2}$ and S E Rozhkov $^{3}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[231,305,695,320]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{1}$ Krasnoyarsk State Agrarian University, Krasnoyarsk, Russia \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[231,320,823,350]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{2}$ Siberian State University of Science and Technology named after Reshetneva, Krasnoyarsk, Russia \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[233,350,610,366]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{3}$ Siberian Federal University, Krasnoyarsk, Russia \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[231,394,430,410]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{4}$ E-mail: dalnata@mail.ru \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[231,423,882,562]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract. Currently, waste-free technologies in the food industry play an important role in the sustainable development of dairy enterprises, as well as in solving food, economic, environmental and energy problems. One of the ways to strengthen the food industry is the introduction of new food processing technologies. This, in turn, requires more carefulness processing of agricultural raw materials and more rational use of useful ingredients. In this regard, the goal is to develop a technology for the production of cottage cheese with certain qualitative and physico-chemical properties. The research results show that albumin cottage cheese (or albumin) obtained with the help of whey protein meets quality standards, and the economic efficiency of this production product is very high which increases the production development and sustainability of agricultural enterprises. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,589,243,602]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,603,882,707]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The sustainable development strategy of the company is to gain, maintain and strengthen the competitive position of the company in the market for a long period of time. The formulation of development strategies is of great importance for companies of all sizes and for various specific activities. The problem and the relevance of its solution lies in the fact that for any organization there are problems of survival and continuity of its development. The formation of an enterprise development strategy is a necessary tool for the economic prosperity of an enterprise in unstable economic conditions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,709,880,769]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sustainable development strategy is very important for companies of any size and with different business characteristics. Companies should allocate and use resources wisely. In market conditions, a business can improve its efficiency, correctly define goals and objectives and analyze the objectivity of the external and internal environment [1-3]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,769,880,844]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Strengthening the company's capacity in the field of sustainable strategic development has a beneficial effect on risk management skills. In such a situation, the available capabilities consider the existence of certain organizational capabilities that can minimize the damage caused by dangerous situations. Due to the specific conditions of their activities, internal and external conditions of development, the potential of each company is unique. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,844,880,874]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The problems faced by agricultural production and its distinctive features have led to delays in the use of modern management tools on farms. Most farms have not yet implemented their strategic plans. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,66,198,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"AEGIS-2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[784,66,882,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Publishing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,81,431,95]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Conf. Series: Earth and Environmental Science \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[463,81,589,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1076 (2022) 012016 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[640,81,882,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"doi:10.1088/1755-1315/1076/1/012016 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,913,198,934]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CC BY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[198,913,880,935]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[112,938,371,950]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Published under licence by IOP Publishing Ltd \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[497,940,507,948]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[112,133,884,180]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, in the absence of a scientific strategy for industrial development at each stage of management, it is impossible to get out of the crisis and lay the foundations for the gradual sustainable development strategy of the agricultural economy. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,193,326,207]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. Materials and methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,207,882,283]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The dairy market in Russia is an integral part of the Russian food industry. The food industry plays a huge role in the economy of any country. Currently, there are 25,000 enterprises in the Russian food industry, and its share in Russian production exceeds $10\\\\%$ . In quantitative terms, the market share of whole milk is about $84\\\\%$ . The most important dairy product consumed is cheese with a market share of about $8\\\\%$ , followed by butter with a market share of $5\\\\%$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,283,880,344]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Milk and dairy products are traditionally an important part of the diet of Russians. Experts believe that the Russian \\\"dairy\\\" business will always be profitable, according to StepbyStep, only $1.8\\\\%$ of the population does not consume dairy products. Most of the produced milk is used for processing and production of dairy products [4-6]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,344,880,387]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dairy products are very popular among almost all categories of the country's population. It is bought at the same price by representatives of all age groups, regardless of residence place and income level. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,388,880,418]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The most famous producers of dairy products are: \\\"Wimm Bill Dan\\\", \\\"Danon\\\", \\\"Unimilk\\\", \\\"Korenovsky Dairy Canning Plant\\\", \\\"Iskra\\\", \\\"Alekseevsky Dairy Canning Plant\\\". \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,419,880,448]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"One of the main diversified agricultural enterprises of the Yemelyanovsky district in the Krasnoyarsk Region is LLC \\\"Yemelyanovo\\\". \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,448,880,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The main goal of the organization is to sell agricultural products in local natural and environmental conditions, market conditions, effectively use land and production materials and achieve benefits for its members and employees. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,522,882,678]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0175/b1bfbfd8d30d3265012eb2194a5ca314b4235fc8b4a4a740e3bbfcba4bab0bd6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Indicator</td><td>2019</td><td>2020</td><td>2021</td><td>Deviation from 2019</td><td>2021</td></tr><tr><td>1. The cost of commercial products in current prices, thousand rubles</td><td>209402</td><td>234188</td><td>267777</td><td>58375</td><td></td></tr><tr><td>2. The average annual number of employees, people</td><td>176</td><td>175</td><td>174</td><td>-2</td><td></td></tr><tr><td>3. The average annual cost of fixed assets, thousand rubles</td><td>100181</td><td>96585</td><td>108818</td><td>8637</td><td></td></tr><tr><td>4. Agricultural land area, ha</td><td>11200</td><td>11200</td><td>11200</td><td>-</td><td></td></tr><tr><td>5. Livestock, conditional head</td><td>1598</td><td>1389</td><td>1568</td><td>-30</td><td></td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. Production sizes \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[112,690,880,720]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The main activity of the enterprise is the production of agricultural products. Cultivation of food crops and production of milk and beef. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,720,880,766]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A particular specialization of the farm is the cultivation of Hereford-a valuable breed of beef cattle. Marbled meat is obtained from it. Using optimal feeding conditions, walking areas and balanced feed - Hereford bulls of LLC \\\"Yemelyanovo\\\" weigh up to 1.3-1.5 tons. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,766,880,811]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The farm was organized in 1956. In 1991, the state farm \\\"Yemelyanovsky\\\" was reorganized into an agricultural joint-stock company. In 2001, the form of ownership changed, and the company was transformed into a closed joint stock company. In 2003, LLC \\\"Yemelyanovo\\\" was established [7-9]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,811,880,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The farm is constantly updating equipment, acquiring new equipment and introducing modern technologies in crop production and animal husbandry. Within walking distance from \\\"Pure field\\\", the chain store presents the entire range of meat, dairy and bakery products of the company. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[134,857,626,871]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Strategic analysis is considered one of the main types of analysis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,871,880,902]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This analysis can help identify the strengths and weaknesses of the company, as well as threats related to the external environment, thereby helping to understand how to solve these problems. First, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,66,198,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"AEGIS-2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[784,66,882,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Publishing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,81,431,95]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Conf. Series: Earth and Environmental Science \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[463,81,589,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1076 (2022) 012016 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[640,81,882,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"doi:10.1088/1755-1315/1076/1/012016 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[497,939,507,948]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[110,134,880,163]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"analyze the external environment of the company through the environmental factors it faces: competitors, suppliers and consumers [10-12]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,163,880,194]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"By analyzing competitors, it was found that there are several agricultural companies in the region, the main of which are the \\\"Chernogorov\\\" farm and the \\\"Andronovo Agricultural\\\" company. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,194,880,223]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The activities of LLC \\\"Yemelyanovo\\\" and its competitors are aimed at the production, processing and sale of crop and livestock products. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,223,880,268]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"LLC \\\"Yemelyanovo\\\" is not inferior to its competitor farm \\\"Chernygorov\\\" in price, quality and distribution channels, but its market share is small, and product promotion lags behind. The \\\"Chernygorov\\\" farm also uses discounts and promotions for wholesalers and ordinary buyers. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,269,882,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If we compare LLC \\\"Yemelyanovo\\\" and SEC \\\"Andronovsky\\\", we can say that the products of these companies are on the same level in price, quality and promotion. In comparison with the SEC \\\"Andronovsky\\\", LLC \\\"Yemelyanovo\\\" has a significant market share, and LLC \\\"Yemelyanovo\\\" has certain advantages in the sales channels of its products (table 2). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,358,882,593]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0226/c9600402734f8044075f2ff607407d239e87639ac1851752240c71faff84d1cc.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td rowspan=\\\"2\\\">Competitors</td><td rowspan=\\\"2\\\">Product Features</td><td>Advantages</td><td>Disadvantages</td></tr><tr><td colspan=\\\"2\\\">In relation to LLC "Yemelyanovo"</td></tr><tr><td rowspan=\\\"5\\\">LLC\\n"Chernogorov"</td><td>1 Price</td><td>On the same level</td><td></td></tr><tr><td>2. Quality</td><td>On the same level</td><td></td></tr><tr><td>3. Market share</td><td>More</td><td></td></tr><tr><td>4. Promotion</td><td>Discount system</td><td>Limited set of promotion tools</td></tr><tr><td>5. Implementation channels</td><td>A wide range of implementation channels</td><td></td></tr><tr><td rowspan=\\\"5\\\">SEC\\n"Andronovsky"</td><td>1 Price</td><td>On the same level</td><td></td></tr><tr><td>2. Quality</td><td>On the same level</td><td></td></tr><tr><td>3. Market share</td><td></td><td>Less</td></tr><tr><td>4. Promotion</td><td>On the same level</td><td></td></tr><tr><td>5. Implementation channels</td><td>Wholesale only</td><td></td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2. Analysis of competitors of LLC \\\\\\\"Yemelyanovo\\\\\\\" \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[112,606,880,637]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The activities of LLC \\\"Yemelyanovo\\\" and its competitors are aimed at the production, processing and sale of crop and livestock products. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,637,880,682]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"LLC \\\"Yemelyanovo\\\" is not inferior to its competitor LLC \\\"Chernogorov\\\" in price, quality and distribution channels, but its market share is small, and product promotion lags behind. The LLC \\\"Chernogorov\\\" also uses discounts and promotions for wholesalers and ordinary buyers [13-15]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,682,880,742]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If we compare LLC \\\"Yemelyanovo\\\" and SEC \\\"Andronovsky\\\", we can say that the products of these companies are on the same level in price, quality and promotion. In comparison with the SEC \\\"Andronovsky\\\", LLC \\\"Yemelyanovo\\\" has a significant market share, and LLC \\\"Yemelyanovo\\\" has certain advantages in the sales channels of its products (table 5). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,742,880,773]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The most optimal direction of sustainable development strategy at present is the introduction of a new product to the regional market and its further promotion, including the international market. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,787,200,801]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. Results \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,801,880,846]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"According to the segmentation of the market by types of milk products - milk occupies $60\\\\%$ of the market share, fermented milk products $25\\\\%$ , sour cream $6\\\\%$ , cottage cheese $7\\\\%$ , other products $2\\\\%$ . The main initiator of the purchase of cottage cheese are women, mostly 25-55 years old. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,847,880,891]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Currently, LLC \\\"Yemelyanovo\\\" follows the strategy of \\\"deeper penetration into the market\\\" (\\\"improvement of activities\\\"), which assumes an increase in the volume of products to the existing group of consumers without making any changes [16-19]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,66,198,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"AEGIS-2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[784,66,880,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Publishing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,81,431,95]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Conf. Series: Earth and Environmental Science \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[463,81,589,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1076 (2022) 012016 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[640,81,882,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"doi:10.1088/1755-1315/1076/1/012016 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[497,939,507,948]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[112,133,880,192]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The main activity of the enterprise remains the same. The principles of successful business development for the company LLC \\\"Yemelyanovskoe\\\" are high quality, reasonable prices, exact terms. High quality is ensured by the appropriate level of technology, professional training and quality control. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,193,880,254]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As a result of the strategic analysis of LLC \\\"Yemelyanovo\\\", it is certain that the company has sufficient capacity to start producing albumin cottage cheese. This product is unique for the region, which creates a significant competitive advantage, increases the production development and sustainability of the strategic development of the enterprise [20-22]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,254,880,299]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Albumin cottage cheese is a cottage cheese made from whey. The sweet whey that remains after cheese production is a by-product of cheese production. It contains a valuable protein albumin, which is perfectly absorbed by the human body and is very useful. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,299,880,344]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Cottage cheese containing albumin does not contain salt. It is recommended for people with diseases of the liver and biliary tract. For healthy people, this is an excellent protein food that is almost completely absorbed, improves metabolic processes in the body and improves metabolism in the body. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,344,880,419]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The value of protein cottage cheese lies in the fact that this type of fermented milk contains whey, which positively affects the function of the digestive system and does not lead to excess fat in the body. This product is rich in vitamin complexes. The product on the market is a novelty, and competitors have not yet mastered this type of product, which is due to the availability of prices for these products [23-25]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,419,880,480]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This product is unique for the region, which creates a significant competitive advantage. Such a project in the Krasnoyarsk Region will be launched for the first time, and the company LLC \\\"Yemelyanovo\\\" will successfully outstrip competitors and increase work efficiency, increase production development and sustainable development strategy of agricultural enterprises. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[137,480,640,495]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The implementation of the project is pursued by a number of tasks: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[137,510,880,603]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"to release albumin cottage cheese; \\\",\\\"to launch an advertising campaign among consumers in the Krasnoyarsk Region to increase demand; \\\",\\\"- to offer goods to kindergartens and schools as wholesale consumers. The products on the market are new, competitors have not mastered this type of cottage cheese, which is due to the price availability of these products. \\\"]\",\n \"page_idx\": \"4\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[112,617,880,676]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"During the study, several options were studied, and it was concluded that this product replaced the usual and grain cottage cheese. In the production of this type of cottage cheese, consumers' interest in the product will be caused by a high concentration of protein molecules with a low-fat content and an affordable price [26-28]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,676,880,752]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Milk albumin was produced according to GOST R 53493-2009 \\\"Milk albumin. Technical conditions. The technology of food-grade milk albumin includes preparation for albumin deposition, albumin milk aging, neutralization, albumin filtration, cooling and packaging. Consider the technological cycle used for the production of albumin cottage cheese and the corresponding operations: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,752,880,888]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1) the whey is heated in the pasteurizer tank to $75^{\\\\\\\\circ}\\\\\\\\mathrm{C}$ , after which it is fed into the curd maker's container, where the whey is rolled into a curd mass, exposed to the temperature factor $(+95^{\\\\\\\\circ}\\\\\\\\mathrm{C})$ , which provides direct steam supply through the barbuter. This stage lasts 1.5-2.0 hours; \\\",\\\"2) for whey, the acid content is adjusted to a value of $24 - 26^{\\\\\\\\circ}\\\\\\\\mathrm{t}$ by adding a solution of citric acid. \\\",\\\"3) at 30 minutes from the formation of the curd mass, the product is decanted into a container, from where the whey is pumped into a buffer vessel. In the tank, the whey is settled before the recovery procedure, then fed into the tank for heat exchange; \\\",\\\"4) for exactly 12 hours, the cottage cheese is in the refrigerator, where it is self-pressed, after which it is ready for sale. \\\"]\",\n \"page_idx\": \"4\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[114,66,198,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"AEGIS-2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[784,66,880,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Publishing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,81,431,95]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Conf. Series: Earth and Environmental Science \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[463,81,589,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1076 (2022) 012016 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[640,81,882,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"doi:10.1088/1755-1315/1076/1/012016 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[497,939,507,948]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[141,148,855,212]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0428/640b6c7ef44fdc94dc4c343028f0624480f412125914d09e12c804531c03b13d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Indicators</td><td>Characteristic</td></tr><tr><td>Taste, smell</td><td>Clean, without foreign odors and tastes</td></tr><tr><td>Colour</td><td>White, uniform throughout the mass</td></tr><tr><td>Appearance, consistency</td><td>Homogeneous, gentle, smearing</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 3. Organoleptic indicators \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[139,239,857,305]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0050/3ad5d17ce5d037af9a0a5f32db79b7b739d44267a1593b41d6455b9b5cb18c7c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Indicators</td><td>Fact</td><td>Norm</td></tr><tr><td>Protein content, %</td><td>12</td><td>12</td></tr><tr><td>Acidity, T</td><td>67±0,5</td><td>65-70</td></tr><tr><td>Mass fraction of dry substances, %</td><td>20</td><td>20</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 4. Basic physical and chemical indicators \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[110,317,882,498]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The cooking technology is very simple: the whey circulates when heated by steam, passes through the filter, settles on it, and the output is whey without protein. Thus, a fine-grained cottage cheese containing valuable albumin milk proteins is obtained. The continuation of the process may be different. Cottage cheese can be sweet, salty and flavored with mint, vanilla, etc., in combination with fruits or berries. The fat content in protein yogurt depends on the fat content in the original whey and the filler used to give the yogurt certain properties. Cottage cheese with albumin is not sour at all, it is delicious and healthy. There is also one advantage: homemade protein cottage cheese is much cheaper than fermented milk. Albumin from cottage cheese is an excellent protein product for a healthy diet. After the conducted research at the company LLC \\\"Yemelyanovo\\\" LLC, it was decided that it was necessary to produce $7,875\\\\mathrm{kg}$ of albumin cottage cheese per month. To produce this amount of product, 175 tons of whey will be required. The distribution channels will be supermarkets such as \\\"Alley\\\", \\\"Commander\\\", \\\"Krasny Yar\\\", \\\"OK\\\". \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,513,231,526]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. Conclusion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,527,882,663]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Only the application of a number of methods from various sectors of the economy can give today's economic and production effect, and bring Russian enterprises to a new level of sustainable strategic development. This has led to the practical necessity of writing this work, which is devoted to the generalization of theoretical research and practical developments of sustainable strategic development in modern economic conditions through the use of waste-free technologies. Industrial processing of milk into cottage cheese based on the principles of waste-free technology is an important reserve for reducing the consumption of raw materials, increasing production efficiency and sustainable development of dairy agricultural enterprises. Due to the use of whey, it is possible to partially solve the problems of shortage of raw materials at agricultural enterprises. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[115,678,206,691]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[115,693,882,903]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[1] Hetmanets V N 2013 Bulletin of ASAU 4 (102) \\\",\\\"[2] Fedorova M A and Gorodov A A 2020 IOP Conference Series: Earth and Environmental Science 548(2) 022013 \\\",\\\"[3] Ozerova M G, Filimonova N G and Ermakova I N 2021 IOP Conference Series: Earth and Environmental Science 677(2) 022070 \\\",\\\"[4] Stepanova E V 2020 IOP Conference Series: Earth and Environmental Science 548(2) 022098 \\\",\\\"[5] Rozhkova A V and Rozhkov S E 2022 IOP Conference Series: Earth and Environmental Science 981(3) 032013 \\\",\\\"[6] Rozhkova A V and Dalisova N A 2021 IOP Conference Series: Earth and Environmental Science 677(2) 022048 \\\",\\\"[7] Nezamova O A and Olentsova J A 2021 IOP Conference Series: Earth and Environmental Science 839(2) 022060 \\\",\\\"[8] Stepanova EV 2021 IOP Conference Series: Earth and Environmental Science 848(1) 012181 \\\",\\\"[9] Rozhkova A 2021 IOP Conference Series: Earth and Environmental Science 677(2) 022045 \\\"]\",\n \"page_idx\": \"5\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[114,66,198,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"AEGIS-2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[784,66,880,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Publishing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,81,431,95]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Conf. Series: Earth and Environmental Science \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[463,81,589,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1076 (2022) 012016 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[640,81,880,95]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"doi:10.1088/1755-1315/1076/1/012016 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[497,939,507,948]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[115,131,884,660]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[10] Stupina, A.A., Zhukov, E.A., Ezhemanskaya, S.N., Karaseva, M.V., Korpacheva, L.N. 2016 IOP Conference Series: Materials Science and Engineering 155(1) 012024 \\\",\\\"[11] Ozerova M G, Pyzhikova N I and Filimonova N G 2020 IOP Conference Series: Earth and Environmental Science 421(3) 032058 \\\",\\\"[12] Ruiga I R, Stupina A A, Kovzunova E S, Chayka A A and Shkradyuk I A 2019 Journal of Physics: Conference Series 1399(3) 033118 \\\",\\\"[13] Gvozkova V.S., Bubin M.N. Modern approach to strategic planning // Modern research. - 2018. - № 1 (05). - Pp. 10-12 \\\",\\\"[14] Kuzmina V.A. Codex Alimentarius. Milk and dairy products / Translated from English. Codex Alimentarius. Milk and milk products - Moscow: Publishing house \\\\\\\"The Whole World\\\\\\\", 2007 118 p. \\\",\\\"[15] Stepanova E 2020 ACM International Conference Proceeding Series 3444479 \\\",\\\"[16] Belyakova G Y, Zabuga E V and Stepanova E V 2021 IOP Conference Series: Earth and Environmental Science 839(2) 022088 \\\",\\\"[17] Stupina A A, Antamoshkina O I, Ruiga I R, Korpacheva L N and Kovzunova E S 2021 IOP Conference Series: Materials Science and Engineering 1047(1) 012039 \\\",\\\"[18] Nezamova O A and Olentsova J A 2022 IOP Conference Series: Earth and Environmental Science 981(3) 032018 \\\",\\\"[19] Stepanova E V and Rozhkova A V 2020 E3S Web of Conferences 161 01075 \\\",\\\"[20] Rozhkova A V and Stepanova E V 2022 IOP Conference Series: Earth and Environmental Science 981(2) 022087 \\\",\\\"[21] Nezamova O and Olentsova J 2020 ACM International Conference Proceeding Series 3444481 \\\",\\\"[22] Filimonova N G, Ozerova M G, Ermakova I N and Miheeva N B 2019 IOP Conference Series: Earth and Environmental Science 315(2) 022098 \\\",\\\"[23] Gorodov, A A, Fedorova M A, Gavrilova O Yu 2019 IOP Conference Series: Earth and Environmental Science 315(2) 022041 \\\",\\\"[24] Gavrilova O Yu and Fedorova M A 2020 IOP Conference Series: Earth and Environmental Science 548(2) 022025 \\\",\\\"[25] Stupina A A, Rozhkova A V, Olentsova J A and Rozhkov S E 2021 r IOP Conference Series: Earth and Environmental Science 839(2) 022092 \\\",\\\"[26] Fedorova M A 2021 IOP Conference Series: Earth and Environmental Science 839(2) 022047 \\\",\\\"[27] Khramtsov A.G., Vasilisin S.V. Handbook of dairy production technologist. Vol. 5: Products from skimmed milk, buttermilk and whey. - St. Petersburg: GIORD, 2004. \\\",\\\"[28] Stupina A A, Shigina A A, Shigin A O, Karaseva M V, Korpacheva L N 2016 IOP Conference Series: Materials Science and Engineering 155(1) 012025 \\\"]\",\n \"page_idx\": \"6\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[114,66,198,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"AEGIS-2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[784,66,880,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Publishing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,81,431,95]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Conf. Series: Earth and Environmental Science \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[463,81,589,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1076 (2022) 012016 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[640,81,882,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"doi:10.1088/1755-1315/1076/1/012016 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[497,939,507,948]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1088/1755-1315/1076/1/012016"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Life Sciences"},"sha256":{"kind":"string","value":"7e137eb1a2656fa11a1dea6f1484e9cdab2dd24fc7a46eeee3249162eeac0110"},"title":{"kind":"string","value":"Sustainable development strategy of the dairy agro-industrial complex through the use of waste-free technologies"}}},{"rowIdx":265,"cells":{"abstract":{"kind":"string","value":"Follicle stimulating hormone (FSH) is an essential glycoprotein hormone for human reproduction, which functions are mediated by a G protein-coupled receptor, FSHR. Aberrant FSH-FSHR signaling causes infertility and ovarian hyperstimulation syndrome. Here we report cryo-EM structures of FSHR in both inactive and active states, with the active structure bound to FSH and an allosteric agonist compound 21 f. The structures of FSHR are similar to other glycoprotein hormone receptors, highlighting a conserved activation mechanism of hormone-induced receptor activation. Compound 21 f formed extensive interactions with the TMD to directly activate FSHR. Importantly, the unique residue H6157.42 in FSHR plays an essential role in determining FSHR selectivity for various allosteric agonists. Together, our structures provide a molecular basis of FSH and small allosteric agonist-mediated FSHR activation, which could inspire the design of FSHR-targeted drugs for the treatment of infertility and controlled ovarian stimulation for in vitro fertilization."},"author":{"kind":"string","value":"Duan, Jia|Xu, Peiyu|Zhang, Huibing|Luan, Xiaodong|Yang, Jiaqi|He, Xinheng|Mao, Chunyou|Shen, Dan-Dan|Ji, Yujie|Cheng, Xi|Jiang, Hualiang|Jiang, Yi|Zhang, Shuyang|Zhang, Yan|Xu, H. Eric"},"content_list":{"kind":"list like","value":[{"bbox":"[63,137,818,246]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mechanism of hormone and allosteric agonist mediated activation of follicle stimulating hormone receptor ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,288,233,303]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received: 2 August 2022 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,313,245,327]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Accepted: 18 January 2023 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,339,265,353]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Published online: 31 January 2023 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[63,364,201,379]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Check for updates ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[359,284,944,351]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Jia Duan $^{1,2,13}$ , Peiyu Xu $^{1,13}$ , Huibing Zhang $^{3,4,5,6,13}$ , Xiaodong Luan $^{7,8,9,10,13}$ , Jiaqi Yang $^{1}$ , Xinheng He $^{1,2}$ , Chunyou Mao $^{3,4,5,6}$ , Dan-Dan Shen $^{3,4,5,6}$ , Yujie Ji $^{1,2}$ , Xi Cheng $^{1}$ , Hualiang Jiang $^{1,2,11,12}$ , Yi Jiang $^{11,12}$ , Shuyang Zhang $^{7,8,9,10}$ , Yan Zhang $^{3,4,5,6}$ & H. Eric Xu $^{1,2,12}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[359,381,944,627]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Follicle stimulating hormone (FSH) is an essential glycoprotein hormone for human reproduction, which functions are mediated by a G protein-coupled receptor, FSHR. Aberrant FSH-FSHR signaling causes infertility and ovarian hyperstimulation syndrome. Here we report cryo-EM structures of FSHR in both inactive and active states, with the active structure bound to FSH and an allosteric agonist compound 21 f. The structures of FSHR are similar to other glycoprotein hormone receptors, highlighting a conserved activation mechanism of hormone-induced receptor activation. Compound 21 f formed extensive interactions with the TMD to directly activate FSHR. Importantly, the unique residue $\\mathrm{H615^{7.42}}$ in FSHR plays an essential role in determining FSHR selectivity for various allosteric agonists. Together, our structures provide a molecular basis of FSH and small allosteric agonist-mediated FSHR activation, which could inspire the design of FSHR-targeted drugs for the treatment of infertility and controlled ovarian stimulation for in vitro fertilization. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,667,497,778]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Follicle-stimulating hormone (FSH) is secreted by pituitary glands and functions as a stimulator of the estrogen production, ovarian follicles maturation and spermatogenesis $^{1,2}$ . FSH acts through FSHR, which is mainly expressed in gonads (ovaries in female and testes in male) $^{3}$ . Mutations in human demonstrate that aberrant signaling of FSH-FSHR can lead to serious diseases $^{4,5}$ , especially infertility and ovarian hyperstimulation syndrome (OHSS). Recently, much more evidence have been found that the function of extra gonadal FSHR is also closely ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,667,946,775]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"relevant to Alzheimer's disease, osteoporosis, obesity, and cancers[6-9]. In clinical, FSH is a main therapeutic drug used in anovulatory infertility and assisted reproductive technologies for women and hypogonadotropic hypogonadism for men[10,11]. To date, several crystal structures of FSH-bound FSHR fragments, including the leucine-rich repeat hormone-binding domain (FSHR_HB) and the complete ECD fragment (FSHR_ECD), have been reported[12,13], offering an opportunity for us to understand the detailed interactions between FSH and FSHR. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,803,946,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"<sup>1</sup>State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 201203 Shanghai, China. <sup>2</sup>University of Chinese Academy of Sciences, 100049 Beijing, China. <sup>3</sup>Department of Biophysics and Department of Pathology of Sir Run Run Shaw Hospital, Zhejiang University School of Medicine, Hangzhou, Zhejiang, China. <sup>4</sup>Liangzhu Laboratory, Zhejiang University Medical Center, Hangzhou, Zhejiang, China. <sup>5</sup>MOE Frontier Science Center for Brain Research and Brain-Machine Integration, Zhejiang University School of Medicine, Hangzhou, Zhejiang, China. <sup>6</sup>Zhejiang Provincial Key Laboratory of Immunity and Inflammatory diseases, Hangzhou, Zhejiang, China. <sup>7</sup>Department of Cardiology, Peking Union Medical College Hospital, Peking Union Medical College and Chinese Academy of Medical Sciences, Beijing, China. <sup>8</sup>Medical Research Center, Peking Union Medical College Hospital, Peking Union Medical College and Chinese Academy of Medical Sciences, Beijing, China. <sup>9</sup>School of medicine, Tsinghua university, Beijing, China. <sup>10</sup>Tsinghua-Peking Center for life science, Tsinghua university, Beijing, China. <sup>11</sup>Lingang Laboratory, 200031 Shanghai, China. <sup>12</sup>School of Life Science and Technology, ShanghaiTech University, 201210 Shanghai, China. <sup>13</sup>These authors contributed equally: Jia Duan, Peiyu Xu, Huibing Zhang, Xiaodong Luan. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,926,549,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\text{電}$ -mail: shuyangzhang103@nrdrs.org; zhang_yan@zju.edu.cn; eric.xu@simm.ac.cn ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,50,369,74]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"nature communications ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[912,48,942,81]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"# ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[62,116,119,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[667,118,944,132]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41467-023-36170-3 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[62,962,302,975]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nature Communications| (2023)14:519 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[932,964,944,974]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[60,58,495,84]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, the molecular basis of how does FSH activate FSHR is still controversial because of the lack of the full-length FSHR structure. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,86,495,288]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"FSH, along with luteinizing hormone (LH), chorionic gonadotropin (CG) and thyroid-stimulating hormone (TSH), constitute the family of glycoprotein hormones $^{14}$ , which share similar 3D architectures and function through binding and activation of a subfamily of G protein-coupled receptors, named glycoprotein hormone receptors $^{15}$ . There are three members of glycoprotein hormone receptors, FSHR, LHCGR and TSHR, which are activated to mainly couple the Gs protein and lead to up-regulation of the secondary message cAMP in cells $^{16}$ . Most recently, the cryo-electron microscopy (cyro-EM) structures of CG-LHCGR-Gs and TSH-TSHR-Gs complexes have also been determined $^{17-19}$ , further providing insights into hormone specificity and hormone-induced receptor activation. The structures of CG-LHCGR-Gs and TSH-TSHR-Gs complexes suggested that there might be a conserved activation mechanism among glycoprotein hormone receptors. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,288,495,450]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As a disease-associated drug target, there is an urgent need for highly selective small molecular agonists of FSHR to replace hormone therapy, and the small molecular antagonists of FSHR could also be used for contraception[20,21]. Over the years, there are many small molecular agonists and antagonists towards FSHR that have been developed[22,23]. For example, compound 21f (Cpd-21f)[24] is a small molecule allosteric agonist of FSHR with high affinity and activation efficacy. However, up to now, small molecular agonists and antagonists have not entered clinical research due to their low specificity. The high homology of glycoprotein hormone receptors and the lack of structure information of full-length FSHR continue to hinder the development of small molecule drugs targeting FSHR. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,451,495,612]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this study, we report two cryo-EM structures, one is the full-length FSHR bound to FSH, Cpd-21f and Gs protein at a global resolution of $2.82\\AA$ , and the other is the inactive FSHR structure with a global resolution of $6.01\\AA$ . Combined with functional studies, our structures reveal a \"push and pull\" mechanism of hormone-induced receptor activation, which is highly conserved in glycoprotein hormone receptors. The high-resolution structure of Cpd-21f bound with FSHR also provides the basis for rational design of small molecule drugs with higher specificity. Moreover, the structures of the full-length FSHR also allow us to investigate the mechanisms of activating and inactivating mutations naturally occurred in FSHR-related diseases. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,626,129,639]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[62,640,487,653]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Structures of FSH-bound FSHR-Gs complex and inactive FSHR ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,654,495,708]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To obtain a high-resolution structure of FSH-bound FSHR-Gs complex, a constitutively active mutation[25], S273I, was introduced to FSHR to enhance the assembly of the FSH-FSHR-Gs complex, in analogous to the constitutively active mutation S277I in the LHCGR[19] ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,58,944,288]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and S281I in TSHR $^{17}$ . Human FSH was incubated with membranes from cells co-expressing FSHR and three subunits of Gs heterotrimer in the presence of $\\mathrm{Nb35}^{26}$ , which stabilizes the Gs heterotrimer conformation. Cpd-21f was also added to further stabilize the FSH-FSHR-Gs complex. The final structure was determined at a global resolution of $2.82\\AA$ (Supplementary Fig. 1 and Supplementary Table 1). The EM map was clear to position all components of the complex, including two subunits of FSH, the three Gs subunits, Nb35 and FSHR, which includes the N-terminal leucine-rich repeats 1-11 (LRR1-11), the hinge region, and the C-terminal TMD (Fig. 1a, Supplementary Fig. 2a, b). The local refinement of FSH-FSHR ECD subcomplex yielded a map with a better density at the extended hinge loop from the receptor hinge region (residues 296-328 are not included) (Supplementary Fig. 2c, d). Interestingly, 13 cholesterol and 5 lipid molecules were found surrounding the FSHR TMD, like a belt, which was similar to what has been observed in TSHR structures (PDB: 7XW5) $^{17}$ (Fig. 1a, Supplementary Fig. 3). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,288,944,437]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To obtain stable inactive FSHR proteins for cryo-EM structure determination, a small molecular antagonist, compound $24^{27}$ , was added during FSHR expression and purification. Through numerous data collection, we were able to obtain a structure of wild type FSHR in the inactive state at a global resolution of 6.01 Å (Fig. 1b, Supplementary Fig. 4). The EM map was sufficient to place the receptor ECD and TMD, while the density of compound 24 was not observed. Due to the relatively low resolution of the inactive FSHR map, we only built a poly-alanine model for the inactive FSHR structure (Fig. 1b). The data and structural statistics are summarized in Supplementary Table 1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,451,813,463]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mechanism of FSH-induced FSHR activation ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,465,944,708]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As a canonical member of glycoprotein hormone receptors, FSHR has been chosen as a research model and widely studied in many decades[3,28,29]. The detail interactions between FSH and FSHR were extensively studied based on the two crystal structures of FSH-FSHR_HB and FSH-FSHR_ECD complexes[12,13]. However, two controversial activation models of FSH-induced FSHR activation were also proposed due to the fact that the structures of FSH-FSHR_HB and FSH-FSHR_ECD complexes were determined in dimeric[12] and trimeric states[13,30], respectively. The full-length FSHR structures we solved in the active and inactive states were both in monomeric states. Structural comparison of active FSHR in the FSH-FSHR-Gs complex with FSH-FSHR_HB and FSH-FSHR_ECD complexes, respectively, which reveals that the FSH-FSHR_ECD in our structure is nearly identical to the monomeric FSH-FSHR_ECD structure from the two crystal structures. However, the presence of FSH and Gs protein would prevent receptor dimerization or trimerization in the same convex membrane layer (Supplementary Fig. 5a, b) as observed in the crystal structures. Interestingly, dimerization of the receptor-Gs ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,727,522,893]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 1 | Cryo-EM structures of the FSH-FSHR-Gs complex and the inactive FSHR. a Cryo-EM density (left panel) and ribbon presentation (right panel) of the FSH-FSHR-Gs complex, the complex density map is shown at level of 0.044. b Cryo-EM \"]","image_footnote":"[]","img_path":"images/0744/bd1ccd4e78b7f96e30801ace45a0d747b1be832be2edf605c7a135651e41f515.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[534,725,806,883]","code_body":null,"code_caption":null,"image_caption":"[\"density (left panel) and ribbon presentation (right panel) of the inactive FSHR, the EM density map is shown at level of 0.017. \"]","image_footnote":"[]","img_path":"images/0190/44125a9570b95fec20830d383793279541f6f81ed5bff1dfee4e1940851c87c0.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[63,27,119,40]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[663,27,942,41]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41467-023-36170-3 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[62,962,302,975]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nature Communications| (2023)14:519 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[931,963,942,973]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[201,60,800,445]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0588/9b1a7bde9668cdb12f4d09ef41a0c5f41601225a0eb69863a1d24d26be319343.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[213,449,806,664]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 2 | Mechanism of FSH-induced FSHR activation. a–d Structural comparison of the active and inactive FSHR. The overall structure (a), the extracellular side of TMD (b), the intracellular side of TMD (c, d). e The Schematic diagram of FSH-induced FSHR activation, the superposition of ECD structures of the active and inactive FSHR (left panel), and the activation conformation of FSHR (right panel), the clash of FSHβ with the membrane layer is marked with a red line and the \",\"extended hinge loop is shown in cyan. f Concentration-response curves for FSHR mutants at the extended hinge loop. The representative concentration-response curves from three independent experiments were shown. Data were shown as mean $\\\\pm$ S.E.M. from three independent experiments. Source data are provided as a Source Data file. \"]","image_footnote":"[]","img_path":"images/0297/2e05b13c7a8aad6ab4cac861b73c3686b8010c8bd45ed984f5c3b6a0f4bda43b.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[60,775,494,803]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"complex could form from receptors in concave or different membrane layers (Supplementary Fig. 5a). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,803,495,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the inactive FSHR structure, the ECD conformation is closely titled toward the membrane layer and the TMD conformation is very similar to the inactive $\\beta_{2\\mathrm{A}}\\mathrm{R}^{31}$ (Supplementary Fig. 5c). Conformational changes on FSHR can be seen after FSH binding by structural comparison between active and inactive FSHR. At the extracellular side, FSHR_ECD shows an upward rotation by about $48^{\\circ}$ after FSH binding (Fig. 2a). Receptor ECD rotation is accompanied by a series of conformational changes in TMD (Fig. 2b-d). At the extracellular ends, TM1, TM6 and TM7 have $2 - 3\\AA$ inward movement, and TM5 has $1 - 2\\AA$ inward movement at the middle of the TM helix (Fig. 2b). In contrast, there is a ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,775,942,829]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"large movement at the TM6 intracellular end as much as $14.9\\AA$ as measured at the $\\mathrm{C}\\alpha$ atom of residue S564<sup>6,27</sup> (superscripts refer to Ballesteros-Weinstein numbering<sup>32</sup>) (Fig. 2c, d), which in agreement with the hallmark of class A GPCR activation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,830,944,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To fully understand how FSH induces FSHR activation, we aligned the ECD structures of the active and inactive FSHR. The superposition of the FSHR ECD structures reveals that the distal region of $\\mathrm{FSH}\\beta$ would clash with the membrane layer (Fig. 2e), suggesting a collision push of FSH to rotate the FSHR ECD away from the membrane layer into the upright ECD position in the active FSHR structure, which is similar to CG binding with $\\mathrm{LHCGR}^{19}$ , and TSH binding with $\\mathrm{TSHR}^{17,18}$ . On the other side, the extended hinge loop ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[63,27,119,40]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[663,27,942,41]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41467-023-36170-3 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[62,962,302,975]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nature Communications| (2023)14:519 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[931,964,942,974]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[60,58,495,287]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"from FSHR hinge region formed direct interactions with FSH (Supplementary Fig. 2c, d), which is also observed in the crystal structure of FSH-FSHR_ECD complex $^{13}$ . Similar hinge loop-hormone interactions were also observed in the structures of both CG-LHCGR-Gs and TSH-TSHR-Gs complexes $^{17,19}$ . A conserved sulfated tyrosine at the hinge loop (Y335 from FSHR, Y331 from LHCGR and Y385 from TSHR) was shown to involve in hormone binding and activation of the receptor $^{17,19,33,34}$ . Consistently, a single point mutation of Y335G in FSHR resulted in more than a 10-fold reduction of FSH activation potency (Fig. 2f; Supplementary Table 2), while more than a 100-fold reduction of FSH activation potency was caused by three combined point mutations D334G/Y335G/D336G (Fig. 2f; Supplementary Table 2), which further indicated that the extended hinge loop play a role to pull the FSH-FSHR_ECD to rotate away from the membrane layer into the active upright configuration (Fig. 2e), in a similar manner to CG binding with LHCGR and TSH binding with TSHR $^{17-19}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,288,495,465]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Structural comparison of the inactive FSHR with the inactive LHCGR and TSHR structures reveals that all three receptors have a similar ECD down conformation (Supplementary Fig. 5d). The ECD of FSHR has a nearly identical position as the LHCGR ECD but a $7^{\\circ} - 8^{\\circ}$ rotation close to the membrane layer relative to the ECD of the inactive TSHR. In addition, the active structure of FSHR also shows high similarities to the active structures of LHCGR and TSHR except subtle differences existing at the receptor ECD configurations (Supplementary Fig. 5e-g). The ECD of active FSHR has an $11.6^{\\circ}$ rotation away from the membrane layer relative to the ECD of the active LHCGR (Supplementary Fig. 5e). Together, these structural observations support a \"push and pull\" model for FSH-mediated FSHR activation, which is also conserved in LHCGR and TSHR. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,477,453,503]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A conserved structural basis of receptor ECD-TMD signal transmission ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,505,495,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Unlike most of class A GPCRs, the glycoprotein hormone-binding sites are located at the distal end of the elongated ECDs of glycoprotein hormone receptors $^{17-19}$ . The common \"push and pull\" model of glycoprotein hormone-induced receptor activation suggests that glycoprotein hormone receptors have evolved a unique paradigm for activation signal transduced from their ECD to TMD, which is distinct from other class A GPCRs. In the active FSHR structure, its ECD contains LRRs 1-11 and a hinge region that comprises a helix termed hinge helix, the extended hinge loop, and LRR12 followed by the conserved P10 region $^{35}$ , which functions as a tethered intramolecular agonist $^{36-38}$ (Supplementary Fig. 2a). The hinge helix is sandwiched between the ECD and TMD, by two conserved disulfide bonds, with one linked to LRR12 and the other linked to the hinge C-terminal P10 region (residues F353-Y362) (Fig. 3a). The links by these two disulfide bonds ensure an integrated and stable conformation of the holo-FSHR structure. Interestingly, the hinge helix in the inactive FSHR structure is elongated and shows different orientation from the hinge helix in the active FSHR structure (Fig. 3b), highlighting that hinge helix plays an important role during FSHR activation. FSHR ECD interacts with the TMD through two major interfaces, which are also observed in LHCGR and TSHR (Fig. 3a, c, e). The first interface is between the hinge helix and the extracellular loop 1 (ECL1) (Fig. 3a, c). The point mutation S273I is located at the N-terminus of hinge helix, where the S273I mutation can enhance the hydrophobic interactions from ECD to TMD, and elevate the activation level of FSHR (Fig. 3c, d). In contrast, the hinge helix in the inactive FSHR structure shows rare interactions with ECL1 by rotating approximately $30^{\\circ}$ counter-clockwise relative to the hinge helix from the active FSHR structure (Fig. 3b), thus confirming that the interactions between hinge helix and ECL1 is critical for FSHR activation. The second interface is between the P10 region and the top half of TMD (Fig. 3e). As one of the most conserved regions in glycoprotein hormone receptors (Supplementary Fig. 6), the P10 region of FSHR ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,58,944,181]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"forms extensive interactions with TM1, TM2, TM7 and the three ECLs (Fig. 3f). The structures of P10 in the three receptors are nearly identical with the RMSD of $\\mathrm{Ca}$ atoms from FSHR to LHCGR and TSHR are only $0.43\\AA$ and $0.46\\AA$ , respectively (Fig. 3e). Mutational studies of P10 residues in LHCGR and TSHR indicated that most of P10 residues were essential for receptor activation[35,38]. Together, the similar ECD-TMD configuration in all three receptors provided a conserved structural basis of ECD-TMD signal transmission of glycoprotein hormone receptors. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,194,847,207]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Basis for FSHR activation by an allosteric agonist ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,207,944,546]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Small molecular FSHR agonists have been proposed to substitute FSH in clinics[21]. Cpd-2If, a 5,6-dihydroimidazoiso [5,1- $\\alpha$ ] quinoline derivative, is an agonist of $\\mathrm{FSHR}^{24}$ . Consistently, Cpd-2If activated FSHR with high affinity and full efficacy (Supplementary Fig. 7a). The EM density map is sufficiently clear to dock Cpd-2If into the FSHR TMD pocket (Fig. 4a), which is created by the top half of TMD, including TM3, TM5, TM6, TM7, ECL2, and ECL3, as well as the N-terminus of P10 region (Fig. 4b, c). Interestingly, the binding site of Cpd-2If was found to be mainly composed of hydrophobic residues (Fig. 4b, d). Our functional data indicated that most of point mutations at pocket residues, except for F353A and M520A, resulted in the decreased activation ability of Cpd-2If to FSHR (Fig. 4e, Supplementary Table 2). Consistently, the binding of Cpd-2If to the FSHR TMD pocket induces inward movements of TM6 and TM7 at the extracellular side (Supplementary Fig. 7b), which directly results in the outward movement of TM6 at the cytoplasmic side of FSHR (Supplementary Fig. 7c), a hallmark of GPCR activation. Compared to LHCGR and TSHR, the location of Cpd-2If is almost completely overlapped with the LHCGR ligand org43553 and the TSHR ligand ML-109 (Fig. 5a), all of which are near the conserved toggle switch residue $\\mathrm{M58S}^{6,48}$ (Supplementary Fig. 7c), indicating a conserved activation mechanism of glycoprotein hormone receptors by small molecular allosteric agonists[17,19]. Interestingly, the location of Cpd-2If is also similar to orthosteric agonists seen in other class A GPCRs (Supplementary Fig. 7d), suggesting a similar way for Cpd-2If to directly induce FSHR TMD conformational changes for receptor activation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,546,944,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"FSHR, LHCGR, and TSHR share similar allosteric binding pockets as their high similarities in their TMD sequences and structures, which hinder the development of selective allosteric agonists targeting these important receptors (Supplementary Fig. 6 and Supplementary Fig. 5f, g). Single point and multipoint mutations were performed in order to determine the key residues from the receptors that were responsible for small allosteric agonist selectivity. ML-109 was analyzed first as it was a specific TSHR agonist, which cannot activate either FSHR or LHCGR (Fig. 5c, Supplementary Fig. 7e). Detailed structure analysis indicated that the orientations of the extracellular side of TM6, which forms part of the allosteric agonist binding pocket, were nearly identical between FSHR and LHCGR but different from that of TSHR (Fig. 5b). Compared with TSHR, FSHR and LHCGR have inward shifts at the extracellular side of their TM6, which would clash with the TSHR-selective ligand ML-109 (Fig. 5b). However, swapping of the extracellular portion of FSHR TM6 (residues 591-599) with the corresponding TSHR TM6 region (residues 643-651) did not convert the mutated receptor to respond to ML-109 (Fig. 5c; Supplementary Table 3). In addition, the extracellular portion of TM5 also contributes to the pocket, which has different residues between FSHR and TSHR (Supplementary Fig. 6). However, the replacement of the extracellular portions of both TM5 and TM6 from FSHR (residues 527-536/591-599) with the corresponding TSHR TM5/TM6 regions (residues 579-588 and 643-651) did not increase FSHR response to ML-109 either (Fig. 5c; Supplementary Table 3). Moreover, A352 in FSHR is located at the top of the binding pocket (Supplementary Fig. 7f). The correspondence residue in LHCGR is A349 and in TSHR is E404. However, mutation of A352E plus TM5/TM6 mutations still cannot elevate FSHR response to ML-109 (Fig. 5c; Supplementary Table 3). Surprisingly, mutations ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[63,27,119,40]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[663,27,942,41]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41467-023-36170-3 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[62,962,302,974]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nature Communications| (2023)14:519 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[931,964,942,973]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[149,77,626,259]","code_body":null,"code_caption":null,"image_caption":"[\"a \"]","image_footnote":"[]","img_path":"images/0633/098cf5581f7483a53a90a432d61b05086b217936b23dd6dd6dfb85e84bdaca82.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[633,77,858,259]","code_body":null,"code_caption":null,"image_caption":"[\"C \"]","image_footnote":"[]","img_path":"images/0919/dff331bdc2b1838a5c4a9625dca254afa05597fcfb1d0de5ca9f3f303c7070c7.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[151,275,329,458]","code_body":null,"code_caption":null,"image_caption":"[\"b \",\"d \"]","image_footnote":"[]","img_path":"images/0114/d6f88074e6442c90d1f206609ea0a22a836673235ba47572935df954bd37de53.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[339,294,586,445]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0319/5c11a74f3e32898c82815273199134095f07cdebf1f691d80540c879beadd5b8.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[591,277,850,456]","code_body":null,"code_caption":null,"image_caption":"[\"e \"]","image_footnote":"[]","img_path":"images/0700/1167f59fdf84a2b14d9fe73cbf3facbd7c665855822b525e291ab15d8503cb96.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[169,465,853,629]","code_body":null,"code_caption":null,"image_caption":"[\"f \",\"Fig. 3 | Structural basis for FSHR activation signal transduced from ECD to \"]","image_footnote":"[\"TMD. a Structural comparison of FSH-FSHR-Gs complex with CG-LHCGR-Gs and TSH-TSHR- complexes. The similar ECD-TMD configuration in three structures is shown, and the two conserved disulfide bonds in FSHR are shown in sticks. \",\"b Structural comparison of the hinge helix in the inactive and active FSHR structures. The angle was measured at the $\\\\mathrm{C}\\\\alpha$ atoms of S273 and R283 from the inactive FSHR and C276 from the active FSHR. c The first conserved interface between hinge \"]","img_path":"images/0394/3e862435a27f041f11912298051cdd4c0e34b0dc5fb113d14dbeb56d31aef955.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[507,637,944,712]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"helix and ECL1. d Concentration-response curves for WT and S273I mutant receptors. The representative concentration-response curves from three independent experiments were shown. Data were shown as mean $\\pm$ S.E.M. from three independent experiments. Source data are provided as a Source Data file. e The second conserved interface between P10 and TMD. fDetailed interactions between P10 and FSHR TMD are shown in sticks. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,748,495,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"of $\\mathrm{H615^{7.42}Y}$ or $\\mathrm{I411^{2.53}M}$ in addition to the above TM5/TM6/A352E mutations can both lead to FSHR fully activated by ML-109, and all mutations combined (H615 $^{7.42}$ Y/I411 $^{2.53}$ M/ TM5/TM6/A352E) can further increase the activation potency and efficacy of ML-109 to FSHR (Fig. 5d, Supplementary Table 3). On the other hand, single point H615 $^{7.42}$ Y mutation of FSHR can only be activated by ML-109 weakly (Supplementary Fig. 7g and Supplementary Table 3). Combined mutations of H615 $^{7.42}$ Y and I411 $^{2.53}$ M further increased FSHR response to ML-109 (Supplementary Fig. 7g and Supplementary Table 3). H615 $^{7.42}$ Y and I411 $^{2.53}$ M are located at the bottom of the pocket and the corresponding residues in TSHR are in direct contacts with ML-109 (Supplementary Fig. 7h). Thus the H615 $^{7.42}$ Y and I411 $^{2.53}$ M mutations in FSHR would increase the interactions of the mutated FSHR with ML-109. Consistently, Molecular Dynamic (MD) simulation experiments indicated ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,748,944,830]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"that the binding free energy of WT FSHR was higher than FSHR with H615 $^{7,42}$ Y and I411 $^{2,53}$ M mutations. Thus, the MD simulations implied that the H615 $^{7,42}$ Y and I411 $^{2,53}$ M mutations favor the binding of ML-109 and increase its activating ability for FSHR. ML-109 is able to activate TSHR, the binding energy of ML109 to TSHR is comparable to ML-109 binding to mutant FSHR but not WT FSHR (Supplementary Fig. 8). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,830,944,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Cpd-21f can activate FSHR, LHCGR and TSHR with high potency and efficacy, while the activation potency for FSHR is more than 10-fold higher than LHCGR and TSHR (Supplementary Fig. 7i, Supplementary Table 2 and 4). Detailed structural analysis indicated that the N-ethyl of the Cpd-21f would clash with the $\\mathrm{Y612^{7.42}}$ in LHCGR and $\\mathrm{Y667^{7.42}}$ in TSHR, thus weakening the activation potency of Cpd-21f to LHCGR and TSHR (Fig. 5e). Consistently, Mutation H615 $^{7.42}$ Y in FSHR resulted in nearly 4-fold reduction of activation potency of Cpd-21f to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[63,27,119,40]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[663,27,942,41]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41467-023-36170-3 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[62,962,302,975]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nature Communications| (2023)14:519 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[931,964,942,973]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[188,81,310,212]","code_body":null,"code_caption":null,"image_caption":"[\"a \",\"b \"]","image_footnote":"[]","img_path":"images/0646/7772f3a2612ea3d466b9021538e3a3aa4d4b12abfb66bdd8fffdd072f8ddb938.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[359,72,598,222]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0902/b4c8eddc2a1749e4ce8c7d914802ff6f90db754e77f8e3147814d5dd17b51629.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[618,77,855,222]","code_body":null,"code_caption":null,"image_caption":"[\"C \"]","image_footnote":"[]","img_path":"images/0632/f053ad2868a616a561ec042f5f2f7d0e5e692b3177723180019ebc4fb5601959.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[166,226,492,432]","code_body":null,"code_caption":null,"image_caption":"[\"d \"]","image_footnote":"[]","img_path":"images/0805/243943f73a416ca453ab10e4141b9bda361c5daa5c50c8dcff5d8c0f152ebacd.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[510,243,847,426]","code_body":null,"code_caption":null,"image_caption":"[\"e \",\"Fig. 4 | Structural basis for FSHR activation by an allosteric agonist Cpd-21f. a The structure and EM density of Cpd-21f in the bound structure. The density map is shown at level of 0.17. b, c The binding pocket of Cpd-21f in FSHR, from the front view (b) and top view (c). d Detailed interactions between Cpd-21f and FSHR. e Effects of different pocket mutations on the potency of Cpd-21f-induced cAMP accumulation. Data were shown as $\\\\Delta pEC_{50} \\\\pm S.E.M.$ from three independent \",\"experiments, which performed in triplicates, with total repeats of nine for each data point. $^{**}P < 0.01$ , $^{***}P < 0.001$ versus WT. Statistical significance of differences between WT and mutants was determined by two-sided one-way ANOVA with Tukey test. Source data are provided as a Source Data file. All the exact P values are listed as follows: $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $\\\\langle 0.0001\\\\rangle$ \"]","image_footnote":"[]","img_path":"images/0371/b8b3a39bb34b9ec225f430faa6fdcfddaab0bc2c1856862d25f3a60bc87b7491.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[60,532,495,721]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"FSHR (Fig. 5f). Moreover, org 214444-0 was reported as a selective FSHR agonist, which activated FSHR with more than 100-fold higher potency comparing to LHCGR $^{39}$ . Org 214444-0 was docked into FSHR TMD binding pocket, which location was also overlapped with Cpd-21f (Supplementary Fig. 7j). The bottom hexahydroquinoline group of Org-214444-0 is larger than the N-tert-Butyl-N-ethyl moiety of Cpd-21f, thus leading to more severe clash of cyclohexanone of Org 214444-0 with $\\mathrm{Y667^{7,42}}$ in TSHR and $\\mathrm{Y612^{7,42}}$ in LHCGR (Supplementary Fig. 7k, l), consistent with the high selectivity of Org 214444-0 for FSHR $^{39}$ . Together, our analysis indicated that H615 $^{7,42}$ in FSHR played essential roles in determining FSHR ligand selectivity and provided new insights for designing more specific small molecular agonists targeting this important receptor for infertility and in vitro fertilization. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,735,465,760]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Distribution of diseases associated mutations on the FSHR structure ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,762,495,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A distinct feature of glycoprotein hormone receptors is that they have many natural mutations associated with endocrine diseases[40,41]. These mutations are classified into inactivating and activating mutations. In the case of FSHR, the inactivating mutations can cause primary or secondary amenorrhea, premature ovarian failure (POF), and even infertility, while activating mutations can result in OHSS[42]. Comparison with LHCGR and TSHR, FSHR has the fewest natural mutations (Supplementary Fig. 9). There are no more than 20 inactivating mutations and four activating mutations that have been identified in FSHR (Supplementary Fig. 9a)[7]. Interestingly, most of the mutations in FSHR are located at the surface of the receptor rather than the TMD hydrophobic core (Supplementary Fig. 9a), providing a clue that FSHR ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,532,942,558]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"TMD is the most constrained structure among glycoprotein hormone receptors. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,559,944,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Based on the active and inactive FSHR structures $^{43}$ , we modeled the FSHR naturally occurring mutations $^{7}$ . Most of inactivating mutations, including P348R, P519I, P587H, are in key structural elements and their mutations could disrupt the stability of FSHR, thus inactivating the receptor. Specifically, P348 is located in the C terminal of LRR12, P587 is located in the receptor TM6 bundle, and P519 is located in the ECL2 (Fig. 6a). On the other hand, the activating mutations, including N431I, T449A/I $^{3,32}$ , I545T $^{5,54}$ , and D567G $^{6,30}$ , are spread in the FSHR TMD (Fig. 6b-e). The N431I mutation is located at the ECL1 near the S273I mutation, which could enhance the hydrophobic interactions between ECL1 and the hinge helix (Fig. 6b), thus elevating the basal activity of FSHR. T449A/I $^{3,32}$ mutations are located at the TMD hydrophobic core, which are likely to break the interaction between T449 $^{3,32}$ and H615 $^{7,42}$ (Fig. 6c). I545T $^{5,54}$ is located near D581 $^{6,44}$ (Fig. 6d), a PIF motif residue that plays important roles in class A GPCR activation $^{44}$ . The I545T $^{5,54}$ mutation is likely to reduce the hydrophobic interactions between I545 $^{5,54}$ , I578 $^{6,41}$ and L460 $^{3,43}$ to disrupt the packing stability of TM3, TM5 and TM6 (Fig. 6d). Consistently, mutations I542L $^{5,54}$ and V597L/F $^{5,54}$ at the same locations in LHCGR and TSHR also make the mutated receptor constitutively active (Supplementary Fig. 9b, c). The D567G $^{6,30}$ mutation, which is also observed in LHCGR and TSHR, is located at the most conserved position at the N-terminus of TM6 (Fig. 6e, Supplementary Fig. 9b, c), which is likely to disrupt the ionic lock between D567 $^{6,30}$ and R467 $^{3,50}$ , a highly conserved structure element in the inactive state of class A GPCRs $^{45}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[63,27,119,40]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[663,27,942,41]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41467-023-36170-3 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[62,962,302,975]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nature Communications| (2023)14:519 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[929,964,942,973]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[97,64,394,273]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0244/730a87265e8f889c40c3d1387dba1507c77611f7a5143248114bdd9e8809b98a.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[401,60,650,259]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0304/0058be7fe5f36d08e223cf60fb3f61810a9646d20c73fc9cf0fd1666dc4fba33.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[658,63,900,259]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0442/d0649073eb79827f762ea2ba6c9da1292fbd2a865d59444acd558f72f5d14e00.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[97,275,363,481]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0029/5ac7d5a3314dd4d27fd1203bf26420544aeb119f05a5df8e59c3e48632f1b849.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[371,275,652,481]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0518/46e63139afcf5d213cb3c9e2ecf9077bb6708adf14e52371ac8f7d96285abbfe.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[658,273,850,315]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0233/14a46f65b6bff23813441267fa811b1e11e6147a59cf6d7e6e591d04cfbe58ba.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[652,341,910,481]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 5 | Structural basis of allosteric agonist selectivity for FSHR. a Structural comparison of Cpd-21f binding pocket in the FSH-FSHR-Gs complex with the Org43553 binding pocket in the CG-LHCGR-Gs complex, and ML-109 binding pocket in the TSH-TSHR-Gs complex. b Structural comparison of the binding pockets in FSHR and LHCGR TMDs. The clashes between ML-109 and the extracellular side of TM6 of FSHR and LHCGR are highlighted in red circles. The shift between FSHR TM6 and TSHR TM6 was measured at residues S594 in FSHR and S646 in TSHR. c, d Concentration-response curves for WT and mutated FSHR. The representative concentration-response curves from three independent experiments were shown. WT refers to wild type receptor; TM6 means swapping of the extracellular portion of FSHR TM6 (residues 591-599) with the corresponding TSHR TM6 region (residues 643-651); TM5/TM6 means the replacement of the extracellular portions of both TM5 and TM6 from FSHR (residues 527-536/591-599) with \",\"the corresponding TSHR TM5/TM6 regions (residues 579-588 and 643-651); TM5/ TM6/A352E means mutation of A352E in addition to the above TM5/TM6 mutations; TM5/TM6/A352E/H615Y means mutation of H615 $^{7,42}$ Y in addition to the above TM5/ TM6/A352E mutations; TM5/TM6/A352E/I411M means mutation of I411 $^{2,53}$ M in addition to the above TM5/TM6/A352E mutations; TM5/TM6/A352E/H615Y/I411M means mutations of H615 $^{7,42}$ Y and I411 $^{2,53}$ M in addition to the above TM5/TM6/A352E mutations. e Structural comparison of the binding pockets in FSHR, LHCGR and TSHR. The clashes between Cpd-21f and residue Y612 $^{7,42}$ of LHCGR and Y667 $^{7,42}$ of TSHR are highlighted in red circle. f Concentration-response curves for WT and mutated FSHR. The representative concentration-response curves from three independent experiments were shown. UD, undetectable. Data were shown as mean $\\\\pm$ S.E.M. from three independent experiments. Source data are provided as a Source Data file. \"]","image_footnote":"[]","img_path":"images/0344/825287b7121ddc74a6c07ec21618856a7b9964a4ef02170d87d2ec9b9e1cbaed.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[60,679,157,694]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Discussion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,694,495,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Glycoprotein hormones and their receptors play central roles in regulating body development, reproduction and metabolism $^{46,47}$ . Being an essential part of endocrine system, they are involved in many endocrine diseases such as infertility, OHSS, male-limited precocious puberty $^{5,48}$ , Graves' and Hashimoto's diseases $^{49,50}$ . In this paper, we report the structures of full-length FSHR in both inactive and active states. The active structure of FSHR bound to its natural hormone FSH and a synthetic allosteric agonist Cpd-21f. Detailed analysis of these two structures reveals that FSH binding to FSHR induces a $48^{\\circ}$ rotation of its ECD toward the upright active conformation, analogous to the $45^{\\circ}$ and $38^{\\circ}$ rotations seen in the CG-LHCGR and TSH-TSHR structures, respectively. Consistently, the activation signal transduction from FSHR ECD to TMD mainly depends on the two ECD-TMD interaction interfaces (P10-TMD and hinge helix-ECL1), which are also highly conserved in the LHCGR and TSHR structures. Together, these observations highlight a universal activation mechanism of glycoprotein hormone receptors. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,681,944,815]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The small molecule agonist of FSHR has been considered as potential oral replacement of protein hormone for infertility treatment. The active FSHR structure with Cpd-21f reveals the binding site of this allosteric agonist in the top half of the FSHR TMD. Structural comparison with LHCGR and TSHR indicates a similar binding pockets for the allosteric agonists, while the unique residue H615 $^{7,42}$ in FSHR plays critical roles for FSHR activation by allosteric agonists, providing inspirations for future design of highly selective FSHR ligands. In addition, the FSHR structures also provide molecular basis for the diseases associated mutations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,816,944,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To date, the structures of FSHR as well as LHCGR and TSHR in both inactive and hormone-bound active states have been solved. In addition, the structures of small molecular allosteric agonists bound with their corresponding receptors also have been solved. Based on our structural observations and functional studies, we proposed a universal model for glycoprotein hormone receptors activation by glycoprotein hormones. In the basal state, the ECD of glycoprotein hormone receptors are tilted toward the membrane layer. Hormone ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[63,27,119,40]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[663,27,942,41]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41467-023-36170-3 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[62,962,302,975]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nature Communications| (2023)14:519 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\"]","image_footnote":"[]","img_path":"images/0304/7215d7e82cc7494416515c69e6c3ca7a73eb28297d41cf8fc2295a9f0806e36a.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[645,448,858,577]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0885/e03bc8afdd0534f88a93df9cc2ebb2396886c579b787480c51af7773ea8c73c9.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[645,578,857,702]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 6 | Detailed structural analysis of mutations in FSHR. a Three inactive mutations in FSHR. b-e The detailed interactions surrounded residues N431 $^{\\\\mathrm{ECL1}}$ (b), T449A/ $^{3.32}$ (c), I545T $^{5.54}$ (d) and D567G $^{6.30}$ (e) mutations. The active FSHR structure is \",\"shown in violet. The inactive FSHR structure, shown in light green, was modeled by swiss model based on the highest similar template structure. The four active point mutations are highlighted in green spheres. \"]","image_footnote":"[]","img_path":"images/0690/1bae0534e51130129230ed6dd499ead54c58a6b6818488a885ad85f59a22408d.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[60,775,495,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"binding induces the rotation of ECD to the upright position to avoid the clash between hormones and membrane layer. The extended hinge loop from the receptors hinge region interact with hormones to further pull the hormone-ECD complexes in the upright position. On the other hand, the small molecular allosteric agonists can activate glycoprotein hormone receptors alone by direct docking into the receptor TMD pocket, which induces conformational changes in the toggle switch residue and outward movement of TM6 at the cytoplasmic side (Supplementary Fig. 7c). Together, our results not only for FSHR, but also for the whole family of glycoprotein hormone receptors, address the long-standing scientific questions ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,775,942,817]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"regarding the mechanisms of hormone-induced receptor activation, disease-associated receptor mutations, and allosteric activation by small molecule agonists. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,827,589,841]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,844,588,856]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Constructs ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,856,942,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Human FSHR (residues 18-695) was cloned with an N-terminal FLAG and C-terminal His8 tags into a pFastBac vector. The native signal peptide was replaced with the haemagglutinin (HA) to increase protein expression. The constitutively active mutation S273I was introduced to form the FSH-FSHR-Gs complex. A dominant-negative bovine Gαs ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[63,27,119,40]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[663,27,942,41]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41467-023-36170-3 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[62,962,302,975]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nature Communications| (2023)14:519 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[929,964,942,973]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[65,58,494,100]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"construct was generated based on mini-Gs $^{51}$ . The three G-protein components, mini-Gαs, rat Gβ1 and bovine Gγ2, were cloned into separately pFastBac vector. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,112,309,125]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Expression and purification of Nb35 ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[65,126,494,193]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nanobody-35 (Nb35) was expressed and purified similarly as previously described[26]. Nb35 was purified by nickel affinity chromatography (Ni Smart Beads 6FF, SMART Lifesciences), followed by size-exclusion chromatography using a HiLoad 16/600 Superdex 75 column and finally spin concentrated to $5\\mathrm{mg/mL}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,207,317,218]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Complex expression and purification ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[65,221,494,600]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"FSHR, miniGαs, Gβ1 and Gy2 were co-expressed in Sf9 insect cells (Invitrogen) using the Bac-to-Bac baculovirus expression system (ThermoFisher). Cell pellets were thawed and lysed in 20 mM HEPES, pH 7.4, 100 mM NaCl, 10% glycerol, 5 mM MgCl₂ and 5 mM CaCl₂ supplemented with Protease Inhibitor Cocktail, EDTA-Free (TargetMol). The FSH-FSHR-Gs complex was formed in membranes by the addition of 10 μM Cpd-21f (synthesized in our lab), 1 μM FSH (urinary source, Shanghai Yuan Ye Bio-Technology Co Ltd), 10 μg/mL Nb35 and 25 mU/mL apyrase. The suspension was incubated for 1 h at room temperature. The membrane was then solubilized using 0.5% (w/v) n-Dodecyl β-D-maltoside (DDM, Anatrace), 0.1% (w/v) cholesterol hemisuccinate (CHS, Anatrace) and 0.1% (w/v) sodium cholate for 2 h at 4 °C. The supernatant was collected by centrifugation at 80,000 × g for 40 min and then incubated with M1 anti-Flag affinity resin (Genscript) for 2 h at 4 °C. After batch binding, the resin was loaded into a plastic gravity flow column and washed with 10 column volumes of 20 mM HEPES, pH 7.4, 100 mM NaCl, 10% glycerol, 2 mM MgCl₂, 2 mM CaCl₂, 0.01% (w/v) DDM, 0.002% (w/v) CHS, and 0.002% (w/v) sodium cholate, 0.1 μM FSH, 10 μM Cpd-21f and further washed with 10 column volumes of same buffer plus 0.1% (w/v) digitonin, and finally eluted using 0.2 mg/mL Flag peptide. The complex was then concentrated using an Amicon Ultra Centrifugal Filter (MWCO 100 kDa) and injected onto a Superdex200 10/300 GL column (GE Healthcare) equilibrated in the buffer containing 20 mM HEPES, pH 7.4, 100 mM NaCl, 2 mM MgCl₂, 2 mM CaCl₂, 0.05 (w/v) digitonin, 0.0005% (w/v) sodium cholate, 0.1 μM FSH and 10 μM Cpd-21f. The complex fractions were collected and concentrated to 20 mg/mL for electron microscopy experiments. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,613,349,627]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Inactive FSHR expression and purification ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[65,627,494,734]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$5\\mu \\mathrm{M}$ compound 24 was added to the culture after $Sf9$ insect cells were infected with FSHR baculovirus for $24\\mathrm{h}$ at $27^{\\circ}C.$ Cells were then collected after another $24\\mathrm{h}$ later. Cell pellets were thawed and lysed in $20~\\mathrm{mM}$ HEPES, pH 7.4, $100~\\mathrm{mM}$ NaCl, $10\\%$ glycerol, supplemented with $10~\\mu \\mathrm{M}$ compound 24 and Protease Inhibitor Cocktail, EDTA-Free (TargetMol). The purification procedures were similar to the FSH-FSHR-Gs complex, except that the procedure of complex formation on membranes was absent. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,749,211,762]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"cAMP response assay ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[65,763,494,937]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The full-length FSHR and FSHR mutants were cloned into pcDNA6.0 vector (Invitrogen) with a FLAG tag at its N-terminus. CHO-K1 cells (ATCC, #CCL-61) were cultured in Ham's F-12 Nutrient Mix (Gibco) supplemented with $10\\%$ $(\\mathrm{W} / \\mathrm{V})$ fetal bovine serum. Cells were maintained at $37^{\\circ}\\mathrm{C}$ in a $5\\%$ $\\mathrm{CO}_{2}$ incubator with 150,000 cells per well in a 12-well plate. Cells were grown overnight and then transfected with $1\\mu \\mathrm{g}$ FSHR constructs by FuGENE® HD transfection reagent in each well for $24\\mathrm{h}$ . cAMP accumulation was measured using the LANCE cAMP kit (PerkinElmer) according to the manufacturer's instructions. The transfected cells were seeded onto 384-well plates with 2500 cells each well, and then incubated with ligands for $30\\mathrm{min}$ at $37^{\\circ}\\mathrm{C}$ , then Eu and Ulight were added separately before cAMP levels were measured. Fluorescence signals were measured at $615\\mathrm{nm}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,58,942,179]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and $665\\mathrm{nm}$ by an Envision multilevel plate reader (PerkinElmer). Data were analyzed using Graphpad Prism8.0, the three-parameter, nonlinear regression equation in Prism suite was used in fitting. The response values were normalized by WT receptors within each individual experiment, with the basal activity for WT as 0, while the fitted $\\mathbf{E}_{\\mathrm{max}}$ of WT as 100. Experiments were performed at least three times, the detail information were attached in the figure legends, each experiment conducted in triplicate. Data were presented as means $\\pm$ SEM. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,194,848,207]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Detection of surface expression of FSHR mutants ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,207,942,424]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The cell seeding and transfection follow the same method as cAMP response assay. After $24\\mathrm{h}$ of transfection, cells were washed once with PBS and then detached with $0.2\\%$ (w/v) EDTA in PBS. Cells were blocked with PBS containing $5\\%$ (w/v) BSA for $15\\mathrm{min}$ at room temperature (RT) before incubating with primary anti-Flag antibody (diluted with PBS containing $5\\%$ BSA at a ratio of 1:150, ABclonal) for $1\\mathrm{h}$ at RT. Cells were then washed three times with PBS containing $1\\%$ (w/v) BSA and then incubated with anti-mouse Alexa-488-conjugated secondary antibody (diluted at a ratio of 1:1000, Invitrogen) at $4^{\\circ}\\mathrm{C}$ in the dark for $1\\mathrm{h}$ . After another three times of wash, cells were harvested, and fluorescence intensity was quantified in a BD Accuri C6 software (BD Biosciences) at excitation $488\\mathrm{nm}$ and emission $519\\mathrm{nm}$ . Approximately 10,000 cellular events per sample were collected and data were normalized to WT. Experiments were performed at least three times. The representative flow cytometry data for the detection of receptor surface expression was shown in Supplementary Fig. 10. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,437,823,451]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Cryo-EM grid preparation and data collection ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,451,942,532]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For the preparation of cryo-EM grids, $3\\mu \\mathrm{L}$ of the purified protein at $20\\mathrm{mg / mL}$ for the FSH-FSHR-Gs complex, $5\\mathrm{mg / mL}$ for the inactive FSHR, were applied onto a glow-discharged holey carbon grid (Quantifoil R1.2/1.3). Grids were plunge-frozen in liquid ethane using Vitrobot Mark IV (Thermo Fischer Scientific). Frozen grids were transferred to liquid nitrogen and stored for data acquisition. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,532,942,775]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Cryo-EM imaging of the FSH-FSHR-Gs complex and the inactive FSHR were performed on a Titan Krios at $300\\mathrm{kV}$ in Advanced Center for Electron Microscopy and Cryo-Electron Microscopy Research Center, respectively, Shanghai Institute of Materia Medica, Chinese Academy of Sciences (Shanghai China), A total of 4,025 movies for the FSH-FSH-Gs complex were collected with a Titan Krios equipped with a Falcon4 direct electron detection device at a pixel size of $1.03\\AA$ using the EPU software (FEI Eindhoven, Netherlands). The micrographs were recorded in counting mode at a dose rate of about $15\\mathrm{e}/\\mathring{\\mathrm{A}}^{2}/\\mathrm{s}$ with a defocus ranging from $-0.8$ to $-2.0\\mu \\mathrm{m}$ . Each movie was divided into 36 frames during motion correction. For the inactive FSHR protein, a total of 4,495 movies were collected by a Gatan K3 Summit direct electron detector with a Gatan energy filter (operated with a slit width of $20\\mathrm{eV}$ ) (GIF) at a pixel size of $1.071\\mathring{\\mathrm{A}}$ using the SerialEM software[52]. The micrographs were recorded in counting mode at a dose rate of about $22\\mathrm{e}/\\mathring{\\mathrm{A}}^{2}/\\mathrm{s}$ with a defocus ranging from $-1.2$ to $-2.2\\mu \\mathrm{m}$ . The total exposure time was 3s and intermediate frames were recorded in 0.083 s intervals, resulting in a total of 36 frames per micrograph. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,789,786,803]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Image processing and map construction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,803,942,937]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For the FSH-FSHR-Gs complex, dose-fractionated image stacks were aligned using MotionCor2.1 $^{53}$ and CryoSPARC-v3.3 $^{54}$ . Contrast transfer function (CTF) parameters for each micrograph were estimated by Gctf $^{55}$ . Particle selections for 2D and 3D classifications were performed using CryoSPARC-v3.3 $^{54}$ . Automated particle picking yielded 6,759,790 particles that were subjected to three rounds reference-free 2D classification to discard poorly defined particles, producing 1748,285 particles. The good subsets were further subjected to 6 rounds of heterogeneous refinement, which produced an initial reconstruction for further 3D classification. The selected subsets were subsequently ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[63,27,119,40]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[663,27,942,41]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41467-023-36170-3 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[63,963,300,975]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nature Communications | (2023)14:519 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[931,964,942,973]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"9 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[60,58,497,275]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"subjected to non-uniform 3D refinement. The final refinement generated a map with an indicated global resolution of $2.82\\AA$ with 477,950 particles projections at a Fourier shell correlation of 0.143. The particles were further subjected to local-refinement focus on the FSHR-ECD and FSH. The local-refinement generated a map with an indicated global resolution of $3.14\\AA$ at a Fourier shell correlation of 0.143. For the inactive FSHR, image stacks were subjected to beam-induced motion correction using MotionCor2[53]. CTF parameters for non-dose weighted micrographs were determined by Gctf[55]. Automated particle selection yielded 2,781,231 particles using RELION-3.1.2[56]. The particles were imported to CryoSPARC-3.3[54] for 2 rounds of 2D Classification. The well-defined subset accounting for 1,148,175 particles was reextracted in RELION-3.1.2[56] and was subjected to 2 rounds of 3D classification, producing one good subset accounting for 356,211 particles. The final refinement generated a map with an indicated global resolution of $6.01\\AA$ at a Fourier shell correlation of 0.143. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,288,278,301]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Model building and refinement ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,302,497,518]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The crystal structure of human FSH-FSHR_ECD (PDB code: 4AY9), the structure of CG-LHCRG-Gs (PDB code: 7fih) were used as the start for model rebuilding and refinement against the electron microscopy map. The model was docked into the electron microscopy density map using Chimera $^{57}$ , followed by iterative manual adjustment and rebuilding in COOT $^{58}$ and ISOLDE $^{59}$ . Real space and reciprocal space refinements were performed using Phenix programs. The model statistics were validated using MolProbity $^{60}$ . Structural figures were prepared in Chimera $^{61}$ and PyMOL (https://pymol.org/2/). For the inactive FSHR, the model of active FSHR from the structure of FSH-FSHR-Gs complex was to generate the initial template. The initial template was docked into the EM density map using Chimera $^{57}$ . The model was further rebuilt in coot and real-space refined in COOT $^{58}$ and ISOLDE $^{59}$ . The final refinement statistics were validated using the module \"comprehensive validation (cryo-EM)\" in Phenix $^{62}$ . The final refinement statistics are provided in Supplementary Table 1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,532,302,545]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Construction of membraned FSHR ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,546,497,600]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"FSHR was first oriented by the Orientations of Proteins in Membranes server $^{63}$ . Then, the structure was inserted in $100\\mathring{\\mathrm{A}}^{*}100\\mathring{\\mathrm{A}}$ 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) membrane according to CHARMM-GUI server $^{64}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,613,194,627]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Molecular docking ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,627,497,750]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The FSH-FSHR-Gs complex was used for docking. The FSHR and small molecules were separated from the complex and prepared in the protein preparation wizard of Schrodinger, Maestro. During the processes, we first assigned bond orders and added hydrogens on the system. Meanwhile, disulfide bonds were created and residue states were generated using Epik at $\\mathrm{pH} = 7.0 \\pm 2.0$ . Then PROPKA method was applied to assign protonation state of each residue. At last, the restrained minimization was used with $0.3\\AA$ RMSD constraint on heavy atoms under OPLS4 force field. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,762,280,775]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Molecular dynamic simulations ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,775,497,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The cryo-EM structure of Cpd-21f-FSH-FSHR and ML-109-TSH-TSHR (PDB ID: 7XW5) complex were used for the construction of the MD simulation systems. Before the simulation, Gs, FSH, TSH, and Cpd-21f were removed from the systems. We first aligned TSHR-ML-109 to FSHR according to the TMD and placed ML-109 in the corresponding FSHR pocket. Then, H615Y and I411M mutations were introduced via PyMOL. In the dual mutation system, we introduced both mutations. We oriented the structures with the Orientations of Proteins in Membranes server and used the CHARMM-GUI server to insert them into POPC (palmitoyl-2-oleoyls-n-glycero-3-phosphocholine) membrane $^{63,65}$ . Then, TIP3P waters were added to the top and bottom of the system. $0.15 \\mathrm{M} / \\mathrm{L}$ NaCl ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,56,947,317]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ions and counterions were applied via the distance method $^{64,65}$ . FF19SB, LIPID17, and GAFF2 force fields were applied for the parameter of amino acids, lipids, and ML-109, respectively $^{66,67}$ . During simulations, the systems were first minimized and equilibrated in the separated 6 processes provided by CHARMM-GUI. Next, 3 parallels of 200 ns production running were applied on the system. The temperature (303.15 K) and pressure (1 atm) were controlled by the Langevin thermostat and isotropic Berendsen barostat, respectively. Long-range electrostatic interactions were treated by the Particle mesh Ewald algorithm and a cutoff of $12\\AA$ was employed for short-range interactions. Between $10\\AA$ and $12\\AA$ , force-based switching was applied for soft changing of interactions. The SHAKE algorithm with hydrogen mass repartitioning was applied to restrain the bond with hydrogens. Hence, the timestep of simulations was $4\\mathrm{fs}^{68}$ . The calculation of binding free energy was finished by MPPBSA.py $^{69}$ . We used the last $1/4$ of trajectories to guarantee that the trajectory had reached equilibrium upon evaluation. The standard deviation was estimated by 3 repeats of simulations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,329,650,341]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Reporting summary ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,341,942,370]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,381,653,397]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data availability ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,397,944,492]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The density maps and structure coordinates have been deposited to the Electron Microscopy Database (EMDB) and the Protein Data Bank (PDB) with accession number of EMD-35135, PDB ID 8I2G for the FSH-FSHR-Gs complex; EMD-35136 and 8I2H for the inactive FSHR. The functional data and protein purification data and MD data generated in this study are provided in the Supplementary Information and Source Data files. Source data are provided with this paper. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,503,608,517]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[510,518,942,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1. Robker, R. L. & Richards, J. S. Hormonal control of the cell cycle in ovarian cells: proliferation versus differentiation. Biol. Reprod. 59, 476-482 (1998). \",\"2. Foulkes, N. S., Schlotter, F., Pevet, P. & Sassone-Corsi, P. 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Garcia-Nafria, J., Lee, Y., Bai, X., Carpenter, B. & Tate, C. G. Cryo-EM structure of the adenosine A2A receptor coupled to an engineered heterotrimeric G protein. *Elife* 7, https://doi.org/10.7554/eLife.35946 (2018). \",\"52. Mastronarde, D. N. Automated electron microscope tomography using robust prediction of specimen movements. J. Struct. Biol. 152, 36-51 (2005). \",\"53. Zheng, S. Q. et al. MotionCor2: anisotropic correction of beam-induced motion for improved cryo-electron microscopy. Nat. Methods 14, 331-332 (2017). \",\"54. Punjani, A., Rubinstein, J. L., Fleet, D. J. & Brubaker, M. A. cryoS-PARC: algorithms for rapid unsupervised cryo-EM structure determination. Nat. Methods 14, 290-296 (2017). \",\"55. Zhang, K. Gctf: Real-time CTF determination and correction. J. Struct. Biol. 193, 1-12 (2016). \",\"56. Scheres, S. H. RELION: implementation of a Bayesian approach to cryo-EM structure determination. J. Struct. Biol. 180, 519-530 (2012). \",\"57. Pettersen, E. F. et al. UCSF Chimera-a visualization system for exploratory research and analysis. J. Comput Chem. 25, 1605-1612 (2004). \"]","page_idx":"10","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[63,27,119,40]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[663,27,942,41]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41467-023-36170-3 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[63,962,302,975]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nature Communications| (2023)14:519 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[927,963,942,973]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"11 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[62,58,495,532]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"58. Emsley, P. & Cowtan, K. Coot: model-building tools for molecular graphics. Acta Crystallogr. D: Biol. Crystallogr. 60, 2126-2132 (2004). \",\"59. Croll, T. I. ISOLDE: a physically realistic environment for model building into low-resolution electron-density maps. Acta Crystallogr. D: Struct. Biol. 74, 519-530 (2018). \",\"60. Chen, V. B. et al. MolProbity: all-atom structure validation for macromolecular crystallography. Acta Crystallogr. D: Biol. Crystallogr 66, 12-21 (2010). \",\"61. Pettersen, E. F. et al. UCSF ChimeraX: structure visualization for researchers, educators, and developers. Protein Sci. https://doi.org/10.1002/pro.3943 (2020). \",\"62. Adams, P. D. et al. PHENIX: a comprehensive Python-based system for macromolecular structure solution. Acta Crystallogr. D: Biol. Crystallogr. 66, 213-221 (2010). \",\"63. Lomize, M. A., Pogozheva, I. D., Joo, H., Mosberg, H. I. & Lomize, A. L. OPM database and PPM web server: resources for positioning of proteins in membranes. *Nucleic Acids Res.* **40**, D370–D376 (2012). \",\"64. Jo, S. et al. CHARMM-GUI 10 years for biomolecular modeling and simulation. J. Comput. Chem. 38, 1114-1124 (2017). \",\"65. Wu, E. L. et al. CHARMM-GUI Membrane Builder toward realistic biological membrane simulations. J. Comput. Chem. 35, 1997-2004 (2014). \",\"66. Tian, C. et al. ff19SB: Amino-acid-specific protein backbone parameters trained against quantum mechanics energy surfaces in solution. J. Chem. Theory Comput. 16, 528-552 (2020). \",\"67. Lee, J. et al. CHARMM-GUI supports the Amber force fields. J. Chem. Phys. 153, 035103 (2020). \",\"68. Balusek, C. et al. Accelerating membrane simulations with hydrogen mass repartitioning. J. Chem. Theory Comput. 15, 4673-4686 (2019). \",\"69. Miller, B. R. 3rd et al. MMPBSA.py: an efficient program for end-state free energy calculations. J. Chem. Theory Comput. 8, 3314-3321 (2012). \"]","page_idx":"11","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[63,544,233,559]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgements ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,560,497,818]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The cryo-EM data were collected at the Cryo-Electron Microscopy Research Center and Advanced Center for Electron Microscopy, Shanghai Institute of Materia Medica (SIMM). The authors thank the staff at the SIMM Cryo-Electron Microscopy Research Center and Advanced Center for Electron Microscopy for their technical support. This work was partially supported by Ministry of Science and Technology (China) grants (2018YFA0507002 to H.E.X.); Shanghai Municipal Science and Technology Major Project (2019SHZDZX02 to H.E.X.); Shanghai Municipal Science and Technology Major Project (H.E.X.); CAS Strategic Priority Research Program (XDB37030103 to H.E.X.); the National Natural Science Foundation of China (32130022 to H.E.X., 32171187 to Y.J., 82121005 to H.E.X. and Y.J., 81922071 to Y.Z.); CAMS Innovation Fund for Medical Sciences (2021-I2M-1-003 to S.Z.); CAMS Innovation Fund for Medical Sciences (2021-CAMS-JZ004 to S.Z.); Tsinghua University-Peking University Center for Life Sciences (045-61020100121 to S. Z.); National Science & Technology Major Project \"Key New Drug Creation and Manufacturing Program\" of China (2018ZX09711002 to H.J.); Science and Technology Commission of Shanghai Municipal (20431900100 to H.J.); Jack Ma Foundation (2020-CMKYGG-05 to H.J.); Zhejiang Provincial ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,58,944,113]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Natural Science Foundation of China (LR19H310001 to Y.Z), the Ministry of Science and Technology (2019YFA050880 to Y.Z.), and the Key R&D Projects of Zhejiang Province (2021C03039 to Y.Z.). Y.Z. is also supported by the Fundamental Research Funds for the Central Universities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,124,697,137]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Author contributions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,140,944,303]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"J.D. designed the expression constructs, purified the FSHR proteins, performed cryo-EM grid preparation and data collection, conducted functional studies, analyzed the structures, prepared the figures, and wrote the manuscript; P.X. and H.Z. performed cryo-EM data calculations, model building, and participated in figure preparation; X.L. supplied the FSH hormone and supervised by S.Z.; Y.-J.J participated in functional studies and protein purification, J.Y. synthesized Cpd-21f and compound 24; C.M. and D.S. participated in cryo-EM data calculations and model building; X.H. performed molecular docking and dynamic stimulations, which were supervised by H.J. and X.C.; Y.J. supervised the studies; H.E.X., Y.Z. and S.Z. conceived and supervised the project and wrote the manuscript with inputs from all authors. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,313,689,329]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Competing interests ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,330,781,343]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The authors declare no competing interests. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,354,712,369]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Additional information ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,370,855,411]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41467-023-36170-3. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,424,929,451]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Correspondence and requests for materials should be addressed to Shuyang Zhang, Yan Zhang or H. Eric Xu. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,465,936,518]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Peer review information Nature Communications thanks Arnau Cordomi, Xin-Yun Huang, Eric Reiter and Irina Tikhonova for their contribution to the peer review of this work. Peer reviewer reports are available. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,532,835,560]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Reprints and permissions information is available at http://www.nature.com/reprints ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,573,919,601]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,613,944,789]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,803,645,816]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"© The Author(s) 2023 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[63,27,119,40]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[663,27,942,41]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41467-023-36170-3 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[63,962,302,975]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nature Communications| (2023)14:519 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[926,963,942,973]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"12 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[63,137,818,246]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mechanism of hormone and allosteric agonist mediated activation of follicle stimulating hormone receptor \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,288,233,303]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received: 2 August 2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,313,245,327]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Accepted: 18 January 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,339,265,353]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Published online: 31 January 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[63,364,201,379]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Check for updates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[359,284,944,351]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Jia Duan $^{1,2,13}$ , Peiyu Xu $^{1,13}$ , Huibing Zhang $^{3,4,5,6,13}$ , Xiaodong Luan $^{7,8,9,10,13}$ , Jiaqi Yang $^{1}$ , Xinheng He $^{1,2}$ , Chunyou Mao $^{3,4,5,6}$ , Dan-Dan Shen $^{3,4,5,6}$ , Yujie Ji $^{1,2}$ , Xi Cheng $^{1}$ , Hualiang Jiang $^{1,2,11,12}$ , Yi Jiang $^{11,12}$ , Shuyang Zhang $^{7,8,9,10}$ , Yan Zhang $^{3,4,5,6}$ & H. Eric Xu $^{1,2,12}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[359,381,944,627]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Follicle stimulating hormone (FSH) is an essential glycoprotein hormone for human reproduction, which functions are mediated by a G protein-coupled receptor, FSHR. Aberrant FSH-FSHR signaling causes infertility and ovarian hyperstimulation syndrome. Here we report cryo-EM structures of FSHR in both inactive and active states, with the active structure bound to FSH and an allosteric agonist compound 21 f. The structures of FSHR are similar to other glycoprotein hormone receptors, highlighting a conserved activation mechanism of hormone-induced receptor activation. Compound 21 f formed extensive interactions with the TMD to directly activate FSHR. Importantly, the unique residue $\\\\mathrm{H615^{7.42}}$ in FSHR plays an essential role in determining FSHR selectivity for various allosteric agonists. Together, our structures provide a molecular basis of FSH and small allosteric agonist-mediated FSHR activation, which could inspire the design of FSHR-targeted drugs for the treatment of infertility and controlled ovarian stimulation for in vitro fertilization. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,667,497,778]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Follicle-stimulating hormone (FSH) is secreted by pituitary glands and functions as a stimulator of the estrogen production, ovarian follicles maturation and spermatogenesis $^{1,2}$ . FSH acts through FSHR, which is mainly expressed in gonads (ovaries in female and testes in male) $^{3}$ . Mutations in human demonstrate that aberrant signaling of FSH-FSHR can lead to serious diseases $^{4,5}$ , especially infertility and ovarian hyperstimulation syndrome (OHSS). Recently, much more evidence have been found that the function of extra gonadal FSHR is also closely \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,667,946,775]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"relevant to Alzheimer's disease, osteoporosis, obesity, and cancers[6-9]. In clinical, FSH is a main therapeutic drug used in anovulatory infertility and assisted reproductive technologies for women and hypogonadotropic hypogonadism for men[10,11]. To date, several crystal structures of FSH-bound FSHR fragments, including the leucine-rich repeat hormone-binding domain (FSHR_HB) and the complete ECD fragment (FSHR_ECD), have been reported[12,13], offering an opportunity for us to understand the detailed interactions between FSH and FSHR. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,803,946,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"<sup>1</sup>State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 201203 Shanghai, China. <sup>2</sup>University of Chinese Academy of Sciences, 100049 Beijing, China. <sup>3</sup>Department of Biophysics and Department of Pathology of Sir Run Run Shaw Hospital, Zhejiang University School of Medicine, Hangzhou, Zhejiang, China. <sup>4</sup>Liangzhu Laboratory, Zhejiang University Medical Center, Hangzhou, Zhejiang, China. <sup>5</sup>MOE Frontier Science Center for Brain Research and Brain-Machine Integration, Zhejiang University School of Medicine, Hangzhou, Zhejiang, China. <sup>6</sup>Zhejiang Provincial Key Laboratory of Immunity and Inflammatory diseases, Hangzhou, Zhejiang, China. <sup>7</sup>Department of Cardiology, Peking Union Medical College Hospital, Peking Union Medical College and Chinese Academy of Medical Sciences, Beijing, China. <sup>8</sup>Medical Research Center, Peking Union Medical College Hospital, Peking Union Medical College and Chinese Academy of Medical Sciences, Beijing, China. <sup>9</sup>School of medicine, Tsinghua university, Beijing, China. <sup>10</sup>Tsinghua-Peking Center for life science, Tsinghua university, Beijing, China. <sup>11</sup>Lingang Laboratory, 200031 Shanghai, China. <sup>12</sup>School of Life Science and Technology, ShanghaiTech University, 201210 Shanghai, China. <sup>13</sup>These authors contributed equally: Jia Duan, Peiyu Xu, Huibing Zhang, Xiaodong Luan. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,926,549,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\text{電}$ -mail: shuyangzhang103@nrdrs.org; zhang_yan@zju.edu.cn; eric.xu@simm.ac.cn \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,50,369,74]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"nature communications \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[912,48,942,81]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"# \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[62,116,119,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[667,118,944,132]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41467-023-36170-3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[62,962,302,975]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nature Communications| (2023)14:519 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[932,964,944,974]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[60,58,495,84]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, the molecular basis of how does FSH activate FSHR is still controversial because of the lack of the full-length FSHR structure. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,86,495,288]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"FSH, along with luteinizing hormone (LH), chorionic gonadotropin (CG) and thyroid-stimulating hormone (TSH), constitute the family of glycoprotein hormones $^{14}$ , which share similar 3D architectures and function through binding and activation of a subfamily of G protein-coupled receptors, named glycoprotein hormone receptors $^{15}$ . There are three members of glycoprotein hormone receptors, FSHR, LHCGR and TSHR, which are activated to mainly couple the Gs protein and lead to up-regulation of the secondary message cAMP in cells $^{16}$ . Most recently, the cryo-electron microscopy (cyro-EM) structures of CG-LHCGR-Gs and TSH-TSHR-Gs complexes have also been determined $^{17-19}$ , further providing insights into hormone specificity and hormone-induced receptor activation. The structures of CG-LHCGR-Gs and TSH-TSHR-Gs complexes suggested that there might be a conserved activation mechanism among glycoprotein hormone receptors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,288,495,450]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As a disease-associated drug target, there is an urgent need for highly selective small molecular agonists of FSHR to replace hormone therapy, and the small molecular antagonists of FSHR could also be used for contraception[20,21]. Over the years, there are many small molecular agonists and antagonists towards FSHR that have been developed[22,23]. For example, compound 21f (Cpd-21f)[24] is a small molecule allosteric agonist of FSHR with high affinity and activation efficacy. However, up to now, small molecular agonists and antagonists have not entered clinical research due to their low specificity. The high homology of glycoprotein hormone receptors and the lack of structure information of full-length FSHR continue to hinder the development of small molecule drugs targeting FSHR. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,451,495,612]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this study, we report two cryo-EM structures, one is the full-length FSHR bound to FSH, Cpd-21f and Gs protein at a global resolution of $2.82\\\\AA$ , and the other is the inactive FSHR structure with a global resolution of $6.01\\\\AA$ . Combined with functional studies, our structures reveal a \\\"push and pull\\\" mechanism of hormone-induced receptor activation, which is highly conserved in glycoprotein hormone receptors. The high-resolution structure of Cpd-21f bound with FSHR also provides the basis for rational design of small molecule drugs with higher specificity. Moreover, the structures of the full-length FSHR also allow us to investigate the mechanisms of activating and inactivating mutations naturally occurred in FSHR-related diseases. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,626,129,639]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,640,487,653]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Structures of FSH-bound FSHR-Gs complex and inactive FSHR \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,654,495,708]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To obtain a high-resolution structure of FSH-bound FSHR-Gs complex, a constitutively active mutation[25], S273I, was introduced to FSHR to enhance the assembly of the FSH-FSHR-Gs complex, in analogous to the constitutively active mutation S277I in the LHCGR[19] \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,58,944,288]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and S281I in TSHR $^{17}$ . Human FSH was incubated with membranes from cells co-expressing FSHR and three subunits of Gs heterotrimer in the presence of $\\\\mathrm{Nb35}^{26}$ , which stabilizes the Gs heterotrimer conformation. Cpd-21f was also added to further stabilize the FSH-FSHR-Gs complex. The final structure was determined at a global resolution of $2.82\\\\AA$ (Supplementary Fig. 1 and Supplementary Table 1). The EM map was clear to position all components of the complex, including two subunits of FSH, the three Gs subunits, Nb35 and FSHR, which includes the N-terminal leucine-rich repeats 1-11 (LRR1-11), the hinge region, and the C-terminal TMD (Fig. 1a, Supplementary Fig. 2a, b). The local refinement of FSH-FSHR ECD subcomplex yielded a map with a better density at the extended hinge loop from the receptor hinge region (residues 296-328 are not included) (Supplementary Fig. 2c, d). Interestingly, 13 cholesterol and 5 lipid molecules were found surrounding the FSHR TMD, like a belt, which was similar to what has been observed in TSHR structures (PDB: 7XW5) $^{17}$ (Fig. 1a, Supplementary Fig. 3). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,288,944,437]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To obtain stable inactive FSHR proteins for cryo-EM structure determination, a small molecular antagonist, compound $24^{27}$ , was added during FSHR expression and purification. Through numerous data collection, we were able to obtain a structure of wild type FSHR in the inactive state at a global resolution of 6.01 Å (Fig. 1b, Supplementary Fig. 4). The EM map was sufficient to place the receptor ECD and TMD, while the density of compound 24 was not observed. Due to the relatively low resolution of the inactive FSHR map, we only built a poly-alanine model for the inactive FSHR structure (Fig. 1b). The data and structural statistics are summarized in Supplementary Table 1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,451,813,463]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mechanism of FSH-induced FSHR activation \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,465,944,708]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As a canonical member of glycoprotein hormone receptors, FSHR has been chosen as a research model and widely studied in many decades[3,28,29]. The detail interactions between FSH and FSHR were extensively studied based on the two crystal structures of FSH-FSHR_HB and FSH-FSHR_ECD complexes[12,13]. However, two controversial activation models of FSH-induced FSHR activation were also proposed due to the fact that the structures of FSH-FSHR_HB and FSH-FSHR_ECD complexes were determined in dimeric[12] and trimeric states[13,30], respectively. The full-length FSHR structures we solved in the active and inactive states were both in monomeric states. Structural comparison of active FSHR in the FSH-FSHR-Gs complex with FSH-FSHR_HB and FSH-FSHR_ECD complexes, respectively, which reveals that the FSH-FSHR_ECD in our structure is nearly identical to the monomeric FSH-FSHR_ECD structure from the two crystal structures. However, the presence of FSH and Gs protein would prevent receptor dimerization or trimerization in the same convex membrane layer (Supplementary Fig. 5a, b) as observed in the crystal structures. Interestingly, dimerization of the receptor-Gs \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,727,522,893]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 1 | Cryo-EM structures of the FSH-FSHR-Gs complex and the inactive FSHR. a Cryo-EM density (left panel) and ribbon presentation (right panel) of the FSH-FSHR-Gs complex, the complex density map is shown at level of 0.044. b Cryo-EM \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0744/bd1ccd4e78b7f96e30801ace45a0d747b1be832be2edf605c7a135651e41f515.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[534,725,806,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"density (left panel) and ribbon presentation (right panel) of the inactive FSHR, the EM density map is shown at level of 0.017. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0190/44125a9570b95fec20830d383793279541f6f81ed5bff1dfee4e1940851c87c0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[63,27,119,40]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[663,27,942,41]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41467-023-36170-3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[62,962,302,975]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nature Communications| (2023)14:519 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[931,963,942,973]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[201,60,800,445]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0588/9b1a7bde9668cdb12f4d09ef41a0c5f41601225a0eb69863a1d24d26be319343.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[213,449,806,664]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 2 | Mechanism of FSH-induced FSHR activation. a–d Structural comparison of the active and inactive FSHR. The overall structure (a), the extracellular side of TMD (b), the intracellular side of TMD (c, d). e The Schematic diagram of FSH-induced FSHR activation, the superposition of ECD structures of the active and inactive FSHR (left panel), and the activation conformation of FSHR (right panel), the clash of FSHβ with the membrane layer is marked with a red line and the \\\",\\\"extended hinge loop is shown in cyan. f Concentration-response curves for FSHR mutants at the extended hinge loop. The representative concentration-response curves from three independent experiments were shown. Data were shown as mean $\\\\\\\\pm$ S.E.M. from three independent experiments. Source data are provided as a Source Data file. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0297/2e05b13c7a8aad6ab4cac861b73c3686b8010c8bd45ed984f5c3b6a0f4bda43b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[60,775,494,803]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"complex could form from receptors in concave or different membrane layers (Supplementary Fig. 5a). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,803,495,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the inactive FSHR structure, the ECD conformation is closely titled toward the membrane layer and the TMD conformation is very similar to the inactive $\\\\beta_{2\\\\mathrm{A}}\\\\mathrm{R}^{31}$ (Supplementary Fig. 5c). Conformational changes on FSHR can be seen after FSH binding by structural comparison between active and inactive FSHR. At the extracellular side, FSHR_ECD shows an upward rotation by about $48^{\\\\circ}$ after FSH binding (Fig. 2a). Receptor ECD rotation is accompanied by a series of conformational changes in TMD (Fig. 2b-d). At the extracellular ends, TM1, TM6 and TM7 have $2 - 3\\\\AA$ inward movement, and TM5 has $1 - 2\\\\AA$ inward movement at the middle of the TM helix (Fig. 2b). In contrast, there is a \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,775,942,829]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"large movement at the TM6 intracellular end as much as $14.9\\\\AA$ as measured at the $\\\\mathrm{C}\\\\alpha$ atom of residue S564<sup>6,27</sup> (superscripts refer to Ballesteros-Weinstein numbering<sup>32</sup>) (Fig. 2c, d), which in agreement with the hallmark of class A GPCR activation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,830,944,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To fully understand how FSH induces FSHR activation, we aligned the ECD structures of the active and inactive FSHR. The superposition of the FSHR ECD structures reveals that the distal region of $\\\\mathrm{FSH}\\\\beta$ would clash with the membrane layer (Fig. 2e), suggesting a collision push of FSH to rotate the FSHR ECD away from the membrane layer into the upright ECD position in the active FSHR structure, which is similar to CG binding with $\\\\mathrm{LHCGR}^{19}$ , and TSH binding with $\\\\mathrm{TSHR}^{17,18}$ . On the other side, the extended hinge loop \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[63,27,119,40]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[663,27,942,41]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41467-023-36170-3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[62,962,302,975]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nature Communications| (2023)14:519 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[931,964,942,974]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[60,58,495,287]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"from FSHR hinge region formed direct interactions with FSH (Supplementary Fig. 2c, d), which is also observed in the crystal structure of FSH-FSHR_ECD complex $^{13}$ . Similar hinge loop-hormone interactions were also observed in the structures of both CG-LHCGR-Gs and TSH-TSHR-Gs complexes $^{17,19}$ . A conserved sulfated tyrosine at the hinge loop (Y335 from FSHR, Y331 from LHCGR and Y385 from TSHR) was shown to involve in hormone binding and activation of the receptor $^{17,19,33,34}$ . Consistently, a single point mutation of Y335G in FSHR resulted in more than a 10-fold reduction of FSH activation potency (Fig. 2f; Supplementary Table 2), while more than a 100-fold reduction of FSH activation potency was caused by three combined point mutations D334G/Y335G/D336G (Fig. 2f; Supplementary Table 2), which further indicated that the extended hinge loop play a role to pull the FSH-FSHR_ECD to rotate away from the membrane layer into the active upright configuration (Fig. 2e), in a similar manner to CG binding with LHCGR and TSH binding with TSHR $^{17-19}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,288,495,465]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Structural comparison of the inactive FSHR with the inactive LHCGR and TSHR structures reveals that all three receptors have a similar ECD down conformation (Supplementary Fig. 5d). The ECD of FSHR has a nearly identical position as the LHCGR ECD but a $7^{\\\\circ} - 8^{\\\\circ}$ rotation close to the membrane layer relative to the ECD of the inactive TSHR. In addition, the active structure of FSHR also shows high similarities to the active structures of LHCGR and TSHR except subtle differences existing at the receptor ECD configurations (Supplementary Fig. 5e-g). The ECD of active FSHR has an $11.6^{\\\\circ}$ rotation away from the membrane layer relative to the ECD of the active LHCGR (Supplementary Fig. 5e). Together, these structural observations support a \\\"push and pull\\\" model for FSH-mediated FSHR activation, which is also conserved in LHCGR and TSHR. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,477,453,503]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A conserved structural basis of receptor ECD-TMD signal transmission \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,505,495,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Unlike most of class A GPCRs, the glycoprotein hormone-binding sites are located at the distal end of the elongated ECDs of glycoprotein hormone receptors $^{17-19}$ . The common \\\"push and pull\\\" model of glycoprotein hormone-induced receptor activation suggests that glycoprotein hormone receptors have evolved a unique paradigm for activation signal transduced from their ECD to TMD, which is distinct from other class A GPCRs. In the active FSHR structure, its ECD contains LRRs 1-11 and a hinge region that comprises a helix termed hinge helix, the extended hinge loop, and LRR12 followed by the conserved P10 region $^{35}$ , which functions as a tethered intramolecular agonist $^{36-38}$ (Supplementary Fig. 2a). The hinge helix is sandwiched between the ECD and TMD, by two conserved disulfide bonds, with one linked to LRR12 and the other linked to the hinge C-terminal P10 region (residues F353-Y362) (Fig. 3a). The links by these two disulfide bonds ensure an integrated and stable conformation of the holo-FSHR structure. Interestingly, the hinge helix in the inactive FSHR structure is elongated and shows different orientation from the hinge helix in the active FSHR structure (Fig. 3b), highlighting that hinge helix plays an important role during FSHR activation. FSHR ECD interacts with the TMD through two major interfaces, which are also observed in LHCGR and TSHR (Fig. 3a, c, e). The first interface is between the hinge helix and the extracellular loop 1 (ECL1) (Fig. 3a, c). The point mutation S273I is located at the N-terminus of hinge helix, where the S273I mutation can enhance the hydrophobic interactions from ECD to TMD, and elevate the activation level of FSHR (Fig. 3c, d). In contrast, the hinge helix in the inactive FSHR structure shows rare interactions with ECL1 by rotating approximately $30^{\\\\circ}$ counter-clockwise relative to the hinge helix from the active FSHR structure (Fig. 3b), thus confirming that the interactions between hinge helix and ECL1 is critical for FSHR activation. The second interface is between the P10 region and the top half of TMD (Fig. 3e). As one of the most conserved regions in glycoprotein hormone receptors (Supplementary Fig. 6), the P10 region of FSHR \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,58,944,181]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"forms extensive interactions with TM1, TM2, TM7 and the three ECLs (Fig. 3f). The structures of P10 in the three receptors are nearly identical with the RMSD of $\\\\mathrm{Ca}$ atoms from FSHR to LHCGR and TSHR are only $0.43\\\\AA$ and $0.46\\\\AA$ , respectively (Fig. 3e). Mutational studies of P10 residues in LHCGR and TSHR indicated that most of P10 residues were essential for receptor activation[35,38]. Together, the similar ECD-TMD configuration in all three receptors provided a conserved structural basis of ECD-TMD signal transmission of glycoprotein hormone receptors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,194,847,207]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Basis for FSHR activation by an allosteric agonist \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,207,944,546]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Small molecular FSHR agonists have been proposed to substitute FSH in clinics[21]. Cpd-2If, a 5,6-dihydroimidazoiso [5,1- $\\\\alpha$ ] quinoline derivative, is an agonist of $\\\\mathrm{FSHR}^{24}$ . Consistently, Cpd-2If activated FSHR with high affinity and full efficacy (Supplementary Fig. 7a). The EM density map is sufficiently clear to dock Cpd-2If into the FSHR TMD pocket (Fig. 4a), which is created by the top half of TMD, including TM3, TM5, TM6, TM7, ECL2, and ECL3, as well as the N-terminus of P10 region (Fig. 4b, c). Interestingly, the binding site of Cpd-2If was found to be mainly composed of hydrophobic residues (Fig. 4b, d). Our functional data indicated that most of point mutations at pocket residues, except for F353A and M520A, resulted in the decreased activation ability of Cpd-2If to FSHR (Fig. 4e, Supplementary Table 2). Consistently, the binding of Cpd-2If to the FSHR TMD pocket induces inward movements of TM6 and TM7 at the extracellular side (Supplementary Fig. 7b), which directly results in the outward movement of TM6 at the cytoplasmic side of FSHR (Supplementary Fig. 7c), a hallmark of GPCR activation. Compared to LHCGR and TSHR, the location of Cpd-2If is almost completely overlapped with the LHCGR ligand org43553 and the TSHR ligand ML-109 (Fig. 5a), all of which are near the conserved toggle switch residue $\\\\mathrm{M58S}^{6,48}$ (Supplementary Fig. 7c), indicating a conserved activation mechanism of glycoprotein hormone receptors by small molecular allosteric agonists[17,19]. Interestingly, the location of Cpd-2If is also similar to orthosteric agonists seen in other class A GPCRs (Supplementary Fig. 7d), suggesting a similar way for Cpd-2If to directly induce FSHR TMD conformational changes for receptor activation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,546,944,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"FSHR, LHCGR, and TSHR share similar allosteric binding pockets as their high similarities in their TMD sequences and structures, which hinder the development of selective allosteric agonists targeting these important receptors (Supplementary Fig. 6 and Supplementary Fig. 5f, g). Single point and multipoint mutations were performed in order to determine the key residues from the receptors that were responsible for small allosteric agonist selectivity. ML-109 was analyzed first as it was a specific TSHR agonist, which cannot activate either FSHR or LHCGR (Fig. 5c, Supplementary Fig. 7e). Detailed structure analysis indicated that the orientations of the extracellular side of TM6, which forms part of the allosteric agonist binding pocket, were nearly identical between FSHR and LHCGR but different from that of TSHR (Fig. 5b). Compared with TSHR, FSHR and LHCGR have inward shifts at the extracellular side of their TM6, which would clash with the TSHR-selective ligand ML-109 (Fig. 5b). However, swapping of the extracellular portion of FSHR TM6 (residues 591-599) with the corresponding TSHR TM6 region (residues 643-651) did not convert the mutated receptor to respond to ML-109 (Fig. 5c; Supplementary Table 3). In addition, the extracellular portion of TM5 also contributes to the pocket, which has different residues between FSHR and TSHR (Supplementary Fig. 6). However, the replacement of the extracellular portions of both TM5 and TM6 from FSHR (residues 527-536/591-599) with the corresponding TSHR TM5/TM6 regions (residues 579-588 and 643-651) did not increase FSHR response to ML-109 either (Fig. 5c; Supplementary Table 3). Moreover, A352 in FSHR is located at the top of the binding pocket (Supplementary Fig. 7f). The correspondence residue in LHCGR is A349 and in TSHR is E404. However, mutation of A352E plus TM5/TM6 mutations still cannot elevate FSHR response to ML-109 (Fig. 5c; Supplementary Table 3). Surprisingly, mutations \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[63,27,119,40]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[663,27,942,41]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41467-023-36170-3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[62,962,302,974]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nature Communications| (2023)14:519 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[931,964,942,973]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[149,77,626,259]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"a \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0633/098cf5581f7483a53a90a432d61b05086b217936b23dd6dd6dfb85e84bdaca82.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[633,77,858,259]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"C \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0919/dff331bdc2b1838a5c4a9625dca254afa05597fcfb1d0de5ca9f3f303c7070c7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[151,275,329,458]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"b \\\",\\\"d \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0114/d6f88074e6442c90d1f206609ea0a22a836673235ba47572935df954bd37de53.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[339,294,586,445]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0319/5c11a74f3e32898c82815273199134095f07cdebf1f691d80540c879beadd5b8.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[591,277,850,456]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"e \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0700/1167f59fdf84a2b14d9fe73cbf3facbd7c665855822b525e291ab15d8503cb96.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[169,465,853,629]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"f \\\",\\\"Fig. 3 | Structural basis for FSHR activation signal transduced from ECD to \\\"]\",\n \"image_footnote\": \"[\\\"TMD. a Structural comparison of FSH-FSHR-Gs complex with CG-LHCGR-Gs and TSH-TSHR- complexes. The similar ECD-TMD configuration in three structures is shown, and the two conserved disulfide bonds in FSHR are shown in sticks. \\\",\\\"b Structural comparison of the hinge helix in the inactive and active FSHR structures. The angle was measured at the $\\\\\\\\mathrm{C}\\\\\\\\alpha$ atoms of S273 and R283 from the inactive FSHR and C276 from the active FSHR. c The first conserved interface between hinge \\\"]\",\n \"img_path\": \"images/0394/3e862435a27f041f11912298051cdd4c0e34b0dc5fb113d14dbeb56d31aef955.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[507,637,944,712]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"helix and ECL1. d Concentration-response curves for WT and S273I mutant receptors. The representative concentration-response curves from three independent experiments were shown. Data were shown as mean $\\\\pm$ S.E.M. from three independent experiments. Source data are provided as a Source Data file. e The second conserved interface between P10 and TMD. fDetailed interactions between P10 and FSHR TMD are shown in sticks. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,748,495,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"of $\\\\mathrm{H615^{7.42}Y}$ or $\\\\mathrm{I411^{2.53}M}$ in addition to the above TM5/TM6/A352E mutations can both lead to FSHR fully activated by ML-109, and all mutations combined (H615 $^{7.42}$ Y/I411 $^{2.53}$ M/ TM5/TM6/A352E) can further increase the activation potency and efficacy of ML-109 to FSHR (Fig. 5d, Supplementary Table 3). On the other hand, single point H615 $^{7.42}$ Y mutation of FSHR can only be activated by ML-109 weakly (Supplementary Fig. 7g and Supplementary Table 3). Combined mutations of H615 $^{7.42}$ Y and I411 $^{2.53}$ M further increased FSHR response to ML-109 (Supplementary Fig. 7g and Supplementary Table 3). H615 $^{7.42}$ Y and I411 $^{2.53}$ M are located at the bottom of the pocket and the corresponding residues in TSHR are in direct contacts with ML-109 (Supplementary Fig. 7h). Thus the H615 $^{7.42}$ Y and I411 $^{2.53}$ M mutations in FSHR would increase the interactions of the mutated FSHR with ML-109. Consistently, Molecular Dynamic (MD) simulation experiments indicated \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,748,944,830]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"that the binding free energy of WT FSHR was higher than FSHR with H615 $^{7,42}$ Y and I411 $^{2,53}$ M mutations. Thus, the MD simulations implied that the H615 $^{7,42}$ Y and I411 $^{2,53}$ M mutations favor the binding of ML-109 and increase its activating ability for FSHR. ML-109 is able to activate TSHR, the binding energy of ML109 to TSHR is comparable to ML-109 binding to mutant FSHR but not WT FSHR (Supplementary Fig. 8). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,830,944,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Cpd-21f can activate FSHR, LHCGR and TSHR with high potency and efficacy, while the activation potency for FSHR is more than 10-fold higher than LHCGR and TSHR (Supplementary Fig. 7i, Supplementary Table 2 and 4). Detailed structural analysis indicated that the N-ethyl of the Cpd-21f would clash with the $\\\\mathrm{Y612^{7.42}}$ in LHCGR and $\\\\mathrm{Y667^{7.42}}$ in TSHR, thus weakening the activation potency of Cpd-21f to LHCGR and TSHR (Fig. 5e). Consistently, Mutation H615 $^{7.42}$ Y in FSHR resulted in nearly 4-fold reduction of activation potency of Cpd-21f to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[63,27,119,40]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[663,27,942,41]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41467-023-36170-3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[62,962,302,975]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nature Communications| (2023)14:519 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[931,964,942,973]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[188,81,310,212]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"a \\\",\\\"b \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0646/7772f3a2612ea3d466b9021538e3a3aa4d4b12abfb66bdd8fffdd072f8ddb938.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[359,72,598,222]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0902/b4c8eddc2a1749e4ce8c7d914802ff6f90db754e77f8e3147814d5dd17b51629.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[618,77,855,222]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"C \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0632/f053ad2868a616a561ec042f5f2f7d0e5e692b3177723180019ebc4fb5601959.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[166,226,492,432]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"d \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0805/243943f73a416ca453ab10e4141b9bda361c5daa5c50c8dcff5d8c0f152ebacd.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[510,243,847,426]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"e \\\",\\\"Fig. 4 | Structural basis for FSHR activation by an allosteric agonist Cpd-21f. a The structure and EM density of Cpd-21f in the bound structure. The density map is shown at level of 0.17. b, c The binding pocket of Cpd-21f in FSHR, from the front view (b) and top view (c). d Detailed interactions between Cpd-21f and FSHR. e Effects of different pocket mutations on the potency of Cpd-21f-induced cAMP accumulation. Data were shown as $\\\\\\\\Delta pEC_{50} \\\\\\\\pm S.E.M.$ from three independent \\\",\\\"experiments, which performed in triplicates, with total repeats of nine for each data point. $^{**}P < 0.01$ , $^{***}P < 0.001$ versus WT. Statistical significance of differences between WT and mutants was determined by two-sided one-way ANOVA with Tukey test. Source data are provided as a Source Data file. All the exact P values are listed as follows: $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $< 0.0001$ , $\\\\\\\\langle 0.0001\\\\\\\\rangle$ \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0371/b8b3a39bb34b9ec225f430faa6fdcfddaab0bc2c1856862d25f3a60bc87b7491.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[60,532,495,721]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"FSHR (Fig. 5f). Moreover, org 214444-0 was reported as a selective FSHR agonist, which activated FSHR with more than 100-fold higher potency comparing to LHCGR $^{39}$ . Org 214444-0 was docked into FSHR TMD binding pocket, which location was also overlapped with Cpd-21f (Supplementary Fig. 7j). The bottom hexahydroquinoline group of Org-214444-0 is larger than the N-tert-Butyl-N-ethyl moiety of Cpd-21f, thus leading to more severe clash of cyclohexanone of Org 214444-0 with $\\\\mathrm{Y667^{7,42}}$ in TSHR and $\\\\mathrm{Y612^{7,42}}$ in LHCGR (Supplementary Fig. 7k, l), consistent with the high selectivity of Org 214444-0 for FSHR $^{39}$ . Together, our analysis indicated that H615 $^{7,42}$ in FSHR played essential roles in determining FSHR ligand selectivity and provided new insights for designing more specific small molecular agonists targeting this important receptor for infertility and in vitro fertilization. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,735,465,760]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Distribution of diseases associated mutations on the FSHR structure \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,762,495,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A distinct feature of glycoprotein hormone receptors is that they have many natural mutations associated with endocrine diseases[40,41]. These mutations are classified into inactivating and activating mutations. In the case of FSHR, the inactivating mutations can cause primary or secondary amenorrhea, premature ovarian failure (POF), and even infertility, while activating mutations can result in OHSS[42]. Comparison with LHCGR and TSHR, FSHR has the fewest natural mutations (Supplementary Fig. 9). There are no more than 20 inactivating mutations and four activating mutations that have been identified in FSHR (Supplementary Fig. 9a)[7]. Interestingly, most of the mutations in FSHR are located at the surface of the receptor rather than the TMD hydrophobic core (Supplementary Fig. 9a), providing a clue that FSHR \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,532,942,558]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"TMD is the most constrained structure among glycoprotein hormone receptors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,559,944,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Based on the active and inactive FSHR structures $^{43}$ , we modeled the FSHR naturally occurring mutations $^{7}$ . Most of inactivating mutations, including P348R, P519I, P587H, are in key structural elements and their mutations could disrupt the stability of FSHR, thus inactivating the receptor. Specifically, P348 is located in the C terminal of LRR12, P587 is located in the receptor TM6 bundle, and P519 is located in the ECL2 (Fig. 6a). On the other hand, the activating mutations, including N431I, T449A/I $^{3,32}$ , I545T $^{5,54}$ , and D567G $^{6,30}$ , are spread in the FSHR TMD (Fig. 6b-e). The N431I mutation is located at the ECL1 near the S273I mutation, which could enhance the hydrophobic interactions between ECL1 and the hinge helix (Fig. 6b), thus elevating the basal activity of FSHR. T449A/I $^{3,32}$ mutations are located at the TMD hydrophobic core, which are likely to break the interaction between T449 $^{3,32}$ and H615 $^{7,42}$ (Fig. 6c). I545T $^{5,54}$ is located near D581 $^{6,44}$ (Fig. 6d), a PIF motif residue that plays important roles in class A GPCR activation $^{44}$ . The I545T $^{5,54}$ mutation is likely to reduce the hydrophobic interactions between I545 $^{5,54}$ , I578 $^{6,41}$ and L460 $^{3,43}$ to disrupt the packing stability of TM3, TM5 and TM6 (Fig. 6d). Consistently, mutations I542L $^{5,54}$ and V597L/F $^{5,54}$ at the same locations in LHCGR and TSHR also make the mutated receptor constitutively active (Supplementary Fig. 9b, c). The D567G $^{6,30}$ mutation, which is also observed in LHCGR and TSHR, is located at the most conserved position at the N-terminus of TM6 (Fig. 6e, Supplementary Fig. 9b, c), which is likely to disrupt the ionic lock between D567 $^{6,30}$ and R467 $^{3,50}$ , a highly conserved structure element in the inactive state of class A GPCRs $^{45}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[63,27,119,40]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[663,27,942,41]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41467-023-36170-3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[62,962,302,975]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nature Communications| (2023)14:519 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[929,964,942,973]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[97,64,394,273]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0244/730a87265e8f889c40c3d1387dba1507c77611f7a5143248114bdd9e8809b98a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[401,60,650,259]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0304/0058be7fe5f36d08e223cf60fb3f61810a9646d20c73fc9cf0fd1666dc4fba33.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n 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null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[371,275,652,481]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0518/46e63139afcf5d213cb3c9e2ecf9077bb6708adf14e52371ac8f7d96285abbfe.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[658,273,850,315]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0233/14a46f65b6bff23813441267fa811b1e11e6147a59cf6d7e6e591d04cfbe58ba.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[652,341,910,481]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 5 | Structural basis of allosteric agonist selectivity for FSHR. a Structural comparison of Cpd-21f binding pocket in the FSH-FSHR-Gs complex with the Org43553 binding pocket in the CG-LHCGR-Gs complex, and ML-109 binding pocket in the TSH-TSHR-Gs complex. b Structural comparison of the binding pockets in FSHR and LHCGR TMDs. The clashes between ML-109 and the extracellular side of TM6 of FSHR and LHCGR are highlighted in red circles. The shift between FSHR TM6 and TSHR TM6 was measured at residues S594 in FSHR and S646 in TSHR. c, d Concentration-response curves for WT and mutated FSHR. The representative concentration-response curves from three independent experiments were shown. WT refers to wild type receptor; TM6 means swapping of the extracellular portion of FSHR TM6 (residues 591-599) with the corresponding TSHR TM6 region (residues 643-651); TM5/TM6 means the replacement of the extracellular portions of both TM5 and TM6 from FSHR (residues 527-536/591-599) with \\\",\\\"the corresponding TSHR TM5/TM6 regions (residues 579-588 and 643-651); TM5/ TM6/A352E means mutation of A352E in addition to the above TM5/TM6 mutations; TM5/TM6/A352E/H615Y means mutation of H615 $^{7,42}$ Y in addition to the above TM5/ TM6/A352E mutations; TM5/TM6/A352E/I411M means mutation of I411 $^{2,53}$ M in addition to the above TM5/TM6/A352E mutations; TM5/TM6/A352E/H615Y/I411M means mutations of H615 $^{7,42}$ Y and I411 $^{2,53}$ M in addition to the above TM5/TM6/A352E mutations. e Structural comparison of the binding pockets in FSHR, LHCGR and TSHR. The clashes between Cpd-21f and residue Y612 $^{7,42}$ of LHCGR and Y667 $^{7,42}$ of TSHR are highlighted in red circle. f Concentration-response curves for WT and mutated FSHR. The representative concentration-response curves from three independent experiments were shown. UD, undetectable. Data were shown as mean $\\\\\\\\pm$ S.E.M. from three independent experiments. Source data are provided as a Source Data file. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0344/825287b7121ddc74a6c07ec21618856a7b9964a4ef02170d87d2ec9b9e1cbaed.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[60,679,157,694]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,694,495,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Glycoprotein hormones and their receptors play central roles in regulating body development, reproduction and metabolism $^{46,47}$ . Being an essential part of endocrine system, they are involved in many endocrine diseases such as infertility, OHSS, male-limited precocious puberty $^{5,48}$ , Graves' and Hashimoto's diseases $^{49,50}$ . In this paper, we report the structures of full-length FSHR in both inactive and active states. The active structure of FSHR bound to its natural hormone FSH and a synthetic allosteric agonist Cpd-21f. Detailed analysis of these two structures reveals that FSH binding to FSHR induces a $48^{\\\\circ}$ rotation of its ECD toward the upright active conformation, analogous to the $45^{\\\\circ}$ and $38^{\\\\circ}$ rotations seen in the CG-LHCGR and TSH-TSHR structures, respectively. Consistently, the activation signal transduction from FSHR ECD to TMD mainly depends on the two ECD-TMD interaction interfaces (P10-TMD and hinge helix-ECL1), which are also highly conserved in the LHCGR and TSHR structures. Together, these observations highlight a universal activation mechanism of glycoprotein hormone receptors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,681,944,815]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The small molecule agonist of FSHR has been considered as potential oral replacement of protein hormone for infertility treatment. The active FSHR structure with Cpd-21f reveals the binding site of this allosteric agonist in the top half of the FSHR TMD. Structural comparison with LHCGR and TSHR indicates a similar binding pockets for the allosteric agonists, while the unique residue H615 $^{7,42}$ in FSHR plays critical roles for FSHR activation by allosteric agonists, providing inspirations for future design of highly selective FSHR ligands. In addition, the FSHR structures also provide molecular basis for the diseases associated mutations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,816,944,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To date, the structures of FSHR as well as LHCGR and TSHR in both inactive and hormone-bound active states have been solved. In addition, the structures of small molecular allosteric agonists bound with their corresponding receptors also have been solved. Based on our structural observations and functional studies, we proposed a universal model for glycoprotein hormone receptors activation by glycoprotein hormones. In the basal state, the ECD of glycoprotein hormone receptors are tilted toward the membrane layer. Hormone \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[63,27,119,40]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[663,27,942,41]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41467-023-36170-3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[62,962,302,975]\",\n 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\"img_path\": \"images/0859/e8d974025d1621603ae7b057acc9cfabee965dcdaef11fb66d6dd9a8b1749071.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[161,586,381,703]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0314/e626f9fba0cbea166b38ef338d24a826a87bcf777bee4eac91738a0fe6165756.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[381,460,620,656]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"e \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0304/7215d7e82cc7494416515c69e6c3ca7a73eb28297d41cf8fc2295a9f0806e36a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[645,448,858,577]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0885/e03bc8afdd0534f88a93df9cc2ebb2396886c579b787480c51af7773ea8c73c9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[645,578,857,702]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 6 | Detailed structural analysis of mutations in FSHR. a Three inactive mutations in FSHR. b-e The detailed interactions surrounded residues N431 $^{\\\\\\\\mathrm{ECL1}}$ (b), T449A/ $^{3.32}$ (c), I545T $^{5.54}$ (d) and D567G $^{6.30}$ (e) mutations. The active FSHR structure is \\\",\\\"shown in violet. The inactive FSHR structure, shown in light green, was modeled by swiss model based on the highest similar template structure. The four active point mutations are highlighted in green spheres. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0690/1bae0534e51130129230ed6dd499ead54c58a6b6818488a885ad85f59a22408d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[60,775,495,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"binding induces the rotation of ECD to the upright position to avoid the clash between hormones and membrane layer. The extended hinge loop from the receptors hinge region interact with hormones to further pull the hormone-ECD complexes in the upright position. On the other hand, the small molecular allosteric agonists can activate glycoprotein hormone receptors alone by direct docking into the receptor TMD pocket, which induces conformational changes in the toggle switch residue and outward movement of TM6 at the cytoplasmic side (Supplementary Fig. 7c). Together, our results not only for FSHR, but also for the whole family of glycoprotein hormone receptors, address the long-standing scientific questions \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,775,942,817]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"regarding the mechanisms of hormone-induced receptor activation, disease-associated receptor mutations, and allosteric activation by small molecule agonists. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,827,589,841]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,844,588,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Constructs \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,856,942,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Human FSHR (residues 18-695) was cloned with an N-terminal FLAG and C-terminal His8 tags into a pFastBac vector. The native signal peptide was replaced with the haemagglutinin (HA) to increase protein expression. The constitutively active mutation S273I was introduced to form the FSH-FSHR-Gs complex. A dominant-negative bovine Gαs \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[63,27,119,40]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[663,27,942,41]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41467-023-36170-3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[62,962,302,975]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nature Communications| (2023)14:519 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[929,964,942,973]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[65,58,494,100]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"construct was generated based on mini-Gs $^{51}$ . The three G-protein components, mini-Gαs, rat Gβ1 and bovine Gγ2, were cloned into separately pFastBac vector. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,112,309,125]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Expression and purification of Nb35 \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,126,494,193]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nanobody-35 (Nb35) was expressed and purified similarly as previously described[26]. Nb35 was purified by nickel affinity chromatography (Ni Smart Beads 6FF, SMART Lifesciences), followed by size-exclusion chromatography using a HiLoad 16/600 Superdex 75 column and finally spin concentrated to $5\\\\mathrm{mg/mL}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,207,317,218]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Complex expression and purification \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,221,494,600]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"FSHR, miniGαs, Gβ1 and Gy2 were co-expressed in Sf9 insect cells (Invitrogen) using the Bac-to-Bac baculovirus expression system (ThermoFisher). Cell pellets were thawed and lysed in 20 mM HEPES, pH 7.4, 100 mM NaCl, 10% glycerol, 5 mM MgCl₂ and 5 mM CaCl₂ supplemented with Protease Inhibitor Cocktail, EDTA-Free (TargetMol). The FSH-FSHR-Gs complex was formed in membranes by the addition of 10 μM Cpd-21f (synthesized in our lab), 1 μM FSH (urinary source, Shanghai Yuan Ye Bio-Technology Co Ltd), 10 μg/mL Nb35 and 25 mU/mL apyrase. The suspension was incubated for 1 h at room temperature. The membrane was then solubilized using 0.5% (w/v) n-Dodecyl β-D-maltoside (DDM, Anatrace), 0.1% (w/v) cholesterol hemisuccinate (CHS, Anatrace) and 0.1% (w/v) sodium cholate for 2 h at 4 °C. The supernatant was collected by centrifugation at 80,000 × g for 40 min and then incubated with M1 anti-Flag affinity resin (Genscript) for 2 h at 4 °C. After batch binding, the resin was loaded into a plastic gravity flow column and washed with 10 column volumes of 20 mM HEPES, pH 7.4, 100 mM NaCl, 10% glycerol, 2 mM MgCl₂, 2 mM CaCl₂, 0.01% (w/v) DDM, 0.002% (w/v) CHS, and 0.002% (w/v) sodium cholate, 0.1 μM FSH, 10 μM Cpd-21f and further washed with 10 column volumes of same buffer plus 0.1% (w/v) digitonin, and finally eluted using 0.2 mg/mL Flag peptide. The complex was then concentrated using an Amicon Ultra Centrifugal Filter (MWCO 100 kDa) and injected onto a Superdex200 10/300 GL column (GE Healthcare) equilibrated in the buffer containing 20 mM HEPES, pH 7.4, 100 mM NaCl, 2 mM MgCl₂, 2 mM CaCl₂, 0.05 (w/v) digitonin, 0.0005% (w/v) sodium cholate, 0.1 μM FSH and 10 μM Cpd-21f. The complex fractions were collected and concentrated to 20 mg/mL for electron microscopy experiments. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,613,349,627]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Inactive FSHR expression and purification \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,627,494,734]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$5\\\\mu \\\\mathrm{M}$ compound 24 was added to the culture after $Sf9$ insect cells were infected with FSHR baculovirus for $24\\\\mathrm{h}$ at $27^{\\\\circ}C.$ Cells were then collected after another $24\\\\mathrm{h}$ later. Cell pellets were thawed and lysed in $20~\\\\mathrm{mM}$ HEPES, pH 7.4, $100~\\\\mathrm{mM}$ NaCl, $10\\\\%$ glycerol, supplemented with $10~\\\\mu \\\\mathrm{M}$ compound 24 and Protease Inhibitor Cocktail, EDTA-Free (TargetMol). The purification procedures were similar to the FSH-FSHR-Gs complex, except that the procedure of complex formation on membranes was absent. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,749,211,762]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"cAMP response assay \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,763,494,937]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The full-length FSHR and FSHR mutants were cloned into pcDNA6.0 vector (Invitrogen) with a FLAG tag at its N-terminus. CHO-K1 cells (ATCC, #CCL-61) were cultured in Ham's F-12 Nutrient Mix (Gibco) supplemented with $10\\\\%$ $(\\\\mathrm{W} / \\\\mathrm{V})$ fetal bovine serum. Cells were maintained at $37^{\\\\circ}\\\\mathrm{C}$ in a $5\\\\%$ $\\\\mathrm{CO}_{2}$ incubator with 150,000 cells per well in a 12-well plate. Cells were grown overnight and then transfected with $1\\\\mu \\\\mathrm{g}$ FSHR constructs by FuGENE® HD transfection reagent in each well for $24\\\\mathrm{h}$ . cAMP accumulation was measured using the LANCE cAMP kit (PerkinElmer) according to the manufacturer's instructions. The transfected cells were seeded onto 384-well plates with 2500 cells each well, and then incubated with ligands for $30\\\\mathrm{min}$ at $37^{\\\\circ}\\\\mathrm{C}$ , then Eu and Ulight were added separately before cAMP levels were measured. Fluorescence signals were measured at $615\\\\mathrm{nm}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,58,942,179]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and $665\\\\mathrm{nm}$ by an Envision multilevel plate reader (PerkinElmer). Data were analyzed using Graphpad Prism8.0, the three-parameter, nonlinear regression equation in Prism suite was used in fitting. The response values were normalized by WT receptors within each individual experiment, with the basal activity for WT as 0, while the fitted $\\\\mathbf{E}_{\\\\mathrm{max}}$ of WT as 100. Experiments were performed at least three times, the detail information were attached in the figure legends, each experiment conducted in triplicate. Data were presented as means $\\\\pm$ SEM. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,194,848,207]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Detection of surface expression of FSHR mutants \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,207,942,424]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The cell seeding and transfection follow the same method as cAMP response assay. After $24\\\\mathrm{h}$ of transfection, cells were washed once with PBS and then detached with $0.2\\\\%$ (w/v) EDTA in PBS. Cells were blocked with PBS containing $5\\\\%$ (w/v) BSA for $15\\\\mathrm{min}$ at room temperature (RT) before incubating with primary anti-Flag antibody (diluted with PBS containing $5\\\\%$ BSA at a ratio of 1:150, ABclonal) for $1\\\\mathrm{h}$ at RT. Cells were then washed three times with PBS containing $1\\\\%$ (w/v) BSA and then incubated with anti-mouse Alexa-488-conjugated secondary antibody (diluted at a ratio of 1:1000, Invitrogen) at $4^{\\\\circ}\\\\mathrm{C}$ in the dark for $1\\\\mathrm{h}$ . After another three times of wash, cells were harvested, and fluorescence intensity was quantified in a BD Accuri C6 software (BD Biosciences) at excitation $488\\\\mathrm{nm}$ and emission $519\\\\mathrm{nm}$ . Approximately 10,000 cellular events per sample were collected and data were normalized to WT. Experiments were performed at least three times. The representative flow cytometry data for the detection of receptor surface expression was shown in Supplementary Fig. 10. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,437,823,451]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Cryo-EM grid preparation and data collection \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,451,942,532]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For the preparation of cryo-EM grids, $3\\\\mu \\\\mathrm{L}$ of the purified protein at $20\\\\mathrm{mg / mL}$ for the FSH-FSHR-Gs complex, $5\\\\mathrm{mg / mL}$ for the inactive FSHR, were applied onto a glow-discharged holey carbon grid (Quantifoil R1.2/1.3). Grids were plunge-frozen in liquid ethane using Vitrobot Mark IV (Thermo Fischer Scientific). Frozen grids were transferred to liquid nitrogen and stored for data acquisition. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,532,942,775]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Cryo-EM imaging of the FSH-FSHR-Gs complex and the inactive FSHR were performed on a Titan Krios at $300\\\\mathrm{kV}$ in Advanced Center for Electron Microscopy and Cryo-Electron Microscopy Research Center, respectively, Shanghai Institute of Materia Medica, Chinese Academy of Sciences (Shanghai China), A total of 4,025 movies for the FSH-FSH-Gs complex were collected with a Titan Krios equipped with a Falcon4 direct electron detection device at a pixel size of $1.03\\\\AA$ using the EPU software (FEI Eindhoven, Netherlands). The micrographs were recorded in counting mode at a dose rate of about $15\\\\mathrm{e}/\\\\mathring{\\\\mathrm{A}}^{2}/\\\\mathrm{s}$ with a defocus ranging from $-0.8$ to $-2.0\\\\mu \\\\mathrm{m}$ . Each movie was divided into 36 frames during motion correction. For the inactive FSHR protein, a total of 4,495 movies were collected by a Gatan K3 Summit direct electron detector with a Gatan energy filter (operated with a slit width of $20\\\\mathrm{eV}$ ) (GIF) at a pixel size of $1.071\\\\mathring{\\\\mathrm{A}}$ using the SerialEM software[52]. The micrographs were recorded in counting mode at a dose rate of about $22\\\\mathrm{e}/\\\\mathring{\\\\mathrm{A}}^{2}/\\\\mathrm{s}$ with a defocus ranging from $-1.2$ to $-2.2\\\\mu \\\\mathrm{m}$ . The total exposure time was 3s and intermediate frames were recorded in 0.083 s intervals, resulting in a total of 36 frames per micrograph. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,789,786,803]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Image processing and map construction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,803,942,937]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For the FSH-FSHR-Gs complex, dose-fractionated image stacks were aligned using MotionCor2.1 $^{53}$ and CryoSPARC-v3.3 $^{54}$ . Contrast transfer function (CTF) parameters for each micrograph were estimated by Gctf $^{55}$ . Particle selections for 2D and 3D classifications were performed using CryoSPARC-v3.3 $^{54}$ . Automated particle picking yielded 6,759,790 particles that were subjected to three rounds reference-free 2D classification to discard poorly defined particles, producing 1748,285 particles. The good subsets were further subjected to 6 rounds of heterogeneous refinement, which produced an initial reconstruction for further 3D classification. The selected subsets were subsequently \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[63,27,119,40]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[663,27,942,41]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41467-023-36170-3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[63,963,300,975]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nature Communications | (2023)14:519 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[931,964,942,973]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"9 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[60,58,497,275]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"subjected to non-uniform 3D refinement. The final refinement generated a map with an indicated global resolution of $2.82\\\\AA$ with 477,950 particles projections at a Fourier shell correlation of 0.143. The particles were further subjected to local-refinement focus on the FSHR-ECD and FSH. The local-refinement generated a map with an indicated global resolution of $3.14\\\\AA$ at a Fourier shell correlation of 0.143. For the inactive FSHR, image stacks were subjected to beam-induced motion correction using MotionCor2[53]. CTF parameters for non-dose weighted micrographs were determined by Gctf[55]. Automated particle selection yielded 2,781,231 particles using RELION-3.1.2[56]. The particles were imported to CryoSPARC-3.3[54] for 2 rounds of 2D Classification. The well-defined subset accounting for 1,148,175 particles was reextracted in RELION-3.1.2[56] and was subjected to 2 rounds of 3D classification, producing one good subset accounting for 356,211 particles. The final refinement generated a map with an indicated global resolution of $6.01\\\\AA$ at a Fourier shell correlation of 0.143. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,288,278,301]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Model building and refinement \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,302,497,518]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The crystal structure of human FSH-FSHR_ECD (PDB code: 4AY9), the structure of CG-LHCRG-Gs (PDB code: 7fih) were used as the start for model rebuilding and refinement against the electron microscopy map. The model was docked into the electron microscopy density map using Chimera $^{57}$ , followed by iterative manual adjustment and rebuilding in COOT $^{58}$ and ISOLDE $^{59}$ . Real space and reciprocal space refinements were performed using Phenix programs. The model statistics were validated using MolProbity $^{60}$ . Structural figures were prepared in Chimera $^{61}$ and PyMOL (https://pymol.org/2/). For the inactive FSHR, the model of active FSHR from the structure of FSH-FSHR-Gs complex was to generate the initial template. The initial template was docked into the EM density map using Chimera $^{57}$ . The model was further rebuilt in coot and real-space refined in COOT $^{58}$ and ISOLDE $^{59}$ . The final refinement statistics were validated using the module \\\"comprehensive validation (cryo-EM)\\\" in Phenix $^{62}$ . The final refinement statistics are provided in Supplementary Table 1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,532,302,545]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Construction of membraned FSHR \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,546,497,600]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"FSHR was first oriented by the Orientations of Proteins in Membranes server $^{63}$ . Then, the structure was inserted in $100\\\\mathring{\\\\mathrm{A}}^{*}100\\\\mathring{\\\\mathrm{A}}$ 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) membrane according to CHARMM-GUI server $^{64}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,613,194,627]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Molecular docking \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,627,497,750]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The FSH-FSHR-Gs complex was used for docking. The FSHR and small molecules were separated from the complex and prepared in the protein preparation wizard of Schrodinger, Maestro. During the processes, we first assigned bond orders and added hydrogens on the system. Meanwhile, disulfide bonds were created and residue states were generated using Epik at $\\\\mathrm{pH} = 7.0 \\\\pm 2.0$ . Then PROPKA method was applied to assign protonation state of each residue. At last, the restrained minimization was used with $0.3\\\\AA$ RMSD constraint on heavy atoms under OPLS4 force field. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,762,280,775]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Molecular dynamic simulations \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,775,497,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The cryo-EM structure of Cpd-21f-FSH-FSHR and ML-109-TSH-TSHR (PDB ID: 7XW5) complex were used for the construction of the MD simulation systems. Before the simulation, Gs, FSH, TSH, and Cpd-21f were removed from the systems. We first aligned TSHR-ML-109 to FSHR according to the TMD and placed ML-109 in the corresponding FSHR pocket. Then, H615Y and I411M mutations were introduced via PyMOL. In the dual mutation system, we introduced both mutations. We oriented the structures with the Orientations of Proteins in Membranes server and used the CHARMM-GUI server to insert them into POPC (palmitoyl-2-oleoyls-n-glycero-3-phosphocholine) membrane $^{63,65}$ . Then, TIP3P waters were added to the top and bottom of the system. $0.15 \\\\mathrm{M} / \\\\mathrm{L}$ NaCl \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,56,947,317]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ions and counterions were applied via the distance method $^{64,65}$ . FF19SB, LIPID17, and GAFF2 force fields were applied for the parameter of amino acids, lipids, and ML-109, respectively $^{66,67}$ . During simulations, the systems were first minimized and equilibrated in the separated 6 processes provided by CHARMM-GUI. Next, 3 parallels of 200 ns production running were applied on the system. The temperature (303.15 K) and pressure (1 atm) were controlled by the Langevin thermostat and isotropic Berendsen barostat, respectively. Long-range electrostatic interactions were treated by the Particle mesh Ewald algorithm and a cutoff of $12\\\\AA$ was employed for short-range interactions. Between $10\\\\AA$ and $12\\\\AA$ , force-based switching was applied for soft changing of interactions. The SHAKE algorithm with hydrogen mass repartitioning was applied to restrain the bond with hydrogens. Hence, the timestep of simulations was $4\\\\mathrm{fs}^{68}$ . The calculation of binding free energy was finished by MPPBSA.py $^{69}$ . We used the last $1/4$ of trajectories to guarantee that the trajectory had reached equilibrium upon evaluation. The standard deviation was estimated by 3 repeats of simulations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,329,650,341]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Reporting summary \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,341,942,370]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,381,653,397]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data availability \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,397,944,492]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The density maps and structure coordinates have been deposited to the Electron Microscopy Database (EMDB) and the Protein Data Bank (PDB) with accession number of EMD-35135, PDB ID 8I2G for the FSH-FSHR-Gs complex; EMD-35136 and 8I2H for the inactive FSHR. The functional data and protein purification data and MD data generated in this study are provided in the Supplementary Information and Source Data files. Source data are provided with this paper. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,503,608,517]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,518,942,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1. Robker, R. L. & Richards, J. S. Hormonal control of the cell cycle in ovarian cells: proliferation versus differentiation. Biol. Reprod. 59, 476-482 (1998). \\\",\\\"2. Foulkes, N. S., Schlotter, F., Pevet, P. & Sassone-Corsi, P. Pituitary hormone FSH directs the CREM functional switch during spermatogenesis. Nature 362, 264-267 (1993). \\\",\\\"3. Simoni, M., Gromoll, J. & Nieschlag, E. The follicle-stimulating hormone receptor: biochemistry, molecular biology, physiology, and pathophysiology. Endocr. Rev. 18, 739-773 (1997). \\\",\\\"4. Kuechler, A. et al. An unbalanced translocation unmasks a recessive mutation in the follicle-stimulating hormone receptor (FSHR) gene and causes FSH resistance. Eur. J. Hum. Genet. 18, 656-661 (2010). \\\",\\\"5. Bhartiya, D. & Patel, H. An overview of FSH-FSHR biology and explaining the existing conundrums. J. Ovarian Res. 14, 144 (2021). \\\",\\\"6. Xiong, J. et al. FSH blockade improves cognition in mice with Alzheimer's disease. Nature 603, 470-476 (2022). \\\",\\\"7. Ulloa-Aguirre, A. & Zarinan, T. The Follitropin receptor: matching structure and function. Mol. Pharm. 90, 596-608 (2016). \\\",\\\"8. Gera, S. et al. FSH-blocking therapeutic for osteoporosis. *Elife* 11, https://doi.org/10.7554/eLife.78022 (2022). \\\",\\\"9. Liu, P. et al. Blocking FSH induces thermogenic adipose tissue and reduces body fat. Nature 546, 107-112 (2017). \\\",\\\"10. Macklon, N. S., Stouffer, R. L., Giudice, L. C. & Fauser, B. C. The science behind 25 years of ovarian stimulation for in vitro fertilization. Endocr. Rev. 27, 170-207 (2006). \\\",\\\"11. Lunenfeld, B. Historical perspectives in gonadotrophin therapy. Hum. Reprod. Update 10, 453-467 (2004). \\\",\\\"12. Fan, Q. R. & Hendrickson, W. A. Structure of human follicle-stimulating hormone in complex with its receptor. Nature 433, 269-277 (2005). \\\"]\",\n \"page_idx\": \"9\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[63,27,119,40]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[663,27,942,41]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41467-023-36170-3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[62,962,302,975]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nature Communications| (2023)14:519 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[924,963,942,974]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[63,58,495,924]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"13. 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Theory Comput. 8, 3314-3321 (2012). \\\"]\",\n \"page_idx\": \"11\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[63,544,233,559]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgements \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,560,497,818]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The cryo-EM data were collected at the Cryo-Electron Microscopy Research Center and Advanced Center for Electron Microscopy, Shanghai Institute of Materia Medica (SIMM). The authors thank the staff at the SIMM Cryo-Electron Microscopy Research Center and Advanced Center for Electron Microscopy for their technical support. This work was partially supported by Ministry of Science and Technology (China) grants (2018YFA0507002 to H.E.X.); Shanghai Municipal Science and Technology Major Project (2019SHZDZX02 to H.E.X.); Shanghai Municipal Science and Technology Major Project (H.E.X.); CAS Strategic Priority Research Program (XDB37030103 to H.E.X.); the National Natural Science Foundation of China (32130022 to H.E.X., 32171187 to Y.J., 82121005 to H.E.X. and Y.J., 81922071 to Y.Z.); CAMS Innovation Fund for Medical Sciences (2021-I2M-1-003 to S.Z.); CAMS Innovation Fund for Medical Sciences (2021-CAMS-JZ004 to S.Z.); Tsinghua University-Peking University Center for Life Sciences (045-61020100121 to S. Z.); National Science & Technology Major Project \\\"Key New Drug Creation and Manufacturing Program\\\" of China (2018ZX09711002 to H.J.); Science and Technology Commission of Shanghai Municipal (20431900100 to H.J.); Jack Ma Foundation (2020-CMKYGG-05 to H.J.); Zhejiang Provincial \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,58,944,113]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Natural Science Foundation of China (LR19H310001 to Y.Z), the Ministry of Science and Technology (2019YFA050880 to Y.Z.), and the Key R&D Projects of Zhejiang Province (2021C03039 to Y.Z.). Y.Z. is also supported by the Fundamental Research Funds for the Central Universities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,124,697,137]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Author contributions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,140,944,303]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"J.D. designed the expression constructs, purified the FSHR proteins, performed cryo-EM grid preparation and data collection, conducted functional studies, analyzed the structures, prepared the figures, and wrote the manuscript; P.X. and H.Z. performed cryo-EM data calculations, model building, and participated in figure preparation; X.L. supplied the FSH hormone and supervised by S.Z.; Y.-J.J participated in functional studies and protein purification, J.Y. synthesized Cpd-21f and compound 24; C.M. and D.S. participated in cryo-EM data calculations and model building; X.H. performed molecular docking and dynamic stimulations, which were supervised by H.J. and X.C.; Y.J. supervised the studies; H.E.X., Y.Z. and S.Z. conceived and supervised the project and wrote the manuscript with inputs from all authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,313,689,329]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Competing interests \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,330,781,343]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The authors declare no competing interests. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,354,712,369]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Additional information \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,370,855,411]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41467-023-36170-3. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,424,929,451]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Correspondence and requests for materials should be addressed to Shuyang Zhang, Yan Zhang or H. Eric Xu. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,465,936,518]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Peer review information Nature Communications thanks Arnau Cordomi, Xin-Yun Huang, Eric Reiter and Irina Tikhonova for their contribution to the peer review of this work. Peer reviewer reports are available. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,532,835,560]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Reprints and permissions information is available at http://www.nature.com/reprints \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,573,919,601]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,613,944,789]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,803,645,816]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"© The Author(s) 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[63,27,119,40]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[663,27,942,41]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41467-023-36170-3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[63,962,302,975]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nature Communications| (2023)14:519 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[926,963,942,973]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"12 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1038/s41467-023-36170-3"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Life Sciences"},"sha256":{"kind":"string","value":"6556b54abc2608dec092866f5f5eea781957a3cef08efdc263e61abf13a76653"},"title":{"kind":"string","value":"Mechanism of hormone and allosteric agonist mediated activation of follicle stimulating hormone receptor"}}},{"rowIdx":266,"cells":{"abstract":{"kind":"string","value":""},"author":{"kind":"string","value":"Zohaib Salahuddin|Matthias Lenga|Hannes Nickisch"},"content_list":{"kind":"list like","value":[{"bbox":"[92,140,907,174]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MULTI-RESOLUTION 3D CONVOLUTIONAL NEURAL NETWORKS FOR AUTOMATIC CORONARY CENTERLINE EXTRACTION IN CARDIAC CT ANGIOGRAPHY SCANS","text_format":null,"text_level":"1","type":"text"},{"bbox":"[223,191,771,210]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Zohaib Salahuddin\\* Matthias Lenga Hannes Nickisch ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[258,225,737,258]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"* Escola Politécnica Superior, Universitat de Girona, Spain † Philips Research Hamburg, Germany ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[231,290,327,304]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABSTRACT ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[70,311,485,524]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We propose a deep learning-based automatic coronary artery tree centerline tracker (AuCoTrack) extending the vessel work of [1]. A multi-resolution 3D Convolutional Neural Network (CNN) is employed to simultaneously predict movement directions and detect bifurcations. Moreover, an automated artery endpoint detector is used to prevent premature termination of the tracking process. On Coronary Computed Tomography Angiography (CCTA or coronary CTA) scans annotated by clinical experts, an average sensitivity of $87.1\\%$ and clinically relevant overlap of $89.1\\%$ could be obtained. In addition, the MICCAI 2008 Coronary Artery Tracking Challenge (CAT08) training and test datasets were used to benchmark the algorithm and to assess its generalization capabilities. On CAT08, an average overlap of $93.6\\%$ and a clinically relevant overlap of $96.4\\%$ were achieved. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[72,530,485,559]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Index Terms—coronary artery centerline tracking, coronary computed tomography angiography, neural networks ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,577,361,591]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. INTRODUCTION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[70,604,487,889]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Coronary artery disease (CAD) results in narrowing or blockage of coronary arteries due to the build-up of cholesterol and fatty deposits on the inner lining of the arterial wall. Such constrictions can result in an inadequate supply of blood to the heart muscles which can be fatal [2]. CAD is one on the leading causes of death worldwide with 9.43 million deaths reported in 2016 [3]. Coronary Angiography (CA) is an interventional procedure for CAD evaluation and treatment. The severity and anatomical extent of CAD can be assessed noninvasively by Coronary Computed Tomography Angiography (CCTA) [4]. Manual reading of volumetric CCTA images is a time-consuming task. Several advanced visualization techniques relying on coronary artery centerlines have been proven to facilitate the clinical workflow. In [5], approaches for the assisted extraction of coronary artery centerlines are categorized as: automatic requiring no user interaction at all [6, 7, 8], semi-automatic requiring one seed point per artery [9, 10, 11] or interactive requiring multiple user interactions per artery [1, 5, 12]. Recently, [1] proposed a CNN-based tracking scheme which iteratively predicts a movement direc ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,290,926,389]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tion and a step-size. As an interactive method, almost state-of-the-art performance could be achieved. Typically, their tracker required multiple seeds per artery in order to successfully extract the related centerline due to premature stopping. The approach did not identify and handle bifurcations. In order to render the algorithm automatic, an additional network was used for seed point extraction. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,390,926,574]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Building on [1], we propose a multi-resolution CNN-based algorithm to extract the entire coronary tree automatically without user interaction. Our approach detects bifurcation points and properly integrates them into the tracking process. In addition, the tracker is guided by another CNN in order to prevent premature termination. The algorithm does not rely on a segmentation network or any other automated method to generate multiple seed points per artery. We show that a simple automated detection of two seeds (one for each coronary tree) suffices and that the proposed method is very robust towards variations of those points. The ostium points obtained from a deformable shape model of the heart [13] are used to initialize the automatic coronary centerline extraction. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[633,592,801,606]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. METHODOLOGY ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,618,926,831]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Our automatic coronary artery tracker (AuCoTrack) sequentially traces the coronary artery centerline while deciding in each step forward in which direction to continue or if a new vessel branches off (direction and bifurcation classifier, DBC-Net). Simultaneously, the tracker monitors whether an endpoint of an artery is reached and the tracking should be stopped (stop classification network, STC-Net), see Figure 1. A global priority queue containing active centerline points is maintained which is initialized with points located at the left and right ostium. Two or three points are added to the queue at each step depending on the discovery of a bifurcation. We avoid double visits by only following centerline points located at a minimum distance from already found centerline points. Processing can be done in parallel and the tracker terminates once no more active centerline points are queued. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,832,926,889]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The direction of movement is found by a multi-class prediction on the unit sphere whose surface is discretised into 1000 admissible directions (DBC-Net). We perform peak detection in order to find two or three likely directions depend ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[0,190,16,805]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI) | 978-1-6654-1246-9/20/$31.00 ©2021 IEEE | DOI: 10.1109/ISBI48211.2021.9434002 ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[70,59,526,81]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI) April 13-16, 2021, Nice, France ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[72,916,314,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"978-1-6654-1246-9/21/$31.00 ©2021 IEEE ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[489,916,507,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"91 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[92,980,895,994]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Authorized licensed use limited to: National University of Singapore. Downloaded on July 04,2021 at 02:25:53 UTC from IEEE Xplore. Restrictions apply. ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[75,114,922,299]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 1. Overview of the AuCoTrack pipeline. At inference time (black arrows), multiresolution image patches $P_{1}$ and $P_{2}$ are fed into the two networks (yellow boxes) which results in a predicted direction on the unit ball (red dots) and the decision whether to branch or stop (orange boxes) by the DBC-Net and the STC-Net, respectively. The stopping prediction is illustrated in the gray box on the bottom left. The main tracking loop (light green box and black dotted arrow) is initialised with the ostiae (blue dots) and results in the coronary tree (red lines). This tree can be mapped back to the underlying CCTA scan via a stretched multiplanar reformat (sMPR). The network architecture of the DBC-Net and STC-Net is essentially an encoder with parallel pathways at two different resolutions whose representations are combined (box top left). For training (red arrows), patches along with their labels (bifurcation/vessel, stop/continue, direction encoded in binary vector) are used. \"]","image_footnote":"[]","img_path":"images/0857/e127ec71d816a91d629a63a01d533c29d1d9e6389bc36bdd6c2cb394822ea039.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[70,452,489,779]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ing on the prediction of a bifurcation. We employ angle constraints to concentrate on meaningful configurations i.e. we require that the (a) highest response (way back) is similar to the previous direction $(\\mathrm{angle} < 60^{\\circ})$ , (b) second response (way ahead) is different from the previous direction $(\\mathrm{angle} > 110^{\\circ})$ , and (c) third response (branching) is different from the other two $(\\mathrm{angle} > 40^{\\circ})$ . The third response is calculated only in the case DBC-Net predicts the presence of a bifurcation. A fixed step of $1\\mathrm{mm}$ is taken in the predicted direction. The STC-Net casts a binary vote on whether the coronary tracking continues. Both DBC-Net and STC-Net use the same network architecture and operate locally on isotropic 3D patches $P_{1}, P_{2}$ of size $19^{3}$ sampled at the two resolutions $0.5\\mathrm{mm}$ and $1.0\\mathrm{mm}$ . Each of the two network branches has 7 convolutional layers with kernels of size 3. Layers 3 and 4 use dilated convolutions with the spacing of 2 and 4 between the kernel points respectively. We use ReLu activation functions and batch normalisation. The result of the two branches is stacked and reduced to the number of direction classes to form Layer $L_{D}$ . Layer $L_{D}$ is then followed by two linear layers and a sigmoid activation for the patch type prediction. In case of DBC-Net, the output of layer $L_{D}$ is followed by a softmax activation to get the direction response. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,783,487,840]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We train and evaluate the two networks on a set of volumetric CCTA scans where the coronary artery tree – as annotated by clinical experts – is represented by a set of centerlines and their topological connections. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,846,489,889]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Binary cross entropy loss $(BCE_{patch})$ is used for the patch type classification and categorical cross entropy loss $(CE_{dir})$ is used for the direction classification. The com ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,451,927,764]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"binned loss function used to train the DBC-Net is $L = CE_{dir} + \\lambda_b BCE_{patch}$ . The weighting factor $\\lambda_b$ is fixed at 5. For STC-Net, we employ only binary cross entropy loss for stop patch type classification. For optimisation, we use Adam with a learning rate of 0.0001 and a mini-batch size of 64. We use several augmentation strategies during training. We use random translations (along three axes) to make the direction prediction more robust and rotational perturbations (along three axes) to introduce a certain degree of rotational invariance. The training of the DBC/STC-Nets requires carefully selected pairs of input patches and output labels in terms of binary vectors encoding the directions, stop and bifurcation indicators. The binary direction vectors are obtained by placing a sphere with radius $R = 1.5mm$ around the centerline point and a subsequent nearest neighbor matching of the vessel intersections with the sphere to the discrete sphere tessellation. The number of intersections with the sphere governs the flag in terms of bifurcation or stop patch. Care was taken to oversample the bifurcations (by a factor of 10, see Section 3). The STC-Net was trained with patches particularly selected beyond the end of the coronary artery, see Figure 1 bottom left box. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[667,809,769,823]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. RESULTS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[509,845,926,889]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We evaluate our AuCoTrack algorithm using the evaluation metrics defined in [5]. Sensitivity was an additional metric used on the training dataset. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[489,916,507,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"92 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[92,982,897,994]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Authorized licensed use limited to: National University of Singapore. Downloaded on July 04,2021 at 02:25:53 UTC from IEEE Xplore. Restrictions apply. ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[73,112,211,190]","code_body":null,"code_caption":null,"image_caption":"[\"(a) \"]","image_footnote":"[]","img_path":"images/0310/bd246fe19f08f8f195b955f35c144668bf94059db8708821855dde7efb0bb658.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[223,112,352,188]","code_body":null,"code_caption":null,"image_caption":"[\"(b) \"]","image_footnote":"[]","img_path":"images/0143/a83ab5d40e133454ae1b990310666179b45983c693bcd65b25aec5748eb3d859.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[364,115,485,187]","code_body":null,"code_caption":null,"image_caption":"[\"(c) \",\"Fig. 2. Rendering of AuCoTrack result: (a) initialization at ostiae, (b) initialization approximately at center of LAD and RCA, (c) detected bifurcation overlayed on tracking result. Green = correct, blue = init points, orange = bifurcations. \"]","image_footnote":"[]","img_path":"images/0096/866af2fc1aaabafabdf0d01ed946b85acf2e97621fc6cc39c8dca8d8f67e2218.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[75,300,231,314]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1. Training Dataset ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[75,321,485,421]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The training dataset consists of 43 CCTA images which were annotated by clinical experts. The number of annotated coronary arteries per CCTA scan varies from 4 to 20. The mean number of annotated coronary arteries per CCTA scan in this dataset is 9. The training dataset contains 428 annotated coronary arteries. Four-fold cross validation has been performed in-order to evaluate the proposed algorithm. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,423,485,634]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 2 (a) shows that the result of the automatic coronary centerline extraction when the seed points for tracker initialization are placed at the left and right coronary ostium. Figure 2 (b) shows the result when the initialization takes place approximately at the center of LAD and RCA. The extracted coronary tree is very similar in both cases. The sensitivity obtained when the seed points are placed at the ostiae is $88.9\\%$ and it is $87.3\\%$ when the seed points are placed in the middle of LAD and RCA. This shows that the seed point can essentially be placed anywhere on the coronary tree. Figure 2 (c) shows the bifurcation detection overlaid on the tracking result. The orange marks on the coronary tree indicate that a bifurcation has been detected at that centerline point by the DBC-Net. This implies that three direction vectors will be obtained to generate the candidate points. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,635,485,804]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An ablation study was performed and revealed the optimal number of equispaced points on the direction sphere to be 1000 (using the spherical Fibonacci mapping). The number of pathways in the multi-resolution DBC-Net and STC-Net was fixed at 2 and the importance sampling parameter for the bifurcation class was found to be around 10 [14]. The patch size of 19 is selected to balance fast processing and enough field-of-view to cover average coronary artery radii. We obtained a sensitivity of $87.1\\% \\pm 3.2\\%$ , a clinically relevant overlap of $89.1\\% \\pm 2.3\\%$ and a total overlap of $80.4\\% \\pm 2.0\\%$ . The accuracy inside was $0.34\\mathrm{mm} \\pm 0.0017\\mathrm{mm}$ which is below the average voxel size of $0.40^2 \\times 0.43\\mathrm{mm}^3$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[75,823,285,837]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2. CAT08 Training Dataset ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[75,846,485,888]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The best model cross-validated on the training dataset was used to extract centerlines on the CAT08 training datasets. Table 1 shows that an average overlap (OV) of $93.4\\%$ ,clinically ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,115,922,229]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 3. Clinically relevant overlap of all the arteries present in the training dataset which occur more than 3 times evaluated using cross validation. The occurrence count of each artery is also shown in the plot. \"]","image_footnote":"[]","img_path":"images/0732/d1c360a10c9b2b196fe1f6867517c046626d9c670b459cc63cb6640a16eee5a1.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[515,317,921,431]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0257/43a837c3341c27dc90826df4cf5650422a5538f2228b8de155ee450f063676b3.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":"<table><tr><td>No.</td><td>Image Quality</td><td>Calcium Score</td><td>OV</td><td>OF</td><td>OT</td><td>AI</td><td>T</td></tr><tr><td>0</td><td>Moderate</td><td>Moderate</td><td>94.2</td><td>77.7</td><td>95.1</td><td>0.4</td><td>55</td></tr><tr><td>1</td><td>Moderate</td><td>Moderate</td><td>97.3</td><td>99.4</td><td>99.6</td><td>0.32</td><td>39</td></tr><tr><td>2</td><td>Good</td><td>Low</td><td>98.3</td><td>99.7</td><td>100</td><td>0.31</td><td>43</td></tr><tr><td>3</td><td>Poor</td><td>Moderate</td><td>86.3</td><td>63.0</td><td>89.1</td><td>0.40</td><td>41</td></tr><tr><td>4</td><td>Moderate</td><td>Low</td><td>92.9</td><td>57.3</td><td>97.9</td><td>0.33</td><td>31</td></tr><tr><td>5</td><td>Poor</td><td>Moderate</td><td>97.6</td><td>77.5</td><td>99.7</td><td>0.43</td><td>33</td></tr><tr><td>6</td><td>Good</td><td>Low</td><td>96.7</td><td>87.2</td><td>99.6</td><td>0.30</td><td>36</td></tr><tr><td>7</td><td>Good</td><td>Severe</td><td>83.9</td><td>49.1</td><td>86.3</td><td>0.38</td><td>48</td></tr><tr><td>Avg</td><td></td><td></td><td>93.4</td><td>76.5</td><td>95.9</td><td>0.36</td><td>41</td></tr></table>","table_caption":"[\"Table 1. Results of our method on CAT08 training set which was used as a test set. For each case, overlap (OV, in %), overlap until first error (OF, in %) and clinically relevant overlap (OT, in %), average accuracy inside (AI, in mm), time taken for coronary tree extraction (T, in s) along with subjective image quality and calcium score is shown. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[512,549,924,619]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"relevant overlap (OT) of $95.9\\%$ and overlap until first error (OF) of $76.5\\%$ was obtained for these 8 CCTA scans. This is a good test of generalization as the CCTA training dataset and the CAT08 dataset used for testing are disjoint and were acquired on scanners from different vendors. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,638,690,652]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.3. CAT08 Test Dataset ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[512,661,924,888]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We tested our algorithm on the CAT08 test set to benchmark the performance of our algorithm against methods available on the leaderboard of the CAT08 challenge. An average overlap of $93.6\\% \\pm 5.2\\%$ , clinically relevant overlap of $96.4\\% \\pm 4.1\\%$ , overlap until first error of $76.3\\% \\pm 22.7\\%$ and accuracy inside of $0.37\\mathrm{mm} \\pm 0.05\\mathrm{mm}$ was obtained for these 24 CCTA scans. Cases 8, 10 and 27 required one additional seed point due to failure in the detection of bifurcations for one of the vessels. There are significant motion artifacts present in case 26 which hamper the bifurcation detection. Hence, additional seed points are provided for 3 of the vessels in this CCTA image. Table 2 shows the comparison of the performance of our algorithm (AuCoTrack) with the current automatic coronary centerline extraction techniques and the state-of-the-art CNN-based technique which requires at-least one seed point per vessel for the centerline extraction. Overall, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[490,916,507,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"93 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[95,982,895,992]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Authorized licensed use limited to: National University of Singapore. Downloaded on July 04,2021 at 02:25:53 UTC from IEEE Xplore. Restrictions apply. ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[77,112,485,198]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0749/624187179d82bd5f60e08ce2a81e15058d341604ee173d13ec83ce0e1f5209e6.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":"<table><tr><td>Method</td><td>OV</td><td>OF</td><td>OT</td><td>AI</td><td>T</td></tr><tr><td>AuCoTrack</td><td>93.6</td><td>76.3</td><td>96.4</td><td>0.37</td><td>42</td></tr><tr><td>Zheng et al.</td><td>93.5</td><td>76.5</td><td>95.6</td><td>0.20</td><td>60</td></tr><tr><td>Kitamura et al.</td><td>90.6</td><td>70.9</td><td>92.5</td><td>0.25</td><td>160</td></tr><tr><td>Yang et al.</td><td>93.7</td><td>74.2</td><td>95.9</td><td>0.30</td><td>120</td></tr><tr><td>Wolterink et al. (Interactive)</td><td>93.7</td><td>81.5</td><td>97.0</td><td>0.21</td><td>10</td></tr></table>","table_caption":"[\"Table 2. We compare of our AuCoTrack pipeline with the top automatic coronary artery centerline algorithms in terms of overlap (OV, in %), overlap until first error (OF, in %) and clinically relevant overlap (OT, in %), average accuracy inside (AI, in mm) and time taken (T, in s) on the CAT08 date. The interactive CNN-based tracker [1] is below the dashed line. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[70,315,489,345]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"AuCoTrack achieves better clinically relevant overlap than other automatic methods. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[213,363,346,378]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.DISCUSSION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[70,391,489,731]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An automatic deep learning-based coronary artery centerline tracker in CCTA images (AuCoTrack) was proposed. Our framework was evaluated on 43 training CCTA images and additional datasets available from the CAT08 challenge. On the training dataset, AuCoTrack was evaluated using fourfold cross validation. To test the generalisation of our approach, the model was applied to the CAT08 training set. For further evaluation, we trained on a combined dataset containing the 43 training CCTA scans and the 8 CCTA scans from the CAT08 training set. The resulting model was then applied to the CAT08 test set and the extracted centerlines were submitted to the CAT08 challenge evaluation framework. Our method obtained an accuracy inside of $0.37\\mathrm{mm}$ , a overlap of $93.6\\%$ and a clinically relevant overlap of $96.4\\%$ on average. Moreover, an overlap rank (OR) of 9.87 was achieved outperforming the available top three automatic algorithms on the CAT08 leaderboard [6] OR=10.43, [7] OR=13.81 and [8] OR=10.55. We remark, that the state-of-the-art automatic centerline extraction algorithm by [6] requires artery segmentation masks as input for their model driven and data driven approach. Their algorithm is trained on 108 training CCTA scans. Similarly, a hybrid learning representation approach that utilizes segmentation masks proposed by [15] was trained on 100 CCTA scans. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,732,487,802]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An analysis of the individual CAT08 cases showed that the performance is not strongly affected by the presence of coronary calcium. For example, on the CAT08 test images with low, moderate and severe calcium scores, an average overlap of $92.9\\%$ , $94.0\\%$ and $94.2\\%$ was obtained. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[70,804,489,891]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The number of annotated centerlines in the training dataset varied from 4 to 20. We observed a high clinically relevant overlap independent of the number of annotated arteries which demonstrates that our algorithm is capable of extracting the entire (left or right) coronary tree from a single seed. In order to address the problem of premature or late stopping, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,115,926,144]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"we employ a voting mechanism combining a CNN-based endpoint detection with a moving average entropy criterion. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,144,927,217]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"AuCoTrack achieves a clinically relevant overlap of $96.4\\%$ on the CAT08 test set and $89.1\\%$ on the training dataset. This difference is due to the fact that the CAT08 test set contains annotations for only 4 coronaries and the training dataset contains a variable number ranging from 4 to 20. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,217,927,445]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"[1] achieved near state-of-the-art performance as an interactive method for the CAT08 dataset. A main constraint of their method is that it requires one or more seed points per vessel as no functionality for detecting and handling bifurcations is available. Our method relies only on a single seed point per coronary tree and bifurcations are properly handled by the tracker. Successful vessel detection $(\\mathrm{OT} > 50\\%)$ was observed in $95\\%$ of the cases from the CAT08 dataset. The ostium points required for initializing AuCoTrack were automatically obtained from a deformable shape model of the heart [13]. Moreover, we observed that our algorithm is very robust towards variations of those point, see Figure 2. In [1] the tracker termination is guided by a moving average entropy criteria which fails in case of a severe stenosis. Consequently, their method may require several initialization points per vessel in order to warm-start the tracking process. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,447,927,532]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A branch-aware coronary centerline extraction approach based on Double Deep Q-Network proposed by [16] was evaluated only on the CAT08 training dataset. This method does not terminate on reaching the end of coronary artery but terminates when the tracker goes out of the CCTA scan or reaches an already visited point. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,533,927,776]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In future work, the accuracy of AuCoTrack can be further boosted by an image-based recentering step of the extracted centerline control points. Furthermore, seed points for potentially missed vessels can be obtained by a rough pre-segmentation and could be integrated into the tracking scheme by adding them directly into the priority queue. False positive detections of vessels e.g. coronary veins or thoracic arteries can be reduced by combing further anatomical prior information with the local tracker. Initialisation at intermediate landmarks different from the ostiae is feasible and can be further explored. The algorithm can be parallelized much stronger in order to decrease runtime per case or to enable intermediate assessment of a partial result. Also, multiscale processing is a possible option for future work. The tracking scheme is very generic and versatile and can potentially also be used to track other 3D tubular structures such as airways, rib centerlines and other blood vessels. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[606,802,831,815]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5. ACKNOWLEDGEMENTS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[507,832,927,890]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"At the time of conducting this study, all authors were associated with Philips Research. Zohaib Salahuddin holds an EACEA Erasmus+ grant for masters in Medical Imaging and Applications (MAIA). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[489,916,509,927]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"94 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[92,980,897,994]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Authorized licensed use limited to: National University of Singapore. Downloaded on July 04,2021 at 02:25:53 UTC from IEEE Xplore. Restrictions apply. ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[87,114,470,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6. COMPLIANCE WITH ETHICAL STANDARDS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[70,142,489,186]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This research was evaluated using human subject data made available in open access. Ethical approval was not required as confirmed by the license attached with the open access data. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[208,205,351,218]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7. REFERENCES ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[82,231,487,888]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[1] Jelmer M. Wolterink, Robbert W. van Hamersvelt, Max A. Viergever, Tim Leiner, and Ivana Isgum, “Coronary artery centerline extraction in cardiac CT angiography using a CNN-based orientation classifier,” Medical Image Analysis, vol. 51, pp. 46 – 60, 2019. \",\"[2] Arup Malakar, Debashree Choudhury, Binata Halder, Prosenjit Paul, Dr Arif Uddin, and Supriyo Chakraborty, “A review on coronary artery disease, its risk factors, and therapeutics,” Journal of Cellular Physiology, vol. 234, 02 2019. \",\"[3] WHO, “Global health estimates 2016: Deaths by cause, age, sex, by country and by region, 2000-2016.” 2018. \",\"[4] Dan Paech and Adele Weston, “A systematic review of the clinical effectiveness of 64-slice or higher computed tomography angiography as an alternative to invasive coronary angiography in the investigation of suspected coronary artery disease,” BMC Cardiovascular Disorders, vol. 11, pp. 32, 06 2011. \",\"[5] Michiel Schaap, Coert Metz, Theo Walsum, Alina van der Giessen, Annick Weustink, Nico Mollet, Christian Bauer, Hrvoje Bogunovic, Carlos Castro, Xiang Deng, Engin Dikici, Thomas O'Donnell, Michel Frenay, Ola Friman, Marcela Hernandez Hoyos, Pieter Kitslaar, Karl Krissian, Caroline Kühnel, Miguel Luengo-Oroz, and W.J. Niessen, \\\"Standardized evaluation methodology and reference database for evaluating coronary artery centerline extraction algorithms,\\\" Medical Image Analysis, vol. 13, pp. 701-14, 07 2009. \",\"[6] Yefeng Zheng, Huseyin Tek, and Gareth Funka-Lea, \\\"Robust and accurate coronary artery centerline extraction in CTA by combining model-driven and data-driven approaches,\\\" International Conference on Medical Image Computing and Computer-Assisted Intervention, vol. 16, pp. 74-81, 09 2013. \",\"[7] Yoshiro Kitamura, Yuanzhong Li, and Wataru Ito, \\\"Automatic coronary extraction by supervised detection and shape matching,\\\" Proceedings - International Symposium on Biomedical Imaging, pp. 234-237, 05 2012. \",\"[8] Guanyu Yang, Pieter Kitslaar, Michel Frenay, Alexander Broersen, Mark Boogers, Jeroen Bax, Johan Reiber, and Jouke Dijkstra, \\\"Automatic centerline extraction of \"]","page_idx":"4","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[512,115,926,802]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"coronary arteries in coronary computed tomographic angiography,\\\" The International Journal of Cardiovascular Imaging, vol. 28, pp. 921-33, 06 2011. \",\"[9] Karl Krissian, Hrvoje Bogunović, Jose Pozo, Maria-Cruz Villa-Uriol, and Alejandro Frangi, \\\"Minimally interactive knowledge-based coronary tracking in CTA using a minimal cost path,\\\" The Insight Journal, 01 2008. \",\"[10] Suheyla Cetin Karayumak, Ali Demir, Anthony Yezzi, Muzaffer Degertekin, and Gozde Unal, \\\"Vessel tractography using an intensity based tensor model with branch detection,\\\" IEEE Transactions on Medical Imaging, vol. 32, 11 2012. \",\"[11] Suheyla Cetin Karayumak and Gozde Unal, “A higher-order tensor vessel tractography for segmentation of vascular structures,” IEEE Transactions on Medical Imaging, vol. 34, 04 2015. \",\"[12] Ola Friman, Caroline Kuehnel, and Heinz-Otto Peitgen, “Coronary centerline extraction using multiple hypothesis tracking and minimal paths,” International Conference on Medical Image Computing and Computer-Assisted Intervention, 08 2008. \",\"[13] Olivier Ecabert, Jochen Peters, Hauke Schramm, Cristian Lorenz, Jens Berg, Matthew Walker, Mani Vembar, Mark Olszewski, Krishna Subramanyan, Guy Lavi, and Jürgen Weese, \\\"Automatic model-based segmentation of the heart in CT images,\\\" IEEE Transactions on Medical Imaging, vol. 27, pp. 1189-201, 10 2008. \",\"[14] Zohaib Salahuddin, Matthias Lenga, and Hannes Nickisch, “Multi-resolution 3d convolutional neural networks for automatic coronary centerline extraction in cardiac CT angiography scans,” arXiv preprint arXiv:2010.00925, 2020. \",\"[15] Jiafa He, Chengwei Pan, Can Yang, Ming Zhang, Yang Wang, Xiaowei Zhou, and Yizhou Yu, “Learning hybrid representations for automatic 3d vessel centerline extraction,” in Medical Image Computing and Computer Assisted Intervention. 2020, pp. 24–34, Springer International Publishing. \",\"[16] Yuyang Zhang, Gongning Luo, Wei Wang, and Kuanquan Wang, “Branch-aware double DQN for centerline extraction in coronary CT angiography,” International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 35–44, 2020. \"]","page_idx":"4","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[489,916,507,926]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"95 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[92,980,895,994]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Authorized licensed use limited to: National University of Singapore. Downloaded on July 04,2021 at 02:25:53 UTC from IEEE Xplore. Restrictions apply. ","text_format":null,"text_level":null,"type":"footer"}],"string":"[\n {\n \"bbox\": \"[92,140,907,174]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MULTI-RESOLUTION 3D CONVOLUTIONAL NEURAL NETWORKS FOR AUTOMATIC CORONARY CENTERLINE EXTRACTION IN CARDIAC CT ANGIOGRAPHY SCANS\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[223,191,771,210]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Zohaib Salahuddin\\\\* Matthias Lenga Hannes Nickisch \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[258,225,737,258]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"* Escola Politécnica Superior, Universitat de Girona, Spain † Philips Research Hamburg, Germany \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[231,290,327,304]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABSTRACT \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,311,485,524]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We propose a deep learning-based automatic coronary artery tree centerline tracker (AuCoTrack) extending the vessel work of [1]. A multi-resolution 3D Convolutional Neural Network (CNN) is employed to simultaneously predict movement directions and detect bifurcations. Moreover, an automated artery endpoint detector is used to prevent premature termination of the tracking process. On Coronary Computed Tomography Angiography (CCTA or coronary CTA) scans annotated by clinical experts, an average sensitivity of $87.1\\\\%$ and clinically relevant overlap of $89.1\\\\%$ could be obtained. In addition, the MICCAI 2008 Coronary Artery Tracking Challenge (CAT08) training and test datasets were used to benchmark the algorithm and to assess its generalization capabilities. On CAT08, an average overlap of $93.6\\\\%$ and a clinically relevant overlap of $96.4\\\\%$ were achieved. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[72,530,485,559]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Index Terms—coronary artery centerline tracking, coronary computed tomography angiography, neural networks \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,577,361,591]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. INTRODUCTION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,604,487,889]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Coronary artery disease (CAD) results in narrowing or blockage of coronary arteries due to the build-up of cholesterol and fatty deposits on the inner lining of the arterial wall. Such constrictions can result in an inadequate supply of blood to the heart muscles which can be fatal [2]. CAD is one on the leading causes of death worldwide with 9.43 million deaths reported in 2016 [3]. Coronary Angiography (CA) is an interventional procedure for CAD evaluation and treatment. The severity and anatomical extent of CAD can be assessed noninvasively by Coronary Computed Tomography Angiography (CCTA) [4]. Manual reading of volumetric CCTA images is a time-consuming task. Several advanced visualization techniques relying on coronary artery centerlines have been proven to facilitate the clinical workflow. In [5], approaches for the assisted extraction of coronary artery centerlines are categorized as: automatic requiring no user interaction at all [6, 7, 8], semi-automatic requiring one seed point per artery [9, 10, 11] or interactive requiring multiple user interactions per artery [1, 5, 12]. Recently, [1] proposed a CNN-based tracking scheme which iteratively predicts a movement direc \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,290,926,389]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tion and a step-size. As an interactive method, almost state-of-the-art performance could be achieved. Typically, their tracker required multiple seeds per artery in order to successfully extract the related centerline due to premature stopping. The approach did not identify and handle bifurcations. In order to render the algorithm automatic, an additional network was used for seed point extraction. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,390,926,574]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Building on [1], we propose a multi-resolution CNN-based algorithm to extract the entire coronary tree automatically without user interaction. Our approach detects bifurcation points and properly integrates them into the tracking process. In addition, the tracker is guided by another CNN in order to prevent premature termination. The algorithm does not rely on a segmentation network or any other automated method to generate multiple seed points per artery. We show that a simple automated detection of two seeds (one for each coronary tree) suffices and that the proposed method is very robust towards variations of those points. The ostium points obtained from a deformable shape model of the heart [13] are used to initialize the automatic coronary centerline extraction. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[633,592,801,606]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. METHODOLOGY \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,618,926,831]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Our automatic coronary artery tracker (AuCoTrack) sequentially traces the coronary artery centerline while deciding in each step forward in which direction to continue or if a new vessel branches off (direction and bifurcation classifier, DBC-Net). Simultaneously, the tracker monitors whether an endpoint of an artery is reached and the tracking should be stopped (stop classification network, STC-Net), see Figure 1. A global priority queue containing active centerline points is maintained which is initialized with points located at the left and right ostium. Two or three points are added to the queue at each step depending on the discovery of a bifurcation. We avoid double visits by only following centerline points located at a minimum distance from already found centerline points. Processing can be done in parallel and the tracker terminates once no more active centerline points are queued. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,832,926,889]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The direction of movement is found by a multi-class prediction on the unit sphere whose surface is discretised into 1000 admissible directions (DBC-Net). We perform peak detection in order to find two or three likely directions depend \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[0,190,16,805]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI) | 978-1-6654-1246-9/20/$31.00 ©2021 IEEE | DOI: 10.1109/ISBI48211.2021.9434002 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[70,59,526,81]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI) April 13-16, 2021, Nice, France \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[72,916,314,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"978-1-6654-1246-9/21/$31.00 ©2021 IEEE \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[489,916,507,927]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"91 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[92,980,895,994]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Authorized licensed use limited to: National University of Singapore. Downloaded on July 04,2021 at 02:25:53 UTC from IEEE Xplore. Restrictions apply. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[75,114,922,299]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 1. Overview of the AuCoTrack pipeline. At inference time (black arrows), multiresolution image patches $P_{1}$ and $P_{2}$ are fed into the two networks (yellow boxes) which results in a predicted direction on the unit ball (red dots) and the decision whether to branch or stop (orange boxes) by the DBC-Net and the STC-Net, respectively. The stopping prediction is illustrated in the gray box on the bottom left. The main tracking loop (light green box and black dotted arrow) is initialised with the ostiae (blue dots) and results in the coronary tree (red lines). This tree can be mapped back to the underlying CCTA scan via a stretched multiplanar reformat (sMPR). The network architecture of the DBC-Net and STC-Net is essentially an encoder with parallel pathways at two different resolutions whose representations are combined (box top left). For training (red arrows), patches along with their labels (bifurcation/vessel, stop/continue, direction encoded in binary vector) are used. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0857/e127ec71d816a91d629a63a01d533c29d1d9e6389bc36bdd6c2cb394822ea039.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[70,452,489,779]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ing on the prediction of a bifurcation. We employ angle constraints to concentrate on meaningful configurations i.e. we require that the (a) highest response (way back) is similar to the previous direction $(\\\\mathrm{angle} < 60^{\\\\circ})$ , (b) second response (way ahead) is different from the previous direction $(\\\\mathrm{angle} > 110^{\\\\circ})$ , and (c) third response (branching) is different from the other two $(\\\\mathrm{angle} > 40^{\\\\circ})$ . The third response is calculated only in the case DBC-Net predicts the presence of a bifurcation. A fixed step of $1\\\\mathrm{mm}$ is taken in the predicted direction. The STC-Net casts a binary vote on whether the coronary tracking continues. Both DBC-Net and STC-Net use the same network architecture and operate locally on isotropic 3D patches $P_{1}, P_{2}$ of size $19^{3}$ sampled at the two resolutions $0.5\\\\mathrm{mm}$ and $1.0\\\\mathrm{mm}$ . Each of the two network branches has 7 convolutional layers with kernels of size 3. Layers 3 and 4 use dilated convolutions with the spacing of 2 and 4 between the kernel points respectively. We use ReLu activation functions and batch normalisation. The result of the two branches is stacked and reduced to the number of direction classes to form Layer $L_{D}$ . Layer $L_{D}$ is then followed by two linear layers and a sigmoid activation for the patch type prediction. In case of DBC-Net, the output of layer $L_{D}$ is followed by a softmax activation to get the direction response. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,783,487,840]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We train and evaluate the two networks on a set of volumetric CCTA scans where the coronary artery tree – as annotated by clinical experts – is represented by a set of centerlines and their topological connections. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,846,489,889]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Binary cross entropy loss $(BCE_{patch})$ is used for the patch type classification and categorical cross entropy loss $(CE_{dir})$ is used for the direction classification. The com \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,451,927,764]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"binned loss function used to train the DBC-Net is $L = CE_{dir} + \\\\lambda_b BCE_{patch}$ . The weighting factor $\\\\lambda_b$ is fixed at 5. For STC-Net, we employ only binary cross entropy loss for stop patch type classification. For optimisation, we use Adam with a learning rate of 0.0001 and a mini-batch size of 64. We use several augmentation strategies during training. We use random translations (along three axes) to make the direction prediction more robust and rotational perturbations (along three axes) to introduce a certain degree of rotational invariance. The training of the DBC/STC-Nets requires carefully selected pairs of input patches and output labels in terms of binary vectors encoding the directions, stop and bifurcation indicators. The binary direction vectors are obtained by placing a sphere with radius $R = 1.5mm$ around the centerline point and a subsequent nearest neighbor matching of the vessel intersections with the sphere to the discrete sphere tessellation. The number of intersections with the sphere governs the flag in terms of bifurcation or stop patch. Care was taken to oversample the bifurcations (by a factor of 10, see Section 3). The STC-Net was trained with patches particularly selected beyond the end of the coronary artery, see Figure 1 bottom left box. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[667,809,769,823]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. RESULTS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,845,926,889]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We evaluate our AuCoTrack algorithm using the evaluation metrics defined in [5]. Sensitivity was an additional metric used on the training dataset. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[489,916,507,927]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"92 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[92,982,897,994]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Authorized licensed use limited to: National University of Singapore. Downloaded on July 04,2021 at 02:25:53 UTC from IEEE Xplore. Restrictions apply. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[73,112,211,190]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(a) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0310/bd246fe19f08f8f195b955f35c144668bf94059db8708821855dde7efb0bb658.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[223,112,352,188]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(b) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0143/a83ab5d40e133454ae1b990310666179b45983c693bcd65b25aec5748eb3d859.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[364,115,485,187]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(c) \\\",\\\"Fig. 2. Rendering of AuCoTrack result: (a) initialization at ostiae, (b) initialization approximately at center of LAD and RCA, (c) detected bifurcation overlayed on tracking result. Green = correct, blue = init points, orange = bifurcations. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0096/866af2fc1aaabafabdf0d01ed946b85acf2e97621fc6cc39c8dca8d8f67e2218.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[75,300,231,314]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1. Training Dataset \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,321,485,421]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The training dataset consists of 43 CCTA images which were annotated by clinical experts. The number of annotated coronary arteries per CCTA scan varies from 4 to 20. The mean number of annotated coronary arteries per CCTA scan in this dataset is 9. The training dataset contains 428 annotated coronary arteries. Four-fold cross validation has been performed in-order to evaluate the proposed algorithm. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,423,485,634]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 2 (a) shows that the result of the automatic coronary centerline extraction when the seed points for tracker initialization are placed at the left and right coronary ostium. Figure 2 (b) shows the result when the initialization takes place approximately at the center of LAD and RCA. The extracted coronary tree is very similar in both cases. The sensitivity obtained when the seed points are placed at the ostiae is $88.9\\\\%$ and it is $87.3\\\\%$ when the seed points are placed in the middle of LAD and RCA. This shows that the seed point can essentially be placed anywhere on the coronary tree. Figure 2 (c) shows the bifurcation detection overlaid on the tracking result. The orange marks on the coronary tree indicate that a bifurcation has been detected at that centerline point by the DBC-Net. This implies that three direction vectors will be obtained to generate the candidate points. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,635,485,804]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An ablation study was performed and revealed the optimal number of equispaced points on the direction sphere to be 1000 (using the spherical Fibonacci mapping). The number of pathways in the multi-resolution DBC-Net and STC-Net was fixed at 2 and the importance sampling parameter for the bifurcation class was found to be around 10 [14]. The patch size of 19 is selected to balance fast processing and enough field-of-view to cover average coronary artery radii. We obtained a sensitivity of $87.1\\\\% \\\\pm 3.2\\\\%$ , a clinically relevant overlap of $89.1\\\\% \\\\pm 2.3\\\\%$ and a total overlap of $80.4\\\\% \\\\pm 2.0\\\\%$ . The accuracy inside was $0.34\\\\mathrm{mm} \\\\pm 0.0017\\\\mathrm{mm}$ which is below the average voxel size of $0.40^2 \\\\times 0.43\\\\mathrm{mm}^3$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,823,285,837]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2. CAT08 Training Dataset \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[75,846,485,888]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The best model cross-validated on the training dataset was used to extract centerlines on the CAT08 training datasets. Table 1 shows that an average overlap (OV) of $93.4\\\\%$ ,clinically \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,115,922,229]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 3. Clinically relevant overlap of all the arteries present in the training dataset which occur more than 3 times evaluated using cross validation. The occurrence count of each artery is also shown in the plot. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0732/d1c360a10c9b2b196fe1f6867517c046626d9c670b459cc63cb6640a16eee5a1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[515,317,921,431]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0257/43a837c3341c27dc90826df4cf5650422a5538f2228b8de155ee450f063676b3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>No.</td><td>Image Quality</td><td>Calcium Score</td><td>OV</td><td>OF</td><td>OT</td><td>AI</td><td>T</td></tr><tr><td>0</td><td>Moderate</td><td>Moderate</td><td>94.2</td><td>77.7</td><td>95.1</td><td>0.4</td><td>55</td></tr><tr><td>1</td><td>Moderate</td><td>Moderate</td><td>97.3</td><td>99.4</td><td>99.6</td><td>0.32</td><td>39</td></tr><tr><td>2</td><td>Good</td><td>Low</td><td>98.3</td><td>99.7</td><td>100</td><td>0.31</td><td>43</td></tr><tr><td>3</td><td>Poor</td><td>Moderate</td><td>86.3</td><td>63.0</td><td>89.1</td><td>0.40</td><td>41</td></tr><tr><td>4</td><td>Moderate</td><td>Low</td><td>92.9</td><td>57.3</td><td>97.9</td><td>0.33</td><td>31</td></tr><tr><td>5</td><td>Poor</td><td>Moderate</td><td>97.6</td><td>77.5</td><td>99.7</td><td>0.43</td><td>33</td></tr><tr><td>6</td><td>Good</td><td>Low</td><td>96.7</td><td>87.2</td><td>99.6</td><td>0.30</td><td>36</td></tr><tr><td>7</td><td>Good</td><td>Severe</td><td>83.9</td><td>49.1</td><td>86.3</td><td>0.38</td><td>48</td></tr><tr><td>Avg</td><td></td><td></td><td>93.4</td><td>76.5</td><td>95.9</td><td>0.36</td><td>41</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. Results of our method on CAT08 training set which was used as a test set. For each case, overlap (OV, in %), overlap until first error (OF, in %) and clinically relevant overlap (OT, in %), average accuracy inside (AI, in mm), time taken for coronary tree extraction (T, in s) along with subjective image quality and calcium score is shown. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[512,549,924,619]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"relevant overlap (OT) of $95.9\\\\%$ and overlap until first error (OF) of $76.5\\\\%$ was obtained for these 8 CCTA scans. This is a good test of generalization as the CCTA training dataset and the CAT08 dataset used for testing are disjoint and were acquired on scanners from different vendors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,638,690,652]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.3. CAT08 Test Dataset \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,661,924,888]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We tested our algorithm on the CAT08 test set to benchmark the performance of our algorithm against methods available on the leaderboard of the CAT08 challenge. An average overlap of $93.6\\\\% \\\\pm 5.2\\\\%$ , clinically relevant overlap of $96.4\\\\% \\\\pm 4.1\\\\%$ , overlap until first error of $76.3\\\\% \\\\pm 22.7\\\\%$ and accuracy inside of $0.37\\\\mathrm{mm} \\\\pm 0.05\\\\mathrm{mm}$ was obtained for these 24 CCTA scans. Cases 8, 10 and 27 required one additional seed point due to failure in the detection of bifurcations for one of the vessels. There are significant motion artifacts present in case 26 which hamper the bifurcation detection. Hence, additional seed points are provided for 3 of the vessels in this CCTA image. Table 2 shows the comparison of the performance of our algorithm (AuCoTrack) with the current automatic coronary centerline extraction techniques and the state-of-the-art CNN-based technique which requires at-least one seed point per vessel for the centerline extraction. Overall, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[490,916,507,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"93 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[95,982,895,992]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Authorized licensed use limited to: National University of Singapore. Downloaded on July 04,2021 at 02:25:53 UTC from IEEE Xplore. Restrictions apply. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[77,112,485,198]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0749/624187179d82bd5f60e08ce2a81e15058d341604ee173d13ec83ce0e1f5209e6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Method</td><td>OV</td><td>OF</td><td>OT</td><td>AI</td><td>T</td></tr><tr><td>AuCoTrack</td><td>93.6</td><td>76.3</td><td>96.4</td><td>0.37</td><td>42</td></tr><tr><td>Zheng et al.</td><td>93.5</td><td>76.5</td><td>95.6</td><td>0.20</td><td>60</td></tr><tr><td>Kitamura et al.</td><td>90.6</td><td>70.9</td><td>92.5</td><td>0.25</td><td>160</td></tr><tr><td>Yang et al.</td><td>93.7</td><td>74.2</td><td>95.9</td><td>0.30</td><td>120</td></tr><tr><td>Wolterink et al. (Interactive)</td><td>93.7</td><td>81.5</td><td>97.0</td><td>0.21</td><td>10</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2. We compare of our AuCoTrack pipeline with the top automatic coronary artery centerline algorithms in terms of overlap (OV, in %), overlap until first error (OF, in %) and clinically relevant overlap (OT, in %), average accuracy inside (AI, in mm) and time taken (T, in s) on the CAT08 date. The interactive CNN-based tracker [1] is below the dashed line. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[70,315,489,345]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"AuCoTrack achieves better clinically relevant overlap than other automatic methods. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[213,363,346,378]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.DISCUSSION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,391,489,731]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An automatic deep learning-based coronary artery centerline tracker in CCTA images (AuCoTrack) was proposed. Our framework was evaluated on 43 training CCTA images and additional datasets available from the CAT08 challenge. On the training dataset, AuCoTrack was evaluated using fourfold cross validation. To test the generalisation of our approach, the model was applied to the CAT08 training set. For further evaluation, we trained on a combined dataset containing the 43 training CCTA scans and the 8 CCTA scans from the CAT08 training set. The resulting model was then applied to the CAT08 test set and the extracted centerlines were submitted to the CAT08 challenge evaluation framework. Our method obtained an accuracy inside of $0.37\\\\mathrm{mm}$ , a overlap of $93.6\\\\%$ and a clinically relevant overlap of $96.4\\\\%$ on average. Moreover, an overlap rank (OR) of 9.87 was achieved outperforming the available top three automatic algorithms on the CAT08 leaderboard [6] OR=10.43, [7] OR=13.81 and [8] OR=10.55. We remark, that the state-of-the-art automatic centerline extraction algorithm by [6] requires artery segmentation masks as input for their model driven and data driven approach. Their algorithm is trained on 108 training CCTA scans. Similarly, a hybrid learning representation approach that utilizes segmentation masks proposed by [15] was trained on 100 CCTA scans. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,732,487,802]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An analysis of the individual CAT08 cases showed that the performance is not strongly affected by the presence of coronary calcium. For example, on the CAT08 test images with low, moderate and severe calcium scores, an average overlap of $92.9\\\\%$ , $94.0\\\\%$ and $94.2\\\\%$ was obtained. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,804,489,891]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The number of annotated centerlines in the training dataset varied from 4 to 20. We observed a high clinically relevant overlap independent of the number of annotated arteries which demonstrates that our algorithm is capable of extracting the entire (left or right) coronary tree from a single seed. In order to address the problem of premature or late stopping, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,115,926,144]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"we employ a voting mechanism combining a CNN-based endpoint detection with a moving average entropy criterion. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,144,927,217]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"AuCoTrack achieves a clinically relevant overlap of $96.4\\\\%$ on the CAT08 test set and $89.1\\\\%$ on the training dataset. This difference is due to the fact that the CAT08 test set contains annotations for only 4 coronaries and the training dataset contains a variable number ranging from 4 to 20. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,217,927,445]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"[1] achieved near state-of-the-art performance as an interactive method for the CAT08 dataset. A main constraint of their method is that it requires one or more seed points per vessel as no functionality for detecting and handling bifurcations is available. Our method relies only on a single seed point per coronary tree and bifurcations are properly handled by the tracker. Successful vessel detection $(\\\\mathrm{OT} > 50\\\\%)$ was observed in $95\\\\%$ of the cases from the CAT08 dataset. The ostium points required for initializing AuCoTrack were automatically obtained from a deformable shape model of the heart [13]. Moreover, we observed that our algorithm is very robust towards variations of those point, see Figure 2. In [1] the tracker termination is guided by a moving average entropy criteria which fails in case of a severe stenosis. Consequently, their method may require several initialization points per vessel in order to warm-start the tracking process. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,447,927,532]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A branch-aware coronary centerline extraction approach based on Double Deep Q-Network proposed by [16] was evaluated only on the CAT08 training dataset. This method does not terminate on reaching the end of coronary artery but terminates when the tracker goes out of the CCTA scan or reaches an already visited point. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,533,927,776]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In future work, the accuracy of AuCoTrack can be further boosted by an image-based recentering step of the extracted centerline control points. Furthermore, seed points for potentially missed vessels can be obtained by a rough pre-segmentation and could be integrated into the tracking scheme by adding them directly into the priority queue. False positive detections of vessels e.g. coronary veins or thoracic arteries can be reduced by combing further anatomical prior information with the local tracker. Initialisation at intermediate landmarks different from the ostiae is feasible and can be further explored. The algorithm can be parallelized much stronger in order to decrease runtime per case or to enable intermediate assessment of a partial result. Also, multiscale processing is a possible option for future work. The tracking scheme is very generic and versatile and can potentially also be used to track other 3D tubular structures such as airways, rib centerlines and other blood vessels. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[606,802,831,815]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5. ACKNOWLEDGEMENTS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,832,927,890]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"At the time of conducting this study, all authors were associated with Philips Research. Zohaib Salahuddin holds an EACEA Erasmus+ grant for masters in Medical Imaging and Applications (MAIA). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[489,916,509,927]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"94 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[92,980,897,994]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Authorized licensed use limited to: National University of Singapore. Downloaded on July 04,2021 at 02:25:53 UTC from IEEE Xplore. Restrictions apply. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[87,114,470,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6. COMPLIANCE WITH ETHICAL STANDARDS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[70,142,489,186]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This research was evaluated using human subject data made available in open access. Ethical approval was not required as confirmed by the license attached with the open access data. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[208,205,351,218]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7. REFERENCES \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[82,231,487,888]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[1] Jelmer M. Wolterink, Robbert W. van Hamersvelt, Max A. Viergever, Tim Leiner, and Ivana Isgum, “Coronary artery centerline extraction in cardiac CT angiography using a CNN-based orientation classifier,” Medical Image Analysis, vol. 51, pp. 46 – 60, 2019. \\\",\\\"[2] Arup Malakar, Debashree Choudhury, Binata Halder, Prosenjit Paul, Dr Arif Uddin, and Supriyo Chakraborty, “A review on coronary artery disease, its risk factors, and therapeutics,” Journal of Cellular Physiology, vol. 234, 02 2019. \\\",\\\"[3] WHO, “Global health estimates 2016: Deaths by cause, age, sex, by country and by region, 2000-2016.” 2018. \\\",\\\"[4] Dan Paech and Adele Weston, “A systematic review of the clinical effectiveness of 64-slice or higher computed tomography angiography as an alternative to invasive coronary angiography in the investigation of suspected coronary artery disease,” BMC Cardiovascular Disorders, vol. 11, pp. 32, 06 2011. \\\",\\\"[5] Michiel Schaap, Coert Metz, Theo Walsum, Alina van der Giessen, Annick Weustink, Nico Mollet, Christian Bauer, Hrvoje Bogunovic, Carlos Castro, Xiang Deng, Engin Dikici, Thomas O'Donnell, Michel Frenay, Ola Friman, Marcela Hernandez Hoyos, Pieter Kitslaar, Karl Krissian, Caroline Kühnel, Miguel Luengo-Oroz, and W.J. Niessen, \\\\\\\"Standardized evaluation methodology and reference database for evaluating coronary artery centerline extraction algorithms,\\\\\\\" Medical Image Analysis, vol. 13, pp. 701-14, 07 2009. \\\",\\\"[6] Yefeng Zheng, Huseyin Tek, and Gareth Funka-Lea, \\\\\\\"Robust and accurate coronary artery centerline extraction in CTA by combining model-driven and data-driven approaches,\\\\\\\" International Conference on Medical Image Computing and Computer-Assisted Intervention, vol. 16, pp. 74-81, 09 2013. \\\",\\\"[7] Yoshiro Kitamura, Yuanzhong Li, and Wataru Ito, \\\\\\\"Automatic coronary extraction by supervised detection and shape matching,\\\\\\\" Proceedings - International Symposium on Biomedical Imaging, pp. 234-237, 05 2012. \\\",\\\"[8] Guanyu Yang, Pieter Kitslaar, Michel Frenay, Alexander Broersen, Mark Boogers, Jeroen Bax, Johan Reiber, and Jouke Dijkstra, \\\\\\\"Automatic centerline extraction of \\\"]\",\n \"page_idx\": \"4\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[512,115,926,802]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"coronary arteries in coronary computed tomographic angiography,\\\\\\\" The International Journal of Cardiovascular Imaging, vol. 28, pp. 921-33, 06 2011. \\\",\\\"[9] Karl Krissian, Hrvoje Bogunović, Jose Pozo, Maria-Cruz Villa-Uriol, and Alejandro Frangi, \\\\\\\"Minimally interactive knowledge-based coronary tracking in CTA using a minimal cost path,\\\\\\\" The Insight Journal, 01 2008. \\\",\\\"[10] Suheyla Cetin Karayumak, Ali Demir, Anthony Yezzi, Muzaffer Degertekin, and Gozde Unal, \\\\\\\"Vessel tractography using an intensity based tensor model with branch detection,\\\\\\\" IEEE Transactions on Medical Imaging, vol. 32, 11 2012. \\\",\\\"[11] Suheyla Cetin Karayumak and Gozde Unal, “A higher-order tensor vessel tractography for segmentation of vascular structures,” IEEE Transactions on Medical Imaging, vol. 34, 04 2015. \\\",\\\"[12] Ola Friman, Caroline Kuehnel, and Heinz-Otto Peitgen, “Coronary centerline extraction using multiple hypothesis tracking and minimal paths,” International Conference on Medical Image Computing and Computer-Assisted Intervention, 08 2008. \\\",\\\"[13] Olivier Ecabert, Jochen Peters, Hauke Schramm, Cristian Lorenz, Jens Berg, Matthew Walker, Mani Vembar, Mark Olszewski, Krishna Subramanyan, Guy Lavi, and Jürgen Weese, \\\\\\\"Automatic model-based segmentation of the heart in CT images,\\\\\\\" IEEE Transactions on Medical Imaging, vol. 27, pp. 1189-201, 10 2008. \\\",\\\"[14] Zohaib Salahuddin, Matthias Lenga, and Hannes Nickisch, “Multi-resolution 3d convolutional neural networks for automatic coronary centerline extraction in cardiac CT angiography scans,” arXiv preprint arXiv:2010.00925, 2020. \\\",\\\"[15] Jiafa He, Chengwei Pan, Can Yang, Ming Zhang, Yang Wang, Xiaowei Zhou, and Yizhou Yu, “Learning hybrid representations for automatic 3d vessel centerline extraction,” in Medical Image Computing and Computer Assisted Intervention. 2020, pp. 24–34, Springer International Publishing. \\\",\\\"[16] Yuyang Zhang, Gongning Luo, Wei Wang, and Kuanquan Wang, “Branch-aware double DQN for centerline extraction in coronary CT angiography,” International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 35–44, 2020. \\\"]\",\n \"page_idx\": \"4\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[489,916,507,926]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"95 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[92,980,895,994]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Authorized licensed use limited to: National University of Singapore. Downloaded on July 04,2021 at 02:25:53 UTC from IEEE Xplore. Restrictions apply. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1109/isbi48211.2021.9434002"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Medicine and Health Sciences"},"sha256":{"kind":"string","value":"59266423b699bf9585a00e53e9041699452d6bb559366459598006a58fe7d728"},"title":{"kind":"string","value":"Multi-Resolution 3D Convolutional Neural Networks for Automatic Coronary\\n Centerline Extraction in Cardiac CT Angiography Scans"}}},{"rowIdx":267,"cells":{"abstract":{"kind":"string","value":"Though algorithms promise many benefits including efficiency, objectivity and accuracy, they may also introduce or amplify biases. Here we study two well-known algorithms, namely PageRank and Who-to-Follow (WTF), and show to what extent their ranks produce inequality and inequity when applied to directed social networks. To this end, we propose a directed network model with preferential attachment and homophily (DPAH) and demonstrate the influence of network structure on the rank distributions of these algorithms. Our main findings suggest that (i) inequality is positively correlated with inequity, (ii) inequality is driven by the interplay between preferential attachment, homophily, node activity and edge density, and (iii) inequity is driven by the interplay between homophily and minority size. In particular, these two algorithms reduce, replicate and amplify the representation of minorities in top ranks when majorities are homophilic, neutral and heterophilic, respectively. Moreover, when this representation is reduced, minorities may improve their visibility in the rank by connecting strategically in the network. For instance, by increasing their out-degree or homophily when majorities are also homophilic. These findings shed light on the social and algorithmic mechanisms that hinder equality and equity in network-based ranking and recommendation algorithms."},"author":{"kind":"string","value":"Espín-Noboa, Lisette|Wagner, Claudia|Strohmaier, Markus|Karimi, Fariba"},"content_list":{"kind":"list like","value":[{"bbox":"[154,166,238,189]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"OPEN ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[258,164,880,278]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Inequality and inequity in network-based ranking and recommendation algorithms ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,283,899,301]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lisette Espín-Noboa $^{1,2,3}$ , Claudia Wagner $^{1,4,5}$ , Markus Strohmaier $^{1,4,6}$ & Fariba Karimi $^{2}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,310,919,524]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Though algorithms promise many benefits including efficiency, objectivity and accuracy, they may also introduce or amplify biases. Here we study two well-known algorithms, namely PageRank and Who-to-Follow (WTF), and show to what extent their ranks produce inequality and inequity when applied to directed social networks. To this end, we propose a directed network model with preferential attachment and homophily (DPAH) and demonstrate the influence of network structure on the rank distributions of these algorithms. Our main findings suggest that (i) inequality is positively correlated with inequity, (ii) inequality is driven by the interplay between preferential attachment, homophily, node activity and edge density, and (iii) inequity is driven by the interplay between homophily and minority size. In particular, these two algorithms reduce, replicate and amplify the representation of minorities in top ranks when majorities are homophilic, neutral and heterophilic, respectively. Moreover, when this representation is reduced, minorities may improve their visibility in the rank by connecting strategically in the network. For instance, by increasing their out-degree or homophily when majorities are also homophilic. These findings shed light on the social and algorithmic mechanisms that hinder equality and equity in network-based ranking and recommendation algorithms. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[253,546,931,714]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Online social networks and information networks have become integral parts of our everyday life. However, the opportunities offered by such networks are often constrained not only by our previous interactions $^{1-5}$ , but also by algorithms. For instance, algorithms could make some people or content more visible than others via classification $^{6}$ , ranking or recommendations $^{7}$ . In this regard, search engines and recommender systems are increasingly used for various applications such as whom to follow, whom to cite, or whom to hire. Typically, these applications use algorithms to order items (e.g., people and academic papers) based on \"importance\" or \"relevance\", and may therefore produce social inequalities by discriminating certain individuals or groups of people in top ranks. In fact, it has been shown that recommender systems such as Who-to-Follow (WTF) $^{8}$ tend to increase the popularity of users who are already popular $^{7,9,10}$ . A similar effect has been found in PageRank $^{11}$ , where nodes in high ranks stabilize their position and give little opportunity to other nodes to occupy higher positions $^{12}$ . This tendency towards the \"popular\" arises because these algorithms harness structural information, in particular, the in- and out-degree of nodes. For this reason, modeling the directionality of links—which is often left out for simplicity—is crucial to really understand how these algorithms work on different types of networks. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[253,713,931,869]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, social networks are complex systems, and many other structural properties may also alter the distribution of nodes and groups in the ranking. For example, previous studies have shown that homophily—the tendency to connect to similar others— affects the visibility of minorities in degree rankings<sup>13</sup> and people recommender systems<sup>14</sup>. Consequently, it can reinforce societal issues such as the glass ceiling effect<sup>15-17</sup> and the invisibility syndrome<sup>18</sup>. Despite these findings, little is known about the extent to which the combination of multiple structural properties can alter the visibility of minorities in top ranks from ranking and recommendation algorithms. A further complication is that debiasing ranking outcomes and making them fair is very challenging since they can be mitigated in different ways<sup>19</sup>: by intervening on the score distribution of candidates<sup>20</sup>, on the ranking algorithm<sup>21</sup>, or on the ranked outcome<sup>22</sup>. While most of these studies tackle fairness in ranking, they do not explore the effects of networked data in ranking. This paper is a step towards this goal. Since such algorithms are so deeply involved in social, economic, and political processes, we need to first understand how our connections affect them to then apply appropriate interventions towards fair results. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,904,931,943]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"<sup>1</sup>Complexity Science Hub, Vienna, Austria. <sup>2</sup>Central European University, Vienna, Austria. <sup>3</sup>University of Koblenz-Landau, Koblenz, Germany. <sup>4</sup>GESIS - Leibniz Institute for the Social Sciences, Cologne, Germany. <sup>5</sup>RwTH Aachen University, Aachen, Germany. <sup>6</sup>University of Mannheim, Mannheim, Germany. <sup>7</sup>email: karimi@csh.ac.at ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[652,14,922,30]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[63,63,453,104]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"scientific reports ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[810,136,831,154]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"# ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[836,140,927,150]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Check for updates ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,282,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2022) 12:2012 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[376,965,633,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-022-05434-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[919,966,931,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[115,60,932,516]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 1. Inequality and inequity. Every column represents a network with certain level of homophily. All networks contain 20 nodes: $20\\\\%$ belong to the minority group (orange), and $80\\\\%$ to the majority group (blue). Edges follow a preferential attachment with homophily mechanism. The top row shows the graph and the level of homophily within groups (MM: majorities and mm: minorities). The second row shows all nodes in descending order (from + to -) based on their PageRank scores. The third row represents the rank inequality: Gini coefficients of the rank distribution for every top- $k\\\\%$ (black line). Gini global refers to the Gini coefficient of the entire rank distribution (i.e., at top- $100\\\\%$ ). We see that the lower the $k$ , the lower the Gini of the rank distribution. The bottom row represents the rank inequity: Percentage of minorities found in each top- $k\\\\%$ of the rank distribution (orange line). ME is the mean error of these percentages compared to a fair baseline or diversity constraint (i.e., how much the orange line deviates from the dotted line across all top-k's). Here we see three main patterns: (a, b) When the majority group is heterophilic, minorities are on average over-represented, $ME > 0.0$ . (d, e) When majorities are homophilic, minorities are on average under-represented, $ME < 0.0$ . (c) When both groups are neutral, the observed fraction of minorities is almost as expected, $ME \\\\approx 0$ . \"]","image_footnote":"[]","img_path":"images/0778/8ea6f6734dd3070088e6f70fa8a185fe2e5568e019936e8983c7b2b4ade0dbdf.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[253,716,931,882]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To this end, we propose DPAH, a network model that generates directed scale-free networks with binary-attributed nodes. It encodes two main mechanisms of edge formation found in social networks: homophily and preferential attachment[23-25] (see Methods for more details). Moreover, it allows to control for the fraction of minorities, edge density, and the skewness of the out-degree distribution. By using this model, we systematically study how these structural properties of social networks impact the ranking of nodes in PageRank and WTF. In particular, we investigate two ranking issues, inequality and inequity, and show how they get affected by the ranking algorithm together with the type of network. We measure inequality by quantifying the skewness of the rank distribution of nodes that PageRank and WTF produce, and inequity as how well-represented the minorities are in the top of the rank compared to the proportion of minorities in the network. In this work we study both ranking issues and measure their correlation. Furthermore, we quantify them globally using the whole rank distribution, and locally within each top- $k\\%$ rank. The goal is to identify both the overall inequality and inequity trend that these algorithms produce, and the tipping points where minorities start gaining visibility in the top of the rank. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,883,931,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As an example, consider the directed networks shown in Fig. 1. Every column represents a network with two types of nodes, minority (orange) and majority (blue), and different levels of homophily within groups. Homophily $h$ , is a parameter ranging from 0 to 1 and determines the tendency of two nodes of the same color to be connected. $h_{MM}$ and $h_{mm}$ represent homophily within majorities and minorities, respectively. When nodes ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,15,337,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2022) 12:2012 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,631,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-022-05434-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[921,965,931,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[258,60,806,400]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 2. Regions of disparity. We measure inequality (y-axis) as the skewness of the rank distribution, and inequality (x-axis) as the mean differences between the proportional representation of groups in top-k% ranks and the network. Highly skewed distributions lie in regions I to III (darker colors), and fair rankings, where minorities are well represented in top ranks, lie in regions II, V, VIII (green). We set $\\\\beta = 0.05$ which is arbitrary and allows for a flexible region of group fairness. \"]","image_footnote":"[]","img_path":"images/0343/7887338b38211d3fa3eb37117cbe74eddb1e4fcf7ea3b6edead31ea17ba7dc4d.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[255,507,931,572]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"are ranked using PageRank (second row), the position of the minorities in the rank varies systematically. For instance, when majorities are heterophilic ( $h_{MM} = 0.2$ , columns a and b), minorities often appear at the top (+). In contrast, when majorities are homophilic ( $h_{MM} = 0.8$ , columns d and e), minorities tend to appear at the tail of the rank (-). Next, we explain this systematic ranking behavior in top ranks by further varying the structure of the network. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,585,319,598]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,599,931,740]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Inequality and inequity in ranking. Inequality refers to the dispersion or distribution of importance among individuals. This importance is the ranking score assigned to every node by the algorithm. We compute the Gini coefficient of the rank distribution to measure how far the ranking scores of individuals deviate from a totally equal distribution (see Methods for more details). As shown in Fig. 2, a very low Gini score ( $\\text{Gini} < 0.3$ ) means that individuals are very similar with respect to their ranking scores. If the Gini score is extremely high ( $\\text{Gini} \\geq 0.6$ ), it means that only a few individuals capture most of the rank. In other words, the rank distribution is very skewed. Values in between ( $0.3 \\leq \\text{Gini} < 0.6$ ) represent moderate skewed distributions. Note that we measure inequality globally by using the whole rank distribution, and locally for each top- $k\\%$ . From our example in Fig. 1, we see that PageRank on average generates moderate skewed ranking distributions for all the depicted networks ( $\\text{Gini}_{\\text{global}} \\approx 0.5$ ). However, for very small top- $k\\%$ 's, the Gini is very low. This means that the top individuals possess very similar ranking scores. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,740,931,934]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Inequity refers to group fairness. In particular, it measures the error distance between the fraction of minorities in the top- $k\\%$ and a given fair baseline (e.g., a diversity constraint or quota). This baseline may be adjusted depending on the context of the application[19,26,27]. Here, a ranking is fair when its top- $k\\%$ preserves the proportional representation of groups in the network (i.e., equivalent to demographic parity[19,28]). Therefore, the error represents the local inequality at each top- $k\\%$ , and $ME$ the mean of these errors across all top- $k\\%$ ranks or global inequality. As shown on the last row of Fig. 1, we measure the local inequality in two steps. First, we compute the fraction of minorities that appear in each top- $k\\%$ rank (orange line). Second, we compute the error between the observed fraction of minorities in each top- $k\\%$ rank and a fair baseline (e.g., the actual fraction of minorities in the network, in this example $20\\%$ ). Then, we average these error scores across all top- $k\\%$ ranks to determine the global inequality score ( $ME$ values). Ideally, a fair ranking should reach $ME = 0$ . However, in order to allow for small fluctuations we introduce the smoothing factor $\\beta$ . Thus, a fair ranking is such that $-\\beta \\leq ME \\leq \\beta$ . The value of $\\beta$ is arbitrary, and allows for a smooth definition of \"low mean error\" or fairness. We set $\\beta = 0.05$ . As shown in Fig. 2, when $ME > \\beta$ , then minorities are over-represented in the top- $k\\%$ (blue region). When $ME < -\\beta$ , then minorities are under-represented (red region), otherwise the ranking is representing very well the minorities in the top of the rank (green region). Alternatively, we can say that the top rank (i) replicates the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,15,337,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2022) 12:2012 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,631,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-022-05434-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[919,965,931,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[124,63,141,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"a) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[157,80,263,94]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"minority (25%) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[159,95,263,109]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"majority (75%) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[285,67,310,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"h++ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[287,80,379,118]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"m M Source M 0.1 0.9 m 0.3 0.7 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[314,80,490,273]","code_body":null,"code_caption":null,"image_caption":"[\"target \"]","image_footnote":"[]","img_path":"images/0723/3728ebd66a3760b9bc8f5c9d2648a2c2c8c20c10a6487551a6dca911be182342.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[115,124,292,273]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0517/87e51e47c08c81e8ffe0bda1e7e7eb69c1bc656d272f905e23081b2702412244.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[531,67,932,277]","code_body":null,"code_caption":null,"image_caption":"[\"b) \",\"Figure 3. DPAH model and ranking of nodes. (a) Illustration of the directed network model with preferential attachment and homophily (DPAH). First, $n = 8$ nodes are created and randomly labeled according to the fraction of minorities $f_{m} = 0.25$ . Then, the following algorithm repeats until a desired edge density is fulfilled. At time $t$ , a source node $p$ is drawn from a power-law (activity) distribution, and a target node $j$ is drawn with a probability proportional to the product of its in-degree $K_{j}^{in} = 4$ and the pair-wise homophily $h_{pj} = h_{mM} = 0.9$ . At time $t + 1$ , a new edge is added between nodes $l \\\\rightarrow o$ based on the same mechanism. (b) The PageRank score of each node is shown under $PR$ . Nodes in each top- $k\\\\%$ of the rank are grouped based on the unique PageRank scores. In this example, the top- $60\\\\%$ of nodes concentrate most of the PageRank and their scores are somewhat similar (i.e., low Gini). Also, the ranking is fair from top- $80\\\\%$ onwards, since they capture the same fraction of minorities as in the population, $25\\\\%$ . Local values are measured per top- $k\\\\%$ , and global values are measured using the whole distribution for inequality (Gini), and the average across all top- $k\\\\%$ ranks for inequity (mean error). \"]","image_footnote":"[]","img_path":"images/0760/1ed34b5a67a96cd4b9349a08e19b3215e6aa1513c4312fb1e16407a1a94e7890.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[255,461,931,526]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"proportional representation of groups when $ME$ is zero or very low, (ii) amplifies the representation of minority nodes when $ME > \\beta$ , and (iii) reduces the representation of minority nodes—and benefits the majority group—when $ME < -\\beta$ . Note that $ME \\approx 0$ may be an artifact of a numerical cancellation as in (c), the neutral case in Fig. 1. In such cases, we could argue that the ranking is still fair since overall it was biased towards both groups across all top-k's. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,525,931,565]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, we refer to the relationship between inequality and inequity as disparity. For example, if a ranking distribution achieves $Gini = 0.65$ and $ME = 0.5$ , we say that the disparity lies in the region III (dark blue), i.e., high inequality and high inequity, see Fig. 2. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[253,578,931,654]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Growth network model with homophily and directed links. In order to examine the effect of homophily on the ranking of minorities in social networks, first we need to develop realistic network models that capture not only a variety of group mixing, but also the directionality of links. Many online social networks are directed networks in their nature, including the follower-followee structure on Twitter, citation networks $^{29}$ , and the hyperlink structure of the Web. Directed links are the key components of many algorithms such as Google Scholar $^{30}$ PageRank and Who-to-Follow. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[253,656,931,796]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To this end, we propose DPAH, a directed preferential attachment with homophily network growth model. We generate these networks by adjusting the number of nodes $n = 2000$ , the edge density $d = 0.0015$ , the fraction of minorities $f_{m} \\in \\{0.1, 0.2, 0.3, 0.4, 0.5\\}$ , the in-class homophily $h_{MM}, h_{mm} \\in \\{0.0, 0.1, \\dots, 1.0\\}$ , and the power-law exponents of the activity distributions $\\gamma_{M} = \\gamma_{m} = 3.0$ . We refer to the minority group as $m$ , and to the majority group as $M$ . Note that the between-class homophily is the complement of the in-class homophily. That is, $h_{Mm} = 1 - h_{MM}$ and $h_{mM} = 1 - h_{mm}$ . Furthermore, an activity score is assigned to every node. This score is drawn from a power-law distribution and determines with what probability the existing node becomes active to create additional links to other nodes. This means that more active nodes possess higher out-degree (see Methods for more details). Each combination of network structure is generated 10 times, nodes are ranked using PageRank and WTF separately, and inequality and inequity scores are computed and averaged across network types (and top-k's for local disparity) for each algorithm. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[253,796,931,938]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 3a illustrates the generation of a network using the DPAH model. First, $n$ labeled nodes are created. In this example $n = 8$ . Then, at time $t$ , node $p$ is selected as source node with a probability proportional to its activity. Then, $p$ connects to an existing node $j$ with a probability related to their pair-wise homophily $h_{pj}$ and preferential attachment that is based on $k_j^{in}$ , the in-degree of node $j$ . By this process, we ensure that the out- and in-degree distributions of nodes follow seemingly power-law distributions that have been observed in many large social networks[31]. The algorithm stops once the network reaches an expected density. Note that source nodes can be either new nodes joining the network for the first time (e.g., node $p$ at time $t$ ) or existing nodes (e.g., node $l$ at time $t + 1$ ). Since the network size is given, \"a node joining the network for the first time\" is a 0-degree node that has been selected to create its first edge. Once a source node connects to a target node successfully, the source node becomes available in the next rounds to become a target candidate. This means that in the beginning the model faces a cold start problem since there are no existing (target) nodes to connect to. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,16,337,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2022) 12:2012 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,631,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-022-05434-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[922,966,929,975]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[117,60,931,191]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 4. The effects of homophily and fraction of minorities in the global disparity of PageRank. Columns represent the fraction of minorities in the network, x-axis indicates the homophily within minorities, and y-axis the homophily within majoritie s. Colors denote the region where the disparity lies in according to our interpretation in Fig. 2. First, we see that, on average, there is never low global inequality (i.e., regions IV to IX—lighter colors—do not appear). This makes sense because these are scale-free networks. Second, depending on the level of homophily within groups, minorities on average can be under-represented (region I, red), or over-represented (region III, blue), or well-represented (region II, green). For example, when $f_{m} = 0.1$ , minorities are on average under-represented when $h_{MM} \\\\geq 0.7$ and $h_{MM} \\\\geq h_{mm}$ . \"]","image_footnote":"[]","img_path":"images/0425/a8d92be36006ce9d30cc4c57ce1bed6a4f5b789b17d3657affc3f9b60c309619.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[255,333,931,375]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Thus, the first $1\\%$ of new edges are between a source node (drawn from the activity distribution) and any other node with probability as in Equation (3). For the sake of completeness we show the computation of local and global disparities of this network in Fig. 3b. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[253,386,931,530]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"How do homophily and directional links influence the ranking of minorities globally and locally? Global disparity. As expected, we found that the Gini coefficient of the rank distributions is large. $Gini_{global} \\geq 0.6$ (regions I, II and III; dark colors) for both PageRank (see Fig. 4) and WTF (see Supplementary Figure S1). As we will see later, this is mainly due to the preferential attachment mechanism $^{32,33}$ . Moreover, we find that on average: (i) Balanced networks ( $f_m = 0.5$ ) can get a fair ranking (green) when both groups possess the same homophily scores ( $h_{MM} = h_{mm}$ ). The same applies for neutral networks ( $h_{MM} = h_{mm} = 0.5$ ) regardless of their fraction of minorities ( $f_m \\leq 0.5$ ). (ii) When the fraction of minorities decreases ( $f_m < 0.5$ ), groups can be fairly represented in the rank in two regimes: First, when both groups are homophilic, homophily within minorities must be higher than homophily within majorities ( $h_{mm} > h_{MM} > 0.5$ ). Second, when both groups are heterophilic, homophily within majorities must be higher than homophily within minorities ( $h_{mm} < h_{MM} < 0.5$ ) to balance the importance of groups. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[253,542,931,748]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Local disparity. We also compute inequality and inequity within each top- $k\\%$ rank in order to see to what extent they ch ange when $k$ increases. In the case of PageRank, we see in Fig. 5 that inequality varies (i.e., from light to dark color or s) in different regimes mainly due to the size of $k$ (x-axis), and inequity due to the interplay between homophily within groups, $h_{MM}$ and $h_{mm}$ . In particular: (i) Only at the top- $5\\%$ of the rank we see a few cases of low inequality (regions VII, VIII and IX; very light colors), this means that nodes at the very top possess very similar ranking scores, but they are very far from the rest of the population, i.e., the larger the top- $k\\%$ , the hig her the Gini (darker colors). This holds for WTF up to roughly the top- $30\\%$ (see Supplementary Figure S2). Overall, PageRank converges to high inequality faster than WTF. (ii) Inequity (regions: red, blue, green) is consistent across all top- $k\\%$ ranks for both algorithms. In other words, if the ranking algorithm favors or harms one group in the top- $5\\%$ , it will continue to do so until converging to the fair regime (regions II, V, VIII; green). With a few exceptions, this fair regime is only reached when $k$ is very large. For example, if a minority group is underrepresented at the top- $5\\%$ , it will remain under-represented at the top- $80\\%$ (see $h_{mm} = 0.1$ and $h_{MM} \\geq 0.7$ in Fig. 5 for PageRank, and Supplementary Figure S2 for WTF). (iii) Minorities are often over-represented when majorities are heterophilic $h_{MM} < 0.5$ ; (regions III, VI, IX; blue). In contrast, minorities are often under-represented when majorities are homophilic $h_{MM} > 0.5$ (regions I, IV, VII; red). This is consistent up to $\\approx$ top- $80\\%$ for both algorithms. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,748,931,801]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In summary, our results suggest that the size of $k$ does not have an influence on inequity. This means that if the algorithm amplifies inequity at the top-5%, it will also amplify inequity at larger top-k%’s. Therefore, increasing the selection pool (larger k) does not improve the representation of minorities. This can be explained by the fact that the preferential attachment mechanism disproportionately affects nodes ranking<sup>12</sup>. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,813,931,943]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Correlation and feature importance. We compute the Spearman correlation between inequality and inequity, and conduct a random forest regression to measure the importance of each network property on both inequality and inequity values (see Supplementary Appendix A.3 for more detail). Results are shown in Table 1 for PageRank and Supplementary Table S2 for WTF. We find that inequality and inequity are positively correlated in both global and local regimes. In other words, the more skewed the rank distribution (i.e., high Gini), the more unfair with either group (i.e., mean error far from zero), and vice versa. This correlation is stronger and more significant in PageRank than in WTF. In terms of feature importance, we find that global inequality (Gini) is mainly explained by both homophily values, whereas g global inequity (ME) is mainly driven by homophily within majorities. Local inequality $(\\text{Gini}_k)$ , however, is mainly explained by the top- $k\\%$ rank, and local inequity $(ME_k)$ by the homophily within the majority group. Notice that we added the variable $\\epsilon$ to verify whether the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,16,337,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2022) 12:2012 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,631,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-022-05434-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[919,965,931,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[147,60,931,586]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 5. The effects of homophily and fraction of minorities in the local disparity of PageRank. Columns represent the fraction of minorities (10%, 30% and 50%) and rows show homophily within minorities (from top to bottom: heterophilic, neutral and homophilic). The x-axis denotes the top-k% rank and the y-axis shows homophily within majorities. Colors refer to the regions of disparity introduced in Fig. 2. One can see that the minority suffers most (red) when the majority is homophilic and the minority is either heterophilic or neutral. Moreover, inequality is lowest (very light colors) only for a few cases at top-5%. This means that the top best ranked nodes are very similar and their ranks are far from the majority of nodes (i.e., due to preferential attachment). Moreover, inequity remains mostly consistent regardless of top-k%. In other words, if the ranking algorithm favors one group in the top-5% (e.g., red or blue), it will continue to do so until entering the fair regime (green). \"]","image_footnote":"[]","img_path":"images/0237/f19bdbd2bc5fa014529fffc51990c63027c90b9998eba4111541e768403467d6.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[258,749,915,828]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0023/3c80f7dc059cb4e4c282fa15516f10f12a97e8e452b6c1c20439e56553b4ecee.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td>Type</td><td>Outcome</td><td>Corr</td><td>R2</td><td>Feature</td><td>Importance</td></tr><tr><td rowspan=\"2\">Global</td><td>Gini</td><td rowspan=\"2\">0.41</td><td>0.91 (0.009)</td><td>hMM, hmm, fm, ε</td><td>0.43, 0.31, 0.21, 0.05</td></tr><tr><td>ME</td><td>0.99 (0.001)</td><td>hMM, hmm, fm, ε</td><td>0.61, 0.31, 0.08, 0.0</td></tr><tr><td rowspan=\"2\">Local</td><td>Gini k</td><td rowspan=\"2\">0.21</td><td>0.95 (0.002)</td><td>k, hMM, hmm, fm, ε</td><td>0.73, 0.11, 0.07, 0.06, 0.03</td></tr><tr><td>MEk</td><td>0.99 (0.001)</td><td>hMM, hmm, k, fm, ε</td><td>0.51, 0.27, 0.14, 0.08, 0.01</td></tr></table>","table_caption":"[\"Table 1. Ten-fold cross-validation for PageRank. We use a Random Forest Regressor to assess feature importance and report the mean and standard deviation of the out-of-sample $R^2$ . Features are ranked in descending order based on their mean importance (from left to right) and highlighted if their importance represents at least $50\\\\%$ of the total importance. Corr shows the Spearman correlation between inequality and inequity scores ( $p$ -values $\\\\approx 0$ ). $\\\\epsilon$ represents random chance. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[65,15,337,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2022) 12:2012 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,631,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-022-05434-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[921,965,931,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[258,61,907,418]","code_body":null,"code_caption":null,"image_caption":"[\"(Mean error of fraction of minorities across all top- $k\\\\%$ ranks) \",\"Figure 6. The effects of homophily and preferential attachment in the global disparity of PageRank. We generated directed networks using four different models of edge formation. DPA: only preferential attachment. DH: only homophily. DPAH: our proposed model that combines DPA and DH. Random: a baseline where nodes are connected randomly. We see the following patterns: (i) Homophily (DH) produces a moderate-to-high level of inequality $(0.3 < Gini < 0.8)$ , while preferential attachment (DPA) produces a consistent moderate inequality $(Gini \\\\approx 0.5)$ . When both mechanisms are combined (DPAH), the rank inequality increases even further $(0.7 < Gini < 0.9)$ . (ii) Random and Preferential attachment (DPA) are always fair $(ME = 0$ or $|ME| \\\\leq \\\\beta)$ , while in the cases where homophily is involved (DH and DPAH) inequity is often high $(|ME| > \\\\beta)$ . Thus, in general preferential attachment is the main driver of inequality, while homophily influences both inequality and inequity. Vertical and horizontal error bars represent the standard deviation over 10 runs of the Gini and ME, respectively. \"]","image_footnote":"[]","img_path":"images/0957/0dddafa223c34bad99f15768a9ffa1a6c237be44d2e3bd2cb9d87ecb4e537abc.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[255,620,931,659]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"network-based features are better than random (see Supplementary Appendix A.3 for more details). In the case of PageRank, all network-based features perform better than by chance. However, randomness seems to be more relevant for explaining rank inequality (Gini) in WTF. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,659,931,723]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"These results are in agreement with what we see in previous figures; even though majority nodes produce most of the inequality and inequity in the rank, their interplay with minority nodes can change or intensify the direction of bias. In fact, both homophily values can explain $75\\%$ (49%) of Gini, the global inequality in PageRank (WTF), 92% (88%) of ME, the global inequity, and 78% (74%) of $ME_{k}$ , the local inequity. However, the top-k% rank together with the homophily within majority nodes explain 84% (86%) of $Gini_{k}$ , the local inequality. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,737,931,801]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"How do different social mechanisms of edge formation contribute to disparity? So far, we show that PageRank and WTF on our network model produce high inequality and a wide-range of possible inequity outcomes. How much of that inequality or inequity was a product of homophily or preferential attachment? To see the effects of these two mechanisms alone, we generate new networks by turning on and off the homophily and preferential attachment features (see Methods for the details of the models). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,801,931,904]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 6 shows the inequality and inequity produced by PageRank on a variety of models: DPA (Directed Preferential Attachment), DH (Directed Homophily), Random, and DPAH (see Supplementary Figure S3 for WTF). Results from both algorithms show that networks whose nodes connect through preferential attachment (DPA) produce on average higher inequality compared to DH and Random. However, when preferential attachment is combined with homophily (DPAH), this inequality increases even further. Additionally, we see that WTF produces higher inequality compared to PageRank (see Supplementary Appendix A.4 for more details). Inequity, on the other hand, is mainly driven by homophily. This means that, homophily (DPAH and DH) influences both, inequality and inequity in both algorithms. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,905,931,943]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Note that in Fig. 6, we fixed the activity of nodes to $\\gamma_{M} = \\gamma_{m} = 3.0$ . However, when we set these parameters to $\\gamma_{M} = \\gamma_{m} < 3.0$ (more active nodes or lower values of $\\gamma$ as found in several scale-free networks<sup>34</sup>), inequality decreases, see Supplementary Figure S5. This behavior holds even if the minority group is the only one increasing ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,15,337,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2022) 12:2012 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,631,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-022-05434-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[922,965,931,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[117,61,932,258]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 7. Global disparity in PageRank on empirical networks. Each column represents an empirical network. Citation/retweet networks (APS and Hate) and Hyper-link networks (Blogs and Wikipedia). Inequality and inequity are shown in the y- and x-axis, respectively. The disparity in ranking that we see in empirical networks are best explained as follows: (i) citation/retweet networks by preferential attachment PA, and (ii) hyper-link networks by preferential attachment and homophily DPAH. \"]","image_footnote":"[]","img_path":"images/0553/6c7a3a3021b12c6d7bc259aa90b23923a6a689d2ac353c43316f0594f99ea456.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[255,365,931,430]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"its activity $(\\gamma_{m} = 1.5 < \\gamma_{M} = 3.0)$ which in turn increases inequity against the majority, see Supplementary Figure S6. Additionally, in Supplementary Figure S4, we see that edge density also plays a role in the inequality produced by PageRank and WTF. This means that, by further adjusting these two parameters (node activity and edge density), we would expect changes only to inequality since inequity is mainly affected by homophily as we saw before. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[253,443,931,638]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Disparities on empirical networks. First, we fit the DPA, DH, and DPAH models to each of the empirical networks in order to find the mechanism that best explains the inequality and inequity found in the rank. The parameters passed to these models are inferred from the real networks and described in Table 3. Second, we rank nodes in the empirical and fitted networks using PageRank and WTF, and compute the disparities (inequality vs. inequity) found in their rank distribution. Results are shown in Fig. 7 for PageRank and Supplementary Figure S9 for WTF. Disparity values from the real-world networks are labeled as empirical (black dot), and disparity values from the fitted networks are labeled according to the model (x marks). We see that each network tells a different story. This can be explained by the nature or domain of these networks. For instance, APS and Hate are best explained by the DPA model. This means that scientists tend to cite authors that have already many citations, and users in Twitter tend to retweet content posted by popular users (i.e., popular in terms of the number of retweets they get). Blogs and Wikipedia on the other hand, are best explained by our DPAH model. Notice that both are hyper-link networks. In other words, people tend to add not only popular references to their Web pages, but also related to their topics (i.e., political leaning in Blogs, and gender in Wikipedia). Note that the Hate network shows the lowest (empirical) inequality. This is due to the fact that it possesses low out-degree exponents $(\\gamma_{M} = 2.2, \\gamma_{m} = 1.7)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[253,650,931,856]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Strategies towards a fair ranking. Results from both algorithms show that while the homophily within majorities is the main driver for inequality and inequity, minorities may overcome unfair rankings by connecting strategically in the network. For instance, when both groups are equally active, minorities should adjust their homophily based on the homophily of the majority. (i) When majorities are homophilic $h_{MM} > 0.5$ , minorities should increase their homophily such that $h_{mm} > h_{MM}$ . (ii) When majorities are (somewhat) neutral ( $h_{MM} = 0.5 \\pm 0.1$ ), minorities may connect arbitrarily with any group without being too homophilic, otherwise they will become over-represented in the rank. (iii) When majorities are heterophilic $h_{MM} < 0.5$ , one solution to achieve a fair rank is to increase the size of the minority group, and make sure that both groups behave similarly in terms of homophily ( $h_{MM} \\approx h_{mm}$ ). Otherwise, minorities will be over-represented regardless of their in-class homophily. On the other hand, when one group is more active than the other, achieving a fair rank becomes challenging. Nevertheless, if the objective is to increase the visibility of minorities in the rank, then the minorities themselves should be more active in the network by creating more connections to increase their out-degree. Note that these \"strategies\" without algorithmic intervention may work in scenarios such as a citation or collaboration networks, but they might not work in other scenarios. In such cases, we need additional recommender systems to help under-represented groups discover those \"strategic\" links that will help them climb to higher ranks. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,870,477,883]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Discussion and future work ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,884,931,937]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this work we have proposed a systematic study to measure the inequality and inequity produced by PageRank and Who-To-Follow (WTF). Our approach disentangles the effect of network structure on the rank distributions of these two algorithms by using synthetic networks. By doing so, we control for the properties of the network and measure how these changes affect the rankings. In particular, we studied six prominent structural properties ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,16,337,30]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2022) 12:2012 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,631,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-022-05434-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[921,965,931,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[260,61,931,189]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"of social networks: homophily, preferential attachment, fraction of minorities, edge density, node activity and the directionality of links. We found that the systemic bias produced by these algorithms in the rank is mainly due to homophily imbalance ( $h_{MM} \\gg h_{mm}$ or $h_{mm} \\gg h_{MM}$ ) for inequity, and the interplay between our six properties of interest for inequality. Consequently, our systematic study makes PageRank and Who-To-Follow interpretable and explainable since our results show the necessary structural conditions to achieve a fair rank. A potential avenue to reduce inequity is to then create synthetic connections before the ranking as it is done for correcting the class imbalance problem in supervised learning<sup>35</sup>. Alternatively, these conditions or strategic connections may be added into the network to change its structure as a collective fairness intervention. For instance, recommender systems could suggest relevant articles not only based on popularity and (keyword) similarity but also based on fairness by fulfilling diversity constraints. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,189,931,393]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Notice that our model simplifies the role of homophily and minorities. First, it assumes that all nodes of the same group have the same in-class and between-class homophily. This means that rich mixing patterns might get ignored since some nodes can exhibit local differences $^{36}$ . Second, while there exist multiple definitions of minorities $^{37}$ we adopted the one by Italian jurist Francesco Capotorti: \"a group numerically inferior to the rest of the population of a State, in a non-dominant position...\" $^{38,39}$ . However, we constrained this population to all nodes in a given network (neither the State nor the world population). Notice as well that the ranking amplifies the representation of minorities by reducing the representation of majorities in top ranks (e.g., when the majority is heterophilic, see Fig. 1). This aligns with the definition of minorities by Wirth $^{40}$ that implies that \"minorities objectively occupy disadvantageous positions in society\". This means that \"a minority may actually, from a numerical standpoint, be the majority\" (e.g., people living in poverty in under-developed countries). In other words, under these two definitions, being in disadvantage in the top- $\\mathbf{k}\\%$ (inequity) is not a group size issue only, but a combination of group size and homophily as we have previously shown. More complex definitions of minorities are out of the scope of this paper. A further limitation is that we focus on a single binary attribute (e.g., color $\\in$ {Black, White}), this means that multiple sources of inequality and inequity (e.g., intersections of disadvantage such as being poor and of color) cannot be captured at once $^{41}$ . Addressing these issues is beyond the scope of this paper and we leave them for future work. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,393,931,471]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, we disentangled the individual effects of preferential attachment and homophily in the rank by comparing the disparities of our proposed DPAH model with two variants and a baseline: networks with preferential attachment only (DPA), networks with homophily only (DH), and directed Erdős-Rényi (Random) $^{42}$ graphs. Further research can investigate other topologies and social mechanisms of edge formation such as clustering $^{43}$ , transitivity $^{44}$ , and reciprocity $^{45}$ . Similarly, other structural properties such as monophily $^{46}$ and second order homophily $^{47}$ can be studied to measure their influence on ranking. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,484,354,497]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conclusions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[260,500,931,575]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this work we have investigated under which conditions PageRank and Who-To-Follow (WTF) reduce, replicate or amplify the representation of minorities in top ranks. In particular, given the rank distribution produced by these algorithms, we computed inequality as the dispersion among individuals in terms of ranking scores, and inequality as whether minorities are over-, under- or well-represented in top ranks compared to their representation in the network. We studied these two metrics separately and in combination to better understand the mechanisms that can explain them. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,576,931,664]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To that end, we proposed DPAH, a growth network model that allows to generate realistic scale-free directed networks with different levels of homophily, fraction of minorities, node activity, and edge density. In these networks, we found that both inequality and inequity are positively correlated and mainly driven by the homophily within majorities. This means that, when the majority group is highly homophilic, the minority group is underrepresented in top ranks. Also, when the majority is highly heterophilic, the minority benefits tremendously since it is over-represented in the top- $k\\%$ . However, minorities can overcome these disparities by connecting strategically with others. Thus, equity in ranking is a trade-off between homophily and the fraction of minorities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,666,931,716]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Our systematic study makes PageRank and Who-to-Follow explainable and interpretable to help data scientists understand and estimate the disparity that these algorithms produce given the structure of networks, which is key for proposing targeted interventions. We hope our results create awareness among majority and minority groups about these disparities since they may replicate and even amplify the biases found in social networks. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,730,408,742]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data and methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[260,744,931,884]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Synthetic networks. Network models have been proposed with various social mechanisms. For instance, the classic stochastic-block model<sup>48</sup> which allows for homophily between and across groups, and the configuration model<sup>49</sup> which generates links among nodes by preserving a given degree distribution. On the other hand, the preferential-attachment model<sup>25</sup> produces scale-free networks due to cumulative advantage<sup>50</sup>. Although these models can reproduce certain properties of real-world networks such as degree or homophily, they fail at guaranteeing similar visibility of minorities as their empirical counterpart. In this direction, Karimi et al.<sup>13</sup> and Fabbri et al.<sup>14</sup> devise social network models with preferential attachment, adjustable homophily and fraction of minorities. They demonstrate how the degree rank of the minority group in a network is a function of the relative group sizes and the presence or absence of homophily. However, the former models undirected networks, and the latter did not control for edge density and node activity (i.e., power-law out-degree distributions) as we do in this work for minority and majority groups. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,900,931,939]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Directed network. We define a directed network as: Let $G = (V, E, C)$ be a node-attributed unweighted graph with $V = \\{v_1, \\dots, v_n\\}$ being a set of $n$ nodes, $E \\subseteq V \\times V$ a set of $e$ directed edges, and $C = \\{c_1, \\dots, c_n\\}$ a list of binary class labels where each element $c_i$ represents the class membership of node $v_i$ . The fraction of minorities ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,16,337,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2022) 12:2012 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,631,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-022-05434-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[921,965,931,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"9 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[255,61,931,113]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$f_{m}$ captures the relative size of the minority class—with respect to $C$ —in the network. We refer to the minority group as $m$ , and to the majority group as $M$ . A network is balanced when all class labels have the same number of nodes ( $f_{m} = 0.5$ ), otherwise it is unbalanced ( $f_{m} < 0.5$ ). Networks fulfill a predefined edge density level $d$ . Since $n$ and $d$ are given, networks stop growing when $e = dn(n - 1)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,112,931,202]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In order to generate directed links, inspired by the activity-driven network model $^{51}$ , we assign an activity score to each node that determines with what probability the existing node becomes active and creates additional links to other nodes. It has been shown that in empirical networks the activity of the nodes follows a power-law distribution $^{51}$ . Therefore, we assign an activity to each node drawn from a power-law distribution $\\rho(\\gamma) = X^{-\\gamma}$ . Note that each group possesses its own activity distribution and they are defined by its power-law exponent $\\gamma_{M}$ and $\\gamma_{m}$ for majority and minority nodes, respectively. The level of activity of a group is inversely proportional to $\\gamma$ . That is, groups with higher out-degree produce lower $\\gamma$ (more skewed). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,202,931,242]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Then, the probability of connecting a source (active) node $\\nu_{i}$ to a target node $\\nu_{j}$ (or in other words the probability of connecting to $\\nu_{j}$ given the source node $\\nu_{i}$ ) is explained by any of the following three mechanisms of edge formation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,255,931,309]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Preferential attachment (DPA). Also known as the rich-get-richer effect or cumulative advantage in social networks[25,50]. It indicates that nodes tend to connect to popular nodes. We define popularity as the in-degree of the node. Therefore, the probability that a source node $\\nu_{i}$ connects to a target node $\\nu_{j}$ is proportional to the in-degree of the target node $\\nu_{j}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[499,315,931,352]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP (i \\rightarrow j) = P (j \\mid i) = \\frac {k _ {j} ^ {\\text {i n}}}{\\sum_ {l = 1} ^ {N} k _ {l} ^ {\\text {i n}}} \\tag {1}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[255,374,931,503]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Homophily (DH). It is the tendency of individuals to connect (or interact) with similar others $^{24,49}$ . Thus, the probability that a source node $\\nu_{i}$ connects to a target node $\\nu_{j}$ is driven by the homophily between their classes $c_{i}$ and $c_{j}$ . We assign a homophily value to each dyad based on pre-defined homophily parameters within majorities and minorities, $h_{MM}$ and $h_{mm}$ , respectively. Homophily values range from 0.0 to 1.0. If the homophily value is high, that means that nodes of the same class are attracted to each other more often than nodes of different attributes. Following the definitions from previous work $^{13,14,52}$ , nodes of the same class with homophily $h_{aa} = 0.5$ are referred to as neutral (i.e., they connect randomly to either class), otherwise they are heterophilic if $h_{aa} < 0.5$ (i.e., more likely to connect to the other class), or homophilic when $h_{aa} > 0.5$ (i.e., more likely to connect to the same class). Note that in- and between-class homophily values are complementary: $h_{mm} = 1 - h_{mM}$ and $h_{MM} = 1 - h_{Mm}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[499,511,931,544]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP (i \\rightarrow j) = P (j \\mid i) = \\frac {h _ {i j}}{\\sum_ {l = 1} ^ {N} h _ {i l}} \\tag {2}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[255,566,931,618]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Preferential attachment with homophily (DPAH). We propose DPAH, a directed growth network model with adjustable homophily and fraction of minorities. DPAH stands for Directed network with Preferential Attachment and Homophily. This mechanism combines DPA and DH, and is an extension of the BA-Homophily model<sup>13</sup>. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[490,627,931,663]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP (i \\rightarrow j) = P (j | i) = \\frac {h _ {i j} k _ {j} ^ {i n}}{\\sum_ {l = 1} ^ {N} h _ {i l} k _ {l} ^ {i n}} \\tag {3}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[255,671,931,749]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Note that DPA and DH are especial cases of DPAH where only the in-degree mechanism varies. This means that, the out-degree distribution remains the same as in DPAH: it is driven by the activity model. Additionally, we include a random model where both source and target nodes are chosen at random (i.e., directed Erdos-Renyi model $^{42}$ ). Table 2 shows the parameters adjusted in each model. Number of nodes $n$ and edge density $d$ are arbitrary in the sense that they are not part of the edge formation mechanism. Thus, we fix them to make a fair comparison across all models. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,762,931,791]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Empirical networks. We inspect four networks from different domains and compute the inequalities and inequities produced by PageRank and WTF. Table 3 shows the most important properties of these networks. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,804,931,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- APS: The American Physical Society citation network wh os nodes represent articles, and edges represent citations. The binary class of each node is pacs and encodes two different Physics sub-field s w he re 05.20.-y (C la ssical statistical mechanics) is the minority. \",\"- Hate: A retweet network<sup>53</sup> where nodes denote users, and edges represent ret weets among them. Users are labeled as either hateful or normal depending on the sentiment of their tweets. Hateful users represent the minority. \",\"- Blogs: An hyper-link network from political blog posts about the 2004 U.S. election<sup>54</sup>. Nodes represent blog pages, and edges hyper-links among them. Each blog is labeled as either right- or left-leaning. The latter represents the minorities. \"]","page_idx":"9","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[65,16,337,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2022) 12:2012 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,633,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-022-05434-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[914,966,929,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[258,62,678,184]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0624/9981a67fc4c0d56fa9ba9b99dda75396d78f37d6959dba3c4c68a885db07b6f3.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":"<table><tr><td></td><td>Random</td><td>DPA</td><td>DH</td><td>DPAH</td></tr><tr><td>n</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>fm</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>d</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>hMM</td><td>-</td><td>-</td><td>✓</td><td>✓</td></tr><tr><td>hmm</td><td>-</td><td>-</td><td>✓</td><td>✓</td></tr><tr><td>γM</td><td>-</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>γm</td><td>-</td><td>✓</td><td>✓</td><td>✓</td></tr></table>","table_caption":"[\"Table 2. Model parameters. Check marks denote that a given model (column) requires a particular parameter (row): number of nodes $n$ , fraction of minorities $f_{m}$ , edge density $d$ , in-class homophily $h_{aa}$ , and the power-law exponent of the activity distribution $\\\\gamma$ . Sub-indices $M$ and $m$ refer to the majority and minority groups, respectively. The difference between DH and DPAH is the preferential attachment (in-degree) mechanism. All models produce directed networks. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[258,301,546,528]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0676/3441350ea3d4b37a8e721e4f9501b73b103cef405f3453e6997739c5faa8702f.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":"<table><tr><td>Dataset</td><td>APS</td><td>Hate</td><td>Blogs</td><td>Wikipedia</td></tr><tr><td>n</td><td>1853</td><td>4971</td><td>1224</td><td>3159</td></tr><tr><td>Class</td><td>pacs</td><td>hate</td><td>leaning</td><td>gender</td></tr><tr><td>M</td><td>05.30.-d</td><td>normal</td><td>right</td><td>male</td></tr><tr><td>m</td><td>05.20.-y</td><td>hateful</td><td>left</td><td>female</td></tr><tr><td>fm</td><td>0.37561</td><td>0.10943</td><td>0.48039</td><td>0.15226</td></tr><tr><td>d</td><td>0.00106</td><td>0.00061</td><td>0.01271</td><td>0.00149</td></tr><tr><td>γM</td><td>3.22246</td><td>2.23026</td><td>4.88733</td><td>4.22425</td></tr><tr><td>γm</td><td>8.93993</td><td>1.73445</td><td>3.22464</td><td>6.16567</td></tr><tr><td>EMM</td><td>0.64981</td><td>0.56898</td><td>0.47070</td><td>0.78469</td></tr><tr><td>EMm</td><td>0.02859</td><td>0.10244</td><td>0.04741</td><td>0.07824</td></tr><tr><td>EmM</td><td>0.02721</td><td>0.07886</td><td>0.04105</td><td>0.10685</td></tr><tr><td>Emm</td><td>0.29439</td><td>0.24972</td><td>0.44084</td><td>0.03022</td></tr><tr><td>hMM</td><td>0.94000</td><td>0.58000</td><td>0.92000</td><td>0.59000</td></tr><tr><td>hmm</td><td>0.96000</td><td>0.95000</td><td>0.90000</td><td>0.62000</td></tr></table>","table_caption":"[\"Table 3. Empirical Networks. APS, a scientific citation network. Hate, a retweet network. Blogs, a political blog hyper-link network. Wikipedia, a hyper-link network of politicians. Each row represents a property of the network. $E_{**}$ represents the fraction of edges within and across groups, and $h_{**}$ homophily values inferred by the DPAH model (see Supplementary Appendix A for derivations). \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[257,636,931,664]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"- Wikipedia: A Wikipedia hyper-link network where nodes represent U.S. politicians $^{55,56}$ labeled as either male or female. Female politicians re present the minorities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,705,931,824]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Ranking and recommendation algorithms. There exist a variety of ranking and recommendation algorithms that follow different strategies depending on the nature of the problem. For instance, in information systems, items such as content, Web pages, and products are ranked to recommend users what to read or buy[57]. In social networks, however, people are ranked to identify their hierarchy or importance[54-60], and recommended to other users in order to establish new connections[61-64]. These rankings and recommendations are based on algorithms that often rely on whom we are already connected with. In this work, we focus on two such algorithms widely used in practice[65]: PageRank[1] and Who-to-Follow (WTF)[8]. While PageRank determines the global ranking of nodes in comparison with all other nodes, WTF deals with ranking nodes in a node level and thus remains a local measure. For that reason, we focus on these two algorithms to capture both dimensions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,837,931,888]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PageRank . It was invented to rank all web pages in the Web<sup>11</sup>, and has been used in several applications<sup>65</sup>. For example, to study citation and co-authorship networks<sup>66-68</sup>. PageRank assigns an importance score to every single node in a network. This score takes into account the number and quality of incoming links of each node. The PageRank of node $i$ is defined as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[495,897,931,932]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP R (i) = (1 - \\alpha) + \\alpha \\sum_ {j \\in N _ {i}} \\frac {P R (j)}{k _ {j} ^ {\\text {o u t}}} \\tag {4}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[65,16,337,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2022) 12:2012 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,633,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-022-05434-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[914,965,929,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"11 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[255,62,932,116]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $i \\in V$ , $N_{i}$ represents all neighbors of node $\\nu_{i}$ (e.g., all nodes $\\nu_{i}$ points to), and $k_{j}^{out}$ the out-degree of node $\\nu_{j}$ . The damping factor $\\alpha$ , or probability of following links using a Random Walker, is set to 0.85 as suggested by Brin and Page[69]. We use the fast-pagerank[70] python package to compute the PageRank score of all nodes using sparse adjacency matrices. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,127,931,232]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Who-to-follow (WTF). This recommendation algorithm was created and used by Twitter to suggest new people to follow. It is based on SALSA which in turn is based on Personalized PageRank. In a nutshell, for each user $u$ (or node $\\nu_{i} \\in V$ ), the algorithm looks for its circle of trust, which is the result of an egocentric random walk (similar to personalized PageRank). Then, based on this circle-of-trust, the algorithm ranks all users that are not yet friends with $u$ but are connected through the circle of trust. Then, we take the top-k of these (recommended) users, and add up the counter of being selected as a recommendation to each of them. This is done for every node $u$ in the network. At the end, the rank of each node encodes the number of times a user was suggested as a recommendation across all nodes in the network. Thus, the WTF score for each node is defined as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,239,931,269]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nW T F (i) = \\sum_ {j \\in V} \\mathbb {1} _ {S A L S A (j)} (i) \\tag {5}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[255,277,932,317]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $SALSA(j)$ refers to the top-k users the SALSA algorithm recommends to node $j$ . In this work we select the top-10 users as recommendations. $\\mathbb{1}_A(x)$ denotes the indicator function or boolean predicate function to test set inclusion (i.e., whether $x \\in A$ ). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,329,931,395]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Gini coefficient. The Gini coefficient was developed by the Italian Statistician Corrado Gini<sup>73</sup> to measure the income inequality of a society. It is defined as the mean of absolute differences between all pairs of individuals for some measure. In our setup this measure is the score given to every node by PageRank and Who-To-Follow. The minimum value is 0 when all individuals' scores are equal, and its maximum value is 1 when there is a big gap or discrepancy between scores<sup>74</sup>. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[275,395,823,407]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We define the Gini coefficient of the rank distribution $X$ as follows. For more details see<sup>75</sup>: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[494,416,931,453]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nG i n i (X) = \\frac {\\sum_ {i = 1} ^ {\\hat {n}} (2 i - \\hat {n} - 1) x _ {i}}{n \\sum_ {i = 1} ^ {\\hat {n}} x _ {i}} \\tag {6}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[255,460,931,488]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $x \\in X$ is an observed value in the rank distribution, $\\hat{n} = |X|$ is the number of values observed, and $i$ is the rank of values in ascending order. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,497,394,512]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data availability ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,512,931,539]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The code and datasets generated during and/or analyzed during the current study are available in the GitHub repository, https://github.com/gesiscs/Homophilic_Directed_ScaleFree_Networks. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,549,589,563]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received: 16 September 2021; Accepted: 7 January 2022 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,563,467,576]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Published online: 07 February 2022 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[260,590,349,604]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[265,604,929,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1. 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Identifying a set of influential spreaders in complex networks. Sci. Rep. 6, 27823 (2016). \",\"65. Gleich, D. F. Pagerank beyond the web. SIAM Rev. 57, 321-363 (2015). \",\"66. Liu, X., Bollen, J., Nelson, M. L. & Van de Sompel, H. Co-authorship networks in the digital library research community. Inf. Process. Manag. 41, 1462-1480 (2005). \",\"67. Jezek, K., Fiala, D. & Steinberger, J. Exploration and evaluation of citation networks. In ELPUB, 351-362 (2008). \",\"68. Fiala, D., Rousselot, F. & Jezek, K. Pagerank for bibliographic networks. Scientometrics 76, 135-158 (2008). \",\"69. Brin, S. & Page, L. The anatomy of a large-scale hypertextual web search engine. Comput. Netw. ISDN Syst. 30, 107-117 (1998). \",\"70. Sajadi, A. Fast personalized pagerank implementation. https://github.com/asajadi/fast-pagerank (2019). Accessed 30 Mar 2021 \",\"71. Lempel, R. & Moran, S. Salsa: the stochastic approach for link-structure analysis. ACM Trans. Inf. Syst. (TOIS) 19, 131-160 (2001). \"]","page_idx":"12","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[65,15,337,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2022) 12:2012 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,631,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-022-05434-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[914,966,929,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"13 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[257,61,932,136]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"72. Jeh, G. & Widom, J. Scaling personalized web search. In Proceedings of the 12th international conference on World Wide Web, 271-279 (2003). \",\"73. Gini, C. Variabilità e mutabilità. Repr. Memorie di metodologica statistica (Ed. Pizetti E (1912). \",\"74. Ceriani, L. & Verme, P. The origins of the gini index: extracts from variabilità e mutabilità (1912) by corrado gini. J. Econ. Inequal. 10, 421-443 (2012). \",\"75. StatsDirect. Gini coefficient of inequality. https://www.statsdirect.com/help/default.htm#nonparametric_methods/gini.htm. Accessed on 09 Nov 2020. \"]","page_idx":"13","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[257,149,421,164]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgements ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,164,932,228]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Special thanks to Nicola Perra, Indira Sen, Mattia Samori, Reinhard Munz who have helped improving this paper and to Antonio Ferrara and Jan Bachmann for their technical support on the revisions of this paper. Also, thanks to LXAI@ICML2020, NetSci2020, and WiDS Guayaquil@ESPOL for their feedback. This work was partially funded by the Austrian Science Promotion Agency FFG project no. 873927. The presented computational results have been achieved in part using the Vienna Scientific Cluster (VSC). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,237,430,251]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Author contributions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,251,932,305]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"L.E.N., F.K., C.W. and M.S. devised the research project. L.E.N. conceived the experiments and analyzed the datasets. F.K. performed analytical derivations. L.E.N., F.K., C.W., and M.S. wrote the paper. All authors reviewed the manuscript. Parts of L.E.N and M.S.'s work on this project have been performed while being at GESIS and RWTH Aachen, respectively. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,317,425,332]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Competing interests ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[257,332,526,345]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The authors declare no competing interests. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,355,445,369]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Additional information ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[255,370,932,393]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Supplementary Information The online version contains supplementary material available at https://doi.org/10.1038/s41598-022-05434-1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,401,692,414]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Correspondence and requests for materials should be addressed to F.K. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,421,747,434]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Reprints and permissions information is available at www.nature.com/reprints. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,439,931,465]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,471,332,494]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0072/69fe8d617e02875965310298bb154f4674e564cb261c4a3ee9cb6fe15fdd348a.jpg","list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[334,471,931,497]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[255,498,931,575]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[257,586,394,599]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"© The Author(s) 2022 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[65,16,337,31]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"www.nature.com/scientificreports/ ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[65,965,290,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Scientific Reports (2022) 12:2012 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[381,965,631,978]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1038/s41598-022-05434-1 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[786,964,880,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"natureportfolio ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[914,966,929,976]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"14 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[154,166,238,189]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"OPEN \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[258,164,880,278]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Inequality and inequity in network-based ranking and recommendation algorithms \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,283,899,301]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lisette Espín-Noboa $^{1,2,3}$ , Claudia Wagner $^{1,4,5}$ , Markus Strohmaier $^{1,4,6}$ & Fariba Karimi $^{2}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,310,919,524]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Though algorithms promise many benefits including efficiency, objectivity and accuracy, they may also introduce or amplify biases. Here we study two well-known algorithms, namely PageRank and Who-to-Follow (WTF), and show to what extent their ranks produce inequality and inequity when applied to directed social networks. To this end, we propose a directed network model with preferential attachment and homophily (DPAH) and demonstrate the influence of network structure on the rank distributions of these algorithms. Our main findings suggest that (i) inequality is positively correlated with inequity, (ii) inequality is driven by the interplay between preferential attachment, homophily, node activity and edge density, and (iii) inequity is driven by the interplay between homophily and minority size. In particular, these two algorithms reduce, replicate and amplify the representation of minorities in top ranks when majorities are homophilic, neutral and heterophilic, respectively. Moreover, when this representation is reduced, minorities may improve their visibility in the rank by connecting strategically in the network. For instance, by increasing their out-degree or homophily when majorities are also homophilic. These findings shed light on the social and algorithmic mechanisms that hinder equality and equity in network-based ranking and recommendation algorithms. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,546,931,714]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Online social networks and information networks have become integral parts of our everyday life. However, the opportunities offered by such networks are often constrained not only by our previous interactions $^{1-5}$ , but also by algorithms. For instance, algorithms could make some people or content more visible than others via classification $^{6}$ , ranking or recommendations $^{7}$ . In this regard, search engines and recommender systems are increasingly used for various applications such as whom to follow, whom to cite, or whom to hire. Typically, these applications use algorithms to order items (e.g., people and academic papers) based on \\\"importance\\\" or \\\"relevance\\\", and may therefore produce social inequalities by discriminating certain individuals or groups of people in top ranks. In fact, it has been shown that recommender systems such as Who-to-Follow (WTF) $^{8}$ tend to increase the popularity of users who are already popular $^{7,9,10}$ . A similar effect has been found in PageRank $^{11}$ , where nodes in high ranks stabilize their position and give little opportunity to other nodes to occupy higher positions $^{12}$ . This tendency towards the \\\"popular\\\" arises because these algorithms harness structural information, in particular, the in- and out-degree of nodes. For this reason, modeling the directionality of links—which is often left out for simplicity—is crucial to really understand how these algorithms work on different types of networks. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,713,931,869]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, social networks are complex systems, and many other structural properties may also alter the distribution of nodes and groups in the ranking. For example, previous studies have shown that homophily—the tendency to connect to similar others— affects the visibility of minorities in degree rankings<sup>13</sup> and people recommender systems<sup>14</sup>. Consequently, it can reinforce societal issues such as the glass ceiling effect<sup>15-17</sup> and the invisibility syndrome<sup>18</sup>. Despite these findings, little is known about the extent to which the combination of multiple structural properties can alter the visibility of minorities in top ranks from ranking and recommendation algorithms. A further complication is that debiasing ranking outcomes and making them fair is very challenging since they can be mitigated in different ways<sup>19</sup>: by intervening on the score distribution of candidates<sup>20</sup>, on the ranking algorithm<sup>21</sup>, or on the ranked outcome<sup>22</sup>. While most of these studies tackle fairness in ranking, they do not explore the effects of networked data in ranking. This paper is a step towards this goal. Since such algorithms are so deeply involved in social, economic, and political processes, we need to first understand how our connections affect them to then apply appropriate interventions towards fair results. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,904,931,943]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"<sup>1</sup>Complexity Science Hub, Vienna, Austria. <sup>2</sup>Central European University, Vienna, Austria. <sup>3</sup>University of Koblenz-Landau, Koblenz, Germany. <sup>4</sup>GESIS - Leibniz Institute for the Social Sciences, Cologne, Germany. <sup>5</sup>RwTH Aachen University, Aachen, Germany. <sup>6</sup>University of Mannheim, Mannheim, Germany. <sup>7</sup>email: karimi@csh.ac.at \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[652,14,922,30]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[63,63,453,104]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"scientific reports \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[810,136,831,154]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"# \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[836,140,927,150]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Check for updates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,282,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2022) 12:2012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[376,965,633,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-022-05434-1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[919,966,931,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[115,60,932,516]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 1. Inequality and inequity. Every column represents a network with certain level of homophily. All networks contain 20 nodes: $20\\\\\\\\%$ belong to the minority group (orange), and $80\\\\\\\\%$ to the majority group (blue). Edges follow a preferential attachment with homophily mechanism. The top row shows the graph and the level of homophily within groups (MM: majorities and mm: minorities). The second row shows all nodes in descending order (from + to -) based on their PageRank scores. The third row represents the rank inequality: Gini coefficients of the rank distribution for every top- $k\\\\\\\\%$ (black line). Gini global refers to the Gini coefficient of the entire rank distribution (i.e., at top- $100\\\\\\\\%$ ). We see that the lower the $k$ , the lower the Gini of the rank distribution. The bottom row represents the rank inequity: Percentage of minorities found in each top- $k\\\\\\\\%$ of the rank distribution (orange line). ME is the mean error of these percentages compared to a fair baseline or diversity constraint (i.e., how much the orange line deviates from the dotted line across all top-k's). Here we see three main patterns: (a, b) When the majority group is heterophilic, minorities are on average over-represented, $ME > 0.0$ . (d, e) When majorities are homophilic, minorities are on average under-represented, $ME < 0.0$ . (c) When both groups are neutral, the observed fraction of minorities is almost as expected, $ME \\\\\\\\approx 0$ . \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0778/8ea6f6734dd3070088e6f70fa8a185fe2e5568e019936e8983c7b2b4ade0dbdf.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[253,716,931,882]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To this end, we propose DPAH, a network model that generates directed scale-free networks with binary-attributed nodes. It encodes two main mechanisms of edge formation found in social networks: homophily and preferential attachment[23-25] (see Methods for more details). Moreover, it allows to control for the fraction of minorities, edge density, and the skewness of the out-degree distribution. By using this model, we systematically study how these structural properties of social networks impact the ranking of nodes in PageRank and WTF. In particular, we investigate two ranking issues, inequality and inequity, and show how they get affected by the ranking algorithm together with the type of network. We measure inequality by quantifying the skewness of the rank distribution of nodes that PageRank and WTF produce, and inequity as how well-represented the minorities are in the top of the rank compared to the proportion of minorities in the network. In this work we study both ranking issues and measure their correlation. Furthermore, we quantify them globally using the whole rank distribution, and locally within each top- $k\\\\%$ rank. The goal is to identify both the overall inequality and inequity trend that these algorithms produce, and the tipping points where minorities start gaining visibility in the top of the rank. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,883,931,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As an example, consider the directed networks shown in Fig. 1. Every column represents a network with two types of nodes, minority (orange) and majority (blue), and different levels of homophily within groups. Homophily $h$ , is a parameter ranging from 0 to 1 and determines the tendency of two nodes of the same color to be connected. $h_{MM}$ and $h_{mm}$ represent homophily within majorities and minorities, respectively. When nodes \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,15,337,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2022) 12:2012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,631,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-022-05434-1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[921,965,931,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[258,60,806,400]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 2. Regions of disparity. We measure inequality (y-axis) as the skewness of the rank distribution, and inequality (x-axis) as the mean differences between the proportional representation of groups in top-k% ranks and the network. Highly skewed distributions lie in regions I to III (darker colors), and fair rankings, where minorities are well represented in top ranks, lie in regions II, V, VIII (green). We set $\\\\\\\\beta = 0.05$ which is arbitrary and allows for a flexible region of group fairness. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0343/7887338b38211d3fa3eb37117cbe74eddb1e4fcf7ea3b6edead31ea17ba7dc4d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[255,507,931,572]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"are ranked using PageRank (second row), the position of the minorities in the rank varies systematically. For instance, when majorities are heterophilic ( $h_{MM} = 0.2$ , columns a and b), minorities often appear at the top (+). In contrast, when majorities are homophilic ( $h_{MM} = 0.8$ , columns d and e), minorities tend to appear at the tail of the rank (-). Next, we explain this systematic ranking behavior in top ranks by further varying the structure of the network. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,585,319,598]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,599,931,740]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Inequality and inequity in ranking. Inequality refers to the dispersion or distribution of importance among individuals. This importance is the ranking score assigned to every node by the algorithm. We compute the Gini coefficient of the rank distribution to measure how far the ranking scores of individuals deviate from a totally equal distribution (see Methods for more details). As shown in Fig. 2, a very low Gini score ( $\\\\text{Gini} < 0.3$ ) means that individuals are very similar with respect to their ranking scores. If the Gini score is extremely high ( $\\\\text{Gini} \\\\geq 0.6$ ), it means that only a few individuals capture most of the rank. In other words, the rank distribution is very skewed. Values in between ( $0.3 \\\\leq \\\\text{Gini} < 0.6$ ) represent moderate skewed distributions. Note that we measure inequality globally by using the whole rank distribution, and locally for each top- $k\\\\%$ . From our example in Fig. 1, we see that PageRank on average generates moderate skewed ranking distributions for all the depicted networks ( $\\\\text{Gini}_{\\\\text{global}} \\\\approx 0.5$ ). However, for very small top- $k\\\\%$ 's, the Gini is very low. This means that the top individuals possess very similar ranking scores. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,740,931,934]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Inequity refers to group fairness. In particular, it measures the error distance between the fraction of minorities in the top- $k\\\\%$ and a given fair baseline (e.g., a diversity constraint or quota). This baseline may be adjusted depending on the context of the application[19,26,27]. Here, a ranking is fair when its top- $k\\\\%$ preserves the proportional representation of groups in the network (i.e., equivalent to demographic parity[19,28]). Therefore, the error represents the local inequality at each top- $k\\\\%$ , and $ME$ the mean of these errors across all top- $k\\\\%$ ranks or global inequality. As shown on the last row of Fig. 1, we measure the local inequality in two steps. First, we compute the fraction of minorities that appear in each top- $k\\\\%$ rank (orange line). Second, we compute the error between the observed fraction of minorities in each top- $k\\\\%$ rank and a fair baseline (e.g., the actual fraction of minorities in the network, in this example $20\\\\%$ ). Then, we average these error scores across all top- $k\\\\%$ ranks to determine the global inequality score ( $ME$ values). Ideally, a fair ranking should reach $ME = 0$ . However, in order to allow for small fluctuations we introduce the smoothing factor $\\\\beta$ . Thus, a fair ranking is such that $-\\\\beta \\\\leq ME \\\\leq \\\\beta$ . The value of $\\\\beta$ is arbitrary, and allows for a smooth definition of \\\"low mean error\\\" or fairness. We set $\\\\beta = 0.05$ . As shown in Fig. 2, when $ME > \\\\beta$ , then minorities are over-represented in the top- $k\\\\%$ (blue region). When $ME < -\\\\beta$ , then minorities are under-represented (red region), otherwise the ranking is representing very well the minorities in the top of the rank (green region). Alternatively, we can say that the top rank (i) replicates the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,15,337,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2022) 12:2012 \",\n \"text_format\": null,\n \"text_level\": null,\n 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\"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"minority (25%) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[159,95,263,109]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"majority (75%) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[285,67,310,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"h++ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[287,80,379,118]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"m M Source M 0.1 0.9 m 0.3 0.7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[314,80,490,273]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"target \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0723/3728ebd66a3760b9bc8f5c9d2648a2c2c8c20c10a6487551a6dca911be182342.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[115,124,292,273]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0517/87e51e47c08c81e8ffe0bda1e7e7eb69c1bc656d272f905e23081b2702412244.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[531,67,932,277]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"b) \\\",\\\"Figure 3. DPAH model and ranking of nodes. (a) Illustration of the directed network model with preferential attachment and homophily (DPAH). First, $n = 8$ nodes are created and randomly labeled according to the fraction of minorities $f_{m} = 0.25$ . Then, the following algorithm repeats until a desired edge density is fulfilled. At time $t$ , a source node $p$ is drawn from a power-law (activity) distribution, and a target node $j$ is drawn with a probability proportional to the product of its in-degree $K_{j}^{in} = 4$ and the pair-wise homophily $h_{pj} = h_{mM} = 0.9$ . At time $t + 1$ , a new edge is added between nodes $l \\\\\\\\rightarrow o$ based on the same mechanism. (b) The PageRank score of each node is shown under $PR$ . Nodes in each top- $k\\\\\\\\%$ of the rank are grouped based on the unique PageRank scores. In this example, the top- $60\\\\\\\\%$ of nodes concentrate most of the PageRank and their scores are somewhat similar (i.e., low Gini). Also, the ranking is fair from top- $80\\\\\\\\%$ onwards, since they capture the same fraction of minorities as in the population, $25\\\\\\\\%$ . Local values are measured per top- $k\\\\\\\\%$ , and global values are measured using the whole distribution for inequality (Gini), and the average across all top- $k\\\\\\\\%$ ranks for inequity (mean error). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0760/1ed34b5a67a96cd4b9349a08e19b3215e6aa1513c4312fb1e16407a1a94e7890.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[255,461,931,526]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"proportional representation of groups when $ME$ is zero or very low, (ii) amplifies the representation of minority nodes when $ME > \\\\beta$ , and (iii) reduces the representation of minority nodes—and benefits the majority group—when $ME < -\\\\beta$ . Note that $ME \\\\approx 0$ may be an artifact of a numerical cancellation as in (c), the neutral case in Fig. 1. In such cases, we could argue that the ranking is still fair since overall it was biased towards both groups across all top-k's. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,525,931,565]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, we refer to the relationship between inequality and inequity as disparity. For example, if a ranking distribution achieves $Gini = 0.65$ and $ME = 0.5$ , we say that the disparity lies in the region III (dark blue), i.e., high inequality and high inequity, see Fig. 2. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,578,931,654]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Growth network model with homophily and directed links. In order to examine the effect of homophily on the ranking of minorities in social networks, first we need to develop realistic network models that capture not only a variety of group mixing, but also the directionality of links. Many online social networks are directed networks in their nature, including the follower-followee structure on Twitter, citation networks $^{29}$ , and the hyperlink structure of the Web. Directed links are the key components of many algorithms such as Google Scholar $^{30}$ PageRank and Who-to-Follow. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,656,931,796]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To this end, we propose DPAH, a directed preferential attachment with homophily network growth model. We generate these networks by adjusting the number of nodes $n = 2000$ , the edge density $d = 0.0015$ , the fraction of minorities $f_{m} \\\\in \\\\{0.1, 0.2, 0.3, 0.4, 0.5\\\\}$ , the in-class homophily $h_{MM}, h_{mm} \\\\in \\\\{0.0, 0.1, \\\\dots, 1.0\\\\}$ , and the power-law exponents of the activity distributions $\\\\gamma_{M} = \\\\gamma_{m} = 3.0$ . We refer to the minority group as $m$ , and to the majority group as $M$ . Note that the between-class homophily is the complement of the in-class homophily. That is, $h_{Mm} = 1 - h_{MM}$ and $h_{mM} = 1 - h_{mm}$ . Furthermore, an activity score is assigned to every node. This score is drawn from a power-law distribution and determines with what probability the existing node becomes active to create additional links to other nodes. This means that more active nodes possess higher out-degree (see Methods for more details). Each combination of network structure is generated 10 times, nodes are ranked using PageRank and WTF separately, and inequality and inequity scores are computed and averaged across network types (and top-k's for local disparity) for each algorithm. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,796,931,938]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 3a illustrates the generation of a network using the DPAH model. First, $n$ labeled nodes are created. In this example $n = 8$ . Then, at time $t$ , node $p$ is selected as source node with a probability proportional to its activity. Then, $p$ connects to an existing node $j$ with a probability related to their pair-wise homophily $h_{pj}$ and preferential attachment that is based on $k_j^{in}$ , the in-degree of node $j$ . By this process, we ensure that the out- and in-degree distributions of nodes follow seemingly power-law distributions that have been observed in many large social networks[31]. The algorithm stops once the network reaches an expected density. Note that source nodes can be either new nodes joining the network for the first time (e.g., node $p$ at time $t$ ) or existing nodes (e.g., node $l$ at time $t + 1$ ). Since the network size is given, \\\"a node joining the network for the first time\\\" is a 0-degree node that has been selected to create its first edge. Once a source node connects to a target node successfully, the source node becomes available in the next rounds to become a target candidate. This means that in the beginning the model faces a cold start problem since there are no existing (target) nodes to connect to. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,16,337,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2022) 12:2012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,631,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-022-05434-1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[922,966,929,975]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[117,60,931,191]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 4. The effects of homophily and fraction of minorities in the global disparity of PageRank. Columns represent the fraction of minorities in the network, x-axis indicates the homophily within minorities, and y-axis the homophily within majoritie s. Colors denote the region where the disparity lies in according to our interpretation in Fig. 2. First, we see that, on average, there is never low global inequality (i.e., regions IV to IX—lighter colors—do not appear). This makes sense because these are scale-free networks. Second, depending on the level of homophily within groups, minorities on average can be under-represented (region I, red), or over-represented (region III, blue), or well-represented (region II, green). For example, when $f_{m} = 0.1$ , minorities are on average under-represented when $h_{MM} \\\\\\\\geq 0.7$ and $h_{MM} \\\\\\\\geq h_{mm}$ . \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0425/a8d92be36006ce9d30cc4c57ce1bed6a4f5b789b17d3657affc3f9b60c309619.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[255,333,931,375]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Thus, the first $1\\\\%$ of new edges are between a source node (drawn from the activity distribution) and any other node with probability as in Equation (3). For the sake of completeness we show the computation of local and global disparities of this network in Fig. 3b. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,386,931,530]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"How do homophily and directional links influence the ranking of minorities globally and locally? Global disparity. As expected, we found that the Gini coefficient of the rank distributions is large. $Gini_{global} \\\\geq 0.6$ (regions I, II and III; dark colors) for both PageRank (see Fig. 4) and WTF (see Supplementary Figure S1). As we will see later, this is mainly due to the preferential attachment mechanism $^{32,33}$ . Moreover, we find that on average: (i) Balanced networks ( $f_m = 0.5$ ) can get a fair ranking (green) when both groups possess the same homophily scores ( $h_{MM} = h_{mm}$ ). The same applies for neutral networks ( $h_{MM} = h_{mm} = 0.5$ ) regardless of their fraction of minorities ( $f_m \\\\leq 0.5$ ). (ii) When the fraction of minorities decreases ( $f_m < 0.5$ ), groups can be fairly represented in the rank in two regimes: First, when both groups are homophilic, homophily within minorities must be higher than homophily within majorities ( $h_{mm} > h_{MM} > 0.5$ ). Second, when both groups are heterophilic, homophily within majorities must be higher than homophily within minorities ( $h_{mm} < h_{MM} < 0.5$ ) to balance the importance of groups. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,542,931,748]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Local disparity. We also compute inequality and inequity within each top- $k\\\\%$ rank in order to see to what extent they ch ange when $k$ increases. In the case of PageRank, we see in Fig. 5 that inequality varies (i.e., from light to dark color or s) in different regimes mainly due to the size of $k$ (x-axis), and inequity due to the interplay between homophily within groups, $h_{MM}$ and $h_{mm}$ . In particular: (i) Only at the top- $5\\\\%$ of the rank we see a few cases of low inequality (regions VII, VIII and IX; very light colors), this means that nodes at the very top possess very similar ranking scores, but they are very far from the rest of the population, i.e., the larger the top- $k\\\\%$ , the hig her the Gini (darker colors). This holds for WTF up to roughly the top- $30\\\\%$ (see Supplementary Figure S2). Overall, PageRank converges to high inequality faster than WTF. (ii) Inequity (regions: red, blue, green) is consistent across all top- $k\\\\%$ ranks for both algorithms. In other words, if the ranking algorithm favors or harms one group in the top- $5\\\\%$ , it will continue to do so until converging to the fair regime (regions II, V, VIII; green). With a few exceptions, this fair regime is only reached when $k$ is very large. For example, if a minority group is underrepresented at the top- $5\\\\%$ , it will remain under-represented at the top- $80\\\\%$ (see $h_{mm} = 0.1$ and $h_{MM} \\\\geq 0.7$ in Fig. 5 for PageRank, and Supplementary Figure S2 for WTF). (iii) Minorities are often over-represented when majorities are heterophilic $h_{MM} < 0.5$ ; (regions III, VI, IX; blue). In contrast, minorities are often under-represented when majorities are homophilic $h_{MM} > 0.5$ (regions I, IV, VII; red). This is consistent up to $\\\\approx$ top- $80\\\\%$ for both algorithms. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,748,931,801]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In summary, our results suggest that the size of $k$ does not have an influence on inequity. This means that if the algorithm amplifies inequity at the top-5%, it will also amplify inequity at larger top-k%’s. Therefore, increasing the selection pool (larger k) does not improve the representation of minorities. This can be explained by the fact that the preferential attachment mechanism disproportionately affects nodes ranking<sup>12</sup>. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,813,931,943]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Correlation and feature importance. We compute the Spearman correlation between inequality and inequity, and conduct a random forest regression to measure the importance of each network property on both inequality and inequity values (see Supplementary Appendix A.3 for more detail). Results are shown in Table 1 for PageRank and Supplementary Table S2 for WTF. We find that inequality and inequity are positively correlated in both global and local regimes. In other words, the more skewed the rank distribution (i.e., high Gini), the more unfair with either group (i.e., mean error far from zero), and vice versa. This correlation is stronger and more significant in PageRank than in WTF. In terms of feature importance, we find that global inequality (Gini) is mainly explained by both homophily values, whereas g global inequity (ME) is mainly driven by homophily within majorities. Local inequality $(\\\\text{Gini}_k)$ , however, is mainly explained by the top- $k\\\\%$ rank, and local inequity $(ME_k)$ by the homophily within the majority group. Notice that we added the variable $\\\\epsilon$ to verify whether the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,16,337,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2022) 12:2012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,631,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-022-05434-1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[919,965,931,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[147,60,931,586]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 5. The effects of homophily and fraction of minorities in the local disparity of PageRank. Columns represent the fraction of minorities (10%, 30% and 50%) and rows show homophily within minorities (from top to bottom: heterophilic, neutral and homophilic). The x-axis denotes the top-k% rank and the y-axis shows homophily within majorities. Colors refer to the regions of disparity introduced in Fig. 2. One can see that the minority suffers most (red) when the majority is homophilic and the minority is either heterophilic or neutral. Moreover, inequality is lowest (very light colors) only for a few cases at top-5%. This means that the top best ranked nodes are very similar and their ranks are far from the majority of nodes (i.e., due to preferential attachment). Moreover, inequity remains mostly consistent regardless of top-k%. In other words, if the ranking algorithm favors one group in the top-5% (e.g., red or blue), it will continue to do so until entering the fair regime (green). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0237/f19bdbd2bc5fa014529fffc51990c63027c90b9998eba4111541e768403467d6.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[258,749,915,828]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0023/3c80f7dc059cb4e4c282fa15516f10f12a97e8e452b6c1c20439e56553b4ecee.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Type</td><td>Outcome</td><td>Corr</td><td>R2</td><td>Feature</td><td>Importance</td></tr><tr><td rowspan=\\\"2\\\">Global</td><td>Gini</td><td rowspan=\\\"2\\\">0.41</td><td>0.91 (0.009)</td><td>hMM, hmm, fm, ε</td><td>0.43, 0.31, 0.21, 0.05</td></tr><tr><td>ME</td><td>0.99 (0.001)</td><td>hMM, hmm, fm, ε</td><td>0.61, 0.31, 0.08, 0.0</td></tr><tr><td rowspan=\\\"2\\\">Local</td><td>Gini k</td><td rowspan=\\\"2\\\">0.21</td><td>0.95 (0.002)</td><td>k, hMM, hmm, fm, ε</td><td>0.73, 0.11, 0.07, 0.06, 0.03</td></tr><tr><td>MEk</td><td>0.99 (0.001)</td><td>hMM, hmm, k, fm, ε</td><td>0.51, 0.27, 0.14, 0.08, 0.01</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. Ten-fold cross-validation for PageRank. We use a Random Forest Regressor to assess feature importance and report the mean and standard deviation of the out-of-sample $R^2$ . Features are ranked in descending order based on their mean importance (from left to right) and highlighted if their importance represents at least $50\\\\\\\\%$ of the total importance. Corr shows the Spearman correlation between inequality and inequity scores ( $p$ -values $\\\\\\\\approx 0$ ). $\\\\\\\\epsilon$ represents random chance. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[65,15,337,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2022) 12:2012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,631,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-022-05434-1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[921,965,931,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[258,61,907,418]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(Mean error of fraction of minorities across all top- $k\\\\\\\\%$ ranks) \\\",\\\"Figure 6. The effects of homophily and preferential attachment in the global disparity of PageRank. We generated directed networks using four different models of edge formation. DPA: only preferential attachment. DH: only homophily. DPAH: our proposed model that combines DPA and DH. Random: a baseline where nodes are connected randomly. We see the following patterns: (i) Homophily (DH) produces a moderate-to-high level of inequality $(0.3 < Gini < 0.8)$ , while preferential attachment (DPA) produces a consistent moderate inequality $(Gini \\\\\\\\approx 0.5)$ . When both mechanisms are combined (DPAH), the rank inequality increases even further $(0.7 < Gini < 0.9)$ . (ii) Random and Preferential attachment (DPA) are always fair $(ME = 0$ or $|ME| \\\\\\\\leq \\\\\\\\beta)$ , while in the cases where homophily is involved (DH and DPAH) inequity is often high $(|ME| > \\\\\\\\beta)$ . Thus, in general preferential attachment is the main driver of inequality, while homophily influences both inequality and inequity. Vertical and horizontal error bars represent the standard deviation over 10 runs of the Gini and ME, respectively. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0957/0dddafa223c34bad99f15768a9ffa1a6c237be44d2e3bd2cb9d87ecb4e537abc.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[255,620,931,659]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"network-based features are better than random (see Supplementary Appendix A.3 for more details). In the case of PageRank, all network-based features perform better than by chance. However, randomness seems to be more relevant for explaining rank inequality (Gini) in WTF. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,659,931,723]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"These results are in agreement with what we see in previous figures; even though majority nodes produce most of the inequality and inequity in the rank, their interplay with minority nodes can change or intensify the direction of bias. In fact, both homophily values can explain $75\\\\%$ (49%) of Gini, the global inequality in PageRank (WTF), 92% (88%) of ME, the global inequity, and 78% (74%) of $ME_{k}$ , the local inequity. However, the top-k% rank together with the homophily within majority nodes explain 84% (86%) of $Gini_{k}$ , the local inequality. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,737,931,801]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"How do different social mechanisms of edge formation contribute to disparity? So far, we show that PageRank and WTF on our network model produce high inequality and a wide-range of possible inequity outcomes. How much of that inequality or inequity was a product of homophily or preferential attachment? To see the effects of these two mechanisms alone, we generate new networks by turning on and off the homophily and preferential attachment features (see Methods for the details of the models). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,801,931,904]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 6 shows the inequality and inequity produced by PageRank on a variety of models: DPA (Directed Preferential Attachment), DH (Directed Homophily), Random, and DPAH (see Supplementary Figure S3 for WTF). Results from both algorithms show that networks whose nodes connect through preferential attachment (DPA) produce on average higher inequality compared to DH and Random. However, when preferential attachment is combined with homophily (DPAH), this inequality increases even further. Additionally, we see that WTF produces higher inequality compared to PageRank (see Supplementary Appendix A.4 for more details). Inequity, on the other hand, is mainly driven by homophily. This means that, homophily (DPAH and DH) influences both, inequality and inequity in both algorithms. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,905,931,943]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Note that in Fig. 6, we fixed the activity of nodes to $\\\\gamma_{M} = \\\\gamma_{m} = 3.0$ . However, when we set these parameters to $\\\\gamma_{M} = \\\\gamma_{m} < 3.0$ (more active nodes or lower values of $\\\\gamma$ as found in several scale-free networks<sup>34</sup>), inequality decreases, see Supplementary Figure S5. This behavior holds even if the minority group is the only one increasing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,15,337,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2022) 12:2012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,631,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-022-05434-1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[922,965,931,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[117,61,932,258]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 7. Global disparity in PageRank on empirical networks. Each column represents an empirical network. Citation/retweet networks (APS and Hate) and Hyper-link networks (Blogs and Wikipedia). Inequality and inequity are shown in the y- and x-axis, respectively. The disparity in ranking that we see in empirical networks are best explained as follows: (i) citation/retweet networks by preferential attachment PA, and (ii) hyper-link networks by preferential attachment and homophily DPAH. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0553/6c7a3a3021b12c6d7bc259aa90b23923a6a689d2ac353c43316f0594f99ea456.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[255,365,931,430]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"its activity $(\\\\gamma_{m} = 1.5 < \\\\gamma_{M} = 3.0)$ which in turn increases inequity against the majority, see Supplementary Figure S6. Additionally, in Supplementary Figure S4, we see that edge density also plays a role in the inequality produced by PageRank and WTF. This means that, by further adjusting these two parameters (node activity and edge density), we would expect changes only to inequality since inequity is mainly affected by homophily as we saw before. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,443,931,638]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Disparities on empirical networks. First, we fit the DPA, DH, and DPAH models to each of the empirical networks in order to find the mechanism that best explains the inequality and inequity found in the rank. The parameters passed to these models are inferred from the real networks and described in Table 3. Second, we rank nodes in the empirical and fitted networks using PageRank and WTF, and compute the disparities (inequality vs. inequity) found in their rank distribution. Results are shown in Fig. 7 for PageRank and Supplementary Figure S9 for WTF. Disparity values from the real-world networks are labeled as empirical (black dot), and disparity values from the fitted networks are labeled according to the model (x marks). We see that each network tells a different story. This can be explained by the nature or domain of these networks. For instance, APS and Hate are best explained by the DPA model. This means that scientists tend to cite authors that have already many citations, and users in Twitter tend to retweet content posted by popular users (i.e., popular in terms of the number of retweets they get). Blogs and Wikipedia on the other hand, are best explained by our DPAH model. Notice that both are hyper-link networks. In other words, people tend to add not only popular references to their Web pages, but also related to their topics (i.e., political leaning in Blogs, and gender in Wikipedia). Note that the Hate network shows the lowest (empirical) inequality. This is due to the fact that it possesses low out-degree exponents $(\\\\gamma_{M} = 2.2, \\\\gamma_{m} = 1.7)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,650,931,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Strategies towards a fair ranking. Results from both algorithms show that while the homophily within majorities is the main driver for inequality and inequity, minorities may overcome unfair rankings by connecting strategically in the network. For instance, when both groups are equally active, minorities should adjust their homophily based on the homophily of the majority. (i) When majorities are homophilic $h_{MM} > 0.5$ , minorities should increase their homophily such that $h_{mm} > h_{MM}$ . (ii) When majorities are (somewhat) neutral ( $h_{MM} = 0.5 \\\\pm 0.1$ ), minorities may connect arbitrarily with any group without being too homophilic, otherwise they will become over-represented in the rank. (iii) When majorities are heterophilic $h_{MM} < 0.5$ , one solution to achieve a fair rank is to increase the size of the minority group, and make sure that both groups behave similarly in terms of homophily ( $h_{MM} \\\\approx h_{mm}$ ). Otherwise, minorities will be over-represented regardless of their in-class homophily. On the other hand, when one group is more active than the other, achieving a fair rank becomes challenging. Nevertheless, if the objective is to increase the visibility of minorities in the rank, then the minorities themselves should be more active in the network by creating more connections to increase their out-degree. Note that these \\\"strategies\\\" without algorithmic intervention may work in scenarios such as a citation or collaboration networks, but they might not work in other scenarios. In such cases, we need additional recommender systems to help under-represented groups discover those \\\"strategic\\\" links that will help them climb to higher ranks. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,870,477,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Discussion and future work \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,884,931,937]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this work we have proposed a systematic study to measure the inequality and inequity produced by PageRank and Who-To-Follow (WTF). Our approach disentangles the effect of network structure on the rank distributions of these two algorithms by using synthetic networks. By doing so, we control for the properties of the network and measure how these changes affect the rankings. In particular, we studied six prominent structural properties \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,16,337,30]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2022) 12:2012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,631,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-022-05434-1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[921,965,931,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[260,61,931,189]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"of social networks: homophily, preferential attachment, fraction of minorities, edge density, node activity and the directionality of links. We found that the systemic bias produced by these algorithms in the rank is mainly due to homophily imbalance ( $h_{MM} \\\\gg h_{mm}$ or $h_{mm} \\\\gg h_{MM}$ ) for inequity, and the interplay between our six properties of interest for inequality. Consequently, our systematic study makes PageRank and Who-To-Follow interpretable and explainable since our results show the necessary structural conditions to achieve a fair rank. A potential avenue to reduce inequity is to then create synthetic connections before the ranking as it is done for correcting the class imbalance problem in supervised learning<sup>35</sup>. Alternatively, these conditions or strategic connections may be added into the network to change its structure as a collective fairness intervention. For instance, recommender systems could suggest relevant articles not only based on popularity and (keyword) similarity but also based on fairness by fulfilling diversity constraints. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,189,931,393]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Notice that our model simplifies the role of homophily and minorities. First, it assumes that all nodes of the same group have the same in-class and between-class homophily. This means that rich mixing patterns might get ignored since some nodes can exhibit local differences $^{36}$ . Second, while there exist multiple definitions of minorities $^{37}$ we adopted the one by Italian jurist Francesco Capotorti: \\\"a group numerically inferior to the rest of the population of a State, in a non-dominant position...\\\" $^{38,39}$ . However, we constrained this population to all nodes in a given network (neither the State nor the world population). Notice as well that the ranking amplifies the representation of minorities by reducing the representation of majorities in top ranks (e.g., when the majority is heterophilic, see Fig. 1). This aligns with the definition of minorities by Wirth $^{40}$ that implies that \\\"minorities objectively occupy disadvantageous positions in society\\\". This means that \\\"a minority may actually, from a numerical standpoint, be the majority\\\" (e.g., people living in poverty in under-developed countries). In other words, under these two definitions, being in disadvantage in the top- $\\\\mathbf{k}\\\\%$ (inequity) is not a group size issue only, but a combination of group size and homophily as we have previously shown. More complex definitions of minorities are out of the scope of this paper. A further limitation is that we focus on a single binary attribute (e.g., color $\\\\in$ {Black, White}), this means that multiple sources of inequality and inequity (e.g., intersections of disadvantage such as being poor and of color) cannot be captured at once $^{41}$ . Addressing these issues is beyond the scope of this paper and we leave them for future work. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,393,931,471]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, we disentangled the individual effects of preferential attachment and homophily in the rank by comparing the disparities of our proposed DPAH model with two variants and a baseline: networks with preferential attachment only (DPA), networks with homophily only (DH), and directed Erdős-Rényi (Random) $^{42}$ graphs. Further research can investigate other topologies and social mechanisms of edge formation such as clustering $^{43}$ , transitivity $^{44}$ , and reciprocity $^{45}$ . Similarly, other structural properties such as monophily $^{46}$ and second order homophily $^{47}$ can be studied to measure their influence on ranking. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,484,354,497]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conclusions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,500,931,575]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this work we have investigated under which conditions PageRank and Who-To-Follow (WTF) reduce, replicate or amplify the representation of minorities in top ranks. In particular, given the rank distribution produced by these algorithms, we computed inequality as the dispersion among individuals in terms of ranking scores, and inequality as whether minorities are over-, under- or well-represented in top ranks compared to their representation in the network. We studied these two metrics separately and in combination to better understand the mechanisms that can explain them. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,576,931,664]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To that end, we proposed DPAH, a growth network model that allows to generate realistic scale-free directed networks with different levels of homophily, fraction of minorities, node activity, and edge density. In these networks, we found that both inequality and inequity are positively correlated and mainly driven by the homophily within majorities. This means that, when the majority group is highly homophilic, the minority group is underrepresented in top ranks. Also, when the majority is highly heterophilic, the minority benefits tremendously since it is over-represented in the top- $k\\\\%$ . However, minorities can overcome these disparities by connecting strategically with others. Thus, equity in ranking is a trade-off between homophily and the fraction of minorities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,666,931,716]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Our systematic study makes PageRank and Who-to-Follow explainable and interpretable to help data scientists understand and estimate the disparity that these algorithms produce given the structure of networks, which is key for proposing targeted interventions. We hope our results create awareness among majority and minority groups about these disparities since they may replicate and even amplify the biases found in social networks. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,730,408,742]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data and methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,744,931,884]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Synthetic networks. Network models have been proposed with various social mechanisms. For instance, the classic stochastic-block model<sup>48</sup> which allows for homophily between and across groups, and the configuration model<sup>49</sup> which generates links among nodes by preserving a given degree distribution. On the other hand, the preferential-attachment model<sup>25</sup> produces scale-free networks due to cumulative advantage<sup>50</sup>. Although these models can reproduce certain properties of real-world networks such as degree or homophily, they fail at guaranteeing similar visibility of minorities as their empirical counterpart. In this direction, Karimi et al.<sup>13</sup> and Fabbri et al.<sup>14</sup> devise social network models with preferential attachment, adjustable homophily and fraction of minorities. They demonstrate how the degree rank of the minority group in a network is a function of the relative group sizes and the presence or absence of homophily. However, the former models undirected networks, and the latter did not control for edge density and node activity (i.e., power-law out-degree distributions) as we do in this work for minority and majority groups. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,900,931,939]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Directed network. We define a directed network as: Let $G = (V, E, C)$ be a node-attributed unweighted graph with $V = \\\\{v_1, \\\\dots, v_n\\\\}$ being a set of $n$ nodes, $E \\\\subseteq V \\\\times V$ a set of $e$ directed edges, and $C = \\\\{c_1, \\\\dots, c_n\\\\}$ a list of binary class labels where each element $c_i$ represents the class membership of node $v_i$ . The fraction of minorities \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[65,16,337,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2022) 12:2012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,631,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-022-05434-1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[921,965,931,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"9 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[255,61,931,113]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$f_{m}$ captures the relative size of the minority class—with respect to $C$ —in the network. We refer to the minority group as $m$ , and to the majority group as $M$ . A network is balanced when all class labels have the same number of nodes ( $f_{m} = 0.5$ ), otherwise it is unbalanced ( $f_{m} < 0.5$ ). Networks fulfill a predefined edge density level $d$ . Since $n$ and $d$ are given, networks stop growing when $e = dn(n - 1)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,112,931,202]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In order to generate directed links, inspired by the activity-driven network model $^{51}$ , we assign an activity score to each node that determines with what probability the existing node becomes active and creates additional links to other nodes. It has been shown that in empirical networks the activity of the nodes follows a power-law distribution $^{51}$ . Therefore, we assign an activity to each node drawn from a power-law distribution $\\\\rho(\\\\gamma) = X^{-\\\\gamma}$ . Note that each group possesses its own activity distribution and they are defined by its power-law exponent $\\\\gamma_{M}$ and $\\\\gamma_{m}$ for majority and minority nodes, respectively. The level of activity of a group is inversely proportional to $\\\\gamma$ . That is, groups with higher out-degree produce lower $\\\\gamma$ (more skewed). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,202,931,242]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Then, the probability of connecting a source (active) node $\\\\nu_{i}$ to a target node $\\\\nu_{j}$ (or in other words the probability of connecting to $\\\\nu_{j}$ given the source node $\\\\nu_{i}$ ) is explained by any of the following three mechanisms of edge formation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,255,931,309]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Preferential attachment (DPA). Also known as the rich-get-richer effect or cumulative advantage in social networks[25,50]. It indicates that nodes tend to connect to popular nodes. We define popularity as the in-degree of the node. Therefore, the probability that a source node $\\\\nu_{i}$ connects to a target node $\\\\nu_{j}$ is proportional to the in-degree of the target node $\\\\nu_{j}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[499,315,931,352]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP (i \\\\rightarrow j) = P (j \\\\mid i) = \\\\frac {k _ {j} ^ {\\\\text {i n}}}{\\\\sum_ {l = 1} ^ {N} k _ {l} ^ {\\\\text {i n}}} \\\\tag {1}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[255,374,931,503]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Homophily (DH). It is the tendency of individuals to connect (or interact) with similar others $^{24,49}$ . Thus, the probability that a source node $\\\\nu_{i}$ connects to a target node $\\\\nu_{j}$ is driven by the homophily between their classes $c_{i}$ and $c_{j}$ . We assign a homophily value to each dyad based on pre-defined homophily parameters within majorities and minorities, $h_{MM}$ and $h_{mm}$ , respectively. Homophily values range from 0.0 to 1.0. If the homophily value is high, that means that nodes of the same class are attracted to each other more often than nodes of different attributes. Following the definitions from previous work $^{13,14,52}$ , nodes of the same class with homophily $h_{aa} = 0.5$ are referred to as neutral (i.e., they connect randomly to either class), otherwise they are heterophilic if $h_{aa} < 0.5$ (i.e., more likely to connect to the other class), or homophilic when $h_{aa} > 0.5$ (i.e., more likely to connect to the same class). Note that in- and between-class homophily values are complementary: $h_{mm} = 1 - h_{mM}$ and $h_{MM} = 1 - h_{Mm}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[499,511,931,544]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP (i \\\\rightarrow j) = P (j \\\\mid i) = \\\\frac {h _ {i j}}{\\\\sum_ {l = 1} ^ {N} h _ {i l}} \\\\tag {2}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[255,566,931,618]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Preferential attachment with homophily (DPAH). We propose DPAH, a directed growth network model with adjustable homophily and fraction of minorities. DPAH stands for Directed network with Preferential Attachment and Homophily. This mechanism combines DPA and DH, and is an extension of the BA-Homophily model<sup>13</sup>. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[490,627,931,663]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP (i \\\\rightarrow j) = P (j | i) = \\\\frac {h _ {i j} k _ {j} ^ {i n}}{\\\\sum_ {l = 1} ^ {N} h _ {i l} k _ {l} ^ {i n}} \\\\tag {3}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[255,671,931,749]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Note that DPA and DH are especial cases of DPAH where only the in-degree mechanism varies. This means that, the out-degree distribution remains the same as in DPAH: it is driven by the activity model. Additionally, we include a random model where both source and target nodes are chosen at random (i.e., directed Erdos-Renyi model $^{42}$ ). Table 2 shows the parameters adjusted in each model. Number of nodes $n$ and edge density $d$ are arbitrary in the sense that they are not part of the edge formation mechanism. Thus, we fix them to make a fair comparison across all models. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,762,931,791]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Empirical networks. We inspect four networks from different domains and compute the inequalities and inequities produced by PageRank and WTF. Table 3 shows the most important properties of these networks. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,804,931,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- APS: The American Physical Society citation network wh os nodes represent articles, and edges represent citations. The binary class of each node is pacs and encodes two different Physics sub-field s w he re 05.20.-y (C la ssical statistical mechanics) is the minority. \\\",\\\"- Hate: A retweet network<sup>53</sup> where nodes denote users, and edges represent ret weets among them. Users are labeled as either hateful or normal depending on the sentiment of their tweets. Hateful users represent the minority. \\\",\\\"- Blogs: An hyper-link network from political blog posts about the 2004 U.S. election<sup>54</sup>. Nodes represent blog pages, and edges hyper-links among them. Each blog is labeled as either right- or left-leaning. The latter represents the minorities. \\\"]\",\n \"page_idx\": \"9\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[65,16,337,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2022) 12:2012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,633,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-022-05434-1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[914,966,929,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[258,62,678,184]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0624/9981a67fc4c0d56fa9ba9b99dda75396d78f37d6959dba3c4c68a885db07b6f3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td></td><td>Random</td><td>DPA</td><td>DH</td><td>DPAH</td></tr><tr><td>n</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>fm</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>d</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>hMM</td><td>-</td><td>-</td><td>✓</td><td>✓</td></tr><tr><td>hmm</td><td>-</td><td>-</td><td>✓</td><td>✓</td></tr><tr><td>γM</td><td>-</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>γm</td><td>-</td><td>✓</td><td>✓</td><td>✓</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2. Model parameters. Check marks denote that a given model (column) requires a particular parameter (row): number of nodes $n$ , fraction of minorities $f_{m}$ , edge density $d$ , in-class homophily $h_{aa}$ , and the power-law exponent of the activity distribution $\\\\\\\\gamma$ . Sub-indices $M$ and $m$ refer to the majority and minority groups, respectively. The difference between DH and DPAH is the preferential attachment (in-degree) mechanism. All models produce directed networks. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[258,301,546,528]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0676/3441350ea3d4b37a8e721e4f9501b73b103cef405f3453e6997739c5faa8702f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Dataset</td><td>APS</td><td>Hate</td><td>Blogs</td><td>Wikipedia</td></tr><tr><td>n</td><td>1853</td><td>4971</td><td>1224</td><td>3159</td></tr><tr><td>Class</td><td>pacs</td><td>hate</td><td>leaning</td><td>gender</td></tr><tr><td>M</td><td>05.30.-d</td><td>normal</td><td>right</td><td>male</td></tr><tr><td>m</td><td>05.20.-y</td><td>hateful</td><td>left</td><td>female</td></tr><tr><td>fm</td><td>0.37561</td><td>0.10943</td><td>0.48039</td><td>0.15226</td></tr><tr><td>d</td><td>0.00106</td><td>0.00061</td><td>0.01271</td><td>0.00149</td></tr><tr><td>γM</td><td>3.22246</td><td>2.23026</td><td>4.88733</td><td>4.22425</td></tr><tr><td>γm</td><td>8.93993</td><td>1.73445</td><td>3.22464</td><td>6.16567</td></tr><tr><td>EMM</td><td>0.64981</td><td>0.56898</td><td>0.47070</td><td>0.78469</td></tr><tr><td>EMm</td><td>0.02859</td><td>0.10244</td><td>0.04741</td><td>0.07824</td></tr><tr><td>EmM</td><td>0.02721</td><td>0.07886</td><td>0.04105</td><td>0.10685</td></tr><tr><td>Emm</td><td>0.29439</td><td>0.24972</td><td>0.44084</td><td>0.03022</td></tr><tr><td>hMM</td><td>0.94000</td><td>0.58000</td><td>0.92000</td><td>0.59000</td></tr><tr><td>hmm</td><td>0.96000</td><td>0.95000</td><td>0.90000</td><td>0.62000</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 3. Empirical Networks. APS, a scientific citation network. Hate, a retweet network. Blogs, a political blog hyper-link network. Wikipedia, a hyper-link network of politicians. Each row represents a property of the network. $E_{**}$ represents the fraction of edges within and across groups, and $h_{**}$ homophily values inferred by the DPAH model (see Supplementary Appendix A for derivations). \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[257,636,931,664]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"- Wikipedia: A Wikipedia hyper-link network where nodes represent U.S. politicians $^{55,56}$ labeled as either male or female. Female politicians re present the minorities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,705,931,824]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Ranking and recommendation algorithms. There exist a variety of ranking and recommendation algorithms that follow different strategies depending on the nature of the problem. For instance, in information systems, items such as content, Web pages, and products are ranked to recommend users what to read or buy[57]. In social networks, however, people are ranked to identify their hierarchy or importance[54-60], and recommended to other users in order to establish new connections[61-64]. These rankings and recommendations are based on algorithms that often rely on whom we are already connected with. In this work, we focus on two such algorithms widely used in practice[65]: PageRank[1] and Who-to-Follow (WTF)[8]. While PageRank determines the global ranking of nodes in comparison with all other nodes, WTF deals with ranking nodes in a node level and thus remains a local measure. For that reason, we focus on these two algorithms to capture both dimensions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,837,931,888]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PageRank . It was invented to rank all web pages in the Web<sup>11</sup>, and has been used in several applications<sup>65</sup>. For example, to study citation and co-authorship networks<sup>66-68</sup>. PageRank assigns an importance score to every single node in a network. This score takes into account the number and quality of incoming links of each node. The PageRank of node $i$ is defined as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[495,897,931,932]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP R (i) = (1 - \\\\alpha) + \\\\alpha \\\\sum_ {j \\\\in N _ {i}} \\\\frac {P R (j)}{k _ {j} ^ {\\\\text {o u t}}} \\\\tag {4}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[65,16,337,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2022) 12:2012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,633,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-022-05434-1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[914,965,929,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"11 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[255,62,932,116]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $i \\\\in V$ , $N_{i}$ represents all neighbors of node $\\\\nu_{i}$ (e.g., all nodes $\\\\nu_{i}$ points to), and $k_{j}^{out}$ the out-degree of node $\\\\nu_{j}$ . The damping factor $\\\\alpha$ , or probability of following links using a Random Walker, is set to 0.85 as suggested by Brin and Page[69]. We use the fast-pagerank[70] python package to compute the PageRank score of all nodes using sparse adjacency matrices. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,127,931,232]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Who-to-follow (WTF). This recommendation algorithm was created and used by Twitter to suggest new people to follow. It is based on SALSA which in turn is based on Personalized PageRank. In a nutshell, for each user $u$ (or node $\\\\nu_{i} \\\\in V$ ), the algorithm looks for its circle of trust, which is the result of an egocentric random walk (similar to personalized PageRank). Then, based on this circle-of-trust, the algorithm ranks all users that are not yet friends with $u$ but are connected through the circle of trust. Then, we take the top-k of these (recommended) users, and add up the counter of being selected as a recommendation to each of them. This is done for every node $u$ in the network. At the end, the rank of each node encodes the number of times a user was suggested as a recommendation across all nodes in the network. Thus, the WTF score for each node is defined as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,239,931,269]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nW T F (i) = \\\\sum_ {j \\\\in V} \\\\mathbb {1} _ {S A L S A (j)} (i) \\\\tag {5}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[255,277,932,317]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $SALSA(j)$ refers to the top-k users the SALSA algorithm recommends to node $j$ . In this work we select the top-10 users as recommendations. $\\\\mathbb{1}_A(x)$ denotes the indicator function or boolean predicate function to test set inclusion (i.e., whether $x \\\\in A$ ). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,329,931,395]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Gini coefficient. The Gini coefficient was developed by the Italian Statistician Corrado Gini<sup>73</sup> to measure the income inequality of a society. It is defined as the mean of absolute differences between all pairs of individuals for some measure. In our setup this measure is the score given to every node by PageRank and Who-To-Follow. The minimum value is 0 when all individuals' scores are equal, and its maximum value is 1 when there is a big gap or discrepancy between scores<sup>74</sup>. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[275,395,823,407]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We define the Gini coefficient of the rank distribution $X$ as follows. For more details see<sup>75</sup>: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[494,416,931,453]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nG i n i (X) = \\\\frac {\\\\sum_ {i = 1} ^ {\\\\hat {n}} (2 i - \\\\hat {n} - 1) x _ {i}}{n \\\\sum_ {i = 1} ^ {\\\\hat {n}} x _ {i}} \\\\tag {6}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[255,460,931,488]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $x \\\\in X$ is an observed value in the rank distribution, $\\\\hat{n} = |X|$ is the number of values observed, and $i$ is the rank of values in ascending order. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,497,394,512]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data availability \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,512,931,539]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The code and datasets generated during and/or analyzed during the current study are available in the GitHub repository, https://github.com/gesiscs/Homophilic_Directed_ScaleFree_Networks. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,549,589,563]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received: 16 September 2021; Accepted: 7 January 2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,563,467,576]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Published online: 07 February 2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[260,590,349,604]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[265,604,929,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1. 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(TOIS) 19, 131-160 (2001). \\\"]\",\n \"page_idx\": \"12\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[65,15,337,31]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"www.nature.com/scientificreports/ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[65,965,290,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Scientific Reports (2022) 12:2012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[381,965,631,978]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1038/s41598-022-05434-1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[786,964,880,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"natureportfolio \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[914,966,929,976]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"13 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[257,61,932,136]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"72. Jeh, G. & Widom, J. Scaling personalized web search. In Proceedings of the 12th international conference on World Wide Web, 271-279 (2003). \\\",\\\"73. Gini, C. Variabilità e mutabilità. Repr. Memorie di metodologica statistica (Ed. Pizetti E (1912). \\\",\\\"74. Ceriani, L. & Verme, P. The origins of the gini index: extracts from variabilità e mutabilità (1912) by corrado gini. J. Econ. Inequal. 10, 421-443 (2012). \\\",\\\"75. StatsDirect. Gini coefficient of inequality. https://www.statsdirect.com/help/default.htm#nonparametric_methods/gini.htm. Accessed on 09 Nov 2020. \\\"]\",\n \"page_idx\": \"13\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[257,149,421,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgements \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,164,932,228]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Special thanks to Nicola Perra, Indira Sen, Mattia Samori, Reinhard Munz who have helped improving this paper and to Antonio Ferrara and Jan Bachmann for their technical support on the revisions of this paper. Also, thanks to LXAI@ICML2020, NetSci2020, and WiDS Guayaquil@ESPOL for their feedback. This work was partially funded by the Austrian Science Promotion Agency FFG project no. 873927. The presented computational results have been achieved in part using the Vienna Scientific Cluster (VSC). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,237,430,251]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Author contributions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,251,932,305]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"L.E.N., F.K., C.W. and M.S. devised the research project. L.E.N. conceived the experiments and analyzed the datasets. F.K. performed analytical derivations. L.E.N., F.K., C.W., and M.S. wrote the paper. All authors reviewed the manuscript. Parts of L.E.N and M.S.'s work on this project have been performed while being at GESIS and RWTH Aachen, respectively. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,317,425,332]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Competing interests \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,332,526,345]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The authors declare no competing interests. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,355,445,369]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Additional information \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[255,370,932,393]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Supplementary Information The online version contains supplementary material available at https://doi.org/10.1038/s41598-022-05434-1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,401,692,414]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Correspondence and requests for materials should be addressed to F.K. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[257,421,747,434]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Reprints and permissions information is available at www.nature.com/reprints. \",\n \"text_format\": null,\n \"text_level\": null,\n 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The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. 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Barbero, Markus J. van Ackeren, Nathan Weisz, Olivier Collignon"},"content_list":{"kind":"list like","value":[{"bbox":"[122,89,875,143]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,179,883,219]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Siddharth Talwar<sup>a</sup>, Francesca M. Barbero<sup>a,b</sup>, Markus J. van Ackerena<sup>a</sup>, Nathan Weisz<sup>c</sup>, and Olivier Collignon<sup>a,b,c</sup> ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,239,883,339]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"<sup>a</sup> Institute of Psychology (IPSY) and Institute of Neuroscience (IoNS), UCLouvain, Louvain-la-Neuve, Belgium \",\"<sup>b</sup> Center for Mind/Brain Sciences, University of Trento, Italy \",\"$^{c}$ Center for Cognitive Neuroscience Salzburg (CCNS) and Division of Physiological Psychology, University of Salzburg, Austria \"]","page_idx":"0","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[109,359,883,458]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Author contributions: O.C., M.J.V.A., and F.M.B. conceived and designed the experiment; M.J.V.A. and F.M.B. performed the experiment, M.J.V.A., F.M.B., S.T. analyzed the data; N.W. provided resources for analysis; M.J.V.A. and O.C. interpreted the results of the experiment; O.C. wrote the first draft of the manuscript; S.T., M.J.V.A., O.C. and N.W. commented on the manuscript. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,479,883,520]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: multisensory integration, steady-state response, MEG, cortical oscillations, functional connectivity, cortical excitability, pre-stimulus activity ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,903,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[117,97,204,113]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,135,887,396]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"How does the brain integrate or segregate multiple sensory inputs? In our study, we used magnetoencephalography to comprehensively investigate local and network dynamics before and after the presentation of sequences of beeps and flashes that are sometimes perceived as synchronous or asynchronous. Frequency-tagging and spectral analysis revealed that under identical physical conditions, subjective perceptual fusion of multisensory signals elicits stronger evoked sensory responses in both visual and auditory cortices. Crucially, perceptual fusion is preceded by locally reduced pre-stimulus alpha activity, as well as enhanced functional connectivity between auditory and visual cortices within the pre-stimulus gamma activity. We also show that pre-stimulus neuronal states in the occipital cortex predict post-stimulus sensory responses to auditory sequences in the temporal cortex, but not the opposite. The current findings provide evidence that the perceptual fusion of multisensory events relate to a complex interplay between local and inter-sensory neuronal states before and after stimulus presentation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,450,334,470]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Significance Statement ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,489,888,650]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"How does the brain blend information from multiple sensory systems into one holistic perception? We developed a novel frequency-tagging paradigm in Magnetoencephalography (MEG) to robustly estimate the sensory responses to a series of flashes and beeps in early sensory areas, and to demonstrate how these responses are shaped by ongoing fluctuations in local, and long-range network activity. By combining the steady-state method with spectral, and functional connectivity analysis of ongoing oscillations in source space, the current study provides novel insights into the relationship between internal brain states and the way we perceive multisensory events. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,903,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,97,253,113]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,135,883,214]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Understanding how information from multiple senses are seamlessly merged into a single coherent percept is a major challenge for the field of cognitive neuroscience. It is argued that integration emerges already at the earliest stages of the cortical hierarchy, within areas once considered exclusively unisensory. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,234,883,515]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To resolve conflicting sensory information the brain prioritizes more reliable sensory channels (Ernst and Banks, 2002). When localizing objects in space, we typically rely more on the visual system (e.g., ventriloquist effect, rubber hand illusion: Alais and Burr, 2004b; Ehrsson et al., 2004; Charbonneau et al., 2013), while audition typically dominates the detection of temporal changes (e.g., auditory capture: Shipley, 1964; Shams et al., 2000). A popular experiment to unravel the interaction between vision and audition is the double-flash illusion (DFI). Participants frequently perceive multiple visual flashes when a single flash is accompanied by multiple temporally interspersed auditory beeps (Shams et al., 2000). The DFI is a classic example where perception of one sensory system (vision) is influenced by another (audition). It is currently believed that such a perceptual effect may emerge already at the earliest stages of the auditory and visual cortical hierarchies (Shams & Kim, 2010), challenging the idea of a strict parcellation of the brain into unisensory and multisensory areas (Ghazanfar and Schroeder, 2006; Kayser and Logothetis, 2007; Lakatos et al., 2007; Driver and Noesselt, 2008). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,537,883,816]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sensory areas are not passive gateways to the cortex. Rather, the neuronal states in early sensory systems as well as their long-range communication profiles with the rest of the brain shape the perception and integration of sensory events (Ebrahimi et al., 2022; Kayser & Logothetis, 2007). Several studies have demonstrated that neuronal states in early sensory systems can predict the detection of a weak sensory stimulus, or whether information from different input channels are combined (Lange et al., 2013, 2014; Keil et al., 2014; Leske et al., 2015). For instance, reduced pre-stimulus alpha power in the early visual cortices increases the likelihood of perceiving the DFI (Lange and colleagues (2013). Both local changes in the gain of sensory areas and modulations in sensory regions mediated by long-range functional connections can lead to fluctuations in excitability, thereby shaping perception (Ruhnau et al., 2014). While both local and long-range neuronal dynamics have been linked to multisensory integration (Lange et al., 2011, 2013, 2014); it is not well understood how the interplay of local and global neuronal dynamics modulate perception. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,837,880,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We used Magnetoencephalography (MEG) and a novel frequency-tagging approach, combined with spectral and functional connectivity analysis of ongoing oscillatory activity that allows us to isolate sensory processing of a single modality in the frequency domain. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,901,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,97,887,356]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Participants saw and heard sequences of flashes and beeps at different presentation frequencies, and were asked if the two sequences are in synchrony. Based on previous research on audio-visual illusions such as the flicker flutter effect (Shipley, 1964; Berger et al., 2003; Recanzone, 2003), we predicted that during some asynchronous trials, participants will perceive beeps and flashes to be in synchrony. Using frequency-tagging, we then isolated auditory and visual responses. Finally, the response magnitude was linked to the pre-stimulus neuronal states in each of the two systems. If pre-stimulus neuronal states operate locally, we predict a negative relationship between pre-stimulus alpha power and post-stimulus sensitivity to the sensory event in the same sensory modality. In contrast, if local fluctuations in alpha power bias the system at a more global level, we expect that local alpha power fluctuations in one sensory modality will affect sensitivity to sensory events in the other modality, potentially supported by enhanced long-range connectivity between sensory modalities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,373,352,390]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. Materials and Methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[112,425,264,444]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.1 Participants ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,446,883,566]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Twenty-two healthy volunteers (10 males, 24-31 years) with no known neurological deficits participated in this study. Participants gave written informed consent and received a small monetary compensation. The project was approved by the local Ethical Committee at University of Trento. Due to a technical error, the behavioral data of one participant was not recorded and could not be considered in the analyses where trials were segregated based on the participant's behavior. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,585,352,604]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.2 Experimental Design ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,608,883,768]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Visual stimuli were delivered into a dimly lit magnetically shielded room using a Dell Alienware Aurora PC running Windows 7 (64 bit). Stimuli were generated using Psychophysics toolbox 3 (Brainard, 1997) on Matlab 7.9 (The MathWorks Inc., Natick, MA). Images were projected onto a translucent screen using a PROPixx DLP LED projector at a refresh rate of $120\\mathrm{Hz}$ , and a screen resolution of $1920\\times 1080$ pixels. Participants viewed the stimulus $(3.44^{\\circ}$ of visual angle) at a distance from the screen of $100\\mathrm{cm}$ . Auditory stimuli were presented via stereo loudspeakers using Panphonics Sound Shower 2 amplifier at a sound level that was audible and comfortable for the participant. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,789,883,907]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The stimuli included a Gaussian red dot, presented in the center of the screen at two different visual flashing frequencies (slow: 5Hz and fast: 7.5Hz) and a pure tone (500 Hz carrier frequency) that was amplitude modulated at three different auditory beep frequencies (5Hz, 6.5Hz, and 7.5Hz), resulting in six different flash-beep combinations. These combinations consisted of two physically synchronous (S) conditions (5.0V-5.0A and 7.5V-7.5A), and four asynchronous (AS) conditions (5.0V-6.5A, 5.0V-7.5A, 7.5V-","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,903,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,97,883,335]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5.0A, 7.5V-6.5A). The asynchronous conditions were further subdivided into two conditions where the difference between frequencies was far (ASf: 5.0V-7.5A, 7.5V-5.0A) versus close (ASc: 5.0V-6.5A, 7.5V-6.5A). The subjective experience of synchrony between the two sensory streams was expected to be stronger during the ASc condition (Fig. 1A, top panel). The choice for these presentation frequencies was based on the constraints introduced by the refresh rate of the screen (120Hz) and a series of behavioral pilot experiments. All S and ASf conditions comprised 80 trials, while the number of trials was doubled (160 trials) in the ASc conditions, to ensure a sufficient trial number when sorting into trials where participants perceptually integrated or segregated the two sensory events. In addition, 80 Null trials were included in the experiment for a baseline comparison. The experiment was divided into 10 blocks of 72 pseudo-randomized trials, resulting in a total of 720 trials. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,357,883,435]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Participants were given a two-alternative forced choice task (2AFC). After a period of fixation $(750\\pm 250~\\mathrm{ms})$ , the audio-visual stimuli were presented for 3 sec. Participants were asked to indicate whether the beeps and flashes were in synchrony (Fig. 1A, bottom panel). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,455,488,474]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.3 MEG Acquisition and Preprocessing ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,478,883,758]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MEG was recorded continuously on a 102 triple sensor (two gradiometer, and one magnetometer) whole-head system (Elekta Neuromag, Helsinki Finland). Data was acquired with a sampling rate of $1\\mathrm{kHz}$ and an online band pass filter between 0.1 and $330\\mathrm{Hz}$ . The headshape of each individual participant was measured using a Polhemus FASTRAK 3D digitizer. The head position was recorded continuously using five localization coils (forehead, mastoids). For source reconstruction, individual structural MRI images of 12 participants were acquired on a 4T scanner (Bruker Biospin Ettlingen, Germany). The images were consequently co-registered into the MEG coordinate system using a set of anatomical landmarks (pre-auricular points and nasion) as well as the individual headshape. When no individual structural MRI was available, a model of the individual anatomy was created by warping an MNI template brain (MNI, Montreal, Quebec, Canada; http://www.bic.mni.mcgill.ca/brainweb) to the individual subject's headshape (10 participants). The structural MRI was used to create a realistic single-shell headmodel (Nolte, 2003). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,777,880,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The data preprocessing and analysis was performed using the open-source toolbox fieldtrip (Oostenveld et al., 2011), as well as custom written code. The continuous data was filtered (high-pass Butterworth filter at $1\\mathrm{Hz}$ ; DFT filter at 50, 100, and $150\\mathrm{Hz}$ ) and downsampled to $500\\mathrm{Hz}$ . The resulting continuous data was epoched around the events of interest and inspected visually for ocular, muscle and jump artifacts. Subsequently, cleaned epochs were band-pass filtered, depending on the analyses to be performed, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,901,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,97,883,137]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and projected onto a 3-dimensional grid (1.5x1.5x1.5cm) using a linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,155,464,172]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.4 Spectral analysis in source space ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,178,883,297]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Analysis of steady-state responses in source space was performed on the band-pass filtered data (4-16Hz), and centered on a covariance window between 1000-3000 ms post-stimulus to avoid evoked activity in the signal during the first second. Individual trials in the time window of interest were baseline corrected, averaged in the time domain, and subjected to a Fast Fourier transformation (FFT). The resulting complex values were used to compute the amplitude of the different frequencies. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,316,883,578]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Time-resolved Fourier spectra of pre-stimulus oscillatory activity were computed in source space, separately for low (4-32Hz) and high frequencies (32-128Hz). For low frequencies, the data was band-pass filtered (4-32Hz) and projected into source space using a covariance window of 600 ms before stimulus onset. Spectral components were estimated in 0.25 octave steps using a single Hanning taper on 500ms sliding time windows (50ms step size). High frequency spectral components were estimated from the high-pass filtered signal (32Hz) in source space using a multitaper approach with three Slepian tapers and sliding time windows of 250ms (Mitra and Pesaran, 1999). This procedure resulted in a frequency resolution of $\\pm 12.5\\mathrm{Hz}$ . The same Fourier spectra were used to test for differences in pre-stimulus spectral power and connectivity. Functional connectivity was operationalized with the Phase Locking Value (PLV) (Lachaux et al., 1999), which quantifies the consistency in phase angle differences between two regions, independent of the amplitude. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,595,339,614]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.5 Regression analysis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,618,883,878]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A linear regression approach was used to study the potential relationship between pre-stimulus alpha power fluctuations in early sensory areas, and post-stimulus activity at the auditory and visual tagging frequencies. First, single trial alpha power was computed at the source level in early visual and auditory areas. Next, trials were binned into quartiles on the basis of single-trial pre-stimulus alpha power, and post-stimulus steady state responses were computed across all trials in each of the four bins. Finally, linear regression was used at all grid points to find which brain regions show an inverse relationship between the alpha power in early auditory and visual areas and post-stimulus activity at the auditory and visual presentation frequencies. To control for multiple comparisons in space, a cluster-based resampling procedure was applied based on the cluster-mass. Correction for multiple comparisons was applied using a maximum statistic; the observed cluster-mass was compared to a permutation distribution of the maximum cluster-mass value from each permutation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,901,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,97,326,116]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.6 Statistical analysis ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,119,887,339]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Statistical analysis of frequency-tagged responses was performed using permutation t-tests (1000 iterations). At the whole brain level, a multiple comparison correction was applied based on the false discovery rate (FDR, Benjamini and Hochberg, 1995; Genovese et al., 2002). For the analysis of pre-stimulus oscillatory activity, second-level random-effects analysis was conducted. First, independent-sample t-tests were computed between conditions for each participant. The resulting t-values were converted to z-values for second level analysis. These z-maps were tested against zero at the group level. To control for multiple comparisons in time-frequency space, a cluster-based permutation approach was used, based on a maximum statistic of the cluster-mass (Maris and Oostenveld, 2007). The same resampling procedure was used to correct for multiple comparisons in space for the pre-post regression analysis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,354,210,372]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. Results ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[112,407,375,425]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1 Behavioral Performance ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,430,888,690]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Paired-sample permutation t-test (1000 iteration) revealed that participants perceived beeps and flashes as synchronous significantly more often during the Synchronous (S) versus the Asynchronous Far (ASf) conditions for slow (5.0V-5.0A versus 5.0V-7.5A Hz: $t(20)=8.13$ , $p<.001$ ) and fast visual presentation frequencies (7.5V-7.5A versus 7.5V-5.0A Hz: $t(20)=14.00$ , $p<.001$ ). Furthermore, synchrony was reported more often during the Asynchronous Close (ASc) versus Asynchronous Far (ASf) condition for fast (7.5V-6.5A versus 7.5V-5.0A Hz: $t(20)=7.28$ , $p<.001$ ), but not for slow visual presentation frequencies (5.0V-6.5A versus 5.0V-7.5A Hz: $t(20)=0.34$ , $p=.774$ ). Taken together, the behavioral results show that we were able to reliably elicit the subjective illusion of synchrony in the ASc condition for fast (7.5Hz), but not for slow (5.0Hz) visual presentation frequencies (see Fig. 1b). Based on these results, the MEG analysis on the neuronal dynamics during subjective experience of synchrony targeted the fast visual presentation frequencies only (7.5 Hz). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,708,797,743]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2 Modality-Specific Responses to Physical and Perceived Audio-Visual Synchrony ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,748,887,909]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To isolate early auditory and visual regions in space, frequency spectra of the ASf conditions (7.5V-5.0A and 5.0V-7.5A) were contrasted directly at the source level. For the localization, we used the 5Hz tagging frequency as it produced the strongest steady-state response in our data, independent of conditions (the results for 7.5Hz are slightly weaker but show a similar spatial distribution). As expected, we observe robust auditory 5Hz responses (7.5V-5.0A) in bilateral auditory cortex, while the visual 5Hz frequency (5.0V-7.5A) is strongest around V1 (Fig 2A). Regions of interest (ROI) for subsequent analysis were selected as the grid points in anatomically defined primary visual, and auditory ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,903,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,97,883,175]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"cortex (www.brainmap.org), which were sensitive to the visual and auditory presentation frequencies respectively (FDR-corrected). This was done to reduce confounding effects from adjacent temporal and parietal regions, as the unmasked statistical maps also extended into association cortices. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,196,883,356]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"While the functional peaks of the frequency-tagged responses are located in primary sensory areas, they potentially may not be restricted to these regions. To explore this possibility, we contrasted the source amplitude at 5Hz for each ASf condition (5.0V-7.5A, max response in visual cortex; 7.5V-5.0A, max response in auditory cortex) against the Null-condition and computed a conjunction analysis (Fig. 2B). We observe a widespread overlap between the responses to auditory and visual signals in temporal and parietal areas that are classically considered multisensory integration zones (Beauchamp et al., 2004; Bremmer et al., 2004; Beauchamp, 2005). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,377,883,478]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The behavioral data revealed that the subjective illusion of synchrony was only reliably perceived in the ASc condition during fast (7.5V-6.5A) but not slow (5.0V-6.5A) visual presentation frequencies. Therefore, subsequent ROI-based analyses were based on the fast visual presentation frequencies (S: 7.5V-7.5A; ASc: 7.5V-6.5A) as well as the two ASf conditions (7.5V-5.0A, and 5.0V-7.5A). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,498,883,676]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For the ROI analysis, paired-sample permutation t-tests were computed at the presentation frequency (7.5Hz) to test whether physical synchrony of beeps and flashes alters neural responses in early sensory areas. In the auditory cortex, we observed a positive difference between the S (7.5V-7.5A) versus ASf (5.0V-7.5A) condition, suggesting that a stronger neuronal response when the two sensory streams are in synchrony $(t(21)=4.23, p=.001$ ; Fig. 2C). In contrast, there was no evidence for an effect of synchrony in the visual ROI $(t(21)=0.69, p=.942)$ . Taken together, we demonstrate that the auditory, but not visual cortex is sensitive to the physical synchrony between the two sensory streams. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,698,883,898]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Next, we tested whether auditory and visual cortices were sensitive to the subjective illusion of synchrony in the ASc condition (7.5V-6.5A), the AS condition which yielded the highest number of behavior responses indicating synchrony. On average, participants perceived the two events as synchronous on $64\\%$ of the trials (see Fig. 1B). Prior to statistical inference, an equal number of trials were randomly selected from the ASc condition where participants reported the two events to be synchronous (integrated) versus asynchronous (segregated). This was done to avoid any spurious effects due to different sample sizes. To enhance robustness of the tagged frequency amplitudes, participants were only considered for this analysis if more than $20\\%$ of the possible number of trials in a condition could be retained. This procedure resulted in the trimming ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,903,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,97,883,137]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"of the data where participants responding predominantly with one type of response (either synchronous or asynchronous) were excluded (5 participants). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,157,883,335]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Paired-sample permutation t-tests were computed at the presentation frequencies (visual: 7.5Hz; auditory: 6.5Hz) on the remaining 16 participants. For the contrast between integrated versus segregated trials, we observed a significant difference in the auditory cortex (6.5Hz; $t(15) = 2.49$ , $p = .021$ ) (see Fig 2C). Specifically, the auditory cortex responds more strongly if the two sensory streams are integrated and perceived as synchronous. The same contrast at the visual tagging frequency (7.5Hz) demonstrated an equivalent effect in the visual ROI ( $t(15) = 2.57$ , $p = .019$ ) (Fig 2D). Thus, the visual cortex responds more strongly to visual information when it is subjectively integrated with the auditory stream. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,358,883,455]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Taken together, the auditory cortex showed enhanced sensory responses to auditory information if the two sensory streams were either physically or perceptually in synchrony. In contrast, the visual cortex showed enhanced sensory responses only if the two asynchronous streams were perceived as synchronous, but not when the stimuli were physically in synchrony. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,476,702,494]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.3 Pre-Stimulus Neuronal States Predict Multisensory Binding ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,500,883,737]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Next, we tested whether neuronal states of early sensory areas preceding stimulus presentation predict whether auditory and visual streams are perceptually integrated during the ASc condition (7.5V-6.5A, the AS condition which yielded the highest number of behavior responses indicating synchrony). To this end, we performed a second-level random-effects analysis. First, independent-samples t-tests were computed for each individual subject contrasting integrated versus segregated trials, and the resulting t-values were converted to z-values for group-level analysis. At the group level, these z-maps were tested against zero using one-sample t-tests. Cluster-based permutation was performed to control for multiple comparisons in time and frequency space (Maris and Oostenveld, 2007). Analyses were conducted on visual and auditory ROI's, separately for low (4-32Hz) and high frequencies (38-128Hz) in a time window of 500-100 ms before stimulus onset. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,758,883,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the visual cortex (Fig 3A), we observed a reduction in spectral power around the alpha band ( $\\sim$ 11.4 Hz) when participants perceived the sensory events as synchronous ( $t_{sum}(15) = -91.61$ , $p = .002$ ). Furthermore, we found enhanced visual gamma activity ( $\\sim$ 64-90.6Hz) in the same region when participants reported seeing the two sensory streams as synchronous ( $t_{sum}(15) = 4.24$ , $p = .042$ ). Thus, reduced alpha and enhanced gamma power in the visual cortex predict the perception of synchrony between auditory and visual events in the ASc condition. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,901,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,117,883,316]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the auditory cortex (Fig. 3B), our analysis revealed a reduction in spectral power in the lower alpha band ( $\\sim6.8\\mathrm{Hz}$ ) when trials were reported as synchronous ( $t_{sum}(15) = -72.90$ , $p = .006$ ). Notably, the peak difference was at a lower frequency than what we observed in the visual cortex. Although there is some variability in the reported auditory alpha peak frequency (Weisz et al., 2011; Weisz and Obleser, 2014), some studies suggest that it is lower than the visual alpha rhythm (Lehtelä et al., 1997). In contrast to the visual cortex, no differences were found in the higher frequencies when participants perceived the trials as synchronous or asynchronous. Taken together, we observed that reduced auditory alpha power predicts the subjective experience of audio-visual synchrony in the auditory cortex. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,337,880,517]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To explore the spatial specificity of these effects, pre-stimulus power in the two conditions were computed for all points in the 3D grid whereby spectral power was averaged in the time-frequency window where the effect was maximal in the ROI analysis (visual alpha: 9.6-11.4Hz, 500-250ms; auditory alpha: 6.8-8Hz, 500-250ms; visual gamma: 64-90.6Hz, 500-350ms). The thresholded maps for the contrast between integrated versus segregated trials revealed peak differences in visual cortices for visual gamma and visual alpha and a peak in the right auditory cortex for auditory alpha (Figure 3C-E, respectively). The majority of additional peaks outside early sensory areas were located in parietal and temporal areas, largely overlapping with the audio-visual conjunction map. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,537,883,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, to test whether there is a relationship between pre-stimulus neuronal states and post-stimulus evoked responses to the stimulus, we used a regression-based approach on the pre-stimulus alpha power, and post stimulus evoked activity at the presentation frequencies in early visual and auditory cortex. First, alpha power was averaged across the time window 500-250 ms before stimulus onset. The decision for this time window was chosen a) to capture the maximum alpha suppression effect from the ROI analysis, and b) to avoid potential leakage from the post-stimulus time window into the pre-stimulus period due to the temporal smoothing of the time-frequency analysis (with a 500ms time window, post-stimulus events may leak into the pre-stimulus period up to 250ms). Averaged pre-stimulus alpha power in early sensory regions was computed for each individual trial, and trials were binned into quartiles. For each of these quartiles we also computed the amplitude at the auditory and visual presentation frequency post-stimulus. This was done for all points in the 3D grid. The procedure was applied separately with bilateral visual, and auditory cortices as seed regions, taking into account the preferred alpha rhythm in each modality (visual 9.6-11.4 Hz; auditory 6.8-8Hz). Statistical analyses were performed using linear regression, and cluster-based permutation was used to control for multiple comparisons (Maris and Oostenveld, 2007; Obleser and Weisz, 2012). Importantly, amplitudes of the presentation frequencies could show a linear increase or ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,901,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,97,883,175]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"decrease with pre-stimulus alpha activity. However, the interpretation of an increase would be highly problematic as it could merely reflect noise fluctuations from trial to trial. Therefore, statistical analysis was performed one-sided to identify negative linear relationships only. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,196,883,513]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Our analysis revealed a significant negative relationship between the pre-stimulus visual alpha rhythm and the amplitude of the visual tagging frequency (7.5Hz: $t_{sum}$ (21)=-165.33, $p=.009$ ). This difference was observed in posterior parietal cortex, predominantly in the right hemisphere, as well as in parieto-occipital regions stretching from extrastriate visual cortex medially towards the Precuneus and cingulate cortex (Fig. 4A,C). Furthermore, we also find a negative linear relationship between pre-stimulus visual alpha power and the auditory presentation frequency ( $t_{sum}$ (21)=-107.38, $p=.026$ ). This effect was observed in the right auditory cortex (Fig. 4B,D). There was no evidence for a negative linear relationship between the auditory alpha rhythm on either visual or auditory tagging frequency. Taken together, these results demonstrate that reduced visual alpha power in the early visual cortex predicts enhanced sensitivity to the flash sequence in downstream parieto-occipital areas, as well as enhanced auditory cortex sensitivity to the beep sequence. As no such effect was observed for the auditory alpha rhythm, we can conclude that in the case of auditory capture, there is an asymmetric relationship between the effects of locally reduced alpha power and cortical excitability in visual and auditory cortices. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,537,883,878]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If pre-stimulus alpha power in visual cortex predicts post-stimulus auditory processing, there might be pre-existing fluctuations in how the visual and auditory cortices communicate with each other that influence whether the two sensory events are perceived as synchronous (Ruhnau et al., 2014; Weisz et al., 2014; Leske et al., 2015). To directly test this idea, we computed the phase locking value (PLV), as a proxy for functional connectivity, between the right auditory and visual ROI for the visual alpha (6.8-11.4Hz, 500-250ms) and gamma band (64-90.6Hz, 500-250ms). Integrated and segregated trials were contrasted using paired-sample permutation t-tests. We found enhanced pre-stimulus functional connectivity between visual and auditory cortices in the gamma band on trials that were perceived as synchronous ( $t(15)=3.16$ , $p=.006$ ). To explore the spatial selectivity of this effect, permutation t-tests were computed contrasting the integrated versus segregated conditions at the whole-brain level. As the thresholded map ( $p<.05$ , unc.) in Fig. 4E illustrates, the strongest and most widespread increase in connectivity was observed between visual cortex and right auditory cortex, largely overlapping with the cluster from the regression analysis. Paired-sample t-tests in the alpha range did not yield a significant difference between integrated versus segregated trials ( $t(15)=0.66$ , $p>.5$ ) (Fig. 4D). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,901,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,97,243,113]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. Discussion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,135,883,435]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We aimed to investigate the network mechanisms underlying the integration of audiovisual sequences by quantifying local representations and connectivity of early auditory and visual cortices. To this end we used a novel frequency tagging approach inspired by auditory capture effects such as the flicker flutter illusion (Ogilvie, 1956; Shipley, 1964; Berger et al., 2003; Noesselt et al., 2008); where a series of beeps and flashes are presented at neighboring frequencies, and the two streams are sometimes perceived as synchronous. Leveraging the intra-individual variability in multisensory perception, we studied physiological responses within and between auditory and visual systems in different perceptual contexts, that is, when the events were perceived as synchronous or not. Moreover, by linking these isolated sensory responses with ongoing oscillatory activity before the stimulus was presented, we were able to investigate how the neuronal state of one system affects the local sensory response, as well as the sensory response in the other sensory system. Such a paradigm and analytical framework allowed us to isolate the brain correlate of multisensory integration versus segregation under constant physical stimulation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,455,883,835]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"First, we observed that the auditory cortex responded more strongly to the auditory stream when the two sensory events were physically synchronous (Fig 2C, bottom panel), which was not true for the visual cortex. We also found enhanced auditory responses when participants perceived an asynchronous series of beeps and flashes as synchronous (Fig 2D, bottom panel). A similar enhancement in the visual response to the flashes emerged when participants report perceiving a stream of asynchronous beeps and flashes as synchronous (Fig 2D, top panel). Furthermore, the perception of synchrony is predicted by fluctuations in oscillatory neuronal activity shortly before stimulus presentation (Fig 3). In the auditory cortex pre-stimulus alpha power is reduced when participants integrate the two sensory events (Fig 3B,E). In the visual cortex, both reduced alpha and enhanced gamma power predict perceptual integration (Fig A,C,D). Most importantly, we demonstrated that these pre-stimulus dynamics have a different relationship with post-stimulus processing in visual and auditory cortices (Fig 4). Reduced visual alpha power predicts enhanced sensory processing in both auditory and visual cortices (Fig 4A-C), while we found no evidence for a relationship between pre-stimulus alpha power and post-stimulus sensory processing in the auditory cortex. Corroborating this idea of direct information transfer between early sensory areas, we show that the subjective perception of synchrony is preceded by enhanced functional connectivity in between sensory areas in the gamma band (Fig 4D-E). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,901,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,97,861,132]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sensory Processing During Physical and Perceptual Synchrony of Audio-Visual Events ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,137,883,377]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the current study, the auditory cortex responded more strongly if auditory and visual events were either physically or perceptually synchronous (Fig 2C-D, bottom panel). In contrast, the visual cortex showed enhanced sensory responses only when the two sensory streams were perceptually synchronous and not physically synchronous (Fig 2D, top panel). This pattern of results is interesting because it attributes different roles to auditory and visual cortices with respect to multisensory integration: While auditory cortex appears to be sensitive to both perceptual and physical synchrony, the response in visual cortex is only linked to the illusory perception of synchrony. These results may relate to the auditory capture, as 'integration' of the two sensory streams shift in perception toward the more reliable auditory stream (Recanzone, 2003). It is important to emphasize that although this asymmetry might hold for auditory capture, it is not likely generalizable to other forms of multisensory integration. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,397,883,676]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Previous studies on synchrony effects in multisensory paradigms using frequency tagging are rare and have produced mixed results (Giani et al., 2012; Nozaradan et al., 2012; Barbero et al., 2025). Nozaradan and colleagues (2012) reported synchrony effects for both auditory and visual presentation frequencies. Moreover, intermodulation frequencies (linear combinations of audio-visual presentation frequencies) were proven to be a marker of audio-visual emotion integration (Barbero et al., 2025). As these results are restricted to sensor space it is not clear whether the effects reside in early sensory areas or in regions in association cortices. Indeed, using conjunction analysis we found a wide network of areas that are sensitive to both the visual and auditory presentation frequencies (Fig. 2B), which could result in multisensory effects observed at the sensor level. Our approach is different as it uses source analysis in a way that preserves the ability to maximally segregate the two sensory events using frequency tagging. By applying this more sensitive approach, we demonstrated that frequency tagging is a versatile tool to target multisensory integration in the brain. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,696,836,732]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Excitability Fluctuations in Early Sensory Regions Link to Local and Network Activity Change ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[109,736,883,893]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The current study further demonstrates that illusory perception of synchrony is associated with reduced power in the pre-stimulus alpha rhythm in both auditory and visual cortices (Fig 3). Current theories suggest that fluctuations in alpha power reflect changes in cortical excitability (Romei et al., 2008a, 2008b, 2010; Lange et al., 2013; Cecere et al., 2014). In the visual cortex, reduced alpha power is accompanied by enhanced visual gamma activity, often associated with visual processing (Gray et al., 1989; Womelsdorf et al., 2007; Fries et al., 2008). We demonstrated a negative relationship between pre-stimulus alpha power in visual areas and post-stimulus processing at the visual ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,901,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,97,883,234]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"presentation frequency in downstream visual areas in parieto-occipital cortex (Fig 4A,C, left panel), as well as with the post-stimulus processing at the auditory presentation frequency in auditory regions (Fig 4B,C, right panel). Importantly, the reduced prestimulus alpha power in the occipital cortex predicted subjective multisensory integration (Fig. 3A,B). The current findings show that fluctuations in alpha power not only reflect local changes in cortical excitability, but also shape the dynamics of transient functional networks at large. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,257,883,416]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"During the double flash illusion (Shams & Kim, 2010), it was argued previously that a second beep elicits the illusory perception of an additional flash when excitability in the visual cortex is high (Lange et al., 2013, 2014). In this study, the perceived synchrony could be predicted by the pre-stimulus alpha, which signifies cortical excitability. Furthermore, only the visual, but not the auditory alpha rhythm could be linked reliably to the amplitude of the tagged visual frequency, suggesting that in the case of auditory capture alpha power in the visual cortex has more direct effects on the global network organization, while auditory alpha operates locally. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,438,883,777]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Another interpretation of the excitability hypothesis is that reduced local alpha power makes visual and auditory cortices more prone to communicate (Lange et al., 2014). Two findings in the current study provide support for this idea. First, we found that enhanced functional connectivity in the gamma frequency band between early visual and auditory areas predicted whether the two sensory events are perceived as synchronous (Fig 4D-E). This is in line with animal studies demonstrating the existence of direct anatomical pathways between early auditory and visual areas (Falchier et al., 2002; Rockland and Ojima, 2003; Cappe and Barone, 2005). Second, and most importantly, we observed that reduced pre-stimulus alpha power in the visual cortex predicts post-stimulus sensory responses in both visual and auditory cortices (Fig 4B-C, right panel). In contrast, local alpha fluctuations in the auditory cortex, while linked to the perception of synchrony, do not affect the sensory response in the visual cortex. This asymmetric relationship between reduced pre-stimulus alpha power and enhanced post-stimulus sensory responses in visual and auditory cortices could arise from the fact that vision is our dominant modality and under most circumstances drives multisensory perception. As such spontaneous fluctuations in the visual cortex will affect both local and global network structure more readily than fluctuations in the auditory cortex. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,799,883,857]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In conclusion, our study demonstrates that temporal integration of multisensory events in time depends on the fluctuating neuronal states of the system, which bias perception in early sensory areas through local and long-range network interactions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,901,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,97,223,113]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[112,135,883,875]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Alais D, Burr D (2004a) The ventriloquist effect results from near-optimal bimodal integration. Curr Biol 14:257-262. \",\"Alais D, Burr D (2004b) Ventriloquist Effect Results from Near-Optimal Bimodal Integration. Curr Biol 14:257-262. \",\"Barbero, F. M., Talwar, S., Calce, R. P., Rossion, B., & Collignon, O. (2025). 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Biophys J 76:691-708. \"]","page_idx":"15","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[84,2,903,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[114,95,883,898]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Nozaradan S, Peretz I, Mouraux A (2012) Steady-state evoked potentials as an index of multisensory temporal binding. Neuroimage 60:21-28. \",\"Obleser J, Weisz N (2012) Suppressed alpha oscillations predict intelligibility of speech and its acoustic details. 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Neuroimage 31:1247-1256. \",\"Weisz N, Wuhle A, Monittola G, Demarchi G, Frey J, Popov T, Braun C (2014) Prestimulus oscillatory power and connectivity patterns predispose conscious somatosensory perception. Proc Natl Acad Sci U S A 111:E417-E425. \",\"Womelsdorf T, Schoffelen J-M, Oostenveld R, Singer W, Desimone R, Engel AK, Fries P (2007) Modulation of Neuronal Interactions Through Neuronal Synchronization. Science (80- ) 316:1609-1612. \"]","page_idx":"16","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[84,2,903,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[145,215,544,532]","code_body":null,"code_caption":null,"image_caption":"[\"Figures \"]","image_footnote":"[]","img_path":"images/0782/97b83bf3166ad46bca293b526a506c75ed94e91f8496408f6fa5dbd0027021ec.jpg","list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[527,215,830,532]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 1. Design and behavioral results of the study. A) The top panel illustrates the set of conditions used in the current study. The rows depict the three beep frequencies (5Hz, 6.5Hz, 7.5Hz), while the columns show the two flash frequencies (5Hz, 7.5Hz). The bottom panel shows the temporal sequence of a single trial. After a variable period of fixation, auditory beeps and visual flashes are presented at variable frequencies for 3 seconds. A trial is always followed by the question if the two sensory sequences were in synchrony or not. B) The behavioral results for the fast visual presentation frequency (7.5 Hz) show a gradual increase in the proportion trials where the two events were perceived as synchronous as the beep frequencies approached the flash frequency. In the ASf condition, synchrony is perceived on $64\\\\%$ of the trials. Error bars depict SEM, adjusted for within subject comparisons. \"]","image_footnote":"[]","img_path":"images/0458/941e94dbe2d740e11b4b03f4f9f1eb3d77915300947ffe66a4135433fa8e3495.jpg","list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[84,3,903,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[117,106,566,252]","code_body":null,"code_caption":null,"image_caption":"[\"A \"]","image_footnote":"[]","img_path":"images/0502/0cd92d6e8f45eb232f60c5a7521c3d9d0161819f2502b8d3b925c8ee3fbe60df.jpg","list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[591,108,736,244]","code_body":null,"code_caption":null,"image_caption":"[\"C \"]","image_footnote":"[]","img_path":"images/0236/cf5a21fcd490af5d58bf0f22c94f6205f77a5c642fd82fa623a6d5ba915e6d08.jpg","list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[756,107,883,242]","code_body":null,"code_caption":null,"image_caption":"[\"D \"]","image_footnote":"[]","img_path":"images/0713/4eefb60e563d59c21b7a64d58ca429fbe904ad5701127b05a777d2ccbad860e7.jpg","list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[117,258,571,398]","code_body":null,"code_caption":null,"image_caption":"[\"B \"]","image_footnote":"[]","img_path":"images/0926/1ff8ae86a57291bbddc3556ca585bfe16e005a5f72d50a93aa6201a55ac2ccb3.jpg","list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[591,252,738,396]","code_body":null,"code_caption":null,"image_caption":"[\"a aee \"]","image_footnote":"[]","img_path":"images/0437/ca9d1043f9d1af6af88279071685a781823402d3b670177aeaf33909db7ac877.jpg","list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[756,252,880,396]","code_body":null,"code_caption":null,"image_caption":"[\"Frequency [Hz] \",\"Figure 2. Analysis of auditory and visual processing at the presentation frequencies. A) The contrast between the two ASf conditions (7.5V-5.0A versus 5.0V-7.5A), at 5Hz was used to localize early sensory regions of interest. Warm colours show sensitivity to the rhythmic auditory stimulation in bilateral superior temporal gyrus. Cold colours reflect sensitivity to the visual presentation frequency in occipital and parietal lobes, with peaks in bilateral calcarine sulci. The statistical maps are thresholded at $p < .05$ (FDR-corrected). B) The activation maps show the multisensory areas from the conjunction between each of the two asynchronous against the Null condition. Minimum t-values are used to show gradient activation. C) Comparison of the S condition (7.5V-7.5A: pink) versus the two ASf conditions (7.5V-5.0A: blue 5.0V-7.5A red) in visual (top panel), and auditory (bottom panel) cortices. A synchrony effect is observed only in the auditory ROI. Shaded areas around the graphs depict SEM, adjusted for within subject comparisons. D) Illusory synchronization effects for the ASc condition during fast visual presentation (7.5V6.5A) in visual (top panel), and auditory (bottom panel) cortices. Enhanced neural activity is observed in both modalities for trials where visual and auditory signals were perceived as synchronous (purple) versus asynchronous (blue). Shaded areas around the graphs depict SEM, adjusted for within subject comparisons. \"]","image_footnote":"[]","img_path":"images/0308/2faec9dbfc45e63f8ce8e73e91432b1a7e5fb8fd0bef8a2f5705f647abf4a65c.jpg","list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[84,3,903,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,95,401,281]","code_body":null,"code_caption":null,"image_caption":"[\"A \"]","image_footnote":"[]","img_path":"images/0532/7028a42eda4d1d7abcf7e597d8e98948a4283718520c6f2d219819c993cee2d7.jpg","list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[405,94,781,281]","code_body":null,"code_caption":null,"image_caption":"[\"B \"]","image_footnote":"[]","img_path":"images/0137/aa6dd9804017519b189f2a01c4f1377b420b0911a4a19bc79f9c1aa956019240.jpg","list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[223,279,370,352]","code_body":null,"code_caption":null,"image_caption":"[\"C \"]","image_footnote":"[]","img_path":"images/0070/f1f68e98faf51daef0abe88606b8cacd9bca8b3dc5cf0ea3956d808c34214d34.jpg","list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[403,277,602,445]","code_body":null,"code_caption":null,"image_caption":"[\"D \"]","image_footnote":"[]","img_path":"images/0373/027a46d8c787b11bfd8f5eb2ae5391cb98df82bd61fb2aa7e0566452aae2366d.jpg","list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[602,277,800,415]","code_body":null,"code_caption":null,"image_caption":"[\"E \"]","image_footnote":"[]","img_path":"images/0842/fc0bfbc0eb1253b4926edb61c1c7512857ca4f3d2c7d7fb2c4012b74de8f3934.jpg","list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[197,352,397,414]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 3. Analysis of pre-stimulus oscillatory activity contrasting trials perceived as synchronous versus asynchronous. Time-frequency representations from visual areas (right panel) depict the statistical differences in pre-stimulus power for the integrated versus segregated trials. A) statistically significant increase (highlighted, top panel) is observed in the gamma band when audio-visual streams were integrated. In addition, there was a reduction in pre-stimulus alpha power B)) In auditory areas (right panel), there was a reduction in pre-stimulus alpha activity when the two sensory streams were perceived as synchronous (highlighted, bottom panel). C-E Whole-brain, statistically thresholded $(p < .05$ , unc.) maps of the three effects in the visual gamma (C), visual alpha (D), and auditory alpha (E) band reveal mostly independent clusters in visual and auditory areas respectively. Additional clusters are observed mostly in temporal and parietal areas, however the peaks are found in the primary sensory regions. \"]","image_footnote":"[]","img_path":"images/0527/c0c4f628881a1ccb3371134a455a813b5815f273952ad85980328b61e135eca0.jpg","list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[84,3,903,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[196,119,803,734]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 4. Pre-post regression and connectivity analysis. A) Statistically thresholded whole-brain activation map (p<.05, cluster-corrected, one-tailed), showing regions where the post-stimulus amplitude at the visual tagging frequency shows a negative linear relationship with pre-stimulus alpha power in visual cortex. This is observed in a network of regions spanning from parieto-occipital regions (POG: I) to posterior parietal cortex (rPPC: II) B) Activation maps show regions where a linear negative relationship is \"]","image_footnote":"[]","img_path":"images/0696/959db5c620d577dd7400295c4d8d2c7991c5910992d81af19233dcf95bbf948d.jpg","list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[84,3,903,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,45,803,59]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[109,97,883,417]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"observed between the amplitude at the auditory tagging frequency post-stimulus, and pre-stimulus alpha power in visual cortex. This relationship is observed most strongly in the right auditory cortex (rAC: III) and insular cortex (rIC: IV). C) Bar graphs illustrate mean post-stimulus amplitude for the visual (blue) and auditory (red) tagging frequencies in each of the alpha quartiles from visual cortex (low alpha: dark shades, high alpha: lighter shades). Values are extracted from two peak regions where alpha is linearly related to the visual tagging frequency (IPOG, rPPC, left panel), and two regions where alpha is linearly related to the auditory tagging frequency (rAC, rIC, right panel). A significant negative linear relationship is marked with a star. Error bars depict SEM adjusted for within subject comparisons. D) Bar graphs show phase-locking between visual and right auditory cortex in the alpha and gamma band for integrated versus segregated trials. Enhanced functional connectivity is observed for integrated trials in the gamma, but not the alpha band. E) Thresholded statistical maps $(p < .05$ , unc.) contrasting functional connectivity maps between the integrated versus segregated conditions considering the visual cortex as the seed region. The map shows that the activity is largely confined to the right superior temporal gyrus and other auditory regions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[84,2,903,37]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. ","text_format":null,"text_level":null,"type":"header"}],"string":"[\n {\n \"bbox\": \"[122,89,875,143]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,179,883,219]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Siddharth Talwar<sup>a</sup>, Francesca M. Barbero<sup>a,b</sup>, Markus J. van Ackerena<sup>a</sup>, Nathan Weisz<sup>c</sup>, and Olivier Collignon<sup>a,b,c</sup> \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,239,883,339]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"<sup>a</sup> Institute of Psychology (IPSY) and Institute of Neuroscience (IoNS), UCLouvain, Louvain-la-Neuve, Belgium \\\",\\\"<sup>b</sup> Center for Mind/Brain Sciences, University of Trento, Italy \\\",\\\"$^{c}$ Center for Cognitive Neuroscience Salzburg (CCNS) and Division of Physiological Psychology, University of Salzburg, Austria \\\"]\",\n \"page_idx\": \"0\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[109,359,883,458]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Author contributions: O.C., M.J.V.A., and F.M.B. conceived and designed the experiment; M.J.V.A. and F.M.B. performed the experiment, M.J.V.A., F.M.B., S.T. analyzed the data; N.W. provided resources for analysis; M.J.V.A. and O.C. interpreted the results of the experiment; O.C. wrote the first draft of the manuscript; S.T., M.J.V.A., O.C. and N.W. commented on the manuscript. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,479,883,520]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: multisensory integration, steady-state response, MEG, cortical oscillations, functional connectivity, cortical excitability, pre-stimulus activity \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,903,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[117,97,204,113]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,135,887,396]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"How does the brain integrate or segregate multiple sensory inputs? In our study, we used magnetoencephalography to comprehensively investigate local and network dynamics before and after the presentation of sequences of beeps and flashes that are sometimes perceived as synchronous or asynchronous. Frequency-tagging and spectral analysis revealed that under identical physical conditions, subjective perceptual fusion of multisensory signals elicits stronger evoked sensory responses in both visual and auditory cortices. Crucially, perceptual fusion is preceded by locally reduced pre-stimulus alpha activity, as well as enhanced functional connectivity between auditory and visual cortices within the pre-stimulus gamma activity. We also show that pre-stimulus neuronal states in the occipital cortex predict post-stimulus sensory responses to auditory sequences in the temporal cortex, but not the opposite. The current findings provide evidence that the perceptual fusion of multisensory events relate to a complex interplay between local and inter-sensory neuronal states before and after stimulus presentation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,450,334,470]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Significance Statement \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,489,888,650]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"How does the brain blend information from multiple sensory systems into one holistic perception? We developed a novel frequency-tagging paradigm in Magnetoencephalography (MEG) to robustly estimate the sensory responses to a series of flashes and beeps in early sensory areas, and to demonstrate how these responses are shaped by ongoing fluctuations in local, and long-range network activity. By combining the steady-state method with spectral, and functional connectivity analysis of ongoing oscillations in source space, the current study provides novel insights into the relationship between internal brain states and the way we perceive multisensory events. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,903,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,97,253,113]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,135,883,214]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Understanding how information from multiple senses are seamlessly merged into a single coherent percept is a major challenge for the field of cognitive neuroscience. It is argued that integration emerges already at the earliest stages of the cortical hierarchy, within areas once considered exclusively unisensory. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,234,883,515]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To resolve conflicting sensory information the brain prioritizes more reliable sensory channels (Ernst and Banks, 2002). When localizing objects in space, we typically rely more on the visual system (e.g., ventriloquist effect, rubber hand illusion: Alais and Burr, 2004b; Ehrsson et al., 2004; Charbonneau et al., 2013), while audition typically dominates the detection of temporal changes (e.g., auditory capture: Shipley, 1964; Shams et al., 2000). A popular experiment to unravel the interaction between vision and audition is the double-flash illusion (DFI). Participants frequently perceive multiple visual flashes when a single flash is accompanied by multiple temporally interspersed auditory beeps (Shams et al., 2000). The DFI is a classic example where perception of one sensory system (vision) is influenced by another (audition). It is currently believed that such a perceptual effect may emerge already at the earliest stages of the auditory and visual cortical hierarchies (Shams & Kim, 2010), challenging the idea of a strict parcellation of the brain into unisensory and multisensory areas (Ghazanfar and Schroeder, 2006; Kayser and Logothetis, 2007; Lakatos et al., 2007; Driver and Noesselt, 2008). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,537,883,816]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sensory areas are not passive gateways to the cortex. Rather, the neuronal states in early sensory systems as well as their long-range communication profiles with the rest of the brain shape the perception and integration of sensory events (Ebrahimi et al., 2022; Kayser & Logothetis, 2007). Several studies have demonstrated that neuronal states in early sensory systems can predict the detection of a weak sensory stimulus, or whether information from different input channels are combined (Lange et al., 2013, 2014; Keil et al., 2014; Leske et al., 2015). For instance, reduced pre-stimulus alpha power in the early visual cortices increases the likelihood of perceiving the DFI (Lange and colleagues (2013). Both local changes in the gain of sensory areas and modulations in sensory regions mediated by long-range functional connections can lead to fluctuations in excitability, thereby shaping perception (Ruhnau et al., 2014). While both local and long-range neuronal dynamics have been linked to multisensory integration (Lange et al., 2011, 2013, 2014); it is not well understood how the interplay of local and global neuronal dynamics modulate perception. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,837,880,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We used Magnetoencephalography (MEG) and a novel frequency-tagging approach, combined with spectral and functional connectivity analysis of ongoing oscillatory activity that allows us to isolate sensory processing of a single modality in the frequency domain. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,901,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,97,887,356]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Participants saw and heard sequences of flashes and beeps at different presentation frequencies, and were asked if the two sequences are in synchrony. Based on previous research on audio-visual illusions such as the flicker flutter effect (Shipley, 1964; Berger et al., 2003; Recanzone, 2003), we predicted that during some asynchronous trials, participants will perceive beeps and flashes to be in synchrony. Using frequency-tagging, we then isolated auditory and visual responses. Finally, the response magnitude was linked to the pre-stimulus neuronal states in each of the two systems. If pre-stimulus neuronal states operate locally, we predict a negative relationship between pre-stimulus alpha power and post-stimulus sensitivity to the sensory event in the same sensory modality. In contrast, if local fluctuations in alpha power bias the system at a more global level, we expect that local alpha power fluctuations in one sensory modality will affect sensitivity to sensory events in the other modality, potentially supported by enhanced long-range connectivity between sensory modalities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,373,352,390]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. Materials and Methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,425,264,444]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.1 Participants \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,446,883,566]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Twenty-two healthy volunteers (10 males, 24-31 years) with no known neurological deficits participated in this study. Participants gave written informed consent and received a small monetary compensation. The project was approved by the local Ethical Committee at University of Trento. Due to a technical error, the behavioral data of one participant was not recorded and could not be considered in the analyses where trials were segregated based on the participant's behavior. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,585,352,604]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2 Experimental Design \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,608,883,768]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Visual stimuli were delivered into a dimly lit magnetically shielded room using a Dell Alienware Aurora PC running Windows 7 (64 bit). Stimuli were generated using Psychophysics toolbox 3 (Brainard, 1997) on Matlab 7.9 (The MathWorks Inc., Natick, MA). Images were projected onto a translucent screen using a PROPixx DLP LED projector at a refresh rate of $120\\\\mathrm{Hz}$ , and a screen resolution of $1920\\\\times 1080$ pixels. Participants viewed the stimulus $(3.44^{\\\\circ}$ of visual angle) at a distance from the screen of $100\\\\mathrm{cm}$ . Auditory stimuli were presented via stereo loudspeakers using Panphonics Sound Shower 2 amplifier at a sound level that was audible and comfortable for the participant. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,789,883,907]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The stimuli included a Gaussian red dot, presented in the center of the screen at two different visual flashing frequencies (slow: 5Hz and fast: 7.5Hz) and a pure tone (500 Hz carrier frequency) that was amplitude modulated at three different auditory beep frequencies (5Hz, 6.5Hz, and 7.5Hz), resulting in six different flash-beep combinations. These combinations consisted of two physically synchronous (S) conditions (5.0V-5.0A and 7.5V-7.5A), and four asynchronous (AS) conditions (5.0V-6.5A, 5.0V-7.5A, 7.5V-\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,903,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,97,883,335]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5.0A, 7.5V-6.5A). The asynchronous conditions were further subdivided into two conditions where the difference between frequencies was far (ASf: 5.0V-7.5A, 7.5V-5.0A) versus close (ASc: 5.0V-6.5A, 7.5V-6.5A). The subjective experience of synchrony between the two sensory streams was expected to be stronger during the ASc condition (Fig. 1A, top panel). The choice for these presentation frequencies was based on the constraints introduced by the refresh rate of the screen (120Hz) and a series of behavioral pilot experiments. All S and ASf conditions comprised 80 trials, while the number of trials was doubled (160 trials) in the ASc conditions, to ensure a sufficient trial number when sorting into trials where participants perceptually integrated or segregated the two sensory events. In addition, 80 Null trials were included in the experiment for a baseline comparison. The experiment was divided into 10 blocks of 72 pseudo-randomized trials, resulting in a total of 720 trials. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,357,883,435]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Participants were given a two-alternative forced choice task (2AFC). After a period of fixation $(750\\\\pm 250~\\\\mathrm{ms})$ , the audio-visual stimuli were presented for 3 sec. Participants were asked to indicate whether the beeps and flashes were in synchrony (Fig. 1A, bottom panel). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,455,488,474]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.3 MEG Acquisition and Preprocessing \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,478,883,758]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MEG was recorded continuously on a 102 triple sensor (two gradiometer, and one magnetometer) whole-head system (Elekta Neuromag, Helsinki Finland). Data was acquired with a sampling rate of $1\\\\mathrm{kHz}$ and an online band pass filter between 0.1 and $330\\\\mathrm{Hz}$ . The headshape of each individual participant was measured using a Polhemus FASTRAK 3D digitizer. The head position was recorded continuously using five localization coils (forehead, mastoids). For source reconstruction, individual structural MRI images of 12 participants were acquired on a 4T scanner (Bruker Biospin Ettlingen, Germany). The images were consequently co-registered into the MEG coordinate system using a set of anatomical landmarks (pre-auricular points and nasion) as well as the individual headshape. When no individual structural MRI was available, a model of the individual anatomy was created by warping an MNI template brain (MNI, Montreal, Quebec, Canada; http://www.bic.mni.mcgill.ca/brainweb) to the individual subject's headshape (10 participants). The structural MRI was used to create a realistic single-shell headmodel (Nolte, 2003). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,777,880,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The data preprocessing and analysis was performed using the open-source toolbox fieldtrip (Oostenveld et al., 2011), as well as custom written code. The continuous data was filtered (high-pass Butterworth filter at $1\\\\mathrm{Hz}$ ; DFT filter at 50, 100, and $150\\\\mathrm{Hz}$ ) and downsampled to $500\\\\mathrm{Hz}$ . The resulting continuous data was epoched around the events of interest and inspected visually for ocular, muscle and jump artifacts. Subsequently, cleaned epochs were band-pass filtered, depending on the analyses to be performed, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,901,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,97,883,137]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and projected onto a 3-dimensional grid (1.5x1.5x1.5cm) using a linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,155,464,172]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.4 Spectral analysis in source space \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,178,883,297]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Analysis of steady-state responses in source space was performed on the band-pass filtered data (4-16Hz), and centered on a covariance window between 1000-3000 ms post-stimulus to avoid evoked activity in the signal during the first second. Individual trials in the time window of interest were baseline corrected, averaged in the time domain, and subjected to a Fast Fourier transformation (FFT). The resulting complex values were used to compute the amplitude of the different frequencies. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,316,883,578]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Time-resolved Fourier spectra of pre-stimulus oscillatory activity were computed in source space, separately for low (4-32Hz) and high frequencies (32-128Hz). For low frequencies, the data was band-pass filtered (4-32Hz) and projected into source space using a covariance window of 600 ms before stimulus onset. Spectral components were estimated in 0.25 octave steps using a single Hanning taper on 500ms sliding time windows (50ms step size). High frequency spectral components were estimated from the high-pass filtered signal (32Hz) in source space using a multitaper approach with three Slepian tapers and sliding time windows of 250ms (Mitra and Pesaran, 1999). This procedure resulted in a frequency resolution of $\\\\pm 12.5\\\\mathrm{Hz}$ . The same Fourier spectra were used to test for differences in pre-stimulus spectral power and connectivity. Functional connectivity was operationalized with the Phase Locking Value (PLV) (Lachaux et al., 1999), which quantifies the consistency in phase angle differences between two regions, independent of the amplitude. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,595,339,614]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.5 Regression analysis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,618,883,878]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A linear regression approach was used to study the potential relationship between pre-stimulus alpha power fluctuations in early sensory areas, and post-stimulus activity at the auditory and visual tagging frequencies. First, single trial alpha power was computed at the source level in early visual and auditory areas. Next, trials were binned into quartiles on the basis of single-trial pre-stimulus alpha power, and post-stimulus steady state responses were computed across all trials in each of the four bins. Finally, linear regression was used at all grid points to find which brain regions show an inverse relationship between the alpha power in early auditory and visual areas and post-stimulus activity at the auditory and visual presentation frequencies. To control for multiple comparisons in space, a cluster-based resampling procedure was applied based on the cluster-mass. Correction for multiple comparisons was applied using a maximum statistic; the observed cluster-mass was compared to a permutation distribution of the maximum cluster-mass value from each permutation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,901,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,97,326,116]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.6 Statistical analysis \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,119,887,339]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Statistical analysis of frequency-tagged responses was performed using permutation t-tests (1000 iterations). At the whole brain level, a multiple comparison correction was applied based on the false discovery rate (FDR, Benjamini and Hochberg, 1995; Genovese et al., 2002). For the analysis of pre-stimulus oscillatory activity, second-level random-effects analysis was conducted. First, independent-sample t-tests were computed between conditions for each participant. The resulting t-values were converted to z-values for second level analysis. These z-maps were tested against zero at the group level. To control for multiple comparisons in time-frequency space, a cluster-based permutation approach was used, based on a maximum statistic of the cluster-mass (Maris and Oostenveld, 2007). The same resampling procedure was used to correct for multiple comparisons in space for the pre-post regression analysis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,354,210,372]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. Results \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,407,375,425]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1 Behavioral Performance \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,430,888,690]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Paired-sample permutation t-test (1000 iteration) revealed that participants perceived beeps and flashes as synchronous significantly more often during the Synchronous (S) versus the Asynchronous Far (ASf) conditions for slow (5.0V-5.0A versus 5.0V-7.5A Hz: $t(20)=8.13$ , $p<.001$ ) and fast visual presentation frequencies (7.5V-7.5A versus 7.5V-5.0A Hz: $t(20)=14.00$ , $p<.001$ ). Furthermore, synchrony was reported more often during the Asynchronous Close (ASc) versus Asynchronous Far (ASf) condition for fast (7.5V-6.5A versus 7.5V-5.0A Hz: $t(20)=7.28$ , $p<.001$ ), but not for slow visual presentation frequencies (5.0V-6.5A versus 5.0V-7.5A Hz: $t(20)=0.34$ , $p=.774$ ). Taken together, the behavioral results show that we were able to reliably elicit the subjective illusion of synchrony in the ASc condition for fast (7.5Hz), but not for slow (5.0Hz) visual presentation frequencies (see Fig. 1b). Based on these results, the MEG analysis on the neuronal dynamics during subjective experience of synchrony targeted the fast visual presentation frequencies only (7.5 Hz). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,708,797,743]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2 Modality-Specific Responses to Physical and Perceived Audio-Visual Synchrony \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,748,887,909]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To isolate early auditory and visual regions in space, frequency spectra of the ASf conditions (7.5V-5.0A and 5.0V-7.5A) were contrasted directly at the source level. For the localization, we used the 5Hz tagging frequency as it produced the strongest steady-state response in our data, independent of conditions (the results for 7.5Hz are slightly weaker but show a similar spatial distribution). As expected, we observe robust auditory 5Hz responses (7.5V-5.0A) in bilateral auditory cortex, while the visual 5Hz frequency (5.0V-7.5A) is strongest around V1 (Fig 2A). Regions of interest (ROI) for subsequent analysis were selected as the grid points in anatomically defined primary visual, and auditory \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,903,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,97,883,175]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"cortex (www.brainmap.org), which were sensitive to the visual and auditory presentation frequencies respectively (FDR-corrected). This was done to reduce confounding effects from adjacent temporal and parietal regions, as the unmasked statistical maps also extended into association cortices. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,196,883,356]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"While the functional peaks of the frequency-tagged responses are located in primary sensory areas, they potentially may not be restricted to these regions. To explore this possibility, we contrasted the source amplitude at 5Hz for each ASf condition (5.0V-7.5A, max response in visual cortex; 7.5V-5.0A, max response in auditory cortex) against the Null-condition and computed a conjunction analysis (Fig. 2B). We observe a widespread overlap between the responses to auditory and visual signals in temporal and parietal areas that are classically considered multisensory integration zones (Beauchamp et al., 2004; Bremmer et al., 2004; Beauchamp, 2005). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,377,883,478]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The behavioral data revealed that the subjective illusion of synchrony was only reliably perceived in the ASc condition during fast (7.5V-6.5A) but not slow (5.0V-6.5A) visual presentation frequencies. Therefore, subsequent ROI-based analyses were based on the fast visual presentation frequencies (S: 7.5V-7.5A; ASc: 7.5V-6.5A) as well as the two ASf conditions (7.5V-5.0A, and 5.0V-7.5A). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,498,883,676]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For the ROI analysis, paired-sample permutation t-tests were computed at the presentation frequency (7.5Hz) to test whether physical synchrony of beeps and flashes alters neural responses in early sensory areas. In the auditory cortex, we observed a positive difference between the S (7.5V-7.5A) versus ASf (5.0V-7.5A) condition, suggesting that a stronger neuronal response when the two sensory streams are in synchrony $(t(21)=4.23, p=.001$ ; Fig. 2C). In contrast, there was no evidence for an effect of synchrony in the visual ROI $(t(21)=0.69, p=.942)$ . Taken together, we demonstrate that the auditory, but not visual cortex is sensitive to the physical synchrony between the two sensory streams. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,698,883,898]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Next, we tested whether auditory and visual cortices were sensitive to the subjective illusion of synchrony in the ASc condition (7.5V-6.5A), the AS condition which yielded the highest number of behavior responses indicating synchrony. On average, participants perceived the two events as synchronous on $64\\\\%$ of the trials (see Fig. 1B). Prior to statistical inference, an equal number of trials were randomly selected from the ASc condition where participants reported the two events to be synchronous (integrated) versus asynchronous (segregated). This was done to avoid any spurious effects due to different sample sizes. To enhance robustness of the tagged frequency amplitudes, participants were only considered for this analysis if more than $20\\\\%$ of the possible number of trials in a condition could be retained. This procedure resulted in the trimming \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,903,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,97,883,137]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"of the data where participants responding predominantly with one type of response (either synchronous or asynchronous) were excluded (5 participants). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,157,883,335]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Paired-sample permutation t-tests were computed at the presentation frequencies (visual: 7.5Hz; auditory: 6.5Hz) on the remaining 16 participants. For the contrast between integrated versus segregated trials, we observed a significant difference in the auditory cortex (6.5Hz; $t(15) = 2.49$ , $p = .021$ ) (see Fig 2C). Specifically, the auditory cortex responds more strongly if the two sensory streams are integrated and perceived as synchronous. The same contrast at the visual tagging frequency (7.5Hz) demonstrated an equivalent effect in the visual ROI ( $t(15) = 2.57$ , $p = .019$ ) (Fig 2D). Thus, the visual cortex responds more strongly to visual information when it is subjectively integrated with the auditory stream. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,358,883,455]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Taken together, the auditory cortex showed enhanced sensory responses to auditory information if the two sensory streams were either physically or perceptually in synchrony. In contrast, the visual cortex showed enhanced sensory responses only if the two asynchronous streams were perceived as synchronous, but not when the stimuli were physically in synchrony. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,476,702,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.3 Pre-Stimulus Neuronal States Predict Multisensory Binding \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,500,883,737]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Next, we tested whether neuronal states of early sensory areas preceding stimulus presentation predict whether auditory and visual streams are perceptually integrated during the ASc condition (7.5V-6.5A, the AS condition which yielded the highest number of behavior responses indicating synchrony). To this end, we performed a second-level random-effects analysis. First, independent-samples t-tests were computed for each individual subject contrasting integrated versus segregated trials, and the resulting t-values were converted to z-values for group-level analysis. At the group level, these z-maps were tested against zero using one-sample t-tests. Cluster-based permutation was performed to control for multiple comparisons in time and frequency space (Maris and Oostenveld, 2007). Analyses were conducted on visual and auditory ROI's, separately for low (4-32Hz) and high frequencies (38-128Hz) in a time window of 500-100 ms before stimulus onset. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,758,883,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the visual cortex (Fig 3A), we observed a reduction in spectral power around the alpha band ( $\\\\sim$ 11.4 Hz) when participants perceived the sensory events as synchronous ( $t_{sum}(15) = -91.61$ , $p = .002$ ). Furthermore, we found enhanced visual gamma activity ( $\\\\sim$ 64-90.6Hz) in the same region when participants reported seeing the two sensory streams as synchronous ( $t_{sum}(15) = 4.24$ , $p = .042$ ). Thus, reduced alpha and enhanced gamma power in the visual cortex predict the perception of synchrony between auditory and visual events in the ASc condition. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,901,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,117,883,316]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the auditory cortex (Fig. 3B), our analysis revealed a reduction in spectral power in the lower alpha band ( $\\\\sim6.8\\\\mathrm{Hz}$ ) when trials were reported as synchronous ( $t_{sum}(15) = -72.90$ , $p = .006$ ). Notably, the peak difference was at a lower frequency than what we observed in the visual cortex. Although there is some variability in the reported auditory alpha peak frequency (Weisz et al., 2011; Weisz and Obleser, 2014), some studies suggest that it is lower than the visual alpha rhythm (Lehtelä et al., 1997). In contrast to the visual cortex, no differences were found in the higher frequencies when participants perceived the trials as synchronous or asynchronous. Taken together, we observed that reduced auditory alpha power predicts the subjective experience of audio-visual synchrony in the auditory cortex. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,337,880,517]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To explore the spatial specificity of these effects, pre-stimulus power in the two conditions were computed for all points in the 3D grid whereby spectral power was averaged in the time-frequency window where the effect was maximal in the ROI analysis (visual alpha: 9.6-11.4Hz, 500-250ms; auditory alpha: 6.8-8Hz, 500-250ms; visual gamma: 64-90.6Hz, 500-350ms). The thresholded maps for the contrast between integrated versus segregated trials revealed peak differences in visual cortices for visual gamma and visual alpha and a peak in the right auditory cortex for auditory alpha (Figure 3C-E, respectively). The majority of additional peaks outside early sensory areas were located in parietal and temporal areas, largely overlapping with the audio-visual conjunction map. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,537,883,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, to test whether there is a relationship between pre-stimulus neuronal states and post-stimulus evoked responses to the stimulus, we used a regression-based approach on the pre-stimulus alpha power, and post stimulus evoked activity at the presentation frequencies in early visual and auditory cortex. First, alpha power was averaged across the time window 500-250 ms before stimulus onset. The decision for this time window was chosen a) to capture the maximum alpha suppression effect from the ROI analysis, and b) to avoid potential leakage from the post-stimulus time window into the pre-stimulus period due to the temporal smoothing of the time-frequency analysis (with a 500ms time window, post-stimulus events may leak into the pre-stimulus period up to 250ms). Averaged pre-stimulus alpha power in early sensory regions was computed for each individual trial, and trials were binned into quartiles. For each of these quartiles we also computed the amplitude at the auditory and visual presentation frequency post-stimulus. This was done for all points in the 3D grid. The procedure was applied separately with bilateral visual, and auditory cortices as seed regions, taking into account the preferred alpha rhythm in each modality (visual 9.6-11.4 Hz; auditory 6.8-8Hz). Statistical analyses were performed using linear regression, and cluster-based permutation was used to control for multiple comparisons (Maris and Oostenveld, 2007; Obleser and Weisz, 2012). Importantly, amplitudes of the presentation frequencies could show a linear increase or \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,901,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,97,883,175]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"decrease with pre-stimulus alpha activity. However, the interpretation of an increase would be highly problematic as it could merely reflect noise fluctuations from trial to trial. Therefore, statistical analysis was performed one-sided to identify negative linear relationships only. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,196,883,513]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Our analysis revealed a significant negative relationship between the pre-stimulus visual alpha rhythm and the amplitude of the visual tagging frequency (7.5Hz: $t_{sum}$ (21)=-165.33, $p=.009$ ). This difference was observed in posterior parietal cortex, predominantly in the right hemisphere, as well as in parieto-occipital regions stretching from extrastriate visual cortex medially towards the Precuneus and cingulate cortex (Fig. 4A,C). Furthermore, we also find a negative linear relationship between pre-stimulus visual alpha power and the auditory presentation frequency ( $t_{sum}$ (21)=-107.38, $p=.026$ ). This effect was observed in the right auditory cortex (Fig. 4B,D). There was no evidence for a negative linear relationship between the auditory alpha rhythm on either visual or auditory tagging frequency. Taken together, these results demonstrate that reduced visual alpha power in the early visual cortex predicts enhanced sensitivity to the flash sequence in downstream parieto-occipital areas, as well as enhanced auditory cortex sensitivity to the beep sequence. As no such effect was observed for the auditory alpha rhythm, we can conclude that in the case of auditory capture, there is an asymmetric relationship between the effects of locally reduced alpha power and cortical excitability in visual and auditory cortices. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,537,883,878]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If pre-stimulus alpha power in visual cortex predicts post-stimulus auditory processing, there might be pre-existing fluctuations in how the visual and auditory cortices communicate with each other that influence whether the two sensory events are perceived as synchronous (Ruhnau et al., 2014; Weisz et al., 2014; Leske et al., 2015). To directly test this idea, we computed the phase locking value (PLV), as a proxy for functional connectivity, between the right auditory and visual ROI for the visual alpha (6.8-11.4Hz, 500-250ms) and gamma band (64-90.6Hz, 500-250ms). Integrated and segregated trials were contrasted using paired-sample permutation t-tests. We found enhanced pre-stimulus functional connectivity between visual and auditory cortices in the gamma band on trials that were perceived as synchronous ( $t(15)=3.16$ , $p=.006$ ). To explore the spatial selectivity of this effect, permutation t-tests were computed contrasting the integrated versus segregated conditions at the whole-brain level. As the thresholded map ( $p<.05$ , unc.) in Fig. 4E illustrates, the strongest and most widespread increase in connectivity was observed between visual cortex and right auditory cortex, largely overlapping with the cluster from the regression analysis. Paired-sample t-tests in the alpha range did not yield a significant difference between integrated versus segregated trials ( $t(15)=0.66$ , $p>.5$ ) (Fig. 4D). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,901,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,97,243,113]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. Discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,135,883,435]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We aimed to investigate the network mechanisms underlying the integration of audiovisual sequences by quantifying local representations and connectivity of early auditory and visual cortices. To this end we used a novel frequency tagging approach inspired by auditory capture effects such as the flicker flutter illusion (Ogilvie, 1956; Shipley, 1964; Berger et al., 2003; Noesselt et al., 2008); where a series of beeps and flashes are presented at neighboring frequencies, and the two streams are sometimes perceived as synchronous. Leveraging the intra-individual variability in multisensory perception, we studied physiological responses within and between auditory and visual systems in different perceptual contexts, that is, when the events were perceived as synchronous or not. Moreover, by linking these isolated sensory responses with ongoing oscillatory activity before the stimulus was presented, we were able to investigate how the neuronal state of one system affects the local sensory response, as well as the sensory response in the other sensory system. Such a paradigm and analytical framework allowed us to isolate the brain correlate of multisensory integration versus segregation under constant physical stimulation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,455,883,835]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"First, we observed that the auditory cortex responded more strongly to the auditory stream when the two sensory events were physically synchronous (Fig 2C, bottom panel), which was not true for the visual cortex. We also found enhanced auditory responses when participants perceived an asynchronous series of beeps and flashes as synchronous (Fig 2D, bottom panel). A similar enhancement in the visual response to the flashes emerged when participants report perceiving a stream of asynchronous beeps and flashes as synchronous (Fig 2D, top panel). Furthermore, the perception of synchrony is predicted by fluctuations in oscillatory neuronal activity shortly before stimulus presentation (Fig 3). In the auditory cortex pre-stimulus alpha power is reduced when participants integrate the two sensory events (Fig 3B,E). In the visual cortex, both reduced alpha and enhanced gamma power predict perceptual integration (Fig A,C,D). Most importantly, we demonstrated that these pre-stimulus dynamics have a different relationship with post-stimulus processing in visual and auditory cortices (Fig 4). Reduced visual alpha power predicts enhanced sensory processing in both auditory and visual cortices (Fig 4A-C), while we found no evidence for a relationship between pre-stimulus alpha power and post-stimulus sensory processing in the auditory cortex. Corroborating this idea of direct information transfer between early sensory areas, we show that the subjective perception of synchrony is preceded by enhanced functional connectivity in between sensory areas in the gamma band (Fig 4D-E). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,901,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,97,861,132]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sensory Processing During Physical and Perceptual Synchrony of Audio-Visual Events \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,137,883,377]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the current study, the auditory cortex responded more strongly if auditory and visual events were either physically or perceptually synchronous (Fig 2C-D, bottom panel). In contrast, the visual cortex showed enhanced sensory responses only when the two sensory streams were perceptually synchronous and not physically synchronous (Fig 2D, top panel). This pattern of results is interesting because it attributes different roles to auditory and visual cortices with respect to multisensory integration: While auditory cortex appears to be sensitive to both perceptual and physical synchrony, the response in visual cortex is only linked to the illusory perception of synchrony. These results may relate to the auditory capture, as 'integration' of the two sensory streams shift in perception toward the more reliable auditory stream (Recanzone, 2003). It is important to emphasize that although this asymmetry might hold for auditory capture, it is not likely generalizable to other forms of multisensory integration. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,397,883,676]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Previous studies on synchrony effects in multisensory paradigms using frequency tagging are rare and have produced mixed results (Giani et al., 2012; Nozaradan et al., 2012; Barbero et al., 2025). Nozaradan and colleagues (2012) reported synchrony effects for both auditory and visual presentation frequencies. Moreover, intermodulation frequencies (linear combinations of audio-visual presentation frequencies) were proven to be a marker of audio-visual emotion integration (Barbero et al., 2025). As these results are restricted to sensor space it is not clear whether the effects reside in early sensory areas or in regions in association cortices. Indeed, using conjunction analysis we found a wide network of areas that are sensitive to both the visual and auditory presentation frequencies (Fig. 2B), which could result in multisensory effects observed at the sensor level. Our approach is different as it uses source analysis in a way that preserves the ability to maximally segregate the two sensory events using frequency tagging. By applying this more sensitive approach, we demonstrated that frequency tagging is a versatile tool to target multisensory integration in the brain. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,696,836,732]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Excitability Fluctuations in Early Sensory Regions Link to Local and Network Activity Change \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,736,883,893]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The current study further demonstrates that illusory perception of synchrony is associated with reduced power in the pre-stimulus alpha rhythm in both auditory and visual cortices (Fig 3). Current theories suggest that fluctuations in alpha power reflect changes in cortical excitability (Romei et al., 2008a, 2008b, 2010; Lange et al., 2013; Cecere et al., 2014). In the visual cortex, reduced alpha power is accompanied by enhanced visual gamma activity, often associated with visual processing (Gray et al., 1989; Womelsdorf et al., 2007; Fries et al., 2008). We demonstrated a negative relationship between pre-stimulus alpha power in visual areas and post-stimulus processing at the visual \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,901,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,97,883,234]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"presentation frequency in downstream visual areas in parieto-occipital cortex (Fig 4A,C, left panel), as well as with the post-stimulus processing at the auditory presentation frequency in auditory regions (Fig 4B,C, right panel). Importantly, the reduced prestimulus alpha power in the occipital cortex predicted subjective multisensory integration (Fig. 3A,B). The current findings show that fluctuations in alpha power not only reflect local changes in cortical excitability, but also shape the dynamics of transient functional networks at large. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,257,883,416]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"During the double flash illusion (Shams & Kim, 2010), it was argued previously that a second beep elicits the illusory perception of an additional flash when excitability in the visual cortex is high (Lange et al., 2013, 2014). In this study, the perceived synchrony could be predicted by the pre-stimulus alpha, which signifies cortical excitability. Furthermore, only the visual, but not the auditory alpha rhythm could be linked reliably to the amplitude of the tagged visual frequency, suggesting that in the case of auditory capture alpha power in the visual cortex has more direct effects on the global network organization, while auditory alpha operates locally. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,438,883,777]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Another interpretation of the excitability hypothesis is that reduced local alpha power makes visual and auditory cortices more prone to communicate (Lange et al., 2014). Two findings in the current study provide support for this idea. First, we found that enhanced functional connectivity in the gamma frequency band between early visual and auditory areas predicted whether the two sensory events are perceived as synchronous (Fig 4D-E). This is in line with animal studies demonstrating the existence of direct anatomical pathways between early auditory and visual areas (Falchier et al., 2002; Rockland and Ojima, 2003; Cappe and Barone, 2005). Second, and most importantly, we observed that reduced pre-stimulus alpha power in the visual cortex predicts post-stimulus sensory responses in both visual and auditory cortices (Fig 4B-C, right panel). In contrast, local alpha fluctuations in the auditory cortex, while linked to the perception of synchrony, do not affect the sensory response in the visual cortex. This asymmetric relationship between reduced pre-stimulus alpha power and enhanced post-stimulus sensory responses in visual and auditory cortices could arise from the fact that vision is our dominant modality and under most circumstances drives multisensory perception. As such spontaneous fluctuations in the visual cortex will affect both local and global network structure more readily than fluctuations in the auditory cortex. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,799,883,857]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In conclusion, our study demonstrates that temporal integration of multisensory events in time depends on the fluctuating neuronal states of the system, which bias perception in early sensory areas through local and long-range network interactions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,901,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,97,223,113]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,135,883,875]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Alais D, Burr D (2004a) The ventriloquist effect results from near-optimal bimodal integration. 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Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[114,95,883,896]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Falchier A, Clavagnier S, Barone P, Kennedy H (2002) Anatomical evidence of multimodal integration in primate striate cortex. 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Biophys J 76:691-708. \\\"]\",\n \"page_idx\": \"15\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[84,2,903,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[114,95,883,898]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Nozaradan S, Peretz I, Mouraux A (2012) Steady-state evoked potentials as an index of multisensory temporal binding. 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J Neurosci 30:8692-8697. \\\",\\\"Romei V, Rihs T, Brodbeck V, Thut G (2008b) Resting electroencephalogram alpha-power over posterior sites indexes baseline visual cortex excitability. Neuroreport 19:203-208. \\\",\\\"Ruhnau P, Hauswald A, Weisz N (2014) Investigating ongoing brain oscillations and their influence on conscious perception - network states and the window to consciousness. Front Psychol 5:1230. \\\",\\\"Shams L, Kamitani Y, Shimojo S (2000) What you see is what you hear. Nature 408:2000. \\\",\\\"Shams L, Kim R (2010) Crossmodal influences on visual perception. Phys Life Rev 7:269-284. \\\",\\\"Shipley (1964) Auditory Flutter-Driving of Visual Flicker. Science (80-) 145:1328-1330. \\\",\\\"Van Veen BD, van Drongelen W, Yuchtman M, Suzuki A (1997) Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Trans Biomed Eng 44:867-880. \\\",\\\"Watkins S, Shams L, Josephs O, Rees G (2007) Activity in human V1 follows multisensory perception. Neuroimage 37:572-578. \\\",\\\"Watkins S, Shams L, Tanaka S, Haynes JD, Rees G (2006) Sound alters activity in human V1 in association with illusory visual perception. Neuroimage 31:1247-1256. \\\",\\\"Weisz N, Wuhle A, Monittola G, Demarchi G, Frey J, Popov T, Braun C (2014) Prestimulus oscillatory power and connectivity patterns predispose conscious somatosensory perception. Proc Natl Acad Sci U S A 111:E417-E425. \\\",\\\"Womelsdorf T, Schoffelen J-M, Oostenveld R, Singer W, Desimone R, Engel AK, Fries P (2007) Modulation of Neuronal Interactions Through Neuronal Synchronization. Science (80- ) 316:1609-1612. \\\"]\",\n \"page_idx\": \"16\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[84,2,903,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,215,544,532]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figures \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0782/97b83bf3166ad46bca293b526a506c75ed94e91f8496408f6fa5dbd0027021ec.jpg\",\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[527,215,830,532]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 1. Design and behavioral results of the study. A) The top panel illustrates the set of conditions used in the current study. The rows depict the three beep frequencies (5Hz, 6.5Hz, 7.5Hz), while the columns show the two flash frequencies (5Hz, 7.5Hz). The bottom panel shows the temporal sequence of a single trial. After a variable period of fixation, auditory beeps and visual flashes are presented at variable frequencies for 3 seconds. A trial is always followed by the question if the two sensory sequences were in synchrony or not. B) The behavioral results for the fast visual presentation frequency (7.5 Hz) show a gradual increase in the proportion trials where the two events were perceived as synchronous as the beep frequencies approached the flash frequency. In the ASf condition, synchrony is perceived on $64\\\\\\\\%$ of the trials. Error bars depict SEM, adjusted for within subject comparisons. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0458/941e94dbe2d740e11b4b03f4f9f1eb3d77915300947ffe66a4135433fa8e3495.jpg\",\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[84,3,903,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[117,106,566,252]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"A \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0502/0cd92d6e8f45eb232f60c5a7521c3d9d0161819f2502b8d3b925c8ee3fbe60df.jpg\",\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[591,108,736,244]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"C \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0236/cf5a21fcd490af5d58bf0f22c94f6205f77a5c642fd82fa623a6d5ba915e6d08.jpg\",\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[756,107,883,242]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"D \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0713/4eefb60e563d59c21b7a64d58ca429fbe904ad5701127b05a777d2ccbad860e7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[117,258,571,398]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"B \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0926/1ff8ae86a57291bbddc3556ca585bfe16e005a5f72d50a93aa6201a55ac2ccb3.jpg\",\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[591,252,738,396]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"a aee \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0437/ca9d1043f9d1af6af88279071685a781823402d3b670177aeaf33909db7ac877.jpg\",\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[756,252,880,396]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Frequency [Hz] \\\",\\\"Figure 2. Analysis of auditory and visual processing at the presentation frequencies. A) The contrast between the two ASf conditions (7.5V-5.0A versus 5.0V-7.5A), at 5Hz was used to localize early sensory regions of interest. Warm colours show sensitivity to the rhythmic auditory stimulation in bilateral superior temporal gyrus. Cold colours reflect sensitivity to the visual presentation frequency in occipital and parietal lobes, with peaks in bilateral calcarine sulci. The statistical maps are thresholded at $p < .05$ (FDR-corrected). B) The activation maps show the multisensory areas from the conjunction between each of the two asynchronous against the Null condition. Minimum t-values are used to show gradient activation. C) Comparison of the S condition (7.5V-7.5A: pink) versus the two ASf conditions (7.5V-5.0A: blue 5.0V-7.5A red) in visual (top panel), and auditory (bottom panel) cortices. A synchrony effect is observed only in the auditory ROI. Shaded areas around the graphs depict SEM, adjusted for within subject comparisons. D) Illusory synchronization effects for the ASc condition during fast visual presentation (7.5V6.5A) in visual (top panel), and auditory (bottom panel) cortices. Enhanced neural activity is observed in both modalities for trials where visual and auditory signals were perceived as synchronous (purple) versus asynchronous (blue). Shaded areas around the graphs depict SEM, adjusted for within subject comparisons. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0308/2faec9dbfc45e63f8ce8e73e91432b1a7e5fb8fd0bef8a2f5705f647abf4a65c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[84,3,903,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,95,401,281]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"A \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0532/7028a42eda4d1d7abcf7e597d8e98948a4283718520c6f2d219819c993cee2d7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[405,94,781,281]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"B \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0137/aa6dd9804017519b189f2a01c4f1377b420b0911a4a19bc79f9c1aa956019240.jpg\",\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[223,279,370,352]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"C \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0070/f1f68e98faf51daef0abe88606b8cacd9bca8b3dc5cf0ea3956d808c34214d34.jpg\",\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[403,277,602,445]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"D \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0373/027a46d8c787b11bfd8f5eb2ae5391cb98df82bd61fb2aa7e0566452aae2366d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[602,277,800,415]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"E \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0842/fc0bfbc0eb1253b4926edb61c1c7512857ca4f3d2c7d7fb2c4012b74de8f3934.jpg\",\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[197,352,397,414]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 3. Analysis of pre-stimulus oscillatory activity contrasting trials perceived as synchronous versus asynchronous. Time-frequency representations from visual areas (right panel) depict the statistical differences in pre-stimulus power for the integrated versus segregated trials. A) statistically significant increase (highlighted, top panel) is observed in the gamma band when audio-visual streams were integrated. In addition, there was a reduction in pre-stimulus alpha power B)) In auditory areas (right panel), there was a reduction in pre-stimulus alpha activity when the two sensory streams were perceived as synchronous (highlighted, bottom panel). C-E Whole-brain, statistically thresholded $(p < .05$ , unc.) maps of the three effects in the visual gamma (C), visual alpha (D), and auditory alpha (E) band reveal mostly independent clusters in visual and auditory areas respectively. Additional clusters are observed mostly in temporal and parietal areas, however the peaks are found in the primary sensory regions. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0527/c0c4f628881a1ccb3371134a455a813b5815f273952ad85980328b61e135eca0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[84,3,903,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[196,119,803,734]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 4. Pre-post regression and connectivity analysis. A) Statistically thresholded whole-brain activation map (p<.05, cluster-corrected, one-tailed), showing regions where the post-stimulus amplitude at the visual tagging frequency shows a negative linear relationship with pre-stimulus alpha power in visual cortex. This is observed in a network of regions spanning from parieto-occipital regions (POG: I) to posterior parietal cortex (rPPC: II) B) Activation maps show regions where a linear negative relationship is \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0696/959db5c620d577dd7400295c4d8d2c7991c5910992d81af19233dcf95bbf948d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[84,3,903,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,45,803,59]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[109,97,883,417]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"observed between the amplitude at the auditory tagging frequency post-stimulus, and pre-stimulus alpha power in visual cortex. This relationship is observed most strongly in the right auditory cortex (rAC: III) and insular cortex (rIC: IV). C) Bar graphs illustrate mean post-stimulus amplitude for the visual (blue) and auditory (red) tagging frequencies in each of the alpha quartiles from visual cortex (low alpha: dark shades, high alpha: lighter shades). Values are extracted from two peak regions where alpha is linearly related to the visual tagging frequency (IPOG, rPPC, left panel), and two regions where alpha is linearly related to the auditory tagging frequency (rAC, rIC, right panel). A significant negative linear relationship is marked with a star. Error bars depict SEM adjusted for within subject comparisons. D) Bar graphs show phase-locking between visual and right auditory cortex in the alpha and gamma band for integrated versus segregated trials. Enhanced functional connectivity is observed for integrated trials in the gamma, but not the alpha band. E) Thresholded statistical maps $(p < .05$ , unc.) contrasting functional connectivity maps between the integrated versus segregated conditions considering the visual cortex as the seed region. The map shows that the activity is largely confined to the right superior temporal gyrus and other auditory regions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[84,2,903,37]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bioRxiv preprint doi: https://doi.org/10.1101/2025.05.20.655148; this version posted May 21, 2025. The copyright holder has placed this preprint (which was not certified by peer review) in the Public Domain. It is no longer restricted by copyright. Anyone can legally share, reuse, remix, or adapt this material for any purpose without crediting the original authors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":""},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Life Sciences"},"sha256":{"kind":"string","value":"ac463590746a5324696f6729958e9ce4f2eb3edbb030c68e97d5b8d44fc8205f"},"title":{"kind":"string","value":"Two senses, one rhythm: Pre- and post-stimulus neural states predict perceived audio-visual synchrony"}}},{"rowIdx":269,"cells":{"abstract":{"kind":"string","value":"The angle of repose-i.e., the angle theta r between the sloping side of a heap of particles and the horizontal-provides one of the most important observables characterizing the packing and flowability of a granular material. However, this angle is determined by still poorly understood particle-scale processes, as the interactions between particles in the heap cause resistance to roll and slide under the action of gravity. A theoretical expression that predicts theta(r) as a function of particle size and gravity would have impact in the engineering, environmental, and planetary sciences. Here we present such an expression, which we have derived from particle-based numerical simulations that account for both sliding and rolling resistance, as well as for nonbonded attractive particle-particle interactions (van der Waals). Our expression is simple and reproduces the angle of repose of experimental conical heaps as a function of particle size, as well as theta(r) obtained from our simulations with gravity from 0.06 to 100 times that of Earth. Furthermore, we find that heaps undergo a transition from conical to irregular shape when the cohesive to gravitational force ratio exceeds a critical value, thus providing a proxy for particle-scale interactions from heap morphology."},"author":{"kind":"string","value":"Elekes, Filip|Parteli, Eric J. R."},"content_list":{"kind":"list like","value":[{"bbox":"[59,60,760,154]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary environments ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[59,160,345,177]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Filip Elekesa,1 and Eric J. R. Partelib,1 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[59,183,909,208]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{a}$ Institute for Geophysics and Meteorology, University of Cologne, 50969 Cologne, Germany; and $^{b}$ Faculty of Physics, University of Duisburg-Essen, 47057 Duisburg, Germany ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[59,215,924,227]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Edited by Risto Nieminen, Department of Applied Physics, Aalto University, Aalto, Finland, and approved August 6, 2021 (received for review April 27, 2021) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[61,234,483,503]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The angle of repose—i.e., the angle $\\theta_{\\mathrm{r}}$ between the sloping side of a heap of particles and the horizontal—provides one of the most important observables characterizing the packing and flowability of a granular material. However, this angle is determined by still poorly understood particle-scale processes, as the interactions between particles in the heap cause resistance to roll and slide under the action of gravity. A theoretical expression that predicts $\\theta_{\\mathrm{r}}$ as a function of particle size and gravity would have impact in the engineering, environmental, and planetary sciences. Here we present such an expression, which we have derived from particle-based numerical simulations that account for both sliding and rolling resistance, as well as for nonbonded attractive particle-particle interactions (van der Waals). Our expression is simple and reproduces the angle of repose of experimental conical heaps as a function of particle size, as well as $\\theta_{\\mathrm{r}}$ obtained from our simulations with gravity from 0.06 to 100 times that of Earth. Furthermore, we find that heaps undergo a transition from conical to irregular shape when the cohesive to gravitational force ratio exceeds a critical value, thus providing a proxy for particle-scale interactions from heap morphology. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[59,515,405,542]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"granular materials | angle of repose | dry cohesive powders | planetary geomorphology | discrete-element method ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[61,558,483,711]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"One of the most fundamental observables used to characterize the mechanical properties of a granular material, such as sand, pebbles, dust aerosols, and industrial powders, is the angle that a heap of particles makes with the horizontal—the angle of repose, $\\theta_{\\mathrm{r}}$ . This angle is affected by particle size, because attractive particle interaction forces due to surface intermolecular and interatomic interactions become the more relevant compared to gravity and contact forces the smaller the particles are. For instance, heaps of millimeter-sized glass beads poured from a hopper display an angle of repose of about $20^{\\circ}$ to $25^{\\circ}$ (1), while the angle of repose of powders of the same material exceeds $50^{\\circ}$ (2). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[61,711,483,876]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, there is no model that reliably predicts the dependence of the angle of repose of a granular material on the particle size, notwithstanding much effort made in previous work (3-6). Such a model would have the potential to substantially improve the design and control of various technological processes involving particulate systems, including in additive manufacturing technologies, in the food and pharmaceutical industry, and in the agricultural sector. Moreover, the capability of quantitatively predicting the angle of repose as a function of particle size has promising applications in the space and planetary sciences, in particular owing to increasing concern about the mechanics of granular materials in reduced-gravity experiments and extraterrestrial environments (7-9). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[59,877,483,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The derivation of an analytical expression for the angle of repose from a theoretical treatment is challenging because $\\theta_{\\mathrm{r}}$ is dictated by still poorly understood dynamics of interparticle interactions in response to gravitational stresses. These interac ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[499,234,926,311]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"tions are mainly due to frictional contact forces and attractive surface potentials, which enhance the cohesive behavior of the granular heap with decreasing particle size. It is uncertain how to predict the dynamics of particle-particle contacts within the granular heap, as well as the resistance to grain sliding and rolling along the heap surface. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[499,311,926,515]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Therefore, here we model the angle of repose by means of particle-based numerical simulations using the discrete-element method (DEM), which consists of solving Newton's equation of motion for every particle in the system by explicitly modeling all main relevant forces acting on the particles. Using such simulations, we compute the angle of repose $\\theta_{\\mathrm{r}}$ of spherical glass particles over the entire broad range of particle size from the micrometer to the decameter scale. As discussed in the subsequent sections, our numerical predictions for $\\theta_{\\mathrm{r}}$ under Earth's gravity match quantitatively a comprehensive set of experimental observations of this angle over the entire range of particle sizes investigated. Furthermore, we derive a physically based analytical expression that reproduces our DEM predictions for the angle of repose over three orders of magnitude in gravity, from Pluto conditions ( $\\approx 6\\%$ of Earth's gravity) up to 100 times Earth's gravity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[499,515,926,592]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the next section we describe our numerical simulations, whereupon we present and discuss our results, the comparison of our numerical predictions with experimental observations, and our analytical model for the angle of repose. Furthermore, we show that our model is consistent with previous observations of the angle of repose in various extraterrestrial gravity conditions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,602,603,616]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Significance ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[511,630,914,786]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The angle between the sloping side of a heap of particles and the horizontal, called angle of repose, is often used to characterize the flowability of granular materials on Earth and planetary environments, such as sand, dust aerosols, and powders. In planetary research, this angle provides an excellent proxy for particle size. The smaller the particle is, the larger the effect of attractive forces between atoms and molecules on the surface of the particles relative to particle weight, the less allowable the material, and the steeper, thus, the angle of repose. We present a model that accurately predicts the angle of repose as a function of particle size, both on Earth and under extraterrestrial gravity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[499,798,926,840]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Author contributions: F.E. and E.J.R.P. designed research; F.E. and E.J.R.P. performed research; F.E. and E.J.R.P. analyzed data; E.J.R.P. wrote the paper; F.E. performed the numerical simulations; and E.J.R.P. developed the analytical model for the angle of repose. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[500,842,712,854]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The authors declare no competing interest. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,856,692,867]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This article is a PNAS Direct Submission. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[500,869,924,891]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,893,924,915]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To whom correspondence may be addressed. Email: f.elekes@uni-koeln.de or eric.parteli@uni-due.de. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,916,652,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Published September 13, 2021. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[871,12,923,49]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Check for updates ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[6,472,25,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[955,355,982,427]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"APPLIED PHYSICAL SCIENCES ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[61,948,285,959]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PNAS 2021 Vol. 118 No. 38 e2107965118 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[656,948,871,960]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1073/pnas.2107965118 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[892,948,926,959]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 of 8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[66,63,490,103]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To conclude this article, we briefly discuss possible implications of our study for future research and present an outlook for model improvements. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,112,232,126]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Numerical Experiments ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[66,127,490,241]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The DEM, which we apply in our numerical simulations, was introduced by Cundall and Strack (10) and has been steadily refined in the course of recent decades to incorporate improved particle-particle interaction models (11-15). Our DEM, revised in Materials and Methods, accounts for all main relevant forces acting on the particles, i.e., gravity, frictional contact forces, and attractive van der Waals forces, and has proved to reproduce quantitatively the solid fraction and the packing structure of powders constituted of different materials (15, 16). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,242,490,418]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"One widely employed method to generate a granular heap is the fixed funnel method, where the granular material is poured through a funnel or orifice onto a rough surface. In another method, a hollow cylinder, placed atop the surface, is filled with the particulate material and then pulled off of the base at low velocity, to allow the particles to flow down through the cylinder's bottom end (17). However, it is difficult to control heap formation using these methods in numerical simulations of strongly cohesive particles, given that such simulations involve a sensibly small number of particles, thus increasing the tendency to form a clump encompassing a large fraction of the particles in the system. Therefore, we employ a different method that can be regarded as a combination of the fixed funnel and the hollow cylinder method. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,420,490,572]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The heap is formed by pouring particles onto a frictional, square horizontal plate, which has sides $40d$ and constitutes the bottom wall of the simulation domain—a rectangular box of horizontal dimensions $40d \\times 40d$ and height $30d$ . The particle insertion region has a square cross-section of side length $4.4d$ , is centered around the vertical symmetry axis of the simulation domain, and extends from the top of the simulation domain down to a height of $20d$ above the bottom plate. At time $t = 0$ , particles are placed at random positions throughout the inner volume of the insertion region, thereby producing a packing of solid fraction $\\approx 20\\%$ . Thereafter, the particles are released from rest. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,573,490,689]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Particle insertion is repeated at an insertion time step $\\Delta t_{\\mathrm{ins}} \\approx 3.5\\sqrt{d / g}$ , i.e., the time interval between two consecutive insertion events, with $g$ standing for gravity. However, during the pouring process, once the height of the growing heap has exceeded $20d$ , only the remaining upper free volume of the insertion region above the heap crest is used for particle insertion. Moreover, the number of poured particles is 25,000, but the pouring process is interrupted if the heap's crest reaches the top of the simulation domain. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,689,490,779]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Open boundary conditions are applied in the horizontal directions. Therefore, the number of particles constituting the final heap can differ depending on $d$ and $g$ , since particles that abandon the simulation domain through its lateral borders are not replaced by new particles. The number of particles constituting the heaps produced in the present study varied between 5,000 and 14,000. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,785,225,798]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results and Discussion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[66,800,490,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Angle of Repose Predicted from DEM Simulations. Fig. 1 displays snapshots of simulations obtained with $d = 30 \\mu \\mathrm{m}$ and $d = 1 \\mathrm{~mm}$ under terrestrial gravity conditions. To measure the angle of repose, the projection of the heap on two orthogonal planes ( $x$ and $y$ ) is computed, which yields two side-view images of the heap separated by a rotation of $90^{\\circ}$ . An image-processing algorithm is then applied to compute the upper boundary of the granular material, i.e., the heap surface, as well as the total surface area associated with the two-dimensional heap projection. Following ref. 18, we define the angle of repose as the base angle ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[512,63,929,164]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 1. Snapshots of granular heaps produced in our simulations. In $A$ we see a heap constituted by particles of diameter $d = 30\\\\mu \\\\mathrm{m}$ , while particle size in $B$ is $d = 1 \\\\mathrm{~mm}$ . The span of each heap is equal to $40d$ , and both heaps have been produced using terrestrial gravity. \"]","image_footnote":"[]","img_path":"images/0478/6f5fb54f1c8a877d4d28dd4f7526bfdcc974fdfde95bed9350b3077674ac4d63.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[507,241,933,318]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"of the isosceles triangle, which has the same surface area as the heap (Fig. 1). Therefore, two values of this angle are obtained for each heap, from which the mean $\\theta_{\\mathrm{r}}$ and SD $\\sigma_{\\theta_{\\mathrm{r}}}$ are computed. We have found no considerable changes in the angle of repose by including computations of this angle from additional projections separated by smaller rotation angles (18). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,318,933,458]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Moreover, we have found that heaps formed by particles of diameter smaller than a value $d_{\\mathrm{c}}$ $(\\approx 50\\mu \\mathrm{m}$ under terrestrial gravity) display a strongly irregular shape, with considerable variations in local slope throughout their surface (Fig. 1A). In this regime of strongly irregular heap morphology, which we call here regime I, particle avalanches are largely inhibited by the formation of large, irregular particle agglomerates along the surface of the heap. By contrast, heaps formed with particles of size $d\\gtrsim d_{\\mathrm{c}}$ (regime II) display rather regular morphology and nearly constant slope along their surface (Fig. 1B). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,458,933,559]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We remark that it becomes increasingly difficult to produce heaps in our simulations as $d$ decreases down to values smaller than $d_{\\mathrm{c}}$ . In particular, we could not obtain any heap for $d$ smaller than about $50\\%$ of $d_{\\mathrm{c}}$ , since particles' sticky behavior for such small particle sizes causes the heap to reach the upper limit of the simulation domain. The conclusions presented in our article are thus applicable to heaps in regime II, i.e., provided particles are not smaller than about $d_{\\mathrm{c}}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,560,933,661]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The solid squares in Fig. 2 denote the values of $\\theta_{\\mathrm{r}}(d)$ obtained from DEM simulations under Earth's gravity. Moreover, Fig. 2 also displays a comprehensive compilation of experimental data for the angle of repose as a function of particle size, taken from measurements of $\\theta_{\\mathrm{r}}$ from granular heaps produced with different materials (see legend and key in Fig. 2). As we can see in Fig. 2, our numerical predictions follow remarkably well the trend of the experimental data. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,661,933,789]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Furthermore, Fig. 3A shows the values of $\\theta_{\\mathrm{r}}$ obtained for different values of gravity, ranging from Pluto gravity ( $g = 0.62 \\, \\mathrm{m/s}^2$ ) to 100 times Earth's gravity. We see that the same qualitative behavior of $\\theta_{\\mathrm{r}}$ as a function of $d$ is found for all values of gravity investigated. Moreover, for a given particle size, a trend of increasing $\\theta_{\\mathrm{r}}$ with decreasing gravity is observed. In the following section we present a mathematical expression that will shed light on our numerical predictions, as well as on the experimental observations of the angle of repose as a function of particle size. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,800,933,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A Mathematical Expression for the Angle of Repose as a Function of Gravity and Particle Size. To obtain a mathematical expression that fits our DEM predictions for $\\theta_{\\mathrm{r}}$ as a function of particle size, we first note that the angle of repose is described via $\\theta_{\\mathrm{r}} \\approx \\tan^{-1}[\\mu_{\\mathrm{eff}}]$ , where $\\mu_{\\mathrm{eff}}$ is an effective coefficient of friction describing the maximal friction resistance of the granular material against sliding through avalanche (23). This coefficient encodes information on material properties, as well as on macroscopic characteristics related to the heap structure, such as packing fraction and surface roughness. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[6,472,25,934]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[68,948,102,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 of 8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[121,950,153,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PNAS ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[121,959,333,969]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1073/pnas.2107965118 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[837,948,931,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Elekes and Parteli ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[420,959,933,969]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[859,970,933,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"environments ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[61,63,487,312]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 2. Angle of repose as a function of the particle diameter. Solid blue squares indicate the predictions from our numerical simulations, performed with the parameters listed in Table 1 and using $g = 9.81 \\\\, \\\\text{m/s}^2$ . The other symbols denote experimental observations made for roughly monodisperse systems, i.e., the scenario of our DEM simulations. All shown experimental data correspond to glass beads (1, 2, 5, 19-22), except for Pilpel (3) (magnesium oxide) and Lumay et al. (18) (silicon carbide abrasives). The solid line denotes the best fit to our numerical predictions using Eq. 1, which yields $D_{E} \\\\approx 87 \\\\, \\\\mu \\\\text{m}$ , and $\\\\mu_{\\\\text{eff},\\\\infty} \\\\approx 0.447$ . \"]","image_footnote":"[]","img_path":"images/0828/637c30648c68189f18dcd0f225837a3418e2037bbcd35fb49c263249311ad4b9.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[58,453,485,583]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, these characteristics are affected by the nature of interparticle interaction forces. As particle size decreases, attractive particle interaction forces become increasingly more relevant compared to gravitational forces, thereby leading to an increase in the bulk porosity and affecting the dynamics of stress distribution within the heap. Experiments and DEM simulations revealed that the solid fraction of powders follows, approximately, a power-law relation with particle size (15). Taking inspiration from this insight, we approximately describe $\\theta_{\\mathrm{r}}$ (in radians) using the expression ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[164,598,483,630]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\theta_ {\\mathrm {r}} \\approx \\tan^ {- 1} \\left\\{\\mu_ {\\text {e f f}, \\infty} \\cdot \\left[ 1 + \\frac {D}{d} \\right] \\right\\}, \\tag {1}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[58,647,485,736]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where the effective friction coefficient $\\mu_{\\mathrm{eff},\\infty}$ and the characteristic length-scale $D$ must be determined from the best fit to observations of the angle of repose as a function of particle size. The best fit to our simulation data (blue solid squares in Fig. 2) using Eq.1 gives $\\mu_{\\mathrm{eff},\\infty}\\approx 0.447$ and $D\\approx 87~{\\mu\\mathrm{m}}$ with coefficient of correlation $R^2\\approx 99\\%$ . This best fit is denoted by the solid line in Fig. 2. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[58,736,485,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Moreover, the solid lines in Fig. 3A denote the best fits to the DEM results associated with various values of $g$ level; i.e., $\\tilde{g} = g / g_{\\mathrm{Earth}}$ , where $g_{\\mathrm{Earth}} = 9.81~\\mathrm{m / s^2}$ , using Eq. 1 and assuming that $\\mu_{\\mathrm{eff},\\infty}\\approx 0.447$ is independent of gravity. The dotted line in Fig. 3A corresponds to the asymptotic value of the angle of repose, $\\theta_{\\mathrm{r,\\infty}}\\equiv \\tan^{-1}[\\mu_{\\mathrm{eff,\\infty}}]$ . Indeed, we find that the angle of repose $\\theta_{\\mathrm{r,\\infty}}$ obtained from simulations without attractive particle interaction forces (i.e., assuming noncohesive materials) is approximately equal to $\\theta_{\\mathrm{r,\\infty}}$ , independent of particle size (Fig. 3B). There is a small trend of increasing $\\theta_{\\mathrm{r,\\infty}}$ with gravity—Fig. 3B suggests an increase of the order of $10\\%$ in $\\theta_{\\mathrm{r,\\infty}}$ with an increase in $\\tilde{g}$ from 0.06 to 100—which we attribute to a slightly greater tendency of particles to interlock upon an increase in gravitational stress, but further work (not in the scope of this article) would be needed to elucidate this small effect. Fig. 3A and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[499,63,926,89]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$B$ thus shows that particle size controls on $\\theta_{\\mathrm{r}}$ are dictated mainly by cohesive particle-particle interactions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[499,89,926,154]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Fig. 3C displays the values of $D$ obtained from the best fits in Fig. 3A, as a function of the $g$ level. As we can see from Fig. 3C, for the range of $\\tilde{g}$ considered in the present work, the characteristic length-scale $D$ can be approximately described by the equation ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[680,154,924,185]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nD = \\frac {D _ {\\mathrm {E}}}{\\sqrt {\\tilde {g}}}, \\tag {2}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[499,187,928,255]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $D_{\\mathrm{E}}$ denotes the terrestrial value of $D$ , i.e., $87\\mu \\mathrm{m}$ . We remark that the solid red line in Fig. 3C is no fit to the simulation data (solid circles). Instead, the red line denotes Eq. 2, i.e., our conjecture that $D$ is equal to $D_{\\mathrm{E}} / \\sqrt{\\tilde{g}}$ . We have found that fitting the DEM results using the equation $D = D_0 / \\tilde{g}^\\alpha$ leads to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[500,288,926,531]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0399/bb3d4e839416979a367c8f44cdb5c3a20484289406d6d84cba133c36ef25d101.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[500,544,928,771]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 3. Effect of gravity on the angle of repose. In $A$ , symbols denote $\\\\theta_{\\\\mathrm{r}}(d)$ for various $g$ levels, ranging from gravity conditions on Pluto to 100 times Earth's gravity. The solid lines in this plot indicate the best fits to the simulation data using Eq. 1, assuming $\\\\mu_{\\\\mathrm{eff},\\\\infty} = 0.447$ . Furthermore, symbols in $B$ denote the angle of repose $\\\\theta_{\\\\mathrm{r,nc}}$ obtained from simulations without cohesive forces, while the dotted line in $A$ and $B$ indicates the value $\\\\theta_{\\\\mathrm{r},\\\\infty} \\\\equiv \\\\tan^{-1}[\\\\mu_{\\\\mathrm{eff},\\\\infty}]$ . The values of $D$ obtained from the best fits in $A$ are shown in $C$ as a function of the $g$ level. The solid line in $C$ represents Eq. 2, using $D_{\\\\mathrm{E}} = 87~\\\\mu \\\\mathrm{m}$ as obtained from the best fit to the DEM data with Earth's gravity (Fig. 2). Furthermore, the dashed line denotes the best fit to our numerical predictions of $D$ as a function of $\\\\tilde{g}$ using $D = D_0 / \\\\tilde{g}^\\\\alpha$ , which yields $D_0 \\\\approx 76~\\\\mu \\\\mathrm{m}$ and $\\\\alpha \\\\approx 0.454$ with coefficient of correlation larger than $99\\\\%$ . \"]","image_footnote":"[]","img_path":"images/0348/3deb9f93b28969252528897f0346b617892be8d4fd614311d3d3f5433997f671.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[6,472,25,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[953,353,986,427]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"APPLIED PHYSICAL SCIENCES ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[61,948,157,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Elekes and Parteli ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[59,959,574,980]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary environments ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[841,948,873,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PNAS ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[892,948,926,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 of 8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,959,926,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1073/pnas.2107965118 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[66,63,490,103]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$D_0 \\approx 76\\mu \\mathrm{m}$ and $\\alpha \\approx 0.45$ with coefficient of correlation larger than $99\\%$ (dashed line in Fig. 3C), which provides, thus, an exponent close to 0.5 as assumed in Eq. 2. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[83,103,319,116]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Using Eq. 2 we can rewrite Eq. 1 as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[138,128,490,162]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\theta_ {\\mathrm {r}} \\approx \\tan^ {- 1} \\left\\{\\mu_ {\\text {e f f}, \\infty} \\cdot \\left[ 1 + \\frac {1}{\\left(d / D _ {\\mathrm {E}}\\right) \\cdot \\sqrt {\\tilde {g}}} \\right] \\right\\}, \\tag {3}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[66,174,490,213]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"which provides a means to estimate $\\theta_{\\mathrm{r}}$ (in radians) for given $g$ and $d$ , provided $D_{\\mathrm{E}}$ and $\\mu_{\\mathrm{eff},\\infty}$ for the granular material are known, e.g., from experiments under terrestrial gravity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,214,490,353]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"From Eq. 3, we see that, in the limit $\\sqrt{\\overline{g}} d / D_{\\mathrm{E}} \\to \\infty$ , the angle of repose asymptotically approaches the value $\\theta_{\\mathrm{r,\\infty}} \\equiv \\tan^{-1}[\\mu_{\\mathrm{eff,\\infty}}]$ , independent of gravity and particle size. For the particulate material investigated here, $\\theta_{\\mathrm{r,\\infty}} \\approx 24^{\\circ}$ (Figs. 2 and 3). Therefore, an approximate value for $\\mu_{\\mathrm{eff,\\infty}}$ can be estimated from experiments using particles that are so large that cohesive effects on the angle of repose can be neglected, whereupon $\\mu_{\\mathrm{eff,\\infty}}$ can be computed using the equation $\\mu_{\\mathrm{eff,\\infty}} = \\tan (\\theta_{\\mathrm{r,\\infty}})$ . Subsequently, experiments under Earth's gravity using different values of $d$ can be performed to estimate $D_{\\mathrm{E}}$ from the best fit to Eq. 3. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,353,490,495]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To shed light on Eq. 3, we note that granular materials display increasing relative cohesiveness the smaller the particle size is (15). We follow refs. 24 and 25 and characterize this cohesiveness by computing the Bond number (Bo), i.e., the ratio of the maximum cohesive force acting on a particle to the gravitational force. For the system investigated here, we obtain $\\mathrm{Bo} = 12\\gamma /(d^2 g\\rho_{\\mathrm{p}})$ (using Eqs. 13 and 14), where $\\rho_{\\mathrm{p}}$ is the material density and $\\gamma$ is the surface energy density, which scales the attractive interparticle (van der Waals) force. Given this expression for the Bond number and the scaling of the angle of repose with the particle size in Eq. 3, we propose the model ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[162,509,490,533]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\theta_ {\\mathrm {r}} \\approx \\tan^ {- 1} \\left\\{\\mu_ {\\text {e f f}, \\infty} \\cdot \\left[ 1 + \\beta \\sqrt {\\mathrm {B o}} \\right] \\right\\}, \\tag {4}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[66,546,490,586]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\mu_{\\mathrm{eff},\\infty}$ and $\\beta$ are empirical parameters. As shown in Fig. 4, using this model, we find an excellent data collapse of our simulation results for all values of particle size and gravity con ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[68,613,490,853]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 4. Main plot: Angle of repose $\\\\theta_{\\\\mathrm{r}}$ as a function of the Bond number. Symbols indicate predictions from numerical simulations under different $g$ levels. Moreover, the solid line in the main plot denotes the best fit to the simulation data using Eq. 4, which yields $\\\\mu_{\\\\mathrm{eff,\\\\infty}} \\\\approx 0.458$ and $\\\\beta \\\\approx 0.014$ ( $R^2 \\\\approx 0.98$ ). The data shown in the main plot are replotted in Inset, which shows the angle of repose $\\\\theta_{\\\\mathrm{r}}$ as a function of $\\\\sqrt{\\\\mathrm{B}\\\\sigma}$ , using linear scale for both axes. \"]","image_footnote":"[]","img_path":"images/0373/bd67681668875fcd7869094f9fbb06cd9e122e8397ea01e9cbb15ca87e100a3c.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[507,63,933,90]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"sidered, with $\\mu_{\\mathrm{eff},\\infty}\\approx 0.458$ and $\\beta \\approx 0.014$ . Furthermore, from the definition of Bo, Eqs. 1 and 4 lead to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[673,102,933,139]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nD = \\beta \\sqrt {\\frac {1 2 \\gamma}{\\rho_ {\\mathrm {p}} g}}, \\tag {5}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,149,933,174]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"which relates the characteristic length-scale $D$ in Eq. 1 to the material parameters. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,174,933,302]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We note that our model is valid in the regime of regular heap morphology (regime II), i.e., when $d \\gtrsim d_{\\mathrm{c}}$ . In particular, Eq. 1 predicts $\\theta_{\\mathrm{r}} \\to 90^{\\circ}$ when $d \\to 0$ , but experiments revealed a nearly constant angle of repose for particle sizes of the order of a few micrometers, i.e., in regime I of irregular heap morphology (26). Our simulations show that $D \\approx 2d_{\\mathrm{c}}$ and that the heap morphology changes from regular (regime II) to irregular (regime I) when the Bond number exceeds approximately $10^{4}$ , thus providing a means to approximately estimate $d_{\\mathrm{c}}$ from the material properties. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,302,933,556]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We have also performed some simulations with heaps $150\\%$ larger than the ones considered in the present discussion, but we could not find a significant change in the values of $\\theta_{\\mathrm{r}}$ . We believe that, qualitatively, even larger heaps should display the same dependence of $\\theta_{\\mathrm{r}}$ on $d$ observed in the experiments quoted in Fig. 2 and in the DEM simulations in this article. However, it is uncertain to which extent our model parameters should be adapted to assess the angle of repose of much larger heaps quantitatively. In particular, the dynamics of much larger systems could be affected by particle-air interactions, which must be incorporated in a future extension of our model. Furthermore, since the packing dynamics are affected by the preparation history of the packing (see the discussion in ref. 15), the pouring height and the size of the insertion region chosen for reproducing experimental conditions could exert an important control on the value of $\\theta_{\\mathrm{r}}$ . We have indeed noticed a trend of increasing avalanche sizes by increasing the width of the particle insertion region in our simulations of larger heaps. Therefore, the quantitative behavior of $\\theta_{\\mathrm{r}}$ for much larger heaps will constitute topic of future research. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,556,935,596]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An argument for the approximate scaling with the square root of the Bond number in Eq. 4. Our model suggests that the effective friction coefficient $\\mu_{\\mathrm{eff}}$ can be written as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[649,606,933,621]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mu_ {\\text {e f f}} \\approx \\mu_ {\\text {e f f}, \\infty} \\cdot [ 1 + f ], \\tag {6}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,632,933,685]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\mu_{\\mathrm{eff},\\infty}$ is the value of $\\mu_{\\mathrm{eff}}$ disregarding the contribution from attractive particle interaction forces, encoded in the value of $f$ . Furthermore, an approximate scaling of $f$ with $\\sqrt{\\mathrm{Bo}}$ is obtained from our simulations (Eq. 4). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,685,933,851]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To shed light on this scaling, we note that, when the local slope exceeds the angle of repose, the heap surface relaxes through avalanches, thus leading to the emergence of a surface avalanche layer—of thickness a few times $d$ and constituted of $N$ particles—flowing downhill atop the immobile granular bulk in the heap's interior. At the angle of repose, the downhill gravitational force on these $N$ particles, i.e., $W = Nmg$ , with m denoting the particle mass, is balanced by frictional contact forces and cohesive interactions with particles in the bulk. However, not all $N$ particles participate in these interactions. Instead, the total cohesive force acts on a subset $N_{\\mathrm{interface}}$ of particles that are at the interface with the bulk. We propose that $f$ scales with the quotient of this total cohesive force and $W$ ; i.e., ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[586,860,933,891]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nf \\propto \\frac {N _ {\\text {i n t e r f a c e}} \\cdot F _ {\\mathrm {v d W}}}{N m g} \\propto \\frac {N _ {\\text {i n t e r f a c e}}}{N} \\cdot \\frac {1}{d ^ {2} g}, \\tag {7}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,902,933,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where we used $m \\propto d^3$ and $F_{\\mathrm{vdW}} \\propto d$ , with $F_{\\mathrm{vdW}}$ standing for the attractive van der Waals force (Eq. 13) between a particle in ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[6,472,25,934]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[68,948,102,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 of 8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[121,948,153,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PNAS ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[121,959,333,969]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1073/pnas.2107965118 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[837,948,933,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Elekes and Parteli ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[420,959,933,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[859,970,933,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"environments ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[61,63,482,117]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the avalanche layer and another particle in the bulk. Therefore, a scaling of $f$ with $\\sqrt{\\mathrm{Bo}}$ , i.e., with $(d\\sqrt{g})^{-1}$ , is obtained if $\\eta \\equiv N_{\\mathrm{interface}} / N \\propto d\\sqrt{g}$ , which must be verified through numerical simulations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[61,117,483,269]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, here we assume that $\\eta$ is, to first order, proportional to the packing density $(\\phi)$ of the granular material. We think that this assumption is reasonable, because the smaller $\\phi$ is, the more porous the granular medium and the smaller, thus, $\\eta$ is. By contrast, the denser the granular material is, the larger the number of particle-particle contacts, and the larger, thus, $\\eta$ is. To verify whether $\\phi$ (and thus $\\eta$ ) follows, to a certain limit, an approximate scaling with $d\\sqrt{g}$ , we have performed numerical experiments adapting the protocol of ref. 15 to investigate the effect of $d$ and $g$ on $\\phi$ . Fig. 5 displays the results of these experiments, which are described at the end of Materials and Methods. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[61,270,483,481]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As can be seen in Fig. 5, the plot of $\\phi$ as a function of $d\\sqrt{\\tilde{g}}$ leads to an excellent data collapse of our simulation results and reveals an asymptotic growth of the packing fraction with $d\\sqrt{\\tilde{g}}$ . Specifically, in the limit of large particle sizes ( $d \\gtrsim 1 \\mathrm{~mm}$ ), the granular material displays a largely noncohesive behavior, with $\\phi$ resulting nearly independent of $d\\sqrt{\\tilde{g}}$ . The dashed line in the main plot in Fig. 5 denotes the best fit using the asymptotic growth function $\\phi = \\phi_{\\infty} \\cdot \\left\\{1 - C \\cdot \\exp \\left[-D_{\\phi}^{-1} \\cdot d\\sqrt{\\tilde{g}}\\right]\\right\\}$ , which gives $\\phi_{\\infty} \\approx 0.57$ (the associated random loose packing fraction) (27), $C \\approx 0.56$ , and $D_{\\phi} \\approx 103 \\mu \\mathrm{m}$ , with correlation coefficient $R^2 \\approx 0.994$ . We remark that a theoretical model is needed to elucidate this scaling, as well as the behavior of $\\phi$ as $d\\sqrt{\\tilde{g}} \\to 0$ . However, such a theoretical model would go beyond the scope of the present discussion, which aims rather at testing for an approximate scaling of $\\phi$ with $d\\sqrt{\\tilde{g}}$ to a certain limit. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[61,482,482,575]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Indeed, a linear fit using $\\phi = A + B\\cdot d\\sqrt{\\tilde{g}}$ describes reasonably well the trend of the simulation results associated with the lower range of $d\\sqrt{\\tilde{g}}$ considered in the present article; i.e., $30\\leq \\left[d\\sqrt{\\tilde{g}}\\right] / \\mu \\mathrm{m}\\leq 210$ with $A\\approx 0.32$ $B\\approx 1.14\\mathrm{mm}^{-1}$ , and correlation coefficient $R^2\\approx 0.947$ (Fig. 5, Inset). The origin of this approximate linear trend is the effect of attractive particle interaction forces—which are relevant in the aforementioned range ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[59,600,485,835]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 5. Packing density $\\\\phi$ as a function of $d\\\\sqrt{\\\\tilde{g}}$ , with $\\\\tilde{g} \\\\equiv g / g_{\\\\mathrm{Earth}}$ . The dashed line in the main plot denotes the best fit to the simulation results (symbols) using the equation $\\\\phi = \\\\phi_{\\\\infty} \\\\cdot \\\\left\\\\{1 - C \\\\cdot \\\\exp \\\\left[-D_{\\\\phi}^{-1} \\\\cdot d\\\\sqrt{\\\\tilde{g}}\\\\right]\\\\right\\\\}$ , which yields $\\\\phi_{\\\\infty} \\\\approx 0.57$ , $C \\\\approx 0.56$ , and $D_{\\\\phi} \\\\approx 103~\\\\mu \\\\mathrm{m}$ , with $R^2 \\\\approx 0.994$ . Furthermore, the solid line in Inset denotes the best linear fit to the simulation results within the range $30 \\\\leq d / \\\\mu \\\\mathrm{m} \\\\leq 210$ , using $\\\\phi = A + B \\\\cdot d\\\\sqrt{\\\\tilde{g}}$ , which gives $A \\\\approx 0.32$ and $B \\\\approx 1.14~\\\\mathrm{mm}^{-1}$ , with $R^2 \\\\approx 0.947$ . \"]","image_footnote":"[]","img_path":"images/0813/9228745e6188d0cac10ab0f5fb95a1cf459211969100e4c697116ad5493d4a0f.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[505,63,924,159]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"of small $d\\sqrt{g}$ , but become negligibly small compared to particle weight when $d\\sqrt{g}$ becomes sufficiently large. We thus find that the approximate linear scaling of $\\phi$ (and, thus, of $\\eta \\equiv N_{\\mathrm{interface}} / N$ ) with $d\\sqrt{g}$ , within the range of small $d\\sqrt{g}$ , provides an argument for the approximate scaling of $f$ with $\\sqrt{\\mathrm{Bo}}$ , owing to Eq. 7. More precisely, $f \\propto \\eta / [d^2 g] \\propto \\phi / [d^2 g] \\propto 1 / [d\\sqrt{g}]$ (i.e., $f \\propto \\sqrt{\\mathrm{Bo}}$ ). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,174,924,314]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Significance of Our Model in the Light of Experimental Observations. Reduced-gravity experiments of granular heap formation (28) in the Bremen drop tower, using basalt beads of diameter $500\\mu \\mathrm{m}$ , revealed a slight trend of increasing angle of repose with decreasing gravity for $0.03\\leq \\tilde{g}\\leq 1$ . Although the experiments were performed using a Hele-Shaw cell to obtain quasi-2D heaps (28), qualitatively, the behavior of $\\theta_{\\mathrm{r}}$ with gravity for these heaps is consistent with the prediction from our model that granular materials behave more cohesively and produce larger angles of repose under lower gravity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,314,924,544]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Furthermore, parabolic flight experiments with slowly rotating drums, operating in the discrete avalanche regime at $g$ levels ranging from 0.1 to 1, revealed a slight trend of increasing angle of repose $\\theta_{\\mathrm{start}}$ the slope above which the granular surface becomes unstable and starts to avalanche (29)with decreasing gravity (30, 31). The increase of $\\theta_{\\mathrm{start}}$ with decreasing $g$ observed in ref. 30 suggests enhanced cohesive behavior of granular materials under reduced gravity (30). Microgravity experiments with rotating drums operating at $g$ levels varying from 0.01 to 1.9 and at high rotational speeds, in the so-called continuous avalanching regime—in which the granular surface undergoes avalanche flow permanently—also revealed increasing cohesive behavior with decreasing $g$ (32, 33). In these experiments, a scaling of the slope angle of the granular surface with $\\sqrt{1 / g}$ was found (32, 33). To compare, experiments in the centrifuge at $g$ levels from 1 to 25 revealed insignificant correlation between this angle and gravity (34), as also predicted from our model. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,545,924,761]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We note that particle interaction forces can be affected by still poorly understood geochemical processes (35), while granular flows under low atmospheric pressure conditions can be further influenced by the presence of interstitial gas. Moreover, for values of Bond number smaller than unity, irregular particle geometries, inherent to natural granular systems, can cause statistical fluctuations comparable to the difference between the angles of repose predicted for spherical particles under $g$ levels of the same order. For instance, parabolic flight experiments using Toyoura sand $(d\\approx 250\\mu \\mathrm{m})$ revealed no significant dependence of the angle of repose on gravity for the range of investigated $g$ levels (1/6 to 2) (36). We conclude, based on our results, that the angle of repose of natural sand under Martian gravity should not differ much from its terrestrial counterpart $(30^{\\circ}$ to $35^{\\circ})$ , which is consistent with observations from the slope of Martian dunes at their avalanche side (37). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,761,924,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Characterization of average particle size of strongly polydisperse systems can be made using different parameters, such as the Sauter mean particle size $d_{\\mathrm{S}}$ i.e., the diameter of the particle that has the same volume to surface area ratio as the entire ensemble. Two comprehensive compilations of experimental datasets on $\\theta_{\\mathrm{r}}$ as a function of $d_{\\mathrm{S}}$ presented in refs. 26 and 38, reveal the same characteristics as in Fig. 2, i.e., a noticeable, power-law-like decrease with $d_{\\mathrm{S}}$ within an intermediate range of particle size, followed by slower decay in the limit of larger $d_{\\mathrm{S}}$ with $\\theta_{\\mathrm{r}}$ asymptotically approaching a value $\\theta_{\\mathrm{r,\\infty}}$ between $20^{\\circ}$ and $30^{\\circ}$ that is roughly independent of particle size. We thus propose that Eq. 1 should be valid without regard of the parameter employed to characterize particle size, since the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[6,472,25,934]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[61,950,155,959]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Elekes and Parteli ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[61,960,572,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[61,970,135,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"environments ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[842,948,871,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PNAS ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[892,948,924,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 of 8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[714,960,924,969]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1073/pnas.2107965118 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[955,356,982,427]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"SENEI 1A ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[66,63,490,90]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"corresponding value of $D$ can be estimated from the best fit to $\\theta_{\\mathrm{r}}(d)$ using Eq. 1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,90,492,255]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We further remark that Eq. 1 should break down when $d$ becomes much smaller than a certain value $(d_{\\mathrm{c}})$ , which, for the system considered in our DEM simulations, is of the order of $50\\mu \\mathrm{m}$ . Indeed, Eq. 1 predicts that $\\theta_{\\mathrm{r}}\\rightarrow 90^{\\circ}$ as $d\\to 0$ . However, measurements of $\\theta_{\\mathrm{r}}$ of strongly polydisperse dust systems (using the Sauter mean diameter $d_{\\mathrm{S}}$ to characterize particle size) revealed a breakdown in the trend of increasing $\\theta_{\\mathrm{r}}$ with decreasing particle size, when particles become sufficiently small (26). As explained by Lanzerstorfer (26), the reason for this behavior is the formation of small agglomerates of dust-sized particles, which roll down the heap slope, thus limiting the angle of repose. An upper limit for $\\theta_{\\mathrm{r}}$ of about $55^{\\circ}$ was reported in the experiments in ref. 26. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,255,492,496]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Although further work will be required to characterize the dynamics of particle agglomerates in DEM simulations and to investigate the factors controlling the value of $d_{\\mathrm{c}}$ we note that the highest values of $\\theta_{\\mathrm{r}}$ in most experimental datasets quoted in Fig. 2 are consistent with the upper bound reported by Lanzerstorfer (26). The only exception is the dataset of Lumay et al. (18) (open squares in Fig. 2), which displays $\\theta_{\\mathrm{r}}$ exceeding $70^{\\circ}$ . A possible explanation for the higher $\\theta_{\\mathrm{r}}$ values in this dataset is that the silicon carbide abrasives adopted in ref. 18 consist of a broad distribution of complex particle geometric shapes, including elongated and sharp-edged particles. DEM simulations (39) have shown that cohesive rods form packings of lower solid fraction than that of cohesive beads; i.e., complex particle shapes can enhance the cohesive behavior of granular materials. By virtue of these observations and in view of our Eqs. 4 and 7, we thus expect that elongated particles, compared to beads, produce steeper heaps, while sharp edges could further enhance friction and heap stability. The present work could be thus continued by elucidating this behavior in DEM simulations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,496,490,550]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, future work should now focus on deepening the understanding of our findings from a theoretical analysis of granular heap stability, which poses a long-standing and challenging research topic in the field of granular matter physics (40). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,556,230,569]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Materials and Methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[66,573,464,584]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This section describes the DEM employed in our numerical simulations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,596,492,620]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Equations of Motion. The equations for the translational and rotational motion of the $i$ th particle in the system read ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,625,492,657]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nm \\ddot {r} _ {i} = \\sum_ {\\substack {1 \\leq j \\leq n \\\\ j \\neq i}} \\mathbf {F} _ {i j} + m \\mathbf {g} \\tag{8}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[223,661,492,693]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nI \\dot {\\boldsymbol {\\omega}} _ {i} = \\sum_ {\\substack {1 \\leq j \\leq n \\\\ j \\neq i}} \\mathbf {M} _ {i j}, \\tag{[9]}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[66,701,492,793]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\mathbf{r}_i$ and $\\omega_{i}$ denote the position and angular velocity of particle $i$ , respectively; $\\mathbf{g}$ is gravity; while $\\mathbf{F}_{ij}$ and $\\mathbf{M}_{ij}$ denote the interaction force and torque, respectively, exerted by particle $j$ on particle $i$ . Furthermore, $n$ is the total number of particles in the system, each particle having diameter $d$ , density $\\rho_{\\mathrm{p}}$ , mass $m = \\pi \\rho_{\\mathrm{p}} d^{3} / 6$ , and moment of inertia $I = m d^{2} / 10$ . In Eq. 8, $\\mathbf{F}_{ij}$ denotes the sum of the contact force $\\mathbf{F}_{ij}^{\\mathrm{c}}$ and the nonbonded attractive interaction force $\\mathbf{F}_{ij}^{\\mathrm{a}}$ exerted by particle $j$ on particle $i$ . These forces are modeled as discussed next. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,805,492,853]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Particle-Particle Interaction Forces. For the normal component of the contact force, $\\mathsf{F}_{ij,n}^{\\mathrm{c}}$ , viscoelastic interaction is assumed (11), while a modified Cundall-Strack model (10) is applied to compute the tangential force, $\\mathsf{F}_{ij,t}^{\\mathrm{c}}$ . The equations for $\\mathsf{F}_{ij,n}^{\\mathrm{c}}$ and $\\mathsf{F}_{ij,t}^{\\mathrm{c}}$ read ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,860,492,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathbf {F} _ {i j, n} ^ {c} = \\min \\left(0, - k _ {n} \\delta_ {i j, n} ^ {3 / 2} - \\frac {3}{2} A _ {n} k _ {n} \\sqrt {\\delta_ {i j , n}} \\dot {\\delta} _ {i j, n}\\right) \\mathbf {e} _ {i j, n} \\tag {10}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[129,892,492,933]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathbf {F} _ {i j, t} ^ {c} = - \\min \\left(\\mu_ {s} \\left| \\mathbf {F} _ {i j, n} ^ {c} \\right|, \\int_ {\\text {p a t h}} k _ {t} \\sqrt {\\delta_ {i j , n}} d s + A _ {t} \\sqrt {\\delta_ {i j , n}} v _ {i j, t}\\right) \\mathbf {e} _ {i j, t}, \\tag {11}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[509,81,933,183]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0725/ac0d56c6597dedf1742fa360fdf261195f6be3ac2b30ad6cd6e4ec53f43f79c9.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":"<table><tr><td>Parameter</td><td>Symbol</td><td>Value</td></tr><tr><td>Young's modulus</td><td>Y</td><td>63 GPa</td></tr><tr><td>Poisson's ratio</td><td>ν</td><td>0.24</td></tr><tr><td>Particle material density</td><td>ρp</td><td>2,500 kg/m3</td></tr><tr><td>Surface energy density</td><td>γ</td><td>0.05 J/m2</td></tr><tr><td>Sliding friction coefficient</td><td>μs</td><td>0.5</td></tr><tr><td>Rolling friction coefficient</td><td>μr</td><td>0.05</td></tr></table>","table_caption":"[\"Table 1. Numerical values of parameters used in the simulations \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[507,205,933,296]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\delta_{ij,n} = d - |r_j - r_i|$ ; $\\mathbf{e}_{ij,n} = \\frac{\\mathbf{r}_j - \\mathbf{r}_i}{|\\mathbf{r}_j - \\mathbf{r}_i|}$ ; $r_i$ and $r_j$ are the positions of particles $i$ and $j$ , respectively; $\\mathbf{v}_{ij,t} = |\\mathbf{v}_{ij,t}|$ , where $\\mathbf{v}_{ij,t} = \\mathbf{v}_{ij} - (\\mathbf{v}_{ij} \\cdot \\mathbf{e}_{ij,n}) \\cdot \\mathbf{e}_{ij,n}$ denotes the relative tangential velocity at the point of contact, with $\\mathbf{v}_{ij} = \\dot{\\mathbf{r}}_j - \\dot{\\mathbf{r}}_i$ ; and $\\mathbf{e}_{ij,t} = \\mathbf{v}_{ij,t} / v_{ij,t}$ is the tangential unit vector; while the contact forces in Eqs. 10 and 11 are set as zero if $\\delta_{ij,n} < 0$ . Furthermore, $k_n$ and $k_t$ are elastic parameters, which are computed from the particle Young's modulus, $Y$ , and the Poisson's ratio, $\\nu$ , through ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[606,307,933,333]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nk _ {\\mathrm {n}} = \\frac {2 Y}{3 \\left(1 - \\nu^ {2}\\right)} \\sqrt {R _ {\\mathrm {e f f}}}, k _ {\\mathrm {t}} = \\frac {4 G}{2 - \\nu} \\sqrt {R _ {\\mathrm {e f f}}} \\tag {12}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,344,933,402]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"with $G = Y / (2 + 2\\nu)$ denoting the shear modulus and $R_{\\mathrm{eff}} = d / 4$ , while $A_{\\mathrm{n}}$ and $A_{\\mathrm{t}}$ are dissipative parameters, $\\mu_{s}$ is the (Coulomb) sliding friction coefficient, and the integral in Eq. 11 is performed over the relative displacement of the particles at the point of contact and over the entire contact duration (15, 41). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,403,933,527]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The dissipative parameter $A_{\\mathrm{n}}$ further depends on material viscosities that are not directly available (11). Therefore, to determine $A_{\\mathrm{n}}$ , we use a relation between this dissipative parameter and the coefficient of restitution for the collision of two isolated particles (42, 43) and employ the Padé approximation from ref. 44. Furthermore, following ref. 45, we choose the tangential dissipative parameter, $A_{\\mathrm{t}}$ , such that the prefactors of $\\dot{\\delta}_{ij,\\mathrm{n}}$ and $v_{ij,\\mathrm{t}}$ in Eqs. 10 and 11, respectively, are of the same order of magnitude, thus yielding $A_{\\mathrm{t}} = 3A_{\\mathrm{n}}k_{\\mathrm{n}} / 2$ . Indeed, ref. 46 showed that this assumption leads to excellent agreement between simulation results and experimental values of particle velocity profiles in a gravity-driven shearing experiment. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,528,933,551]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Furthermore, the nonbonded attractive van der Waals interaction force between two particles in the system, labeled $i$ and $j$ , is given by (15, 47, 48) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[570,565,933,630]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathbf {F} _ {i j, n} ^ {a} = \\left\\{ \\begin{array}{l l} \\frac {A _ {H} R _ {\\text {e f f}}}{6 D _ {\\min } ^ {2}} \\mathbf {e} _ {i j, n} & \\text {i f} \\delta_ {i j, n} > 0, \\\\ \\frac {A _ {H} R _ {\\text {e f f}}}{6 \\left(\\delta_ {i j , n} - D _ {\\min }\\right) ^ {2}} \\mathbf {e} _ {i j, n} & \\text {i f} - D _ {\\max } \\leq \\delta_ {i j, n} \\leq 0 \\\\ 0, & \\text {i f} \\delta_ {i j, n} < - D _ {\\max }, \\end{array} \\right. \\tag {13}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,644,933,669]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $A_{\\mathsf{H}}$ is the Hamaker constant, which is computed from the surface energy density, $\\gamma$ , using the expression (49) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[673,681,933,696]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nA _ {H} = 2 4 \\pi D _ {\\min } ^ {2} \\gamma . \\tag {14}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,708,933,777]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In Eq. 13, $D_{\\mathrm{max}}$ is the maximal (cutoff) distance of the van der Waals interaction, which is set as $1\\mu \\mathrm{m}$ (15), while the constant $D_{\\mathrm{min}}$ is introduced to avoid the singularity of the Hamaker equation at $\\delta_{ij,n} = 0$ and accounts for the fact that particles are not perfectly smooth. We take the value $D_{\\mathrm{min}} = 1.65\\mathring{\\mathrm{A}}$ , which corresponds to the minimal distance between particles at contact (49, 50). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,789,933,837]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Torque and Rolling Friction. The total torque $\\mathbf{M}_{ij}$ is given by $\\mathbf{M}_{ij} = \\mathbf{M}_{ij}^{\\mathrm{t}} + \\mathbf{M}_{ij}^{\\mathrm{r}}$ , where $\\mathbf{M}_{ij}^{\\mathrm{t}} = \\Theta (\\delta_{ij,n})[d / 2 - \\delta_{ij,n}]\\mathbf{e}_{ij,n}\\times \\mathbf{F}_{ij,t}^{c}$ , and $\\mathbf{M}_{ij}^{\\mathrm{r}}$ is the torque associated with the rolling resistance at the contact point between particles $i$ and $j$ and is computed through the model (14, 17) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[536,850,933,881]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathbf {M} _ {i j} ^ {r} (t + \\Delta t) = \\min \\left(\\mathbf {M} _ {i j} ^ {r m}, | \\mathbf {M} _ {i j} ^ {r} (t) - k _ {r} \\omega_ {i j} \\Delta t |\\right) \\frac {\\mathbf {M} _ {i j} ^ {r} (t) - k _ {r} \\omega_ {i j} \\Delta t}{| \\mathbf {M} _ {i j} ^ {r} (t) - k _ {r} \\omega_ {i j} \\Delta t |}, \\tag {15}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[507,893,933,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $M_{ij}^{\\mathrm{rm}} = \\mu_{\\mathrm{r}}R_{\\mathrm{eff}}|\\mathbf{F}_{ij,n}^{\\mathrm{c}}|$ , with $\\mu_{\\mathrm{r}}$ standing for the coefficient of rolling resistance. Furthermore, $\\omega_{ij} = \\omega_{i} - \\omega_{j}$ , $\\Delta t$ denotes the time step, and $k_{\\mathrm{r}} = k_{\\mathrm{t}}\\sqrt{\\delta_{ij,n}} R_{\\mathrm{eff}}^{2}$ (17, 51, 52). The magnitude of the spring torque $\\mathbf{M}_{ij}^{\\mathrm{r}}$ is, thus, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[6,472,25,934]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[68,948,102,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 of 8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[121,948,153,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PNAS ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[121,959,333,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1073/pnas.2107965118 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[837,948,933,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Elekes and Parteli ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[420,959,933,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[859,970,933,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"environments ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[59,65,485,90]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"upper bounded by the full mobilization torque $\\mu_{\\mathrm{r}}R_{\\mathrm{eff}}|\\mathbf{F}_{ij,n}^{\\mathrm{c}}|$ , which means that rolling resistance behaves perfectly plastic beyond this upper bound. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[59,100,485,229]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Numerical Integration. The integration was performed using the open source Discrete Element Method particle simulation software LIGGGHTS (which stands for LAMMPS Improved for General Granular and Granular Heat Transfer Simulations) (52), along with the extensions introduced in ref. 15, to account for the computation of the dissipative term in the contact model (Eqs. 10 and 11), following ref. 44, and the attractive particle interaction force model (15, 47, 48) defined in Eq. 13. The integration time step $\\Delta t$ has been about $10\\%$ of the collision time $T_{\\mathrm{col}}$ between two particles, defined from Hertz's elastic theory for the undamped, noncohesive situation; i.e., $T_{\\mathrm{col}} \\approx 3.21(m_{\\mathrm{eff}} / k_{\\mathrm{n}})^{2 / 5} \\cdot v_{\\mathrm{imp}}^{-1 / 5}$ (12), where $m_{\\mathrm{eff}} = m / 2$ , and $v_{\\mathrm{imp}}$ denotes the relative normal velocity of the particles at impact. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[59,241,485,333]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Model Parameters. The values of Young's modulus, Poisson's ratio, particle density, and surface energy density, listed in Table 1, are consistent with glass beads (15, 49), and we take the coefficients of sliding and rolling friction following calibration results from previous DEM simulations (6, 14-17, 46, 53, 54). The collisions of the particles with the frictional bottom wall are modeled using the same material parameters, while the wall is regarded as cohesionless and one of the collision partners has infinite mass and radius (15). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[59,333,485,461]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Furthermore, the normal damping coefficient $A_{n}$ is computed based on the coefficient of restitution $\\varepsilon_{\\mathrm{ref}}$ associated with a reference collisional velocity $\\nu_{\\mathrm{imp}}$ , assuming only contact forces (no cohesion) (44). Based on previous calibration of the coefficient of restitution for use in DEM studies of the angle of repose (53, 54), here we adopt $\\varepsilon_{\\mathrm{ref}}$ in the range between 0.2 and 0.4, for $\\nu_{\\mathrm{imp}} = 1.0~\\mathrm{m / s}$ . All results presented in this article refer to $\\varepsilon_{\\mathrm{ref}} = 0.2$ , but we have found that using $\\varepsilon_{\\mathrm{ref}} = 0.4$ still leads to a reasonable quantitative agreement between our numerical predictions for $\\theta_{\\mathrm{r}}$ and the experimental data in Fig. 2. However, we reinforce that the main contribution of our article consists of a mathematical expression that is robust with respect to details of interparticle ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[500,65,926,112]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"interactions, encoded in the parameters $\\mu_{\\mathrm{eff},\\infty}$ and $\\beta$ . The role of various ingredients that have been neglected in our simulations, such as torsion (13) and long-range electrostatic interactions, should be elucidated in future work. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[500,123,928,376]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Numerical Experiments to Estimate the Packing Fraction, $\\phi$ , as a Function of Particle Size and Gravity. Fig. 5 displays the results from numerical experiments to estimate the packing fraction $\\phi$ as a function of $d$ and $g$ . Each of these experiments consists of releasing from rest a monodisperse packing of $20\\%$ initial volume fraction composed of 11,039 (initially noncontacting) particles randomly distributed over the simulation domain—a vertical rectangular box of horizontal dimensions $L_{x} \\times L_{y}$ , with $L_{x} = L_{y} = 17d$ and height $100d$ . Boundary conditions are the same as in the experiments of the angle of repose, except that periodic boundary conditions are applied in the horizontal directions (15). Once the particles have settled due to the action of gravity, we compute the packing density of the granular column using $\\phi = n_{\\phi} \\cdot (\\pi/6)d^{3}/[L_{x} \\cdot L_{y} \\cdot (H_{u} - H_{l})]$ , where $n_{\\phi}$ is the number of particles with center-of-mass position between $H_{l} = 0.3z_{\\max}$ and $H_{u} = 0.7z_{\\max}$ with $z_{\\max}$ denoting the center-of-mass position of the highest particle in the granular column (15). We find that $\\phi$ differs negligibly over different realizations of the same experiment (each realization with different initial random positions of the particles). Therefore, each value of $\\phi$ presented in Fig. 5 has been obtained based on one realization for the corresponding value of $d$ and $g$ , but by averaging over the four vertical subcolumns obtained by halving $L_{x}$ and $L_{y}$ (15), the associated SD corresponding to the error bars in Fig. 5 (i.e., the same protocol as in ref. 15 but including the effect of gravity in the investigation). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[500,386,852,399]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Data Availability. All study data are included in the main text. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[500,406,926,459]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ACKNOWLEDGMENTS. We thank Sandesh Kamath for assistance with the numerical interface between the DEM implementation of ref. 15 and the latest version of LIGGGHTS, Yaping Shao for discussions, and the German Research Foundation for funding through the Heisenberg Programme and Grant RI 2497/6-1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[59,477,485,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1. H. Chen, Y. L. Liu, X. Q. Zhao, Y. G. Xiao, Y. Liu, Numerical investigation on angle of repose and force network from granular pile in variable gravitational environments. Powder Technol. 283, 607-617 (2015). \",\"2. A. C.-Y. Wong, Characterization of the flowability of glass beads by bulk densities ratio. Chem. Eng. Sci. 55, 3855-3859 (2000). \",\"3. N. Pilpel, The flow properties of magnesia. J. Pharm. Pharmacol. 16, 705-716 (1964). \",\"4. J. T. Carstensen, P.-C. Chan, Relation between particle size and repose angles of powders. Powder Technol. 15, 129-131 (1976). \",\"5. Y. C. Zhou, B. H. Xu, A. B. Yu, P. Zulli, An experimental and numerical study of the angle of repose of coarse spheres. Powder Technol. 125, 45-54 (2002). \",\"6. V. Hassanzadeh, C. M. Wensrich, R. Moreno-Atanasio, Elucidation of the role of cohesion in the macroscopic behaviour of coarse particulate systems using DEM. Powder Technol. 361, 374-388 (2020). \",\"7. S. Ji, H. H. Shen, Contrasting terrestrial and lunar gravity: Angle of repose and incline flows. Earth Space 2006, 1-8 (2006). \",\"8. M. W. Telfer et al., Dunes on Pluto. Science 360, 992-997 (2018). \",\"9. C. B. Beddingfield et al., Landslides on Charon. Icarus 335, 113383 (2020). \",\"10. P. A. Cundall, O. D. L. Strack, A discrete numerical model for granular assemblies. Geotechnique 29, 47-65 (1979). \",\"11. N. V. Brilliantov, F. Spahn, J.-M. Hertzsch, T. Poschel, Model for collisions in granular gases. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53, 5382-5392 (1996). \",\"12. J. Schäfer, S. Dippel, D. E. Wolf, Force schemes in simulations of granular materials. J. Phys. I France 6, 5-20 (1996). \",\"13. S. Luding, Cohesive, frictional powders: Contact models for tension. Granul. Matter 10, 235 (2008). \",\"14. J. Ai, J. F. Chen, J. M. Rotter, J. Y. Ooi, Assessment of rolling resistance models in discrete element simulations. Powder Technol. 206, 269-282 (2011). \",\"15. E. J. R. Parteli et al., Attractive particle interaction forces and packing density of fine glass powders. Sci. Rep. 4, 6227 (2014). \",\"16. J. Schmidt et al., Packings of micron-sized spherical particles: Insights from bulk density determination, X-ray tomography and discrete element simulations. Adv. Powder Technol. 31, 2293-2304 (2020). \",\"17. C. M. Wensrich, A. Katterfeld, Rolling friction as a technique for modelling particle shape in DEM. Powder Technol. 217, 409-417 (2012). \",\"18. G. Lumay et al., Measuring the flowing properties of powders and grains. Powder Technol. 224, 19-27 (2012). \",\"19. Y. Li, Y. Xu, C. Thornton, A comparison of discrete element simulations and experiments for 'sandpiles' composed of spherical particles. Powder Technol. 160, 219-228 (2005). \",\"20. Y. Matsukara, H. Obanawa, Effect of grain diameter and packing condition on the avalanching depth on a slope composed of dry granular materials. Tsukuba Geoenvironmental Sciences 1, 19-25 (2005). \"]","page_idx":"6","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[499,477,924,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"21. E. M. Culligan, H. K. Christenson, Cohesion of granular matter in subzero humidity. J. Phys. Chem. C 118, 15929-15933 (2014). \",\"22. J. H. Choi, E. T. Kang, J. W. Lee, U. S. Kim, W. S. Cho, Materials and process development for manufacturing porcelain figure using a binder jetting 3D printer. J. Ceram. Process. Res. 19, 43-49 (2018). \",\"23. J. R. Metcalf, Angle of repose and internal friction. Int. J. Rock Mech. Min. Sci. 3, 155-161 (1966). \",\"24. A. Anand, J. S. Curtis, C. R. Wassgren, B. C. Hancock, W. R. Ketterhagen, Segregation of cohesive granular materials during discharge from a rectangular hopper. Granul. Matter 12, 193-200 (2010). \",\"25. A. Gans, O. Pouliquen, M. Nicolas, Cohesion-controlled granular material. Phys. Rev. E 101, 032904 (2020). \",\"26. C. Lanzerstorfer, Dusts from dry off-gas cleaning: Comparison of flowability determined by angle of repose and with shear cells. Granul. Matter 19, 58 (2017). \",\"27. C. Song, P. Wang, H. A. Makse, A phase diagram for jammed matter. Nature 453, 629-632 (2008). \",\"28. P. G. Hofmeister, J. Blum, D. Heisselmann, The flow of granular matter under reduced gravity conditions. AIP Conf. Proc. 1145, 71-74 (2009). \",\"29. P. G. Hofmeister, J. Blum, D. Heisselmann, Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 1-24 (2008). \",\"30. M. G. Kleinhans, H. Markies, S. J. de Vet, A. C. in 't Veld, F. N. Postema, Static and dynamic angles of repose in loose granular materials under reduced gravity. J. Geophys. Res. 116, E11004 (2011). \",\"31. C. M. Dury, G. H. Ristow, J. L. Moss, M. Nakagawa, Boundary effects on the angle of repose in rotating cylinders. Phys. Rev. E 57, 4491-4497 (1998). \",\"32. B. R. White, S. P. Klein, Dynamic shear of granular material under variable gravity conditions. Am. Inst. Aeronaut. J. 28, 1701-1702 (1990). \",\"33. O. R. Walton, C. Pamela de Moor, K. S. Gill, Effects of gravity on cohesive behavior of fine powders: Implications for processing Lunar regolith. Granul. Matter 9, 353-363 (2007). \",\"34. A. Brucks, T. Arndt, J. M. Ottino, R. M. Lueptow, Behavior of flowing granular materials under variable g. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75, 032301 (2007). \",\"35. V. Schatz, H. Tsoar, K. S. Edgett, E. J. R. Parteli, H. J. Herrmann, Evidence for indurated sand dunes in the Martian north polar region. J. Geophys. Res. 111, E04006 (2006). \",\"36. H. Nakashima et al., Determining the angle of repose of sand under low-gravity conditions using discrete element method. J. Terramechs. 48, 17-26 (2011). \",\"37. C. Atwood-Stone, A. S. McEwen, Avalanche slope angles in low-gravity environments from active Martian sand dunes. Geophys. Res. Lett. 40, 2929-2934 (2013). \",\"38. D. Geldart, E. C. Abdullah, A. Hassanpour, L. C. Nwoke, I. Wouters, Characterization of powder flowability using measurement of angle of repose. China Particuology 4, 104-107 (2006). \",\"39. X. L. Deng, R. N. Dave, Dynamic simulation of particle packing influenced by size, aspect ratio and surface energy. Granul. Matter 15, 401-415 (2013). \"]","page_idx":"6","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[6,472,25,934]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[953,353,982,427]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"APPLIED PHYSICAL SCIENCES ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[61,948,155,959]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Elekes and Parteli ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[842,948,873,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PNAS ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[892,948,924,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7 of 8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[61,960,572,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[61,970,135,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"environments ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[714,960,924,970]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1073/pnas.2107965118 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[66,67,490,260]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"40. R. P. Behringer, B. Chakraborty, The physics of jamming for granular materials: A review. Rep. Prog. Phys. 82, 012601 (2019). \",\"41. L. E. Silbert et al., Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64, 051302 (2001). \",\"42. R. Ramirez, T. Pöschel, N. V. Brilliantov, T. Schwager, Coefficient of restitution of colliding viscoelastic spheres. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60, 4465-4472 (1999). \",\"43. T. Schwager, T. Pöschel, Coefficient of restitution for viscoelastic spheres: The effect of delayed recovery. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78, 051304 (2008). \",\"44. P. Müller, T. Pöschel, Collision of viscoelastic spheres: Compact expressions for the coefficient of normal restitution. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84, 021302 (2011). \",\"45. T. Schwager, V. Becker, T. Pöschel, Coefficient of tangential restitution for viscoelastic spheres. Eur. Phys. J. E Soft Matter 27, 107-114 (2008). \",\"46. C. H. Rycroft, A. V. Orpe, A. Kudrolli, Physical test of a particle simulation model in a sheared granular system. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80, 031305 (2009). \"]","page_idx":"7","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[507,67,933,260]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"47. H. C. Hamaker, The London-van der Waals attraction between spherical particles. Physica 4, 1058-1072 (1937). \",\"48. M. L. Eggersdorfer, D. Kadau, H. J. Herrmann, S. E. Pratsinis, Fragmentation and restructuring of soft-agglomerates under shear. J. Colloid Interface Sci. 342, 261-268 (2010). \",\"49. M. Götzinger, W. Peukert, Dispersive forces of particle-surface interactions: Direct AFM measurements and modelling. Powder Technol. 130, 102-109 (2003). \",\"50. J. Israelachvili, *Intermolecular & Surface Forces* (Academic Press, London, UK, 1998). \",\"51. K. Iwashita, M. Oda, Rolling resistance at contacts in simulation of shear band development by DEM. J. Eng. Mech. 124, 285-292 (1998). \",\"52. C. Kloss, C. Goniva, A. Hager, S. Amberger, S. Pirker, Models, algorithms and validation for opensource DEM and CFD-DEM. Prog. Comput. Fluid Dyn. 12, 140-152 (2012). \",\"53. P. Frankowski, M. Morgeneyer, Calibration and validation of DEM rolling and sliding friction coefficients in angle of repose and shear measurements. AIP Conf. Proc. 1542, 851 (2013). \",\"54. R. Poisel, A. Preh, \\\"Modifications of PFC $^{3D}$ for rock mass fall modeling\\\" in Continuum and Distinct Element Numerical Modeling in Geo-Engineering, R. Hart, C. Detournay, P. Cundall, Eds. (Itasca Consulting Group, Inc., Minneapolis, MN, 2008), pp. 29-38. \"]","page_idx":"7","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[6,472,25,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[68,948,102,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 of 8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[123,950,153,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PNAS ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[123,960,333,969]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1073/pnas.2107965118 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[839,948,933,957]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Elekes and Parteli ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[422,960,933,969]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[861,971,933,979]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"environments ","text_format":null,"text_level":null,"type":"footer"}],"string":"[\n {\n \"bbox\": \"[59,60,760,154]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary environments \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[59,160,345,177]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Filip Elekesa,1 and Eric J. R. Partelib,1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[59,183,909,208]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{a}$ Institute for Geophysics and Meteorology, University of Cologne, 50969 Cologne, Germany; and $^{b}$ Faculty of Physics, University of Duisburg-Essen, 47057 Duisburg, Germany \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[59,215,924,227]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Edited by Risto Nieminen, Department of Applied Physics, Aalto University, Aalto, Finland, and approved August 6, 2021 (received for review April 27, 2021) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[61,234,483,503]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The angle of repose—i.e., the angle $\\\\theta_{\\\\mathrm{r}}$ between the sloping side of a heap of particles and the horizontal—provides one of the most important observables characterizing the packing and flowability of a granular material. However, this angle is determined by still poorly understood particle-scale processes, as the interactions between particles in the heap cause resistance to roll and slide under the action of gravity. A theoretical expression that predicts $\\\\theta_{\\\\mathrm{r}}$ as a function of particle size and gravity would have impact in the engineering, environmental, and planetary sciences. Here we present such an expression, which we have derived from particle-based numerical simulations that account for both sliding and rolling resistance, as well as for nonbonded attractive particle-particle interactions (van der Waals). Our expression is simple and reproduces the angle of repose of experimental conical heaps as a function of particle size, as well as $\\\\theta_{\\\\mathrm{r}}$ obtained from our simulations with gravity from 0.06 to 100 times that of Earth. Furthermore, we find that heaps undergo a transition from conical to irregular shape when the cohesive to gravitational force ratio exceeds a critical value, thus providing a proxy for particle-scale interactions from heap morphology. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[59,515,405,542]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"granular materials | angle of repose | dry cohesive powders | planetary geomorphology | discrete-element method \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[61,558,483,711]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"One of the most fundamental observables used to characterize the mechanical properties of a granular material, such as sand, pebbles, dust aerosols, and industrial powders, is the angle that a heap of particles makes with the horizontal—the angle of repose, $\\\\theta_{\\\\mathrm{r}}$ . This angle is affected by particle size, because attractive particle interaction forces due to surface intermolecular and interatomic interactions become the more relevant compared to gravity and contact forces the smaller the particles are. For instance, heaps of millimeter-sized glass beads poured from a hopper display an angle of repose of about $20^{\\\\circ}$ to $25^{\\\\circ}$ (1), while the angle of repose of powders of the same material exceeds $50^{\\\\circ}$ (2). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[61,711,483,876]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, there is no model that reliably predicts the dependence of the angle of repose of a granular material on the particle size, notwithstanding much effort made in previous work (3-6). Such a model would have the potential to substantially improve the design and control of various technological processes involving particulate systems, including in additive manufacturing technologies, in the food and pharmaceutical industry, and in the agricultural sector. Moreover, the capability of quantitatively predicting the angle of repose as a function of particle size has promising applications in the space and planetary sciences, in particular owing to increasing concern about the mechanics of granular materials in reduced-gravity experiments and extraterrestrial environments (7-9). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[59,877,483,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The derivation of an analytical expression for the angle of repose from a theoretical treatment is challenging because $\\\\theta_{\\\\mathrm{r}}$ is dictated by still poorly understood dynamics of interparticle interactions in response to gravitational stresses. These interac \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[499,234,926,311]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"tions are mainly due to frictional contact forces and attractive surface potentials, which enhance the cohesive behavior of the granular heap with decreasing particle size. It is uncertain how to predict the dynamics of particle-particle contacts within the granular heap, as well as the resistance to grain sliding and rolling along the heap surface. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[499,311,926,515]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Therefore, here we model the angle of repose by means of particle-based numerical simulations using the discrete-element method (DEM), which consists of solving Newton's equation of motion for every particle in the system by explicitly modeling all main relevant forces acting on the particles. Using such simulations, we compute the angle of repose $\\\\theta_{\\\\mathrm{r}}$ of spherical glass particles over the entire broad range of particle size from the micrometer to the decameter scale. As discussed in the subsequent sections, our numerical predictions for $\\\\theta_{\\\\mathrm{r}}$ under Earth's gravity match quantitatively a comprehensive set of experimental observations of this angle over the entire range of particle sizes investigated. Furthermore, we derive a physically based analytical expression that reproduces our DEM predictions for the angle of repose over three orders of magnitude in gravity, from Pluto conditions ( $\\\\approx 6\\\\%$ of Earth's gravity) up to 100 times Earth's gravity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[499,515,926,592]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the next section we describe our numerical simulations, whereupon we present and discuss our results, the comparison of our numerical predictions with experimental observations, and our analytical model for the angle of repose. Furthermore, we show that our model is consistent with previous observations of the angle of repose in various extraterrestrial gravity conditions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,602,603,616]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Significance \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[511,630,914,786]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The angle between the sloping side of a heap of particles and the horizontal, called angle of repose, is often used to characterize the flowability of granular materials on Earth and planetary environments, such as sand, dust aerosols, and powders. In planetary research, this angle provides an excellent proxy for particle size. The smaller the particle is, the larger the effect of attractive forces between atoms and molecules on the surface of the particles relative to particle weight, the less allowable the material, and the steeper, thus, the angle of repose. We present a model that accurately predicts the angle of repose as a function of particle size, both on Earth and under extraterrestrial gravity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[499,798,926,840]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Author contributions: F.E. and E.J.R.P. designed research; F.E. and E.J.R.P. performed research; F.E. and E.J.R.P. analyzed data; E.J.R.P. wrote the paper; F.E. performed the numerical simulations; and E.J.R.P. developed the analytical model for the angle of repose. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,842,712,854]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The authors declare no competing interest. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,856,692,867]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This article is a PNAS Direct Submission. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,869,924,891]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,893,924,915]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To whom correspondence may be addressed. Email: f.elekes@uni-koeln.de or eric.parteli@uni-due.de. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,916,652,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Published September 13, 2021. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[871,12,923,49]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Check for updates \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[6,472,25,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[955,355,982,427]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"APPLIED PHYSICAL SCIENCES \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[61,948,285,959]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PNAS 2021 Vol. 118 No. 38 e2107965118 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[656,948,871,960]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1073/pnas.2107965118 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[892,948,926,959]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[66,63,490,103]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To conclude this article, we briefly discuss possible implications of our study for future research and present an outlook for model improvements. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,112,232,126]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Numerical Experiments \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,127,490,241]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The DEM, which we apply in our numerical simulations, was introduced by Cundall and Strack (10) and has been steadily refined in the course of recent decades to incorporate improved particle-particle interaction models (11-15). Our DEM, revised in Materials and Methods, accounts for all main relevant forces acting on the particles, i.e., gravity, frictional contact forces, and attractive van der Waals forces, and has proved to reproduce quantitatively the solid fraction and the packing structure of powders constituted of different materials (15, 16). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,242,490,418]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"One widely employed method to generate a granular heap is the fixed funnel method, where the granular material is poured through a funnel or orifice onto a rough surface. In another method, a hollow cylinder, placed atop the surface, is filled with the particulate material and then pulled off of the base at low velocity, to allow the particles to flow down through the cylinder's bottom end (17). However, it is difficult to control heap formation using these methods in numerical simulations of strongly cohesive particles, given that such simulations involve a sensibly small number of particles, thus increasing the tendency to form a clump encompassing a large fraction of the particles in the system. Therefore, we employ a different method that can be regarded as a combination of the fixed funnel and the hollow cylinder method. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,420,490,572]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The heap is formed by pouring particles onto a frictional, square horizontal plate, which has sides $40d$ and constitutes the bottom wall of the simulation domain—a rectangular box of horizontal dimensions $40d \\\\times 40d$ and height $30d$ . The particle insertion region has a square cross-section of side length $4.4d$ , is centered around the vertical symmetry axis of the simulation domain, and extends from the top of the simulation domain down to a height of $20d$ above the bottom plate. At time $t = 0$ , particles are placed at random positions throughout the inner volume of the insertion region, thereby producing a packing of solid fraction $\\\\approx 20\\\\%$ . Thereafter, the particles are released from rest. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,573,490,689]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Particle insertion is repeated at an insertion time step $\\\\Delta t_{\\\\mathrm{ins}} \\\\approx 3.5\\\\sqrt{d / g}$ , i.e., the time interval between two consecutive insertion events, with $g$ standing for gravity. However, during the pouring process, once the height of the growing heap has exceeded $20d$ , only the remaining upper free volume of the insertion region above the heap crest is used for particle insertion. Moreover, the number of poured particles is 25,000, but the pouring process is interrupted if the heap's crest reaches the top of the simulation domain. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,689,490,779]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Open boundary conditions are applied in the horizontal directions. Therefore, the number of particles constituting the final heap can differ depending on $d$ and $g$ , since particles that abandon the simulation domain through its lateral borders are not replaced by new particles. The number of particles constituting the heaps produced in the present study varied between 5,000 and 14,000. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,785,225,798]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results and Discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,800,490,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Angle of Repose Predicted from DEM Simulations. Fig. 1 displays snapshots of simulations obtained with $d = 30 \\\\mu \\\\mathrm{m}$ and $d = 1 \\\\mathrm{~mm}$ under terrestrial gravity conditions. To measure the angle of repose, the projection of the heap on two orthogonal planes ( $x$ and $y$ ) is computed, which yields two side-view images of the heap separated by a rotation of $90^{\\\\circ}$ . An image-processing algorithm is then applied to compute the upper boundary of the granular material, i.e., the heap surface, as well as the total surface area associated with the two-dimensional heap projection. Following ref. 18, we define the angle of repose as the base angle \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[512,63,929,164]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 1. Snapshots of granular heaps produced in our simulations. In $A$ we see a heap constituted by particles of diameter $d = 30\\\\\\\\mu \\\\\\\\mathrm{m}$ , while particle size in $B$ is $d = 1 \\\\\\\\mathrm{~mm}$ . The span of each heap is equal to $40d$ , and both heaps have been produced using terrestrial gravity. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0478/6f5fb54f1c8a877d4d28dd4f7526bfdcc974fdfde95bed9350b3077674ac4d63.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[507,241,933,318]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"of the isosceles triangle, which has the same surface area as the heap (Fig. 1). Therefore, two values of this angle are obtained for each heap, from which the mean $\\\\theta_{\\\\mathrm{r}}$ and SD $\\\\sigma_{\\\\theta_{\\\\mathrm{r}}}$ are computed. We have found no considerable changes in the angle of repose by including computations of this angle from additional projections separated by smaller rotation angles (18). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,318,933,458]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Moreover, we have found that heaps formed by particles of diameter smaller than a value $d_{\\\\mathrm{c}}$ $(\\\\approx 50\\\\mu \\\\mathrm{m}$ under terrestrial gravity) display a strongly irregular shape, with considerable variations in local slope throughout their surface (Fig. 1A). In this regime of strongly irregular heap morphology, which we call here regime I, particle avalanches are largely inhibited by the formation of large, irregular particle agglomerates along the surface of the heap. By contrast, heaps formed with particles of size $d\\\\gtrsim d_{\\\\mathrm{c}}$ (regime II) display rather regular morphology and nearly constant slope along their surface (Fig. 1B). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,458,933,559]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We remark that it becomes increasingly difficult to produce heaps in our simulations as $d$ decreases down to values smaller than $d_{\\\\mathrm{c}}$ . In particular, we could not obtain any heap for $d$ smaller than about $50\\\\%$ of $d_{\\\\mathrm{c}}$ , since particles' sticky behavior for such small particle sizes causes the heap to reach the upper limit of the simulation domain. The conclusions presented in our article are thus applicable to heaps in regime II, i.e., provided particles are not smaller than about $d_{\\\\mathrm{c}}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,560,933,661]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The solid squares in Fig. 2 denote the values of $\\\\theta_{\\\\mathrm{r}}(d)$ obtained from DEM simulations under Earth's gravity. Moreover, Fig. 2 also displays a comprehensive compilation of experimental data for the angle of repose as a function of particle size, taken from measurements of $\\\\theta_{\\\\mathrm{r}}$ from granular heaps produced with different materials (see legend and key in Fig. 2). As we can see in Fig. 2, our numerical predictions follow remarkably well the trend of the experimental data. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,661,933,789]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Furthermore, Fig. 3A shows the values of $\\\\theta_{\\\\mathrm{r}}$ obtained for different values of gravity, ranging from Pluto gravity ( $g = 0.62 \\\\, \\\\mathrm{m/s}^2$ ) to 100 times Earth's gravity. We see that the same qualitative behavior of $\\\\theta_{\\\\mathrm{r}}$ as a function of $d$ is found for all values of gravity investigated. Moreover, for a given particle size, a trend of increasing $\\\\theta_{\\\\mathrm{r}}$ with decreasing gravity is observed. In the following section we present a mathematical expression that will shed light on our numerical predictions, as well as on the experimental observations of the angle of repose as a function of particle size. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,800,933,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A Mathematical Expression for the Angle of Repose as a Function of Gravity and Particle Size. To obtain a mathematical expression that fits our DEM predictions for $\\\\theta_{\\\\mathrm{r}}$ as a function of particle size, we first note that the angle of repose is described via $\\\\theta_{\\\\mathrm{r}} \\\\approx \\\\tan^{-1}[\\\\mu_{\\\\mathrm{eff}}]$ , where $\\\\mu_{\\\\mathrm{eff}}$ is an effective coefficient of friction describing the maximal friction resistance of the granular material against sliding through avalanche (23). This coefficient encodes information on material properties, as well as on macroscopic characteristics related to the heap structure, such as packing fraction and surface roughness. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[6,472,25,934]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[68,948,102,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[121,950,153,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PNAS \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[121,959,333,969]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1073/pnas.2107965118 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[837,948,931,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Elekes and Parteli \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[420,959,933,969]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[859,970,933,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"environments \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[61,63,487,312]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 2. Angle of repose as a function of the particle diameter. Solid blue squares indicate the predictions from our numerical simulations, performed with the parameters listed in Table 1 and using $g = 9.81 \\\\\\\\, \\\\\\\\text{m/s}^2$ . The other symbols denote experimental observations made for roughly monodisperse systems, i.e., the scenario of our DEM simulations. All shown experimental data correspond to glass beads (1, 2, 5, 19-22), except for Pilpel (3) (magnesium oxide) and Lumay et al. (18) (silicon carbide abrasives). The solid line denotes the best fit to our numerical predictions using Eq. 1, which yields $D_{E} \\\\\\\\approx 87 \\\\\\\\, \\\\\\\\mu \\\\\\\\text{m}$ , and $\\\\\\\\mu_{\\\\\\\\text{eff},\\\\\\\\infty} \\\\\\\\approx 0.447$ . \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0828/637c30648c68189f18dcd0f225837a3418e2037bbcd35fb49c263249311ad4b9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[58,453,485,583]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, these characteristics are affected by the nature of interparticle interaction forces. As particle size decreases, attractive particle interaction forces become increasingly more relevant compared to gravitational forces, thereby leading to an increase in the bulk porosity and affecting the dynamics of stress distribution within the heap. Experiments and DEM simulations revealed that the solid fraction of powders follows, approximately, a power-law relation with particle size (15). Taking inspiration from this insight, we approximately describe $\\\\theta_{\\\\mathrm{r}}$ (in radians) using the expression \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[164,598,483,630]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\theta_ {\\\\mathrm {r}} \\\\approx \\\\tan^ {- 1} \\\\left\\\\{\\\\mu_ {\\\\text {e f f}, \\\\infty} \\\\cdot \\\\left[ 1 + \\\\frac {D}{d} \\\\right] \\\\right\\\\}, \\\\tag {1}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[58,647,485,736]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where the effective friction coefficient $\\\\mu_{\\\\mathrm{eff},\\\\infty}$ and the characteristic length-scale $D$ must be determined from the best fit to observations of the angle of repose as a function of particle size. The best fit to our simulation data (blue solid squares in Fig. 2) using Eq.1 gives $\\\\mu_{\\\\mathrm{eff},\\\\infty}\\\\approx 0.447$ and $D\\\\approx 87~{\\\\mu\\\\mathrm{m}}$ with coefficient of correlation $R^2\\\\approx 99\\\\%$ . This best fit is denoted by the solid line in Fig. 2. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[58,736,485,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Moreover, the solid lines in Fig. 3A denote the best fits to the DEM results associated with various values of $g$ level; i.e., $\\\\tilde{g} = g / g_{\\\\mathrm{Earth}}$ , where $g_{\\\\mathrm{Earth}} = 9.81~\\\\mathrm{m / s^2}$ , using Eq. 1 and assuming that $\\\\mu_{\\\\mathrm{eff},\\\\infty}\\\\approx 0.447$ is independent of gravity. The dotted line in Fig. 3A corresponds to the asymptotic value of the angle of repose, $\\\\theta_{\\\\mathrm{r,\\\\infty}}\\\\equiv \\\\tan^{-1}[\\\\mu_{\\\\mathrm{eff,\\\\infty}}]$ . Indeed, we find that the angle of repose $\\\\theta_{\\\\mathrm{r,\\\\infty}}$ obtained from simulations without attractive particle interaction forces (i.e., assuming noncohesive materials) is approximately equal to $\\\\theta_{\\\\mathrm{r,\\\\infty}}$ , independent of particle size (Fig. 3B). There is a small trend of increasing $\\\\theta_{\\\\mathrm{r,\\\\infty}}$ with gravity—Fig. 3B suggests an increase of the order of $10\\\\%$ in $\\\\theta_{\\\\mathrm{r,\\\\infty}}$ with an increase in $\\\\tilde{g}$ from 0.06 to 100—which we attribute to a slightly greater tendency of particles to interlock upon an increase in gravitational stress, but further work (not in the scope of this article) would be needed to elucidate this small effect. Fig. 3A and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[499,63,926,89]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$B$ thus shows that particle size controls on $\\\\theta_{\\\\mathrm{r}}$ are dictated mainly by cohesive particle-particle interactions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[499,89,926,154]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Fig. 3C displays the values of $D$ obtained from the best fits in Fig. 3A, as a function of the $g$ level. As we can see from Fig. 3C, for the range of $\\\\tilde{g}$ considered in the present work, the characteristic length-scale $D$ can be approximately described by the equation \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[680,154,924,185]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nD = \\\\frac {D _ {\\\\mathrm {E}}}{\\\\sqrt {\\\\tilde {g}}}, \\\\tag {2}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[499,187,928,255]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $D_{\\\\mathrm{E}}$ denotes the terrestrial value of $D$ , i.e., $87\\\\mu \\\\mathrm{m}$ . We remark that the solid red line in Fig. 3C is no fit to the simulation data (solid circles). Instead, the red line denotes Eq. 2, i.e., our conjecture that $D$ is equal to $D_{\\\\mathrm{E}} / \\\\sqrt{\\\\tilde{g}}$ . We have found that fitting the DEM results using the equation $D = D_0 / \\\\tilde{g}^\\\\alpha$ leads to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,288,926,531]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0399/bb3d4e839416979a367c8f44cdb5c3a20484289406d6d84cba133c36ef25d101.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[500,544,928,771]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 3. Effect of gravity on the angle of repose. In $A$ , symbols denote $\\\\\\\\theta_{\\\\\\\\mathrm{r}}(d)$ for various $g$ levels, ranging from gravity conditions on Pluto to 100 times Earth's gravity. The solid lines in this plot indicate the best fits to the simulation data using Eq. 1, assuming $\\\\\\\\mu_{\\\\\\\\mathrm{eff},\\\\\\\\infty} = 0.447$ . Furthermore, symbols in $B$ denote the angle of repose $\\\\\\\\theta_{\\\\\\\\mathrm{r,nc}}$ obtained from simulations without cohesive forces, while the dotted line in $A$ and $B$ indicates the value $\\\\\\\\theta_{\\\\\\\\mathrm{r},\\\\\\\\infty} \\\\\\\\equiv \\\\\\\\tan^{-1}[\\\\\\\\mu_{\\\\\\\\mathrm{eff},\\\\\\\\infty}]$ . The values of $D$ obtained from the best fits in $A$ are shown in $C$ as a function of the $g$ level. The solid line in $C$ represents Eq. 2, using $D_{\\\\\\\\mathrm{E}} = 87~\\\\\\\\mu \\\\\\\\mathrm{m}$ as obtained from the best fit to the DEM data with Earth's gravity (Fig. 2). Furthermore, the dashed line denotes the best fit to our numerical predictions of $D$ as a function of $\\\\\\\\tilde{g}$ using $D = D_0 / \\\\\\\\tilde{g}^\\\\\\\\alpha$ , which yields $D_0 \\\\\\\\approx 76~\\\\\\\\mu \\\\\\\\mathrm{m}$ and $\\\\\\\\alpha \\\\\\\\approx 0.454$ with coefficient of correlation larger than $99\\\\\\\\%$ . \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0348/3deb9f93b28969252528897f0346b617892be8d4fd614311d3d3f5433997f671.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[6,472,25,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[953,353,986,427]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"APPLIED PHYSICAL SCIENCES \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[61,948,157,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Elekes and Parteli \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[59,959,574,980]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary environments \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[841,948,873,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PNAS \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[892,948,926,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,959,926,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1073/pnas.2107965118 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[66,63,490,103]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$D_0 \\\\approx 76\\\\mu \\\\mathrm{m}$ and $\\\\alpha \\\\approx 0.45$ with coefficient of correlation larger than $99\\\\%$ (dashed line in Fig. 3C), which provides, thus, an exponent close to 0.5 as assumed in Eq. 2. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[83,103,319,116]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Using Eq. 2 we can rewrite Eq. 1 as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[138,128,490,162]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\theta_ {\\\\mathrm {r}} \\\\approx \\\\tan^ {- 1} \\\\left\\\\{\\\\mu_ {\\\\text {e f f}, \\\\infty} \\\\cdot \\\\left[ 1 + \\\\frac {1}{\\\\left(d / D _ {\\\\mathrm {E}}\\\\right) \\\\cdot \\\\sqrt {\\\\tilde {g}}} \\\\right] \\\\right\\\\}, \\\\tag {3}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[66,174,490,213]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"which provides a means to estimate $\\\\theta_{\\\\mathrm{r}}$ (in radians) for given $g$ and $d$ , provided $D_{\\\\mathrm{E}}$ and $\\\\mu_{\\\\mathrm{eff},\\\\infty}$ for the granular material are known, e.g., from experiments under terrestrial gravity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,214,490,353]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"From Eq. 3, we see that, in the limit $\\\\sqrt{\\\\overline{g}} d / D_{\\\\mathrm{E}} \\\\to \\\\infty$ , the angle of repose asymptotically approaches the value $\\\\theta_{\\\\mathrm{r,\\\\infty}} \\\\equiv \\\\tan^{-1}[\\\\mu_{\\\\mathrm{eff,\\\\infty}}]$ , independent of gravity and particle size. For the particulate material investigated here, $\\\\theta_{\\\\mathrm{r,\\\\infty}} \\\\approx 24^{\\\\circ}$ (Figs. 2 and 3). Therefore, an approximate value for $\\\\mu_{\\\\mathrm{eff,\\\\infty}}$ can be estimated from experiments using particles that are so large that cohesive effects on the angle of repose can be neglected, whereupon $\\\\mu_{\\\\mathrm{eff,\\\\infty}}$ can be computed using the equation $\\\\mu_{\\\\mathrm{eff,\\\\infty}} = \\\\tan (\\\\theta_{\\\\mathrm{r,\\\\infty}})$ . Subsequently, experiments under Earth's gravity using different values of $d$ can be performed to estimate $D_{\\\\mathrm{E}}$ from the best fit to Eq. 3. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,353,490,495]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To shed light on Eq. 3, we note that granular materials display increasing relative cohesiveness the smaller the particle size is (15). We follow refs. 24 and 25 and characterize this cohesiveness by computing the Bond number (Bo), i.e., the ratio of the maximum cohesive force acting on a particle to the gravitational force. For the system investigated here, we obtain $\\\\mathrm{Bo} = 12\\\\gamma /(d^2 g\\\\rho_{\\\\mathrm{p}})$ (using Eqs. 13 and 14), where $\\\\rho_{\\\\mathrm{p}}$ is the material density and $\\\\gamma$ is the surface energy density, which scales the attractive interparticle (van der Waals) force. Given this expression for the Bond number and the scaling of the angle of repose with the particle size in Eq. 3, we propose the model \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[162,509,490,533]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\theta_ {\\\\mathrm {r}} \\\\approx \\\\tan^ {- 1} \\\\left\\\\{\\\\mu_ {\\\\text {e f f}, \\\\infty} \\\\cdot \\\\left[ 1 + \\\\beta \\\\sqrt {\\\\mathrm {B o}} \\\\right] \\\\right\\\\}, \\\\tag {4}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[66,546,490,586]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\mu_{\\\\mathrm{eff},\\\\infty}$ and $\\\\beta$ are empirical parameters. As shown in Fig. 4, using this model, we find an excellent data collapse of our simulation results for all values of particle size and gravity con \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[68,613,490,853]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 4. Main plot: Angle of repose $\\\\\\\\theta_{\\\\\\\\mathrm{r}}$ as a function of the Bond number. Symbols indicate predictions from numerical simulations under different $g$ levels. Moreover, the solid line in the main plot denotes the best fit to the simulation data using Eq. 4, which yields $\\\\\\\\mu_{\\\\\\\\mathrm{eff,\\\\\\\\infty}} \\\\\\\\approx 0.458$ and $\\\\\\\\beta \\\\\\\\approx 0.014$ ( $R^2 \\\\\\\\approx 0.98$ ). The data shown in the main plot are replotted in Inset, which shows the angle of repose $\\\\\\\\theta_{\\\\\\\\mathrm{r}}$ as a function of $\\\\\\\\sqrt{\\\\\\\\mathrm{B}\\\\\\\\sigma}$ , using linear scale for both axes. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0373/bd67681668875fcd7869094f9fbb06cd9e122e8397ea01e9cbb15ca87e100a3c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[507,63,933,90]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"sidered, with $\\\\mu_{\\\\mathrm{eff},\\\\infty}\\\\approx 0.458$ and $\\\\beta \\\\approx 0.014$ . Furthermore, from the definition of Bo, Eqs. 1 and 4 lead to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[673,102,933,139]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nD = \\\\beta \\\\sqrt {\\\\frac {1 2 \\\\gamma}{\\\\rho_ {\\\\mathrm {p}} g}}, \\\\tag {5}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,149,933,174]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"which relates the characteristic length-scale $D$ in Eq. 1 to the material parameters. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,174,933,302]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We note that our model is valid in the regime of regular heap morphology (regime II), i.e., when $d \\\\gtrsim d_{\\\\mathrm{c}}$ . In particular, Eq. 1 predicts $\\\\theta_{\\\\mathrm{r}} \\\\to 90^{\\\\circ}$ when $d \\\\to 0$ , but experiments revealed a nearly constant angle of repose for particle sizes of the order of a few micrometers, i.e., in regime I of irregular heap morphology (26). Our simulations show that $D \\\\approx 2d_{\\\\mathrm{c}}$ and that the heap morphology changes from regular (regime II) to irregular (regime I) when the Bond number exceeds approximately $10^{4}$ , thus providing a means to approximately estimate $d_{\\\\mathrm{c}}$ from the material properties. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,302,933,556]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We have also performed some simulations with heaps $150\\\\%$ larger than the ones considered in the present discussion, but we could not find a significant change in the values of $\\\\theta_{\\\\mathrm{r}}$ . We believe that, qualitatively, even larger heaps should display the same dependence of $\\\\theta_{\\\\mathrm{r}}$ on $d$ observed in the experiments quoted in Fig. 2 and in the DEM simulations in this article. However, it is uncertain to which extent our model parameters should be adapted to assess the angle of repose of much larger heaps quantitatively. In particular, the dynamics of much larger systems could be affected by particle-air interactions, which must be incorporated in a future extension of our model. Furthermore, since the packing dynamics are affected by the preparation history of the packing (see the discussion in ref. 15), the pouring height and the size of the insertion region chosen for reproducing experimental conditions could exert an important control on the value of $\\\\theta_{\\\\mathrm{r}}$ . We have indeed noticed a trend of increasing avalanche sizes by increasing the width of the particle insertion region in our simulations of larger heaps. Therefore, the quantitative behavior of $\\\\theta_{\\\\mathrm{r}}$ for much larger heaps will constitute topic of future research. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,556,935,596]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An argument for the approximate scaling with the square root of the Bond number in Eq. 4. Our model suggests that the effective friction coefficient $\\\\mu_{\\\\mathrm{eff}}$ can be written as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[649,606,933,621]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mu_ {\\\\text {e f f}} \\\\approx \\\\mu_ {\\\\text {e f f}, \\\\infty} \\\\cdot [ 1 + f ], \\\\tag {6}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,632,933,685]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\mu_{\\\\mathrm{eff},\\\\infty}$ is the value of $\\\\mu_{\\\\mathrm{eff}}$ disregarding the contribution from attractive particle interaction forces, encoded in the value of $f$ . Furthermore, an approximate scaling of $f$ with $\\\\sqrt{\\\\mathrm{Bo}}$ is obtained from our simulations (Eq. 4). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,685,933,851]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To shed light on this scaling, we note that, when the local slope exceeds the angle of repose, the heap surface relaxes through avalanches, thus leading to the emergence of a surface avalanche layer—of thickness a few times $d$ and constituted of $N$ particles—flowing downhill atop the immobile granular bulk in the heap's interior. At the angle of repose, the downhill gravitational force on these $N$ particles, i.e., $W = Nmg$ , with m denoting the particle mass, is balanced by frictional contact forces and cohesive interactions with particles in the bulk. However, not all $N$ particles participate in these interactions. Instead, the total cohesive force acts on a subset $N_{\\\\mathrm{interface}}$ of particles that are at the interface with the bulk. We propose that $f$ scales with the quotient of this total cohesive force and $W$ ; i.e., \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[586,860,933,891]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nf \\\\propto \\\\frac {N _ {\\\\text {i n t e r f a c e}} \\\\cdot F _ {\\\\mathrm {v d W}}}{N m g} \\\\propto \\\\frac {N _ {\\\\text {i n t e r f a c e}}}{N} \\\\cdot \\\\frac {1}{d ^ {2} g}, \\\\tag {7}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,902,933,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where we used $m \\\\propto d^3$ and $F_{\\\\mathrm{vdW}} \\\\propto d$ , with $F_{\\\\mathrm{vdW}}$ standing for the attractive van der Waals force (Eq. 13) between a particle in \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[6,472,25,934]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[68,948,102,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[121,948,153,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PNAS \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[121,959,333,969]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1073/pnas.2107965118 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[837,948,933,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Elekes and Parteli \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[420,959,933,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[859,970,933,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"environments \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[61,63,482,117]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the avalanche layer and another particle in the bulk. Therefore, a scaling of $f$ with $\\\\sqrt{\\\\mathrm{Bo}}$ , i.e., with $(d\\\\sqrt{g})^{-1}$ , is obtained if $\\\\eta \\\\equiv N_{\\\\mathrm{interface}} / N \\\\propto d\\\\sqrt{g}$ , which must be verified through numerical simulations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[61,117,483,269]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, here we assume that $\\\\eta$ is, to first order, proportional to the packing density $(\\\\phi)$ of the granular material. We think that this assumption is reasonable, because the smaller $\\\\phi$ is, the more porous the granular medium and the smaller, thus, $\\\\eta$ is. By contrast, the denser the granular material is, the larger the number of particle-particle contacts, and the larger, thus, $\\\\eta$ is. To verify whether $\\\\phi$ (and thus $\\\\eta$ ) follows, to a certain limit, an approximate scaling with $d\\\\sqrt{g}$ , we have performed numerical experiments adapting the protocol of ref. 15 to investigate the effect of $d$ and $g$ on $\\\\phi$ . Fig. 5 displays the results of these experiments, which are described at the end of Materials and Methods. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[61,270,483,481]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As can be seen in Fig. 5, the plot of $\\\\phi$ as a function of $d\\\\sqrt{\\\\tilde{g}}$ leads to an excellent data collapse of our simulation results and reveals an asymptotic growth of the packing fraction with $d\\\\sqrt{\\\\tilde{g}}$ . Specifically, in the limit of large particle sizes ( $d \\\\gtrsim 1 \\\\mathrm{~mm}$ ), the granular material displays a largely noncohesive behavior, with $\\\\phi$ resulting nearly independent of $d\\\\sqrt{\\\\tilde{g}}$ . The dashed line in the main plot in Fig. 5 denotes the best fit using the asymptotic growth function $\\\\phi = \\\\phi_{\\\\infty} \\\\cdot \\\\left\\\\{1 - C \\\\cdot \\\\exp \\\\left[-D_{\\\\phi}^{-1} \\\\cdot d\\\\sqrt{\\\\tilde{g}}\\\\right]\\\\right\\\\}$ , which gives $\\\\phi_{\\\\infty} \\\\approx 0.57$ (the associated random loose packing fraction) (27), $C \\\\approx 0.56$ , and $D_{\\\\phi} \\\\approx 103 \\\\mu \\\\mathrm{m}$ , with correlation coefficient $R^2 \\\\approx 0.994$ . We remark that a theoretical model is needed to elucidate this scaling, as well as the behavior of $\\\\phi$ as $d\\\\sqrt{\\\\tilde{g}} \\\\to 0$ . However, such a theoretical model would go beyond the scope of the present discussion, which aims rather at testing for an approximate scaling of $\\\\phi$ with $d\\\\sqrt{\\\\tilde{g}}$ to a certain limit. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[61,482,482,575]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Indeed, a linear fit using $\\\\phi = A + B\\\\cdot d\\\\sqrt{\\\\tilde{g}}$ describes reasonably well the trend of the simulation results associated with the lower range of $d\\\\sqrt{\\\\tilde{g}}$ considered in the present article; i.e., $30\\\\leq \\\\left[d\\\\sqrt{\\\\tilde{g}}\\\\right] / \\\\mu \\\\mathrm{m}\\\\leq 210$ with $A\\\\approx 0.32$ $B\\\\approx 1.14\\\\mathrm{mm}^{-1}$ , and correlation coefficient $R^2\\\\approx 0.947$ (Fig. 5, Inset). The origin of this approximate linear trend is the effect of attractive particle interaction forces—which are relevant in the aforementioned range \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[59,600,485,835]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 5. Packing density $\\\\\\\\phi$ as a function of $d\\\\\\\\sqrt{\\\\\\\\tilde{g}}$ , with $\\\\\\\\tilde{g} \\\\\\\\equiv g / g_{\\\\\\\\mathrm{Earth}}$ . The dashed line in the main plot denotes the best fit to the simulation results (symbols) using the equation $\\\\\\\\phi = \\\\\\\\phi_{\\\\\\\\infty} \\\\\\\\cdot \\\\\\\\left\\\\\\\\{1 - C \\\\\\\\cdot \\\\\\\\exp \\\\\\\\left[-D_{\\\\\\\\phi}^{-1} \\\\\\\\cdot d\\\\\\\\sqrt{\\\\\\\\tilde{g}}\\\\\\\\right]\\\\\\\\right\\\\\\\\}$ , which yields $\\\\\\\\phi_{\\\\\\\\infty} \\\\\\\\approx 0.57$ , $C \\\\\\\\approx 0.56$ , and $D_{\\\\\\\\phi} \\\\\\\\approx 103~\\\\\\\\mu \\\\\\\\mathrm{m}$ , with $R^2 \\\\\\\\approx 0.994$ . Furthermore, the solid line in Inset denotes the best linear fit to the simulation results within the range $30 \\\\\\\\leq d / \\\\\\\\mu \\\\\\\\mathrm{m} \\\\\\\\leq 210$ , using $\\\\\\\\phi = A + B \\\\\\\\cdot d\\\\\\\\sqrt{\\\\\\\\tilde{g}}$ , which gives $A \\\\\\\\approx 0.32$ and $B \\\\\\\\approx 1.14~\\\\\\\\mathrm{mm}^{-1}$ , with $R^2 \\\\\\\\approx 0.947$ . \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0813/9228745e6188d0cac10ab0f5fb95a1cf459211969100e4c697116ad5493d4a0f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[505,63,924,159]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"of small $d\\\\sqrt{g}$ , but become negligibly small compared to particle weight when $d\\\\sqrt{g}$ becomes sufficiently large. We thus find that the approximate linear scaling of $\\\\phi$ (and, thus, of $\\\\eta \\\\equiv N_{\\\\mathrm{interface}} / N$ ) with $d\\\\sqrt{g}$ , within the range of small $d\\\\sqrt{g}$ , provides an argument for the approximate scaling of $f$ with $\\\\sqrt{\\\\mathrm{Bo}}$ , owing to Eq. 7. More precisely, $f \\\\propto \\\\eta / [d^2 g] \\\\propto \\\\phi / [d^2 g] \\\\propto 1 / [d\\\\sqrt{g}]$ (i.e., $f \\\\propto \\\\sqrt{\\\\mathrm{Bo}}$ ). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,174,924,314]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Significance of Our Model in the Light of Experimental Observations. Reduced-gravity experiments of granular heap formation (28) in the Bremen drop tower, using basalt beads of diameter $500\\\\mu \\\\mathrm{m}$ , revealed a slight trend of increasing angle of repose with decreasing gravity for $0.03\\\\leq \\\\tilde{g}\\\\leq 1$ . Although the experiments were performed using a Hele-Shaw cell to obtain quasi-2D heaps (28), qualitatively, the behavior of $\\\\theta_{\\\\mathrm{r}}$ with gravity for these heaps is consistent with the prediction from our model that granular materials behave more cohesively and produce larger angles of repose under lower gravity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,314,924,544]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Furthermore, parabolic flight experiments with slowly rotating drums, operating in the discrete avalanche regime at $g$ levels ranging from 0.1 to 1, revealed a slight trend of increasing angle of repose $\\\\theta_{\\\\mathrm{start}}$ the slope above which the granular surface becomes unstable and starts to avalanche (29)with decreasing gravity (30, 31). The increase of $\\\\theta_{\\\\mathrm{start}}$ with decreasing $g$ observed in ref. 30 suggests enhanced cohesive behavior of granular materials under reduced gravity (30). Microgravity experiments with rotating drums operating at $g$ levels varying from 0.01 to 1.9 and at high rotational speeds, in the so-called continuous avalanching regime—in which the granular surface undergoes avalanche flow permanently—also revealed increasing cohesive behavior with decreasing $g$ (32, 33). In these experiments, a scaling of the slope angle of the granular surface with $\\\\sqrt{1 / g}$ was found (32, 33). To compare, experiments in the centrifuge at $g$ levels from 1 to 25 revealed insignificant correlation between this angle and gravity (34), as also predicted from our model. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,545,924,761]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We note that particle interaction forces can be affected by still poorly understood geochemical processes (35), while granular flows under low atmospheric pressure conditions can be further influenced by the presence of interstitial gas. Moreover, for values of Bond number smaller than unity, irregular particle geometries, inherent to natural granular systems, can cause statistical fluctuations comparable to the difference between the angles of repose predicted for spherical particles under $g$ levels of the same order. For instance, parabolic flight experiments using Toyoura sand $(d\\\\approx 250\\\\mu \\\\mathrm{m})$ revealed no significant dependence of the angle of repose on gravity for the range of investigated $g$ levels (1/6 to 2) (36). We conclude, based on our results, that the angle of repose of natural sand under Martian gravity should not differ much from its terrestrial counterpart $(30^{\\\\circ}$ to $35^{\\\\circ})$ , which is consistent with observations from the slope of Martian dunes at their avalanche side (37). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,761,924,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Characterization of average particle size of strongly polydisperse systems can be made using different parameters, such as the Sauter mean particle size $d_{\\\\mathrm{S}}$ i.e., the diameter of the particle that has the same volume to surface area ratio as the entire ensemble. Two comprehensive compilations of experimental datasets on $\\\\theta_{\\\\mathrm{r}}$ as a function of $d_{\\\\mathrm{S}}$ presented in refs. 26 and 38, reveal the same characteristics as in Fig. 2, i.e., a noticeable, power-law-like decrease with $d_{\\\\mathrm{S}}$ within an intermediate range of particle size, followed by slower decay in the limit of larger $d_{\\\\mathrm{S}}$ with $\\\\theta_{\\\\mathrm{r}}$ asymptotically approaching a value $\\\\theta_{\\\\mathrm{r,\\\\infty}}$ between $20^{\\\\circ}$ and $30^{\\\\circ}$ that is roughly independent of particle size. We thus propose that Eq. 1 should be valid without regard of the parameter employed to characterize particle size, since the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[6,472,25,934]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[61,950,155,959]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Elekes and Parteli \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[61,960,572,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[61,970,135,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"environments \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[842,948,871,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PNAS \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[892,948,924,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[714,960,924,969]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1073/pnas.2107965118 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[955,356,982,427]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"SENEI 1A \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[66,63,490,90]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"corresponding value of $D$ can be estimated from the best fit to $\\\\theta_{\\\\mathrm{r}}(d)$ using Eq. 1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,90,492,255]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We further remark that Eq. 1 should break down when $d$ becomes much smaller than a certain value $(d_{\\\\mathrm{c}})$ , which, for the system considered in our DEM simulations, is of the order of $50\\\\mu \\\\mathrm{m}$ . Indeed, Eq. 1 predicts that $\\\\theta_{\\\\mathrm{r}}\\\\rightarrow 90^{\\\\circ}$ as $d\\\\to 0$ . However, measurements of $\\\\theta_{\\\\mathrm{r}}$ of strongly polydisperse dust systems (using the Sauter mean diameter $d_{\\\\mathrm{S}}$ to characterize particle size) revealed a breakdown in the trend of increasing $\\\\theta_{\\\\mathrm{r}}$ with decreasing particle size, when particles become sufficiently small (26). As explained by Lanzerstorfer (26), the reason for this behavior is the formation of small agglomerates of dust-sized particles, which roll down the heap slope, thus limiting the angle of repose. An upper limit for $\\\\theta_{\\\\mathrm{r}}$ of about $55^{\\\\circ}$ was reported in the experiments in ref. 26. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,255,492,496]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Although further work will be required to characterize the dynamics of particle agglomerates in DEM simulations and to investigate the factors controlling the value of $d_{\\\\mathrm{c}}$ we note that the highest values of $\\\\theta_{\\\\mathrm{r}}$ in most experimental datasets quoted in Fig. 2 are consistent with the upper bound reported by Lanzerstorfer (26). The only exception is the dataset of Lumay et al. (18) (open squares in Fig. 2), which displays $\\\\theta_{\\\\mathrm{r}}$ exceeding $70^{\\\\circ}$ . A possible explanation for the higher $\\\\theta_{\\\\mathrm{r}}$ values in this dataset is that the silicon carbide abrasives adopted in ref. 18 consist of a broad distribution of complex particle geometric shapes, including elongated and sharp-edged particles. DEM simulations (39) have shown that cohesive rods form packings of lower solid fraction than that of cohesive beads; i.e., complex particle shapes can enhance the cohesive behavior of granular materials. By virtue of these observations and in view of our Eqs. 4 and 7, we thus expect that elongated particles, compared to beads, produce steeper heaps, while sharp edges could further enhance friction and heap stability. The present work could be thus continued by elucidating this behavior in DEM simulations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,496,490,550]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, future work should now focus on deepening the understanding of our findings from a theoretical analysis of granular heap stability, which poses a long-standing and challenging research topic in the field of granular matter physics (40). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,556,230,569]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Materials and Methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,573,464,584]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This section describes the DEM employed in our numerical simulations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,596,492,620]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Equations of Motion. The equations for the translational and rotational motion of the $i$ th particle in the system read \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,625,492,657]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nm \\\\ddot {r} _ {i} = \\\\sum_ {\\\\substack {1 \\\\leq j \\\\leq n \\\\\\\\ j \\\\neq i}} \\\\mathbf {F} _ {i j} + m \\\\mathbf {g} \\\\tag{8}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[223,661,492,693]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nI \\\\dot {\\\\boldsymbol {\\\\omega}} _ {i} = \\\\sum_ {\\\\substack {1 \\\\leq j \\\\leq n \\\\\\\\ j \\\\neq i}} \\\\mathbf {M} _ {i j}, \\\\tag{[9]}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[66,701,492,793]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\mathbf{r}_i$ and $\\\\omega_{i}$ denote the position and angular velocity of particle $i$ , respectively; $\\\\mathbf{g}$ is gravity; while $\\\\mathbf{F}_{ij}$ and $\\\\mathbf{M}_{ij}$ denote the interaction force and torque, respectively, exerted by particle $j$ on particle $i$ . Furthermore, $n$ is the total number of particles in the system, each particle having diameter $d$ , density $\\\\rho_{\\\\mathrm{p}}$ , mass $m = \\\\pi \\\\rho_{\\\\mathrm{p}} d^{3} / 6$ , and moment of inertia $I = m d^{2} / 10$ . In Eq. 8, $\\\\mathbf{F}_{ij}$ denotes the sum of the contact force $\\\\mathbf{F}_{ij}^{\\\\mathrm{c}}$ and the nonbonded attractive interaction force $\\\\mathbf{F}_{ij}^{\\\\mathrm{a}}$ exerted by particle $j$ on particle $i$ . These forces are modeled as discussed next. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,805,492,853]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Particle-Particle Interaction Forces. For the normal component of the contact force, $\\\\mathsf{F}_{ij,n}^{\\\\mathrm{c}}$ , viscoelastic interaction is assumed (11), while a modified Cundall-Strack model (10) is applied to compute the tangential force, $\\\\mathsf{F}_{ij,t}^{\\\\mathrm{c}}$ . The equations for $\\\\mathsf{F}_{ij,n}^{\\\\mathrm{c}}$ and $\\\\mathsf{F}_{ij,t}^{\\\\mathrm{c}}$ read \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,860,492,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathbf {F} _ {i j, n} ^ {c} = \\\\min \\\\left(0, - k _ {n} \\\\delta_ {i j, n} ^ {3 / 2} - \\\\frac {3}{2} A _ {n} k _ {n} \\\\sqrt {\\\\delta_ {i j , n}} \\\\dot {\\\\delta} _ {i j, n}\\\\right) \\\\mathbf {e} _ {i j, n} \\\\tag {10}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[129,892,492,933]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathbf {F} _ {i j, t} ^ {c} = - \\\\min \\\\left(\\\\mu_ {s} \\\\left| \\\\mathbf {F} _ {i j, n} ^ {c} \\\\right|, \\\\int_ {\\\\text {p a t h}} k _ {t} \\\\sqrt {\\\\delta_ {i j , n}} d s + A _ {t} \\\\sqrt {\\\\delta_ {i j , n}} v _ {i j, t}\\\\right) \\\\mathbf {e} _ {i j, t}, \\\\tag {11}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[509,81,933,183]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0725/ac0d56c6597dedf1742fa360fdf261195f6be3ac2b30ad6cd6e4ec53f43f79c9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Parameter</td><td>Symbol</td><td>Value</td></tr><tr><td>Young's modulus</td><td>Y</td><td>63 GPa</td></tr><tr><td>Poisson's ratio</td><td>ν</td><td>0.24</td></tr><tr><td>Particle material density</td><td>ρp</td><td>2,500 kg/m3</td></tr><tr><td>Surface energy density</td><td>γ</td><td>0.05 J/m2</td></tr><tr><td>Sliding friction coefficient</td><td>μs</td><td>0.5</td></tr><tr><td>Rolling friction coefficient</td><td>μr</td><td>0.05</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. Numerical values of parameters used in the simulations \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[507,205,933,296]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\delta_{ij,n} = d - |r_j - r_i|$ ; $\\\\mathbf{e}_{ij,n} = \\\\frac{\\\\mathbf{r}_j - \\\\mathbf{r}_i}{|\\\\mathbf{r}_j - \\\\mathbf{r}_i|}$ ; $r_i$ and $r_j$ are the positions of particles $i$ and $j$ , respectively; $\\\\mathbf{v}_{ij,t} = |\\\\mathbf{v}_{ij,t}|$ , where $\\\\mathbf{v}_{ij,t} = \\\\mathbf{v}_{ij} - (\\\\mathbf{v}_{ij} \\\\cdot \\\\mathbf{e}_{ij,n}) \\\\cdot \\\\mathbf{e}_{ij,n}$ denotes the relative tangential velocity at the point of contact, with $\\\\mathbf{v}_{ij} = \\\\dot{\\\\mathbf{r}}_j - \\\\dot{\\\\mathbf{r}}_i$ ; and $\\\\mathbf{e}_{ij,t} = \\\\mathbf{v}_{ij,t} / v_{ij,t}$ is the tangential unit vector; while the contact forces in Eqs. 10 and 11 are set as zero if $\\\\delta_{ij,n} < 0$ . Furthermore, $k_n$ and $k_t$ are elastic parameters, which are computed from the particle Young's modulus, $Y$ , and the Poisson's ratio, $\\\\nu$ , through \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[606,307,933,333]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nk _ {\\\\mathrm {n}} = \\\\frac {2 Y}{3 \\\\left(1 - \\\\nu^ {2}\\\\right)} \\\\sqrt {R _ {\\\\mathrm {e f f}}}, k _ {\\\\mathrm {t}} = \\\\frac {4 G}{2 - \\\\nu} \\\\sqrt {R _ {\\\\mathrm {e f f}}} \\\\tag {12}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,344,933,402]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"with $G = Y / (2 + 2\\\\nu)$ denoting the shear modulus and $R_{\\\\mathrm{eff}} = d / 4$ , while $A_{\\\\mathrm{n}}$ and $A_{\\\\mathrm{t}}$ are dissipative parameters, $\\\\mu_{s}$ is the (Coulomb) sliding friction coefficient, and the integral in Eq. 11 is performed over the relative displacement of the particles at the point of contact and over the entire contact duration (15, 41). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,403,933,527]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The dissipative parameter $A_{\\\\mathrm{n}}$ further depends on material viscosities that are not directly available (11). Therefore, to determine $A_{\\\\mathrm{n}}$ , we use a relation between this dissipative parameter and the coefficient of restitution for the collision of two isolated particles (42, 43) and employ the Padé approximation from ref. 44. Furthermore, following ref. 45, we choose the tangential dissipative parameter, $A_{\\\\mathrm{t}}$ , such that the prefactors of $\\\\dot{\\\\delta}_{ij,\\\\mathrm{n}}$ and $v_{ij,\\\\mathrm{t}}$ in Eqs. 10 and 11, respectively, are of the same order of magnitude, thus yielding $A_{\\\\mathrm{t}} = 3A_{\\\\mathrm{n}}k_{\\\\mathrm{n}} / 2$ . Indeed, ref. 46 showed that this assumption leads to excellent agreement between simulation results and experimental values of particle velocity profiles in a gravity-driven shearing experiment. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,528,933,551]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Furthermore, the nonbonded attractive van der Waals interaction force between two particles in the system, labeled $i$ and $j$ , is given by (15, 47, 48) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[570,565,933,630]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathbf {F} _ {i j, n} ^ {a} = \\\\left\\\\{ \\\\begin{array}{l l} \\\\frac {A _ {H} R _ {\\\\text {e f f}}}{6 D _ {\\\\min } ^ {2}} \\\\mathbf {e} _ {i j, n} & \\\\text {i f} \\\\delta_ {i j, n} > 0, \\\\\\\\ \\\\frac {A _ {H} R _ {\\\\text {e f f}}}{6 \\\\left(\\\\delta_ {i j , n} - D _ {\\\\min }\\\\right) ^ {2}} \\\\mathbf {e} _ {i j, n} & \\\\text {i f} - D _ {\\\\max } \\\\leq \\\\delta_ {i j, n} \\\\leq 0 \\\\\\\\ 0, & \\\\text {i f} \\\\delta_ {i j, n} < - D _ {\\\\max }, \\\\end{array} \\\\right. \\\\tag {13}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,644,933,669]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $A_{\\\\mathsf{H}}$ is the Hamaker constant, which is computed from the surface energy density, $\\\\gamma$ , using the expression (49) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[673,681,933,696]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nA _ {H} = 2 4 \\\\pi D _ {\\\\min } ^ {2} \\\\gamma . \\\\tag {14}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,708,933,777]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In Eq. 13, $D_{\\\\mathrm{max}}$ is the maximal (cutoff) distance of the van der Waals interaction, which is set as $1\\\\mu \\\\mathrm{m}$ (15), while the constant $D_{\\\\mathrm{min}}$ is introduced to avoid the singularity of the Hamaker equation at $\\\\delta_{ij,n} = 0$ and accounts for the fact that particles are not perfectly smooth. We take the value $D_{\\\\mathrm{min}} = 1.65\\\\mathring{\\\\mathrm{A}}$ , which corresponds to the minimal distance between particles at contact (49, 50). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,789,933,837]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Torque and Rolling Friction. The total torque $\\\\mathbf{M}_{ij}$ is given by $\\\\mathbf{M}_{ij} = \\\\mathbf{M}_{ij}^{\\\\mathrm{t}} + \\\\mathbf{M}_{ij}^{\\\\mathrm{r}}$ , where $\\\\mathbf{M}_{ij}^{\\\\mathrm{t}} = \\\\Theta (\\\\delta_{ij,n})[d / 2 - \\\\delta_{ij,n}]\\\\mathbf{e}_{ij,n}\\\\times \\\\mathbf{F}_{ij,t}^{c}$ , and $\\\\mathbf{M}_{ij}^{\\\\mathrm{r}}$ is the torque associated with the rolling resistance at the contact point between particles $i$ and $j$ and is computed through the model (14, 17) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[536,850,933,881]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathbf {M} _ {i j} ^ {r} (t + \\\\Delta t) = \\\\min \\\\left(\\\\mathbf {M} _ {i j} ^ {r m}, | \\\\mathbf {M} _ {i j} ^ {r} (t) - k _ {r} \\\\omega_ {i j} \\\\Delta t |\\\\right) \\\\frac {\\\\mathbf {M} _ {i j} ^ {r} (t) - k _ {r} \\\\omega_ {i j} \\\\Delta t}{| \\\\mathbf {M} _ {i j} ^ {r} (t) - k _ {r} \\\\omega_ {i j} \\\\Delta t |}, \\\\tag {15}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[507,893,933,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $M_{ij}^{\\\\mathrm{rm}} = \\\\mu_{\\\\mathrm{r}}R_{\\\\mathrm{eff}}|\\\\mathbf{F}_{ij,n}^{\\\\mathrm{c}}|$ , with $\\\\mu_{\\\\mathrm{r}}$ standing for the coefficient of rolling resistance. Furthermore, $\\\\omega_{ij} = \\\\omega_{i} - \\\\omega_{j}$ , $\\\\Delta t$ denotes the time step, and $k_{\\\\mathrm{r}} = k_{\\\\mathrm{t}}\\\\sqrt{\\\\delta_{ij,n}} R_{\\\\mathrm{eff}}^{2}$ (17, 51, 52). The magnitude of the spring torque $\\\\mathbf{M}_{ij}^{\\\\mathrm{r}}$ is, thus, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[6,472,25,934]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[68,948,102,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[121,948,153,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PNAS \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[121,959,333,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1073/pnas.2107965118 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[837,948,933,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Elekes and Parteli \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[420,959,933,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[859,970,933,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"environments \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[59,65,485,90]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"upper bounded by the full mobilization torque $\\\\mu_{\\\\mathrm{r}}R_{\\\\mathrm{eff}}|\\\\mathbf{F}_{ij,n}^{\\\\mathrm{c}}|$ , which means that rolling resistance behaves perfectly plastic beyond this upper bound. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[59,100,485,229]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Numerical Integration. The integration was performed using the open source Discrete Element Method particle simulation software LIGGGHTS (which stands for LAMMPS Improved for General Granular and Granular Heat Transfer Simulations) (52), along with the extensions introduced in ref. 15, to account for the computation of the dissipative term in the contact model (Eqs. 10 and 11), following ref. 44, and the attractive particle interaction force model (15, 47, 48) defined in Eq. 13. The integration time step $\\\\Delta t$ has been about $10\\\\%$ of the collision time $T_{\\\\mathrm{col}}$ between two particles, defined from Hertz's elastic theory for the undamped, noncohesive situation; i.e., $T_{\\\\mathrm{col}} \\\\approx 3.21(m_{\\\\mathrm{eff}} / k_{\\\\mathrm{n}})^{2 / 5} \\\\cdot v_{\\\\mathrm{imp}}^{-1 / 5}$ (12), where $m_{\\\\mathrm{eff}} = m / 2$ , and $v_{\\\\mathrm{imp}}$ denotes the relative normal velocity of the particles at impact. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[59,241,485,333]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Model Parameters. The values of Young's modulus, Poisson's ratio, particle density, and surface energy density, listed in Table 1, are consistent with glass beads (15, 49), and we take the coefficients of sliding and rolling friction following calibration results from previous DEM simulations (6, 14-17, 46, 53, 54). The collisions of the particles with the frictional bottom wall are modeled using the same material parameters, while the wall is regarded as cohesionless and one of the collision partners has infinite mass and radius (15). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[59,333,485,461]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Furthermore, the normal damping coefficient $A_{n}$ is computed based on the coefficient of restitution $\\\\varepsilon_{\\\\mathrm{ref}}$ associated with a reference collisional velocity $\\\\nu_{\\\\mathrm{imp}}$ , assuming only contact forces (no cohesion) (44). Based on previous calibration of the coefficient of restitution for use in DEM studies of the angle of repose (53, 54), here we adopt $\\\\varepsilon_{\\\\mathrm{ref}}$ in the range between 0.2 and 0.4, for $\\\\nu_{\\\\mathrm{imp}} = 1.0~\\\\mathrm{m / s}$ . All results presented in this article refer to $\\\\varepsilon_{\\\\mathrm{ref}} = 0.2$ , but we have found that using $\\\\varepsilon_{\\\\mathrm{ref}} = 0.4$ still leads to a reasonable quantitative agreement between our numerical predictions for $\\\\theta_{\\\\mathrm{r}}$ and the experimental data in Fig. 2. However, we reinforce that the main contribution of our article consists of a mathematical expression that is robust with respect to details of interparticle \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,65,926,112]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"interactions, encoded in the parameters $\\\\mu_{\\\\mathrm{eff},\\\\infty}$ and $\\\\beta$ . The role of various ingredients that have been neglected in our simulations, such as torsion (13) and long-range electrostatic interactions, should be elucidated in future work. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,123,928,376]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Numerical Experiments to Estimate the Packing Fraction, $\\\\phi$ , as a Function of Particle Size and Gravity. Fig. 5 displays the results from numerical experiments to estimate the packing fraction $\\\\phi$ as a function of $d$ and $g$ . Each of these experiments consists of releasing from rest a monodisperse packing of $20\\\\%$ initial volume fraction composed of 11,039 (initially noncontacting) particles randomly distributed over the simulation domain—a vertical rectangular box of horizontal dimensions $L_{x} \\\\times L_{y}$ , with $L_{x} = L_{y} = 17d$ and height $100d$ . Boundary conditions are the same as in the experiments of the angle of repose, except that periodic boundary conditions are applied in the horizontal directions (15). Once the particles have settled due to the action of gravity, we compute the packing density of the granular column using $\\\\phi = n_{\\\\phi} \\\\cdot (\\\\pi/6)d^{3}/[L_{x} \\\\cdot L_{y} \\\\cdot (H_{u} - H_{l})]$ , where $n_{\\\\phi}$ is the number of particles with center-of-mass position between $H_{l} = 0.3z_{\\\\max}$ and $H_{u} = 0.7z_{\\\\max}$ with $z_{\\\\max}$ denoting the center-of-mass position of the highest particle in the granular column (15). We find that $\\\\phi$ differs negligibly over different realizations of the same experiment (each realization with different initial random positions of the particles). Therefore, each value of $\\\\phi$ presented in Fig. 5 has been obtained based on one realization for the corresponding value of $d$ and $g$ , but by averaging over the four vertical subcolumns obtained by halving $L_{x}$ and $L_{y}$ (15), the associated SD corresponding to the error bars in Fig. 5 (i.e., the same protocol as in ref. 15 but including the effect of gravity in the investigation). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,386,852,399]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Data Availability. All study data are included in the main text. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[500,406,926,459]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ACKNOWLEDGMENTS. We thank Sandesh Kamath for assistance with the numerical interface between the DEM implementation of ref. 15 and the latest version of LIGGGHTS, Yaping Shao for discussions, and the German Research Foundation for funding through the Heisenberg Programme and Grant RI 2497/6-1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[59,477,485,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1. H. Chen, Y. L. Liu, X. Q. Zhao, Y. G. Xiao, Y. Liu, Numerical investigation on angle of repose and force network from granular pile in variable gravitational environments. Powder Technol. 283, 607-617 (2015). \\\",\\\"2. A. C.-Y. Wong, Characterization of the flowability of glass beads by bulk densities ratio. Chem. Eng. Sci. 55, 3855-3859 (2000). \\\",\\\"3. N. Pilpel, The flow properties of magnesia. J. Pharm. Pharmacol. 16, 705-716 (1964). \\\",\\\"4. J. T. Carstensen, P.-C. Chan, Relation between particle size and repose angles of powders. Powder Technol. 15, 129-131 (1976). \\\",\\\"5. Y. C. Zhou, B. H. Xu, A. B. Yu, P. Zulli, An experimental and numerical study of the angle of repose of coarse spheres. Powder Technol. 125, 45-54 (2002). \\\",\\\"6. V. Hassanzadeh, C. M. Wensrich, R. Moreno-Atanasio, Elucidation of the role of cohesion in the macroscopic behaviour of coarse particulate systems using DEM. Powder Technol. 361, 374-388 (2020). \\\",\\\"7. S. Ji, H. H. Shen, Contrasting terrestrial and lunar gravity: Angle of repose and incline flows. Earth Space 2006, 1-8 (2006). \\\",\\\"8. M. W. Telfer et al., Dunes on Pluto. Science 360, 992-997 (2018). \\\",\\\"9. C. B. Beddingfield et al., Landslides on Charon. Icarus 335, 113383 (2020). \\\",\\\"10. P. A. Cundall, O. D. L. Strack, A discrete numerical model for granular assemblies. Geotechnique 29, 47-65 (1979). \\\",\\\"11. N. V. Brilliantov, F. Spahn, J.-M. Hertzsch, T. Poschel, Model for collisions in granular gases. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53, 5382-5392 (1996). \\\",\\\"12. J. Schäfer, S. Dippel, D. E. Wolf, Force schemes in simulations of granular materials. J. Phys. I France 6, 5-20 (1996). \\\",\\\"13. S. Luding, Cohesive, frictional powders: Contact models for tension. Granul. Matter 10, 235 (2008). \\\",\\\"14. J. Ai, J. F. Chen, J. M. Rotter, J. Y. Ooi, Assessment of rolling resistance models in discrete element simulations. Powder Technol. 206, 269-282 (2011). \\\",\\\"15. E. J. R. Parteli et al., Attractive particle interaction forces and packing density of fine glass powders. Sci. Rep. 4, 6227 (2014). \\\",\\\"16. J. Schmidt et al., Packings of micron-sized spherical particles: Insights from bulk density determination, X-ray tomography and discrete element simulations. Adv. Powder Technol. 31, 2293-2304 (2020). \\\",\\\"17. C. M. Wensrich, A. Katterfeld, Rolling friction as a technique for modelling particle shape in DEM. Powder Technol. 217, 409-417 (2012). \\\",\\\"18. G. Lumay et al., Measuring the flowing properties of powders and grains. Powder Technol. 224, 19-27 (2012). \\\",\\\"19. Y. Li, Y. Xu, C. Thornton, A comparison of discrete element simulations and experiments for 'sandpiles' composed of spherical particles. Powder Technol. 160, 219-228 (2005). \\\",\\\"20. Y. Matsukara, H. Obanawa, Effect of grain diameter and packing condition on the avalanching depth on a slope composed of dry granular materials. Tsukuba Geoenvironmental Sciences 1, 19-25 (2005). \\\"]\",\n \"page_idx\": \"6\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[499,477,924,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"21. E. M. Culligan, H. K. Christenson, Cohesion of granular matter in subzero humidity. J. Phys. Chem. C 118, 15929-15933 (2014). \\\",\\\"22. J. H. Choi, E. T. Kang, J. W. Lee, U. S. Kim, W. S. Cho, Materials and process development for manufacturing porcelain figure using a binder jetting 3D printer. J. Ceram. Process. Res. 19, 43-49 (2018). \\\",\\\"23. J. R. Metcalf, Angle of repose and internal friction. Int. J. Rock Mech. Min. Sci. 3, 155-161 (1966). \\\",\\\"24. A. Anand, J. S. Curtis, C. R. Wassgren, B. C. Hancock, W. R. Ketterhagen, Segregation of cohesive granular materials during discharge from a rectangular hopper. Granul. Matter 12, 193-200 (2010). \\\",\\\"25. A. Gans, O. Pouliquen, M. Nicolas, Cohesion-controlled granular material. Phys. Rev. E 101, 032904 (2020). \\\",\\\"26. C. Lanzerstorfer, Dusts from dry off-gas cleaning: Comparison of flowability determined by angle of repose and with shear cells. Granul. Matter 19, 58 (2017). \\\",\\\"27. C. Song, P. Wang, H. A. Makse, A phase diagram for jammed matter. Nature 453, 629-632 (2008). \\\",\\\"28. P. G. Hofmeister, J. Blum, D. Heisselmann, The flow of granular matter under reduced gravity conditions. AIP Conf. Proc. 1145, 71-74 (2009). \\\",\\\"29. P. G. Hofmeister, J. Blum, D. Heisselmann, Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 1-24 (2008). \\\",\\\"30. M. G. Kleinhans, H. Markies, S. J. de Vet, A. C. in 't Veld, F. N. Postema, Static and dynamic angles of repose in loose granular materials under reduced gravity. J. Geophys. Res. 116, E11004 (2011). \\\",\\\"31. C. M. Dury, G. H. Ristow, J. L. Moss, M. Nakagawa, Boundary effects on the angle of repose in rotating cylinders. Phys. Rev. E 57, 4491-4497 (1998). \\\",\\\"32. B. R. White, S. P. Klein, Dynamic shear of granular material under variable gravity conditions. Am. Inst. Aeronaut. J. 28, 1701-1702 (1990). \\\",\\\"33. O. R. Walton, C. Pamela de Moor, K. S. Gill, Effects of gravity on cohesive behavior of fine powders: Implications for processing Lunar regolith. Granul. Matter 9, 353-363 (2007). \\\",\\\"34. A. Brucks, T. Arndt, J. M. Ottino, R. M. Lueptow, Behavior of flowing granular materials under variable g. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75, 032301 (2007). \\\",\\\"35. V. Schatz, H. Tsoar, K. S. Edgett, E. J. R. Parteli, H. J. Herrmann, Evidence for indurated sand dunes in the Martian north polar region. J. Geophys. Res. 111, E04006 (2006). \\\",\\\"36. H. Nakashima et al., Determining the angle of repose of sand under low-gravity conditions using discrete element method. J. Terramechs. 48, 17-26 (2011). \\\",\\\"37. C. Atwood-Stone, A. S. McEwen, Avalanche slope angles in low-gravity environments from active Martian sand dunes. Geophys. Res. Lett. 40, 2929-2934 (2013). \\\",\\\"38. D. Geldart, E. C. Abdullah, A. Hassanpour, L. C. Nwoke, I. Wouters, Characterization of powder flowability using measurement of angle of repose. China Particuology 4, 104-107 (2006). \\\",\\\"39. X. L. Deng, R. N. Dave, Dynamic simulation of particle packing influenced by size, aspect ratio and surface energy. Granul. Matter 15, 401-415 (2013). \\\"]\",\n \"page_idx\": \"6\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[6,472,25,934]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[953,353,982,427]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"APPLIED PHYSICAL SCIENCES \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[61,948,155,959]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Elekes and Parteli \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[842,948,873,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PNAS \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[892,948,924,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[61,960,572,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[61,970,135,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"environments \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[714,960,924,970]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1073/pnas.2107965118 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[66,67,490,260]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"40. R. P. Behringer, B. Chakraborty, The physics of jamming for granular materials: A review. Rep. Prog. Phys. 82, 012601 (2019). \\\",\\\"41. L. E. Silbert et al., Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64, 051302 (2001). \\\",\\\"42. R. Ramirez, T. Pöschel, N. V. Brilliantov, T. Schwager, Coefficient of restitution of colliding viscoelastic spheres. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60, 4465-4472 (1999). \\\",\\\"43. T. Schwager, T. Pöschel, Coefficient of restitution for viscoelastic spheres: The effect of delayed recovery. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78, 051304 (2008). \\\",\\\"44. P. Müller, T. Pöschel, Collision of viscoelastic spheres: Compact expressions for the coefficient of normal restitution. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84, 021302 (2011). \\\",\\\"45. T. Schwager, V. Becker, T. Pöschel, Coefficient of tangential restitution for viscoelastic spheres. Eur. Phys. J. E Soft Matter 27, 107-114 (2008). \\\",\\\"46. C. H. Rycroft, A. V. Orpe, A. Kudrolli, Physical test of a particle simulation model in a sheared granular system. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80, 031305 (2009). \\\"]\",\n \"page_idx\": \"7\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[507,67,933,260]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"47. H. C. Hamaker, The London-van der Waals attraction between spherical particles. Physica 4, 1058-1072 (1937). \\\",\\\"48. M. L. Eggersdorfer, D. Kadau, H. J. Herrmann, S. E. Pratsinis, Fragmentation and restructuring of soft-agglomerates under shear. J. Colloid Interface Sci. 342, 261-268 (2010). \\\",\\\"49. M. Götzinger, W. Peukert, Dispersive forces of particle-surface interactions: Direct AFM measurements and modelling. Powder Technol. 130, 102-109 (2003). \\\",\\\"50. J. Israelachvili, *Intermolecular & Surface Forces* (Academic Press, London, UK, 1998). \\\",\\\"51. K. Iwashita, M. Oda, Rolling resistance at contacts in simulation of shear band development by DEM. J. Eng. Mech. 124, 285-292 (1998). \\\",\\\"52. C. Kloss, C. Goniva, A. Hager, S. Amberger, S. Pirker, Models, algorithms and validation for opensource DEM and CFD-DEM. Prog. Comput. Fluid Dyn. 12, 140-152 (2012). \\\",\\\"53. P. Frankowski, M. Morgeneyer, Calibration and validation of DEM rolling and sliding friction coefficients in angle of repose and shear measurements. AIP Conf. Proc. 1542, 851 (2013). \\\",\\\"54. R. Poisel, A. Preh, \\\\\\\"Modifications of PFC $^{3D}$ for rock mass fall modeling\\\\\\\" in Continuum and Distinct Element Numerical Modeling in Geo-Engineering, R. Hart, C. Detournay, P. Cundall, Eds. (Itasca Consulting Group, Inc., Minneapolis, MN, 2008), pp. 29-38. \\\"]\",\n \"page_idx\": \"7\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[6,472,25,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Downloaded from https://www.pnas.org by 218.70.106.126 on January 3, 2024 from IP address 218.70.106.126. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[68,948,102,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[123,950,153,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PNAS \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[123,960,333,969]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1073/pnas.2107965118 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[839,948,933,957]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Elekes and Parteli \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[422,960,933,969]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[861,971,933,979]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"environments \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1073/pnas.2107965118"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Engineering and Manufacturing Science"},"sha256":{"kind":"string","value":"0cea94f002c97475f820f66c7fb8aaefddbf21f77ddf96f1a0cc2717384763a9"},"title":{"kind":"string","value":"An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary environments"}}},{"rowIdx":270,"cells":{"abstract":{"kind":"string","value":"\n \nThis paper is a survey about the Thurston metric on the Teichmüller space. The central issue is the constructions of extremal Lipschitz maps between hyperbolic surfaces. We review several constructions, including the original work of Thurston. Coarse geometry and isometry rigidity of the Thurston metric, relation between the Thurston metric and the Thurston compactification are discussed. Some recent generalizations and developments of the Thurston metric are sketched.\n "},"author":{"kind":"string","value":"Weixu Su|Huiping Pan"},"content_list":{"kind":"list like","value":[{"bbox":"[220,183,774,219]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[372,241,620,257]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[259,323,736,443]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABSTRACT. This chapter is a survey about the Thurston metric on the Teichmüller space. The central issue is the constructions of extremal Lipschitz maps between hyperbolic surfaces. We review several constructions, including the original work of Thurston. Coarse geometry and isometry rigidity of the Thurston metric, relation between the Thurston metric and the Thurston compactification are discussed. Some recent generalizations and developments of the Thurston metric are sketched. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,455,702,472]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mathematical classification (2010) 32G15; 30F45; 30F60. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[447,541,549,556]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CONTENTS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[223,575,795,830]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1. Introduction 2 \",\"2. Background 3 \",\"3. Extremal Lipschitz maps and geodesic rays 8 \",\"4. Harmonic stretch lines 19 \",\"5. Thurston boundary 22 \",\"6. Isometry Rigidity 24 \",\"7. Coarse Geometry 26 \",\"8. Counting lattice points 32 \",\"9. Shearing coordinates 33 \",\"10. Generalization of the Thurston metric 36 \"]","page_idx":"0","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[223,840,792,856]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References 37 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[223,867,792,883]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Index 41 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[22,238,60,688]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"arXiv:2307.03874v1 [math.GT] 8 Jul 2023 ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[493,886,503,896]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[416,145,581,160]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. INTRODUCTION ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[200,180,794,303]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This survey aims to give a brief exposition of recent results on the Thurston metric. This asymmetric metric, defined by Thurston in his 1986 preprint [74], has a lot of beautiful geometric and analytic properties. Thurston's original investigation, just like his many other masterpieces, are based on first principles. Until now, that preprint [74] together with Chapter 8 and Chapter 9 of [73], are excellent references for learning hyperbolic geometry. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,311,795,383]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Aiming for a geometric understanding of the Teichmüller space from the point of view of hyperbolic surfaces and Lipschitz maps, in parallel with the point of view of Riemann surfaces and quasiconformal maps, Thurston [74] considered the following problem: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[259,398,736,434]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Given any two hyperbolic surfaces $X$ and $Y$ , what is the least possible value of the global Lipschitz constant ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[392,441,607,483]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nL (\\phi) := \\sup _ {p \\neq q} \\frac {d (\\phi (p)) , \\phi (q)}{d (p , q)}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[259,491,736,525]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"for a homeomorphism $\\phi : X \\to Y$ in a given homotopy class? ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,541,794,612]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Thurston gave a geometric construction of extremal Lipschitz homeomorphisms realizing the extremal Lipschitz constant $\\operatorname{Lip}(X, Y)$ in the homotopy class of the identity map, and proved that the extremal Lipschitz constant is the same as another geometric quantity: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[403,621,596,659]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nK (X, Y) := \\sup _ {\\alpha} \\frac {\\ell_ {\\alpha} (Y)}{\\ell_ {\\alpha} (X)}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,667,794,720]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\ell_{\\alpha}(\\cdot)$ is the length of the geodesic representative of $\\alpha$ on the corresponding surface and $\\alpha$ ranges over all nontrivial homotopy classes of simple closed curves. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,729,795,763]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For any two points $X$ and $Y$ in the Teichmüller space, the Thurston metric is defined as: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[382,777,616,796]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nd _ {T h} (X, Y) := \\log \\operatorname {L i p} (X, Y).\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,805,794,842]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Among others, Thurston proved that this metric is Finslerian, asymmetric, geodesic but not uniquely geodesic [74]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,849,794,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Through the efforts of many mathematicians, we now have a fairly clear picture of this metric: the horofunction boundary, the isometry ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,118,215,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,145,794,217]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"group, the coarse geometry, the analytic construction of extremal Lipschitz maps and geodesic rays, to name a few. Due to its geometric inspiration, the Thurston metric has been generalized to deformation spaces of other geometric structures and provides new perspectives there. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,223,795,383]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this survey about the Thurston metric, we restrict our attention to recent research. We will look more carefully at several constructions of the extremal Lipschitz maps. Relevant developments will be briefly sketched or summarized without proofs. Other surveys on the Thurston metrics include [54, 50, 68]. In particular, the article [54] contains foundational background material, both on the Teichmüller metric and the Thurston metric. As for prerequisites, the reader is expected to be familiar with hyperbolic geometry and Teichmüller theory. We recommend [23, 35]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,391,795,602]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Here is the outline of this paper. In §2, we review some of the standard facts on Teichmüller space, including the Thurston norm. In §3, we provide various constructions of extremal Lipschitz maps and geodesic rays of the Thurston metric. In §4, we deal with a special type of geodesics, called harmonic stretch lines, and discuss two versions of the Thurston (co-)geodesic flows. In §5, we describe the Thurston boundary and its identification with the horofunction boundary. In §6, we illustrate the isometry rigidity of the Thurston metric, both globally and infinitesimally. In §7 we discuss the coarse geometry of the Thurston metric. In §8, we are concerned with the lattice counting problem. In §9, we discuss the shearing coordinates. In §10, we sketch several generalizations of the Thurston metric. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,611,795,681]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgements. We would like to thank Athanase Papadopoulos for the opportunity of writing this article, for his patience during the preparation of the manuscript, and for suggesting several improvements on the exposition. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[426,709,570,724]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. BACKGROUD ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[200,743,795,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.1. Teichmüller space. Let $S$ be an orientable closed surface of genus at least two. The Teichmüller space $T(S)$ is the space of equivalence classes of complex structures on $S$ , where two complex structures $X$ and $Y$ are said to be equivalent if there exists a conformal map $X \\to Y$ which is homotopic to the identity map. By the Uniformization Theorem, the Teichmüller space $T(S)$ is also the space of equivalence classes of hyperbolic structures on $S$ , where two hyperbolic structures $X$ and $Y$ are said to be equivalent if there exists an isometry $X \\to Y$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[782,118,794,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,143,794,181]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"which is homotopic to the identity map. For simplicity, we denote the equivalence class of the complex/hyperbolic structure $X$ by $X$ itself. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,217,792,306]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.2. Geodesic laminations and measured geodesic laminations. Let $X \\in \\mathcal{T}(S)$ be a hyperbolic surface. A geodesic lamination $\\lambda$ on $X$ is a closed subset of $X$ which can be decomposed as a disjoint union of simple geodesics. Typical examples are simple closed geodesics. A multicurve is a disjoint union of distinct simple closed geodesics. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,314,542,330]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $\\lambda$ be a geodesic lamination. Then ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[245,349,792,417]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- $\\\\lambda$ is called maximal if it cuts $X$ into ideal triangles, i.e. $X \\\\backslash \\\\lambda$ is a union of ideal triangles; \",\"- $\\\\lambda$ is called chain-recurrent if it is the Hausdorff limit of multicurves. \"]","page_idx":"3","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[200,436,794,472]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A chain-recurrent geodesic lamination is said to be maximal if it is not contained in any other chain-recurrent geodesic lamination. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,479,795,551]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"One can equip the set of geodesic laminations on $X$ with the Hausdorff metric and the corresponding Hausdorff topology. With this topology, the set of chain-recurrent geodesic laminations is a closed subset of the space of geodesic laminations [74, Proposition 6.2]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,559,795,664]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Notice that the space of geodesic laminations is independent of the choice of hyperbolic metrics in the following sense. Let $X' \\in \\mathcal{T}(S)$ be another hyperbolic surface. There is a natural one-to-one correspondence between the space of (resp. chain-recurrent) geodesic laminations on $X$ and the space of (resp. chain-recurrent) geodesic laminations on $X'$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,674,794,728]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $\\lambda$ be a geodesic lamination. A transverse measure $\\mu$ on $\\lambda$ is an assignment of a Radon measure $d\\mu_{\\tau}$ on each arc $\\tau$ transverse to $\\lambda$ , subject to the following conditions: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[245,744,792,797]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- if the arc $\\\\tau'$ is a subarc of $\\\\tau$ then $d\\\\mu_{\\\\tau'} = d\\\\mu_{\\\\tau}|_{\\\\tau'}$ , \",\"- if two arcs $\\\\tau$ and $\\\\tau'$ are homotopic through a family of arcs transverse to $\\\\lambda$ , then the homotopy sends $d\\\\mu_{\\\\tau'}$ to $d\\\\mu_{\\\\tau}$ . \"]","page_idx":"3","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[200,813,794,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A geodesic lamination $\\lambda$ with a transverse measure $d\\mu$ is called a measured geodesic lamination. Typical examples of measured laminations are weighed simple closed curves and weighted multicurves. Usually, we will simply denote a measured geodesic lamination $(\\lambda, d\\mu)$ by $\\lambda$ . For ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,118,215,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,143,794,162]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"any simple closed curve $\\gamma$ , the intersection number $i(\\lambda, \\gamma)$ is defined as: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[415,167,583,208]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\ni (\\lambda , \\gamma) := \\inf \\int_ {\\gamma^ {\\prime}} d \\mu\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,212,720,231]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\gamma^\\prime$ ranges over all simple closed curves homopotic to $\\gamma$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,238,797,417]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As we mentioned above, the space of geodesic laminations is independent of the choice of the hyperbolic metrics. So is the space of measured geodesic laminations. Let $\\mathcal{ML}(S)$ be the space of measured geodesic laminations, equipped with the weak- $*$ topology: a sequence of measured laminations $\\lambda_{n}$ converges to $\\lambda$ if $i(\\lambda_n,\\gamma)\\to i(\\lambda ,\\gamma)$ for every simple closed curve $\\alpha$ . With this topology, $\\mathcal{ML}(S)$ is homeomorphic to $\\mathbb{R}^{6g - 6 + 2n}$ , where $g$ and $n$ are respectively the genus and the number of punctures of $S$ (see for instance [57]). Let $\\mathcal{PML}(S)\\coloneqq \\mathcal{ML}(S) / _{\\mathbb{R}^+}$ be the space of projective classes of measured laminations. The set of weighted simple closed curves is dense in both $\\mathcal{ML}(S)$ and $\\mathcal{PML}(S)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,434,794,487]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.3. The Thurston metric and the maximally stretched lamination. For any two hyperbolic surfaces $X$ and $Y$ in $\\mathcal{T}(S)$ , the extremal Lipschitz constant from $X$ to $Y$ is defined as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[395,493,601,520]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\operatorname {L i p} (X, Y) := \\inf _ {f} \\{L (f) \\}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,526,794,580]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $L(f)$ is the Lipschitz constant of $f$ and where $f$ ranges over all Lipschitz homeomorphsims from $X$ to $Y$ in the homotopy class of the identity map. The Thurston metric $d_{Th}$ is defined as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[204,585,614,606]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\quad \\left. d _ {T h} (X, Y) := \\log \\operatorname {L i p} (X, Y) \\right. \\tag {1}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,611,794,646]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Thurston [74, Theorem 8.5] gave another characterization of this metric in terms of simple closed curves: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[204,651,614,691]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nd _ {T h} (X, Y) = \\log \\sup _ {\\alpha} \\frac {\\ell_ {\\alpha} (Y)}{\\ell_ {\\alpha} (X)} \\tag {2}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,695,794,767]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\ell_{\\alpha}(\\cdot)$ represents the length of the (unique) geodesic representative of $\\alpha$ and where $\\alpha$ ranges over all homotopically nontrivial simple closed curves. Since weighted simple closed curves are dense in $\\mathcal{ML}(S)$ , one can rewrite the above identity as: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[362,771,635,810]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nd _ {T h} (X, Y) = \\log \\max _ {\\alpha \\in \\mathcal {M L} (S)} \\frac {\\ell_ {\\alpha} (Y)}{\\ell_ {\\alpha} (X)}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,813,795,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In general, the measured laminations realizing the maximal ratio of length are not unique. For instance, if $\\lambda$ is a non-uniquely ergodic measured lamination which realizes the maximal ratio of length from $X$ to $Y$ , then any measured lamination with the same support as $\\lambda$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[782,118,794,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,143,794,217]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"also realizes the maximal ratio from $X$ to $Y$ . Nevertheless, Thurston introduced the notion of maximal ratio-maximizing chain-recurrent geodesic lamination (the maximally stretched lamination for short) from $X$ to $Y$ , which is unique. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[205,222,795,489]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Given $X$ and $Y$ in $\\mathcal{T}(S)$ , the maximally stretched lamination $\\Lambda(X, Y)$ from $X$ to $Y$ is the largest chain recurrent geodesic lamination $\\lambda$ with a following property: there exists an $\\exp(d_{Th}(X, Y))$ -Lipschitz map, homotopic to the identity map, from a neighbourhood of $\\lambda$ on $X$ to a neighbourhood of $\\lambda$ on $Y$ which takes leaves of $\\lambda$ on $X$ to corresponding leaves of $\\lambda$ on $Y$ by multiplying arc length by a factor of $\\exp(d_{Th}(X, Y))$ . It is also the union of all chain recurrent geodesic laminations with the aforementioned property [74, Theorem 8.2]. Equivalently, the maximally stretched lamination is also the union of chain-recurrent laminations to which the restriction of every Lipschitz map from $X$ to $Y$ with the extremal Lipschitz constant, which is homotopic to the identity, takes leaves of $\\lambda$ on $X$ to corresponding leaves of $\\lambda$ on $Y$ by multiplying arclength by a factor of $\\exp(d_{Th}(X, Y))$ . (For the equivalence between these two descriptions, we refer to [28, Section 9], see also [17, Section 5] for a related discussion.) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,497,794,515]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Regarding the behavior of maximally stretched laminations, we have: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,518,795,592]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 2.1 ([74], Theorem 8.4). Let $X, Y \\in \\mathcal{T}(S)$ be any two distinct hyperbolic surfaces. If $X_{i}$ and $Y_{i}$ are sequences of hyperbolic surfaces converging to $X$ and $Y$ respectively, then $\\Lambda(X, Y)$ contains any lamination in the limit set of $\\Lambda(X_{i}, Y_{i})$ in the Hausdorff topology. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,604,794,676]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Any Lipschitz map $f$ from $X$ to $Y$ realizing the extremal Lipschitz constant $\\operatorname{Lip}(X, Y)$ is called an extremal Lipschitz map. If moreover, $f$ maximally stretches exactly along the maximally stretched lamination $\\Lambda(X, Y)$ , then it is called an optimal Lipschitz map from $X$ to $Y$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,684,777,703]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Before closing this subsection, let us mention the following result: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,707,658,728]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 2.2 ([74], Theorem 8.5). Let $X, Y \\in \\mathcal{T}(S)$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[230,736,790,789]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(1) The extremal Lipschitz constant $\\\\operatorname{Lip}(X, Y)$ can always be realized by a homeomorphism. \",\"(2) There exists a Thurston geodesic from $X$ to $Y$ . \"]","page_idx":"5","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[200,796,795,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 2.3. (i) For various constructions of \"extremal Lipschitz maps\" and Thurston geodesic rays, see Section 3. (ii) In general, there may be more than one geodesic from $X$ to $Y$ . The union of all such geodesics is called the envelope from $X$ to $Y$ . For more information about envelopes, we refer to [19], [6], and [48]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,118,215,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,143,795,181]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.4. The Thurston norm. Let $X \\in \\mathcal{T}(S)$ . The Thurston norm on the tangent space $T_X\\mathcal{T}(S)$ is defined as: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[205,185,725,217]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\| v \\| _ {\\mathrm {T h}} := \\sup _ {\\lambda \\in \\mathcal {P M L} (S)} \\left(d _ {X} \\log \\ell_ {\\lambda}\\right) [ v ], \\quad \\forall v \\in T _ {X} \\mathcal {T} \\left(S _ {g, n}\\right),\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,220,795,294]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\mathcal{PML}(S) = \\mathcal{ML}(S) / _{\\mathbb{R}_{>0}}$ is the space of projective measured laminations and $\\mathcal{ML}(S)$ is the space of measured laminations on $S$ . The Thurston norm is the infinitesimal norm of the Thurston metric ([74, Page 20], see also [50, Theorem 2.3]). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,301,795,335]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The unit sphere in the cotangent bundle has a very nice description as follows. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,344,797,380]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 2.4 ([74], Theorem 5.1). For any hyperbolic surface $X$ of finite type, the map ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[346,383,645,421]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} d \\log \\ell : \\mathcal {P M L} (S) \\longrightarrow T _ {X} ^ {*} \\mathcal {T} (S) \\\\ [ \\mu ] \\quad \\longmapsto d _ {X} \\log \\ell_ {\\mu} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,426,795,481]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"embeds $\\mathcal{PM}\\mathcal{L}(S)$ as the boundary of a convex neighbourhood of the origin. This convex neighbourhood is dual to the unit ball $\\{v\\in T_X\\mathcal{T}(S):\\| v\\|_{\\mathrm{Th}}\\leq 1\\}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,496,795,551]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"There are flat places on the unit sphere $T_X^1\\mathcal{T}(S)$ of $T_{X}\\mathcal{T}(S)$ . A facet is a maximal flat portion of $T_{X}^{1}\\mathcal{T}(S)$ which has maximum possible dimension so that it has interior. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,558,797,628]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 2.5 ([74], Theorem 10.1). There is a bijection between the set of facets on the unit sphere $T_X^1 \\mathcal{T}(S)$ and the set of simple closed curves. In other words, every facet is contained in a plane $d_X \\log \\ell_\\alpha = 1$ for some simple closed curve $\\alpha$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,646,517,662]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For each simple closed curve $\\alpha$ , let ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[307,667,687,689]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nF _ {X} (\\alpha) := \\left\\{v \\in T _ {X} ^ {1} \\mathcal {T} (S): \\left(d _ {X} \\log \\ell_ {\\alpha}\\right) (v) = 1 \\right\\}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,694,648,710]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"be the corresponding facet obtained in Theorem 2.5. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,720,795,755]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Lemma 2.6 ([47], Lemma 4.2; [33], Corollary 6.13). Let $\\alpha, \\beta$ be two simple closed curves. Then ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[325,761,669,781]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\ni (\\alpha , \\beta) = 0 \\iff \\partial \\mathrm {F} _ {X} (\\alpha) \\cap \\partial \\mathrm {F} _ {X} (\\beta) \\neq \\emptyset .\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,796,795,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The unit sphere of the Thurston norm in the tangent space encodes not only the intersection patterns of simple closed curves, but also their hyperbolic lengths. In [19], Dumas-Lenzhen-Rafi-Tao proved that one can recognize lengths and intersection numbers of curves on $X$ from the lengths of facets in the unit sphere in $T_{X}\\mathcal{T}(S_{1,1})$ , based on the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[782,118,794,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,145,795,321]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"observation that extremal points of any facet in the unit sphere in $T_X\\mathcal{T}(S_{1,1})$ are exactly those vectors tangent to the Thurston stretch lines directed by the two canonical completions of the corresponding simple closed curve. This idea is further exploited and extended to surfaces of higher complexity by Huang-Ohshika-Papadopoulos [33]. Huang-Ohshika-Papadopoulos first observed that stretch vectors with respect to maximal chain-recurrent laminations necessarily arise as the Hausdorff limit of a sequence of shrinking faces of the unit spheres in $T_X\\mathcal{T}(S)$ , and then proceeded to prove that one can recognize lengths of simple closed curves on $X$ using such stretch vectors. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,330,797,455]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 2.7. (i) In his thesis, Bar-Natan [6] proved that the set of tangent vectors to the stretch lines corresponding to completions of maximal chain-recurrent laminations is precisely the set of extreme points in the unit sphere of $\\mathcal{T}_X\\mathcal{T}(S)$ . (ii) For more information about the unit sphere in $T_{X}\\mathcal{T}(S)$ , we refer to [33]. (iii) For the comparison of the Thurston norm with the Teichmüller norm, the Weil-Petersson norm, and the earthquake norm, we refer to [32]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[264,481,732,498]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. EXTREMAL LIPSCHITZ MAPS AND GEODESIC RAYS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[200,516,794,569]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this section, we shall sketch various constructions of extremal Lipschitz maps between hyperbolic surfaces, and the corresponding geodesic rays in the Teichmüller space. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,590,794,662]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1. Deforming polygons via explicit homeomorphisms. One way of constructing extremal Lipschitz maps between surfaces is to consider a pair of orthogonal measured (partial) foliations and to control the effect of the map on the leaves of these foliations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,669,795,792]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Following Thurston's idea, one can deform hyperbolic surfaces by cutting the surface into polygons, deforming each polygon individually, and then gluing the deformed polygons to get new surfaces. One of the advantages of this construction is that the involved deformations/homeomorphisms can be explicitly written down. In the following, we shall introduce this idea with more details, starting with Thurston's original construction. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,813,795,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1.1. Thurston's construction. Let $X$ be a complete hyperbolic surface of finite area. Let $\\lambda$ be a maximal geodesic lamination on $X$ , that is, the complementary region $X \\backslash \\lambda$ is the union of ideal triangles. Suppose further that $\\lambda$ admits at least one leaf which does not go to a cusp ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,118,215,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,614,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[233,142,763,324]","code_body":null,"code_caption":null,"image_caption":"[\"FIGURE 1. In both pictures, the black arcs are leaves of the horocycle foliation $F$ while the red dashed arcs are leaves of $G$ . \"]","image_footnote":"[]","img_path":"images/0780/542251631f1c5c4560d1fcb3ec6d6f5e93a84eb9ac7892fd30dd764462548dff.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[200,404,795,633]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"on both sides. Let $\\Delta$ be an arbitrary ideal triangle in $X\\backslash \\lambda$ . Notice that each corner of $\\Delta$ can be foliated by horocycles. Extend these foliations until they fill all but the region in the center bounded by three horocycles. Let $F$ be the extended partial foliation, called the horocycle foliation of $\\Delta$ . Let $G$ be the partial foliation whose leaves are geodesics rays orthogonal to the leaves of $F$ . Consider the $e^t$ -Lipschitz (self)homeomorphism $f_{t}:\\Delta \\to \\Delta$ which fixes the central region, and maps a horocycle which has distance $r$ from the central region to the horocycle with distance $e^{t}r$ linearly with respect to arc length on the horocycles, see Figure 1. In particular, $f_{t}$ sends leaves of $F$ to (other) leaves of $F$ and keeps each leaf of $G$ invariant (as a set). Thurston proved that the collection of pullback metrics on $X\\backslash \\lambda$ by all such $\\{f_t\\}$ extends to a new hyperbolic metric on $X$ , denoted by $\\mathbf{stretch}(X,\\lambda ,t)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,642,795,715]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 3.1 ([74]). For any complete hyperbolic surface $X$ of finite area, for any maximal geodesic lamination $\\lambda$ not all of whose leaves go to a cusp on both sides, there exists a new hyperbolic surface $\\operatorname{stretch}(X, \\lambda, t)$ depending analytically on $t > 0$ , such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[230,724,794,796]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(1) the identity map $X \\\\to \\\\mathbf{stretch}(X, \\\\lambda, t)$ is Lipschitz with Lipschitz constant $e^t$ , and \",\"(2) the identity map exactly expands arc length of $\\\\lambda$ by the constant factor $e^t$ . \"]","page_idx":"8","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[200,813,795,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The family $\\{\\mathbf{stretch}(X,\\lambda ,t):t > 0\\}$ is called the Thurston stretch ray directed by $\\lambda$ . It is a geodesic under the Thurston metric. For the proof of Theorem 3.1, we refer to [74, Section 4] and [54, Chapter 2, Section 3.5]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[782,118,794,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"9 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,143,794,252]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 3.2. Thurston stretch lines are rare in the sense that at any point $X \\in \\mathcal{T}(S)$ , the set of unit vectors tangent to Thurston stretch lines through $X$ is of Hausdorff dimension zero [74, Theorem 10.5]. However, for any pair of distinct points in $\\mathcal{T}(S)$ , there exists a geodesic from the first point to the second point which a concatenation of finitely many stretch segments [74, Theorem 8.5] ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,285,795,339]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 3.3. Calderon and Farre [13, Lemma 15.11 and Proposition 15.12] generalized Thurston's construction to the case where $X \\backslash \\lambda$ is a union of regular ideal polygons. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,382,797,664]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1.2. The construction of Papadopoulos-Theret. A right-angled hyperbolic hexagon is said to be symmetric if it has three nonadjacent edges of equal length. Using symmetric right-angled hyperbolic hexagons, Papadopoulos and Theret [55] constructed the first examples of Thurston geodesics which are also geodesics in the reversed direction (up to reparametrization). Their construction starts by constructing extremal Lipschitz homeomorphisms between symmetric right-angled hyperbolic hexagons with controlled Lipschitz constant. By doubling the hexagons, they then obtain extremal Lipschitz homeomorphisms between symmetric hyperbolic pairs of pants, that is, hyperbolic pairs of pants which have three geodesic boundary components of equal length. By gluing pairs of pants along their boundary components without twist and by combining the resulting Lipschitz maps between pairs of pants, they obtain new stretch lines in the Teichmüller space of any hyperbolic surface of finite type which are also geodesics (up to reparametrization) in the opposite direction. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,672,797,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Lipschitz homeomorphisms between symmetric right-angled hyperbolic hexagons is constructed as follows. Consider a symmetric right-angled hyperbolic hexagon $H$ . There are two triples of pairwise non-consecutive edges, one of which is called long with common length $L$ while the other is called short with common length $l$ . Similarly as in the case of ideal triangles, one can equip $H$ with two orthogonal partial measured foliations $(F, G)$ defined as follows. The leaves of $F$ are the loci of equidistant points from the short edges. Those leaves foliate $H$ except a triangle-shaped central region. The transverse measure on $F$ is induced by the arclength of the long edges of $H$ . The leaves of $G$ are geodesics orthogonal to the leaves of $F$ and the transverse measure of $G$ is induced by the arclength of short edges of $H$ (see Figure 2.) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[204,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[204,143,795,354]","code_body":null,"code_caption":null,"image_caption":"[\"FIGURE 2. Each of the hexagons has three long sides of equal length (red) and three short sides of equal length (black). The black arcs are leaves of $F$ , which are loci of equidistant points from the short edges. The red dashed arcs are leaves of $G$ , which are geodesics orthogonal to the leaves of $F$ \"]","image_footnote":"[]","img_path":"images/0505/ea803a0bb689ad835e90be706a5c4b6ca77b480a5904512d6dea8f21c3ecdaeb.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[200,511,803,566]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Now Let $H_{t}$ be a family of symmetric right-angled hyperbolic hexagons with long edges being of length $t > 0$ . For any $t > 1$ , Papadopoulos and Théret constructed a homeomorphism $f_{t}: H \\to H_{t}$ such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[243,583,792,705]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- $f_{t}$ sends the central region on $H$ to the central region on $H_{t}$ , \",\"- $f_{t}$ sends affinely the leaves of $F$ at distance $r$ from the central region on $H$ to the leaves at distance $tr$ from the central region on $H_{t}$ , \",\"- $f_{t}$ sends leaves of $G$ on $H$ to the corresponding leaves of $G$ on $H_{t}$ by multiplying arclength by the factor $t$ , \",\"- $f_{t}$ is a $t$ -Lipschitz homeomorphism. \"]","page_idx":"10","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[200,726,797,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Doubling the symmetric right-angled hexagons along short edges and then gluing the resulting pairs of pants without twist, Papadopoulos and Thérét constructed a family of hyperbolic surfaces $\\{X_{t}\\}_{t > 0}$ which is a Thurston geodesic in the forward direction. Notice that the set of short edges of hexagons are glued together to form a pants decomposition of $X_{t}$ while the set of long edges are glued together to form several closed geodesics orthogonal to the aforementioned pants decomposition. Interchanging the role of short edges and long edges, we see that $\\{X_{t}\\}_{t > 0}$ is also a Thurston geodesic in the backward direction. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,118,790,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"11 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,143,797,409]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1.3. The construction of Papadopoulos-Yamada. Starting with an arbitrary right-angled hyperbolic hexagon, Papadopoulos and Yamada constructed a one-parameter family of right-angled hexagons with a Lipschitz map between any two elements in this family, realizing the smallest Lipschitz constant in the homotopy class of this map relative to the boundary [56]. Let $H$ be an arbitrary right-angled hexagon. Notice that there are two triples of non-consecutive edges on $H$ , one of which called long while the other is called short. Let $\\alpha_{1}, \\alpha_{2}, \\alpha_{3}$ be the three long edges of $H$ . Considering the equidistant curves to the long edges of $H$ and the corresponding orthogonal geodesic arcs, Papadopoulos and Yamada constructed a pair of orthogonal measured (partial) foliations $(F, G)$ on $H$ , which extends the construction in [52]. (The construction here is more involved depending on whether the lengths of short edges satisfy the triangle inequality or not, see [56, Section 2]). Let $H_{t}$ be a family of right-angled hyperbolic hexagons such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[426,412,571,452]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\frac {\\cosh \\ell_ {H _ {t}} (\\alpha_ {i})}{\\cosh \\ell_ {H} (\\alpha_ {i})} = t.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[202,455,235,470]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[328,468,666,507]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nk _ {i} (t) := \\frac {\\ell_ {H _ {t}} (\\alpha_ {i})}{\\ell_ {H} (\\alpha_ {i})}, \\qquad k (t) = \\max \\{k _ {i} (t) \\}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,508,794,544]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For any $t > 1$ , Papadopoulos and Yamada constructed a homeomorphism $f_t: H \\to H_t$ such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[245,555,790,660]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- $f_{t}$ sends the central region on $H$ to the central region on $H_{t}$ , \",\"- $f_{t}$ linearly sends the leaves of $F$ on $H$ to the corresponding leaves on $H_{t}$ , \",\"- $f_{t}$ (nonlinearly) sends leaves of $G$ on $H$ to the corresponding leaves of $G$ on $H_{t}$ , \",\"- $f_{t}$ is a $k(t)$ -Lipschitz homeomorphism. \"]","page_idx":"11","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[200,672,794,709]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Notice that each long side $\\alpha_{i}$ is a leaf of $F$ , and hence is stretched under $f$ by the factor $k_{i}(t)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,717,795,838]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Unlike the construction of Thurston and Papadopoulos-Theret, where the constructed homeomorphism linearly stretches the leaves of $G$ with a common factor and linearly shrinks the leaves of $F$ , the map here linearly stretches leaves of $F$ with varying factors and non-linearly shrinks leaves of $G$ . In particular, the map $f: H \\to H_t$ is linear on each of the three long sides of $H$ but not linear on any of the three short sides of $H$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,849,794,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Now we consider an arbitrary hyperbolic surface $X$ of genus $g$ with $b$ geodesic boundary components. Let $\\{\\gamma_i\\}_{1\\leq i\\leq 6g - 6 + 3n}$ be a collection ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[204,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"12 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,143,794,338]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"of pairwise disjoint geodesic arcs orthogonal to the geodesic boundary components of $X$ , i.e. $\\{\\gamma_i\\}_{1 \\leq i \\leq 6g - 6 + 3n}$ is a triangulation of $X$ . The complementary region $X \\setminus (\\cup_{i} \\gamma_{i})$ is a union of right-angled hexagons $\\{H^i\\}$ . Viewing those $\\{\\gamma_i\\}$ as long sides of $H^i$ and applying the previously constructed Lipschitz homeomorphisms to $H^i$ , we arrive at a family of hyperbolic surfaces $X_t$ and a family of Lipschitz homeomorphisms $f_t: X \\to X_t$ attaining the optimal Lipschitz constant on some of the $\\{\\gamma_i\\}$ . Doubling $X_t$ along the geodesic boundary components, we get a family of closed hyperbolic surfaces $\\{X_t^d\\}$ and a family of Lipschitz homeomorphisms $f_t^d: X^d \\to X_t^d$ attaining the optimal Lipschitz constant on some of the double of $\\{\\gamma_i\\}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,380,794,468]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1.4. The construction of Huang-Papadopoulos. Since the optimal Lipschitz map is not as rigid outside the maximally stretched loci, one may hope to construct Thurston geodesics which keep some non-trivial subsurface invariant. This is partially done by Huang and Papadopoulos under some conditions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,478,795,585]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Extending the previous constructions to ideal Saccheri quadrilaterals, Huang and Papadopoulos [34, Theorem 3.3 and Theorem 4.7] constructed, for any complete hyperbolic torus $\\mathbb{T}$ with one boundary component and any chain-recurrent geodesic lamination $\\lambda$ in the convex hull of $\\mathbb{T}$ , a family of complete hyperbolic tori $\\{\\mathbb{T}_t\\}_{t\\geq 1}$ and a family of Lipschitz homeomorphisms $f_{t}:\\mathbb{T}\\to \\mathbb{T}_{t}$ such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[245,601,818,741]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- the convex hull of $\\\\mathbb{T}_t$ has the same boundary length as that of $\\\\mathbb{T}$ , \",\"- $f_{t}$ is $t$ -Lipschitz and multiplies the arclength of $\\\\lambda$ by the factor $t$ , \",\"- $f_{t}$ is an isometry outside a compact neighbourhood of the convex hull of $\\\\mathbb{T}$ , \",\"- if the boundary length of the convex hull of $\\\\mathbb{T}$ is at most $4\\\\operatorname{arcsinh}(1)$ , $f_{t}$ maps the convex hull of $\\\\mathbb{T}$ onto the convex hull of $\\\\mathbb{T}_t$ . \"]","page_idx":"12","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[200,760,794,847]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In particular, for any hyperbolic torus $T$ with one geodesic boundary component of length at most $4\\arcsinh(1)$ , the construction above gives a family of hyperbolic tori $\\{T_t\\}_{t \\geq 1}$ , each of which has exactly one geodesic boundary component, and a family of Lipschitz homeomorphisms $f_t: T \\to T_t$ such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[245,866,656,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"- $T_{t}$ has the same boundary length as that of $T$ , ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[776,118,790,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"13 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[245,143,794,196]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"- $f_{t}$ is $t$ -Lipschitz, multiplies the arclength of $\\lambda$ by the factor $t$ , and maps the boundary of $T$ linearly to the boundary of $T_{t}$ by the factor 1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,210,795,316]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Consider a hyperbolic surface $X$ with punctures or geodesic boundary components. If $X$ contains a hyperbolic torus $T$ with one geodesic boundary component, whose boundary length is at most 4arcsinh(1), then for any chain-recurrent geodesic lamination in $T$ the above construction gives a family of hyperbolic surfaces $X_{t}$ and a family of Lipschitz homeomorphisms $f_{t}: X \\to X_{t}$ such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[245,329,691,364]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- $f_{t}$ is $t$ -Lipschitz, and multiplies the arclength of $\\\\lambda$ ; \",\"- $f_{t}$ is an isometry on the closure of $X \\\\backslash T$ . \"]","page_idx":"13","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[200,388,805,493]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2. Deforming crowned surfaces via harmonic diffeomorphisms. Using harmonic maps of high energy, Pan and Wolf constructed piecewise harmonic stretch lines and harmonic stretch lines [49]. Recall that a differentiable map $f: (M, \\sigma | dz|^2) \\to (N, \\rho | dw|^2)$ between Riemannian surfaces is said to be harmonic if it satisfies the Euler-Lagrange equation: ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[401,496,596,516]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nf _ {z \\bar {z}} + (\\log \\rho) _ {w} f _ {z} f _ {\\bar {z}} = 0.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,518,794,555]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If $M$ and $N$ are compact, then $f$ is harmonic if and only if it is a critical point of the energy functional ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[401,561,596,599]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nE (f) := \\int_ {M} e (f) \\sigma | d z | ^ {2}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,607,794,662]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $e(f) \\coloneqq \\frac{\\rho(f(z))}{\\sigma(z)} (|f_z|^2 + |f_{\\bar{z}}|^2)$ is the energy density of $f$ . Notice that the energy depends on the conformal structure on $M$ and the metric on $N$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,672,795,830]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The basic existence result of harmonic maps was established by Eells and Sampson in [20] and by Hamilton in [30], if the target manifold has nonpositive sectional curvature. The uniqueness was obtained by Al'ber [1] and Hartman [31] if the target manifold has negative sectional curvature and if the image is not contractible to a point or a geodesic. Moreover, Sampson [61] and Schoen-Yau [65] proved that any harmonic map between compact surfaces which is homotopic to a diffeomorphism is a diffeomorphism, provided that the target surface has nonpositive curvature. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[218,839,743,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Suppose that $f$ is harmonic. Consider the pullback of $\\rho$ by $f$ : ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[318,864,678,887]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nf ^ {*} (\\rho) = \\rho f _ {z} \\overline {{f _ {\\bar {z}}}} d z ^ {2} + e (f) \\sigma d z d \\bar {z} + \\rho \\overline {{f _ {z}}} f _ {\\bar {z}} d \\bar {z} ^ {2}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[202,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"14 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[382,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,143,795,233]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The $(2,0)$ -part of $f^{*}(\\rho)$ is called the Hopf differential of $f$ . The harmonicity of $f$ implies that the Hopf differential of $f$ is holomorphic (see [66, 36]). If we choose the coordinate $z = x + iy$ such that the Hopf differential $\\Phi = dz^2$ and choose $\\sigma$ to be the singular flat metric induced by $|\\Phi|$ , then $f^{*}(\\rho)$ can be simply expressed as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[367,239,627,262]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nf ^ {*} \\rho = (e + 2) d x ^ {2} + (e - 2) d y ^ {2}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,268,795,428]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"By [43, Lemma 3.2 and Lemma 3.3], the energy density satisfies $e(z) = 2 + O(e^{-2r})$ where $r$ represents the distance from $z$ to the zeros of the Hopf differential. In particular, for points far away from the zeros of the Hopf differential, the pullback metric $f^{*}\\rho$ is nearly $4dx^{2}$ . Roughly speaking, at regions far away from the zeros of the Hopf differential, the harmonic map $f$ linearly maps horizontal leaves of the Hopf differential to hyperbolic geodesics by a factor of 2 while contracting the vertical leaves exponentially. This observation is the starting point of the construction of Pan and Wolf. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,436,795,526]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 3.4 ([49], Theorem 1.7). Let $Y \\in \\mathcal{T}(S)$ be any closed hyperbolic surface, and let $\\lambda$ be any geodesic lamination. Then for any surjective harmonic diffeomorphism $f: X \\to Y \\setminus \\lambda$ from some (possibly disconnected) punctured surface $X$ , there is a family of new hyperbolic surfaces ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[362,529,633,547]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nY _ {t} := \\mathbf {s t r e t c h} (Y, \\lambda , f; t) \\in \\mathcal {T} (S)\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[202,553,573,571]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"depending analytically on $\\{t > 0\\}$ such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,584,795,680]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(a) the identity map $f_{t}: X \\\\to Y_{t} \\\\setminus \\\\lambda$ is a surjective harmonic map $f_{t}: X \\\\to Y_{t} \\\\setminus \\\\lambda$ with Hopf differential $t\\\\mathrm{Hopf}(f)$ ; \",\"(b) for any $0 < s < t$ , the identity map $(f_t \\\\circ f_s^{-1})$ is $\\\\sqrt{t / s}$ -Lipschitz with (pointwise) Lipschitz constant strictly less than $\\\\sqrt{t / s}$ in $S - \\\\lambda$ , and exactly expands arc length of $\\\\lambda$ by the constant factor $\\\\sqrt{t / s}$ . \"]","page_idx":"14","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[200,699,795,808]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A family of hyperbolic structures stretch $(X, \\lambda; \\widehat{\\Phi}, \\widehat{f}; t)$ constructed above is called a piecewise harmonic stretch line. It admits a canonical orientation coming from the orientation of the positive real ray $\\{t > 0\\}$ . With that orientation, a piecewise harmonic stretch line is a (reparametrized) geodesic in the Thurston metric. Whenever we say a piecewise harmonic stretch line, we mean a directed line. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,830,794,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.3. The constructions of Guéritaud-Kassel and Alessandrini-Disarlo. Using a totally different method, Guéritaud and Kassel extended Thurston's construction to a geometrically finite setting and to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[776,118,790,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"15 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,143,794,356]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"higher dimension. Let $\\Gamma_0$ be a discrete group. For a pair $(j,\\rho)$ of representations of $\\Gamma_0$ into $\\mathrm{PO}(n,1) = \\mathrm{Isom}(\\mathbb{H}^n)$ with $j$ geometrically finite. Guéritaud and Kassel investigate the set of $(j,\\rho)$ -equivariant Lipschitz maps from $\\mathbb{H}^n$ to itself having the minimal Lipschitz constants (such maps do exist if $\\rho$ is reductive [28, Lemma 4.10]), establish the existence of maximally stretched locus $E(j,\\rho)$ (which is a geodesic lamination if the minimal Lipschitz constant is at least one), and prove the existence of optimal Lipschitz maps whose stretched locus is exactly the maximally stretched locus $E(j,\\rho)$ of the representations $(j,\\rho)$ [28, Theorem 1.3]. This allows Guéritaud and Kassel to study proper actions of discrete subgroups of $\\mathrm{PO}(n,1)\\times \\mathrm{PO}(n,1)$ on $\\mathrm{PO}(n,1)$ by left and right multiplication [28, Theorem 1.8 and Theorem 1.9]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,364,795,436]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"One of the key ideas of Guéritaud and Kassel is to consider the \"average of Lipchitz maps\". This idea is used by Alessandrini and Disarlo to construct extremal Lipschitz maps between hyperbolic surfaces with geodesic boundary components [3]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,444,795,655]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We now sketch the construction of Alessandrini and Disarlo [3]. Let $X$ be a finite-area hyperbolic surface with geodesic boundary components. A geodesic lamination $\\lambda$ on $X$ is called maximal if any connected component of its complementary region $X \\backslash \\lambda$ is either an ideal triangle, a right-angled quadrilateral with two consecutive ideal vertices, a right-angled pentagon with one ideal vertex, or a right-angled hexagon. These four types of polygons are called geometric pieces. For any maximal geodesic lamination on $X$ , Alessandrini and Disarlo constructed a family of hyperbolic surface $X_{\\lambda}^{t}$ homeomorphic to $X$ and a family of generalized stretch maps $\\Psi^t: X \\to X_{\\lambda}^t$ which realizes the minimal Lipschitz constant from $X$ to $X_{\\lambda}^{t}$ and maximally stretches along $\\lambda$ . Their construction has three steps. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,664,795,806]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Step 1: Generalized stretch map between geometric pieces. Combine Thurston's stretch maps and Guéritaud-Kassel's idea of averaging Lipschitz maps to construct implicit extremal maps between geometric pieces of the same type which stretch along certain sides. However, it is unclear whether the resulting maps between geometric pieces are homeomorphic or not. So one can't simply \"glue\" these new pieces and the corresponding stretch maps. To overcome this issue, Alessandrini and Disarlo adapted a different idea in the remaining steps. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,813,794,849]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Step 2: Decomposition of $X$ . Let $B \\subset X$ be the union of geometric pieces of $X \\backslash \\lambda$ which are not ideal triangles. The surface $B$ is a crowned ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[204,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"16 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,143,795,181]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"hyperbolic surface. Let $C \\subset B$ be the union of crown ends of $B$ and set $B_{C} = \\overline{B \\setminus C} \\subset B$ . Finally, let $X_{C} := \\overline{X \\setminus B_{C}} \\subset X$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,188,795,279]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Step 3: Define $X_{\\lambda}^{t}$ and the generalized stretch map $\\psi^t:X\\to X_\\lambda^t$ For each $t\\geq 0$ , Alessandrini and Disarlo construct hyperbolic surfaces $B^{t},B_{C}^{t},X_{C}^{t}$ homeomorphic to $B,B_{C},X_{C}$ respectively. The new surfaces come with preferred (locally) isometric embeddings $\\xi^t:C^t\\to B^t$ and $h^t:C^t\\to B_C^t$ . The new surface $X_{\\lambda}^{t}$ is then defined to be ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[411,285,591,306]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nX _ {\\lambda} ^ {t} := \\left(B ^ {t} \\cup B _ {C} ^ {t}\\right) / \\sim ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,313,795,404]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\xi^t(z) \\sim h^t(z)$ for all $z \\in C^t$ . The generalized stretch map $\\Psi^t: X \\to X_\\lambda^t$ is defined by glueing together suitable generalized stretch maps $\\beta^t: B \\to B^t$ and $\\psi^t$ from an open dense subset of $B_C$ to $X_C^t$ . (For the details of the construction, we refer to [3, Section 6.2, 7.4, 8.1 and 8.2]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,412,795,518]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 3.5. (1) It is unclear whether the generalized stretch maps are homeomorphisms or not. (2) Based on the generalized stretch maps and the generalized stretch lines, Alessandrini and Disarlo proved that the Teichmüller space of bordered hyperbolic surfaces with the arc metric is geodesic, and provided new geodesics of the Thurston metric in the Teichmüller space of closed surface. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,537,795,609]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.4. The construction of Daskalopoulos-Uhlenbeck. In [16, 17], Daskalopoulos and Uhlenbeck constructed extremal Lipschitz maps between manifolds using infinity harmonic maps. Here we sketch the construction of [17], which works more generally than hyperbolic surfaces. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,617,795,705]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $(M,g)$ be a compact Riemannian manifold with boundary $\\partial M$ (possibly empty) and $\\dim(M) = n$ . Let $(N,h)$ be a closed Riemannian manifold of non-positive sectional curvature and let $W^{1,p}(M,N)$ denote the Soblev space of maps $f:M\\to N$ such that $f$ and its weak derivative have a finite $L^p$ norm. For any map ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[334,712,665,734]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nf: M \\to N \\in W ^ {1, p} (M, N) \\cap C ^ {0} (M, N),\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,742,470,760]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"define the $J_{p}$ -functional of $f$ as ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[383,768,616,806]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nJ _ {p} (f) := \\int_ {M} \\mathrm {T r} (Q (d f) ^ {p}) * 1,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,813,795,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $1 \\leq p < \\infty$ and where $Q(df)^2 = dfdf^T$ is a non-negative symmetric linear map mapping the tangent space $TN$ to itself. The integrand $\\mathrm{Tr}(Q(df)^p)$ is essentially the sum of the $p$ -th powers of the singular eigenvalues of $df$ . The Euler-Lagrange equations of the $J_p$ functional ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,118,792,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"16","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"17 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[202,147,233,159]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"are ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[405,161,591,181]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nD ^ {*} Q (d f) ^ {q - 2} (d f) ^ {2} = 0,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,184,792,203]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $D = D_{f}$ is the pullback of the Levi-Civita connection on $f^{-1}TN$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,210,795,335]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If the domain manifold $(M,g)$ has nonempty boundary, there are two types minimizing problems: the Dirichlet problem and the Neumann problem. For the Dirichlet problem we fix a continuous map $f:M\\to N$ and seek a minimizer in the homotopy class of $f$ relative to the boundary values of $f$ . For the Neumann problem we only fix a homotopy class and no boundary condition at all. Here is the existence theorem concerning the $J_{p}$ functional. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,342,797,467]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 3.6 ([17], Theorem 1.1). Let $(M,g)$ be a compact Riemannian manifold with boundary $\\partial M$ (possibly empty) and $\\dim(M) = n$ . Let $(N,h)$ be a closed Riemannian manifold of non-positive sectional curvature. Then for each $p > N$ , there exists a minimizer $f$ in $W^{1,p}(M,N)$ of the functional $J_p$ with either the Dirichlet or the Neumann boundary conditions in a homotopy (relative homotopy) class. Furthermore, if $\\partial M \\neq \\emptyset$ , the solution of Dirichlet problem is unique. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,484,795,556]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The next result is about the construction of extremal Lipschitz maps using $J_{p}$ harmonic maps. Recall that a Riemannian manifold $M$ with boundary is said to be convex if it can be isometrically embedded as a convex subset of a manifold of the same dimension without boundary. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,563,797,670]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 3.7 ([17], Theorem 1.4). Let $M, N$ be Riemannian manifolds where $M$ is convex with possibly non-empty boundary and $N$ is closed and has non-positive curvature. Given a sequence $p \\to \\infty$ , there exists a subsequence (denoted also by $p$ ) and a sequence of $J_p$ minimizers $f_p: M \\to N$ in the same homotopy class (either in the absolute sense or relative to the boundary depending on the context) such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[346,675,648,702]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nf = \\lim _ {p \\to \\infty} f _ {p} \\in W ^ {1, s} (M, N) f o r a l l s.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,707,794,743]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Furthermore, $f_{p} \\to f$ uniformly and $f$ is an extremal Lipschitz map in the (relative) homotopy class. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,760,795,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A critical point of the $J_{p}$ functional (with either the Dirichlet problem or the Neumann problem) is called a Schatten-von Neumann $p$ -harmonic map or simply a $J_{p}$ harmonic map. The limit map obtained in Theorem 3.7 is called infinity harmonic map. About the regularity, Daskalopoulos and Uhlenbeck conjecture that for $p > 2$ , any $J_{p}$ harmonic map between hyperbolic surfaces is of $C^{1,\\alpha}$ [17, Conjecture 4.19]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"18 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"17","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,143,797,321]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We now return to the hyperbolic surface setting. Let $f: M \\to N$ be a Lipschitz map between hyperbolic surfaces $M$ and $N$ . Here $M$ and $N$ are not necessary homeomorphic. Suppose further that the minimal Lipschitz constant in the homotopy class of $f$ is at least one. In this setting, the maximally stretched loci of all extremal Lipschitz maps from $M$ to $N$ in the given homotopy class, is a chain recurrent geodesic lamination. In particular, the maximally stretched loci of the infinity harmonic map obtained in Theorem 3.7 contains the maximally stretched lamination. For the inverse direction, they proved: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,330,797,404]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 3.8 ([17], Theorem 1.7). If the maximally stretched lamination $\\lambda$ for a homotopy class of maps $M\\to N$ consists of a finite number of simple closed geodesics, then the maximally stretched loci of the infinity harmonic map obtained in Theorem 3.7 is exactly $\\lambda$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,422,797,532]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Daskalopoulos and Uhlenbeck conjectured that Theorem 3.8 holds in general [17, Conjecture 8.12]: the maximally stretched loci of any infinity harmonic map, whose Lipschitz constant is at least one, is the maximally stretched lamination [17, Conjecture 8.12]. Furthermore, they conjectured that the limit infinity harmonic maps are not homeomorphisms [17, Conjecture 8.5]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,555,816,643]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.5. Concatenations of geodesic segments. In the previous subsections, we discussed the constructions of various geodesic rays. Thurston constructed another type of geodesics, that is, concatenations of Thurston stretch segments [74, Theorem 8.5]. This construction applies to other segments as well. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[362,679,633,696]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. HARMONIC STRETCH LINES ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[200,713,795,801]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In Section 3, we discussed various constructions of geodesic rays under the Thurston metric. In this section, we will focus on a special type of piecewise harmonic stretch lines, namely, the harmonic stretch lines. Throughout this section, we assume that the underlying topological surface $S$ is a closed orientable surface with genus at least two. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[776,118,790,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"19 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,821,795,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"<sup>1</sup>If the minimal Lipschitz constant is less than one, then the maximally stretched loci may not be a geodesic lamination [28, Section 9.4]. In fact, Guéritaud and Kassel conjectured that in this case the maximally stretched loci is a \"grammation\" (contraction of \"graph\" and \"lamination\") [28, Conjecture 1.4]. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[200,143,794,320]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.1. Harmonic stretch lines. Recall that the construction of piecewise harmonic stretch lines through $Y \\in \\mathcal{T}(S)$ depends on the choice of a geodesic lamination $\\lambda$ and a surjective harmonic diffeomorphism $f: X \\to Y \\backslash \\lambda$ from some (possibly disconnected) punctured surface $X$ . If $X$ has several components, the harmonic map $f$ can be prescribed independently on each component. If we impose some additional \"compatibility conditions\" on the harmonic maps from distinct components, we arrive at the harmonic stretch lines. Originally, the harmonic stretch lines are defined via harmonic map rays, of which we now recall the definition. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,329,795,402]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $X \\in \\mathcal{T}(S)$ and let $\\Phi$ be a holomorphic quadratic differential on $X$ . The harmonic map $ray$ determined by $X$ and $\\Phi$ is the set of hyperbolic surfaces $\\{Y_t\\}_{t > 0}$ such that the Hopf differential of harmonic map from $X$ to $Y_t$ is $t\\Phi$ [77]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,409,794,479]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A piecewise harmonic stretch line is said to be a harmonic stretch line if it arises as a limit of some sequence of harmonic map rays in $\\mathcal{T}(S)$ . The basic theorem about those harmonic stretch lines is the following. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,484,795,539]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 4.1 ([49], Theorem 1.8). For any two distinct hyperbolic surfaces $Y, Z \\in \\mathcal{T}(S)$ , there exists a unique harmonic stretch line proceeding from $Y$ to $Z$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,554,795,712]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Actually, one can say more about the relationship between harmonic map rays and Thurston geodesic rays. To that end, we need another definition, the harmonic map dual rays. Let $X \\in \\mathcal{T}(S)$ and let $\\lambda$ be a measured foliation on $X$ . The harmonic map dual ray determined by $X$ and $\\lambda$ is the of hyperbolic surfaces such that the horizontal foliation of the Hopf differential of the harmonic map from $X_{t}$ to $X$ is $t\\lambda$ (for the existence and uniqueness of such a $X_{t}$ , see [78, Theorem 3.1]). For any two hyperbolic surfaces $X', X$ , we denote by $\\mathbf{HR}(X', X)$ the harmonic map which starts at $X'$ and passes through $X$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,719,795,806]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 4.2 ([49], Theorem 1.1). Let $X \\in \\mathcal{T}(S)$ be a hyperbolic surface and $\\lambda$ a measured lamination. Then the family of harmonic map rays $\\mathrm{HR}(X_t, X)$ converge to a Thurston geodesic locally uniformly as $X_t$ diverges along the harmonic map dual ray determined by $X$ and $\\lambda$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,813,794,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 4.3. The conclusion still holds if we replace the harmonic map dual ray by a Teichmüller ray [49, Theorem 1.2]. Similar results also hold for harmonic map dual rays. We fixed $X \\in \\mathcal{T}(S)$ and a holomorphic quadratic differential $\\Phi$ on $X$ . Suppose that $Y_{t}$ diverges along ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"20 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,143,795,217]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the harmonic map ray determined by $X$ and $\\Phi$ . Then the family of harmonic map dual rays, each of which starts at $Y_{t}$ and passes through $X$ , converges to the Teichmüller geodesic determined by $X$ and $\\Phi$ locally uniformly [49, Theorem 1.4]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,232,795,268]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If we remove the assumption that $X_{t}$ diverges along a harmonic map ray, then we have the following sub-convergence result: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,275,797,348]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 4.4 ([49], Theorem 1.3). For any fixed $X \\in \\mathcal{T}(S)$ , let $X_{n} \\in \\mathcal{T}(S)$ be an arbitrary divergent sequence. with $X_{n} \\to \\infty$ . Then the sequence of harmonic map rays $\\mathbf{HR}(X_n, X)$ contains a subsequence which converges to some Thurston geodesic locally uniformly. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,363,795,436]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Next, we extend the existence/ uniqueness theory of harmonic stretch lines to rays whose terminal point is a projective measured lamination, representing a point on the boundary of the Thurston compactification of the Teichmüller space $\\mathcal{T}(S)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,441,795,497]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 4.5 ([49], Theorem 1.11). For any $Y \\in \\mathcal{T}(S)$ and any $[\\eta] \\in \\mathcal{PML}(S)$ , there exists a unique harmonic stretch ray starting at $Y$ , which converges to $[\\eta] \\in \\mathcal{PML}(S)$ in the Thurston compactification. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,503,795,540]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Moreover, these rays foliate $\\mathcal{T}(S)$ if we fix $Y$ and let $[\\eta]$ vary in $\\mathcal{PML}(S)$ , or if we fix $[\\eta]$ and let $Y$ vary in $\\mathcal{T}(S)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,556,843,609]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, let us mention the following continuity property, where $\\mathrm{HSL}(X,X^{\\prime})$ represents the harmonic stretch line proceeding from $X\\in \\mathcal{T}(S)$ to $X^{\\prime}\\in \\mathcal{T}(S)\\cup \\mathcal{PM}\\mathcal{L}(S)$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,617,797,655]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proposition 4.6 ([49], Proposition 12.14 and Proposition 13.8). Let $Y$ and $Z$ be two distinct points in $\\mathcal{T}(S)$ . Let $[\\eta] \\in \\mathcal{PML}(S)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[210,662,795,771]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(i) Suppose that $Y_{n} \\\\to Y$ and $Z_{n} \\\\to Z$ in $\\\\mathcal{T}(S)$ , then the sequence of harmonic stretch lines $\\\\mathrm{HSL}(Y_n,Z_n)$ locally uniformly converges to the harmonic stretch line $\\\\mathrm{HSL}(Y,Z)$ . \",\"(ii) Suppose that $Y_{n} \\\\to Y$ in $\\\\mathcal{T}(S)$ and $[\\\\eta_n] \\\\to [\\\\eta]$ in $\\\\mathcal{PM}\\\\mathcal{L}(S)$ , then the sequence of harmonic stretch lines $\\\\mathrm{HSL}(Y_n, [\\\\eta]_n)$ locally uniformly converges to the harmonic stretch line $\\\\mathrm{HSL}(Y, [\\\\eta])$ . \"]","page_idx":"20","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[200,777,795,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 4.7. Using the identification between $\\mathcal{ML}(S)$ and $T_{Y}^{*}\\mathcal{T}(S)$ , Theorem 4.5 induces a bijection from $T_{Y}^{*}\\mathcal{T}(S)$ to $\\mathcal{T}(S)$ which sends rays through the origin in $T_{Y}^{*}\\mathcal{T}(S)$ to harmonic stretch rays in $\\mathcal{T}(S)$ . (By Proposition 4.6 such a bijection is a homeomorphism.) A natural question is to improve Theorem 4.5 to an exponential map from $T_{Y}\\mathcal{T}(S)$ to $\\mathcal{T}(S)$ . Since the Thurston norm is not strictly convex, this does not ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,118,790,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"20","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"21 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,143,794,198]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"follow directly from Theorem 4.5. The existence part of the exponential map is clear, see [49, Remark 1.12]. However, the uniqueness part is unknown yet. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,217,792,233]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.2. Two versions of the geodesic flow for the Thurston metric. ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[200,234,702,252]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 4.5 allows us to define the Thurston geodesic flow ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[308,260,684,280]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\psi_ {t}: \\mathcal {T} (S) \\times \\mathcal {P M L} (S) \\longrightarrow \\mathcal {T} (S) \\times \\mathcal {P M L} (S)\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,287,795,342]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"such that the orbit through $(Y, [\\eta]) \\in \\mathcal{T}(S) \\times \\mathcal{PML}(S)$ is the harmonic stretch line determined by $Y$ and $[\\eta]$ via Theorem 4.5. Moreover, every harmonic stretch line appears as a (forward) orbit. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,349,683,367]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"There is another version of the Thurston geodesic flow ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[313,376,679,396]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\phi_ {t}: \\mathcal {T} (S) \\times \\mathcal {P M L} (S) \\rightarrow \\mathcal {T} (S) \\times \\mathcal {P M L} (S)\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,402,794,439]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"such that the orbit through $(Y, [\\eta]) \\in \\mathcal{T}(S) \\times \\mathcal{PML}(S)$ is the stretch line obtained from Theorem 4.2. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,446,720,467]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For a further discussion about those flows, we refer to [49]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[383,496,611,513]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5. THURSTON BOUNDARY ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[200,531,794,604]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Teichmüller space $\\mathcal{T}(S)$ parametrizes hyperbolic structures on the topological surface $S$ . A sequence of hyperbolic surfaces $X_{n}\\in \\mathcal{T}(S)$ which tends to infinity has the property that some closed curve $\\gamma$ on $S$ becomes infinitely long, that is, the hyperbolic length $\\ell_{\\gamma}(X_n)\\to \\infty$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,611,795,681]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The length of long curves can be measured quantitatively by looking at their transverse measures with respect to measured foliations. This observation of Thurston [72] resulted in a natural compactification of $\\mathcal{T}(S)$ , which is called the Thurston compactification. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,689,794,779]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Recall that a measured foliation $(F, \\mu)$ is a foliation $F$ on $S$ equipped with an invariant transverse measure $\\mu$ . We require that the singularities of $F$ are similar to the singularities of holomorphic quadratic differentials (or meromorphic quadratic differentials with at most simple pole at the punctures, when $S$ is a punctured surface). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,786,794,823]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For simplicity, we denote $(F,\\mu)$ by $\\mu$ . For any simple closed curve $\\gamma$ , the intersection number $i(\\gamma ,\\mu)$ is defined by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[415,845,583,887]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\ni (\\gamma , \\mu) = \\inf _ {\\gamma^ {\\prime}} \\int_ {\\gamma^ {\\prime}} d \\mu ,\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[202,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"22 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"21","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,143,794,233]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\gamma'$ is taken over all simple closed curves homotopic to $\\gamma$ . Two measured foliations $\\mu_1, \\mu_2$ are said to be equivalent if $i(\\gamma, \\mu_1) = i(\\gamma, \\mu_2)$ for all simple closed curves $\\gamma$ on $S$ . Let $\\mathcal{MF}$ be the set of equivalence classes of measured foliations on $S$ . The set of projective equivalence classes of measured foliations is denoted by $\\mathcal{PMF}(S)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,241,795,313]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As shown by Thurston (see [23]), $\\mathcal{PMF}(S)$ is topologically a sphere of dimension $6g - 7 + 2n$ . Moreover, $\\mathcal{PMF}(S)$ is the Thurston boundary of $\\mathcal{T}(S)$ . By definition, a sequence of hyperbolic surfaces $X_{n}\\in \\mathcal{T}(S)$ converges to the projective class of $\\mu$ if there is some $c_{n} > 0$ such that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[415,318,580,339]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nc _ {n} \\ell_ {\\gamma} (X _ {n}) \\rightarrow i (\\gamma , \\mu)\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,344,794,380]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"for all simple closed curves $\\gamma$ on $S$ . To glue $\\mathcal{T}(S)$ together with $\\mathcal{PMF}(S)$ , we can embed both $\\mathcal{T}(S)$ and $\\mathcal{PMF}(S)$ into $\\mathbb{P}\\mathbb{R}^{\\infty}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,388,794,441]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"There are many applications of Thurston's theory of measured foliations. Below, we will limit ourselves to illustrating some of the results related to the Thurston metric. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,449,794,503]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The following result, first proved by Papadopoulos [51, Theorem 5.1], implies there is direct relation between the Thurston metric and the Thurston boundary: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,511,795,583]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 5.1. Let $\\lambda$ be a maximal geodesic lamination on $X \\in \\mathcal{T}(S)$ with $\\mu = F_{\\lambda}(X)$ being the transverse horocycle foliation. Then the corresponding Thurston stretch ray converges to the projective class $[\\mu] \\in \\mathcal{PMF}(S)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,590,795,715]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 5.2. The problem of the convergence of anti-stretch lines (stretch lines in backward direction) towards the Thurston boundary was studied by Théret [70]. If the anti-stretch line is directed by a complete geodesic lamination $\\lambda$ which is the completion of a uniquely ergodic measured lamination $\\mu$ , then it converges to the projective class of $\\mu$ . For general stretch lines, the problem of the convergence or non-convergence remains open. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,733,794,787]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It is true that every geodesic ray of the Thurston metric has a unique limit in the Thurston boundary. This is a corollary of the following result by Walsh [76, Theorem 3.6]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,795,794,830]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 5.3. The horofunction boundary of $\\mathcal{T}(S)$ , endowed with the Thurston metric, is homeomorphic to the Thurston boundary. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,849,794,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The horofunction compactification and the corresponding boundary of a proper metric space are introduced by Gromov [27]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,118,792,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"22","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"23 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,143,794,303]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 5.4. An asymmetric metric, called arc metric, is defined on the Teichmüller space of compact hyperbolic surfaces with boundary. It is an analogue of the Thurston metric defined on the Teichmüller space of complete finite area hyperbolic surfaces without boundary. Theorem 5.3 was generalized to the arc metric by [2]. Geodesics for the arc metric, which are analogues of Thurston's stretch lines, were constructed by [3]. By [49, Theorem 14.1], the arc metric coincides with the Lipschitz metric, which is defined using Lipschitz maps similarly as (1). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,324,794,378]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let us briefly mention the work of Bonahon [9] on geodesic currents. Let us endow the surface $S$ with a hyperbolic metric. For simplicity, we assume that $S$ is a closed hyperbolic surface. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,386,795,476]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A geodesic current is a locally finite Radon (positive) measure on the space of geodesics on $S$ . Alternatively, a geodesic current is a finite Radon measure on the unique tangent bundle of $S$ that is invariant under the geodesic flow. Closed geodesics or weighted sums of closed geodesics on $S$ are examples of geodesic currents. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,483,795,608]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Denote the space of geodesic currents on $S$ by $\\mathcal{C}(S)$ , endowed with the weak* topology. We can embed $\\mathcal{MF}(S)$ into $\\mathcal{C}(S)$ , by representing each measured foliation as a geodesic lamination with an invariant transverse measure. On the other hand, every hyperbolic structure $X \\in \\mathcal{T}(S)$ corresponds to a Liouville current. By taking projective classes, the Teichmüller space embeds into $\\mathrm{PC}(S)$ , and Bonahon [9] proved that the boundary of the image is exactly $\\mathcal{PMF}(S)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[393,647,602,664]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6. ISOMETRY RIGIDITY","text_format":null,"text_level":"1","type":"text"},{"bbox":"[200,681,794,719]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this section, we will discuss the rigidity of the Thurston metric, especially the isometry rigidity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,747,812,801]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6.1. Global rigidity. We start with the global rigidity due to Walsh [76]. Using an identification of the horofunction boundary of the Thurston metric with the Thurston boundary (Theorem 5.3), Walsh proved that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,813,797,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 6.1 ([76], Theorem 7.8). If $S$ is not a sphere with four or less punctures, nor a torus with two or fewer punctures, then every isometry of $(\\mathcal{T}(S), d_{Th})$ is an element of the extended mapping class group. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"24 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"23","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,143,795,215]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 6.1 is an analogue of Royden's theorem for the Teichmüller metric. Note that the proof of Walsh is geometric. An important step consists of reducing the problem into showing that every isometry of the Thurston metric induces an automorphism of the curve complex. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,223,795,242]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Furthermore, distinct surfaces give rise to distinct Teichmüller spaces: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,250,795,305]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 6.2 ([76], Theorem 7.8). Let $S_{g,n}$ and $S_{g',n'}$ be orientable surfaces of finite type with negative Euler characteristics. Assume that $\\{(g,n),(g',n')\\}$ is not one of the three sets: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[305,309,687,330]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\{(1, 1), (0, 4) \\}, \\{(1, 2), (0, 5) \\}, \\{(2, 0), (0, 6) \\}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,334,794,369]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If $(g,n)\\neq (g^{\\prime},n^{\\prime})$ , then $(\\mathcal{T}(S),d_{Th})$ and $(\\mathcal{T}(S_{g^{\\prime},n^{\\prime}}),d_{Th})$ are not isometric. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,387,794,460]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6.2. Infinitesimal rigidity. The infinitesimal rigidity of the Thurston metric was first studied by Dumas-Lenzhen-Rafi-Tao [19] for once-punctured tori, then independently by Pan [47] and Huang-Ohshika-Papadopoulos [33] for surfaces of higher complexity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,467,795,521]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 6.3 ([19, 47, 33]). Let $S$ be a surface of finite type with negative characteristic. Let $X, Y \\in \\mathcal{T}(S)$ . Then there exists an isometry of normed vector spaces ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[331,526,663,547]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left(T _ {X} \\mathcal {T} (S), \\| \\bullet \\| _ {\\mathrm {T h}}\\right)\\rightarrow \\left(T _ {Y} \\mathcal {T} (S), \\| \\bullet \\| _ {\\mathrm {T h}}\\right)\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,551,794,585]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"if and only $X$ and $Y$ are in the same extended mapping class group orbit. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,604,795,642]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We can also use the Thurston norm to distinguish the topology of the underlying hyperbolic surfaces. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,648,795,702]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 6.4 ([47]). Let $S$ and $S'$ be two surfaces of finite type with negative Euler characteristics. Then there exists an isometry of normed vector spaces ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[330,708,665,729]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left(T _ {X} \\mathcal {T} (S), \\| \\bullet \\| _ {\\mathrm {T h}}\\right)\\rightarrow \\left(T _ {Y} \\mathcal {T} \\left(S ^ {\\prime}\\right), \\| \\bullet \\| _ {\\mathrm {T h}}\\right)\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,733,794,770]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"for some $X \\in \\mathcal{T}(S)$ and $Y \\in \\mathcal{T}(S')$ if and only if and only if $S$ and $S'$ are homeomorphic. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,777,795,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 6.5. The original statement of Theorem 6.4 is slightly differently from the statement here. In [47, Theorem 1.6], the isometry is assumed to be $\\mathbb{R}$ -linear. As pointed out in [33, Remark 1.16], this assumption is unnecessary, as isometries of the Thurston norm are also isometries of its (additive) symmetrisation, and the Mazur-Ulam theorem ensures that any isometry of the Thurston norm must be affine, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,118,792,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"24","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"25 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,143,794,181]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and hence there exists an isometric translate of the affine isometry which is a linear map. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,196,709,214]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Using the infinitesimal rigidity, we have the local rigidity: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,222,797,313]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 6.6 ([19, 47, 33]). Let $S$ be a surface of finite type with negative Euler characteristic. Let $U \\subset \\mathcal{T}(S)$ be a connected open subset, considered as a metric space with the restriction of the Thurston metric. Then any isometric embedding $(U, d_{Th}) \\to (\\mathcal{T}(S), d_{Th})$ is the restriction to $U$ of an element of the extended mapping class group. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,327,794,398]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Intuitively, this says that the quotient of $\\mathcal{T}(S)$ by the mapping class group is \"totally unsymmetric\": each ball fits into the space isometrically in only one place. As a direct consequence of Theorem 6.6, this proves Theorem 6.1 and extends it to the exceptional surfaces: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,406,797,460]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 6.7 ([76, 19, 47, 33]). Let $S$ be a surface of finite type with negative characteristic. Then every isometry of $\\mathcal{T}(S), d_{Th}$ is induced by an element of the extended mapping class group. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,476,794,512]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To pass from the infinitesimal rigidity to the local rigidity, one needs the following regularity result about the Thurston norm: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,518,797,574]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 6.8 ([19], Theorem 6.1). Let $S$ be a surface of finite type with negative characteristic. Then the Thurston norm function $T\\mathcal{T}(S) \\to \\mathbb{R}$ is locally Lipschitz. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[393,594,604,611]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7. COARSE GEOMETRY ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[200,628,794,664]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this section, we will discuss the coarse geometry of the Thurston metric. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,681,797,824]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7.1. Short markings. A pants decomposition on $S$ is a collection of mutually disjoint curves which cut $S$ into pairs of pants. A marking $\\mu$ on $S$ is a pants curve system $P$ with additionally a set of transverse curves $Q$ satisfying the following properties. We require each curve $\\alpha \\in P$ to have a unique transverse curve $\\beta \\in Q$ that intersects $\\alpha$ minimally (once or twice) and is disjoint from all other curves in $P$ . We will often say $\\alpha$ and $\\beta$ are dual to each other, and write $\\bar{\\alpha} = \\beta$ or $\\bar{\\beta} = \\alpha$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,830,797,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Given $X \\in \\mathcal{T}(S)$ , a short marking $\\mu_{X}$ on $X$ is a marking where the pants curve system is constructed using the algorithm that picks the shortest curve on $X$ , then the second shortest disjoint from the first, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"26 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"25","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,145,795,233]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and so on. Once the pants curve system is complete, the transverse curves are then chosen to be as short as possible. Note that a short marking on $X$ may not be unique, but all short markings on $X$ form a bounded set in the curve complex. Thus, we will refer to $\\mu_{X}$ as the associated short marking on $X$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,260,795,367]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7.2. Curve graphs. Given two curves $\\alpha$ and $\\beta$ on $S$ , we define their intersection numberi $(\\alpha, \\beta)$ to be the minimal number of intersections between any representatives of homotopy classes of $\\alpha$ and $\\beta$ . Notice that the minimum of intersection numbers for any two distinct (homotopy classes of) simple closed curves is 1 for the once-punctured torus, 2 for the four-holed sphere, and 0 for all other surfaces. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,375,795,465]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The curve graph $C(S)$ is defined as follows: the vertices are homotopy classes of nontrivial simple closed curves and two vertices are connected by an edge if the corresponding curves can be realized to have minimal possible intersection numbers. We equip $C(S)$ with a metric by assigning length one to every edge. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,472,795,667]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"If $S$ is an annulus, the above definition does not give interesting objects since there is only one homotopy class of simple closed curves on any annulus. We need a different definition. To emphasize the difference, we denote by $A$ the (topological) annulus. By an arc on $A$ we always mean a homotopy class of a simple arc $\\omega$ connecting the two boundary components of $A$ where the homotopy is taken relative to the endpoints of $\\omega$ . The intersection $i(\\omega, \\omega')$ of two arcs is the minimal number of intersections between any representatives of homotopy classes of $\\omega$ and $\\omega'$ . The vertices of the curve graph $C(A)$ are arcs on $A$ and the edges are pairs of arcs with zero intersection. We also equip $C(A)$ with a metric as above. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,694,794,729]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7.3. Subsurface projection. For any subsurface $Y$ of $S$ , the subsurface projection ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[403,734,594,753]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\pi_ {Y}: C (S) \\to \\mathcal {P} (C (Y))\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,760,795,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"from $C(S)$ to the set of subsets of the vertices of $C(Y)$ is defined as follows. Suppose first that $Y$ is not an annulus. If $\\alpha$ is disjoint from $Y$ , then $\\pi_Y(\\alpha) = \\emptyset$ . If $\\alpha$ is contained in $Y$ , then $\\pi_Y(\\alpha) = \\alpha$ . If $\\alpha$ intersects $Y$ , then $\\alpha \\cap Y$ is a union of arcs. Let $\\omega$ be such an arc. Let $\\delta$ and $\\delta'$ be the boundary components of $Y$ intersecting $\\omega$ . Let $\\alpha_{\\omega}$ be the collection of boundary components of the $\\epsilon$ -regular neighbourhood of $\\delta \\cup \\omega \\cup \\delta'$ for sufficiently small $\\epsilon$ . The projection $\\pi_Y(\\alpha)$ is then defined ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,118,792,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"26","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"27 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,143,794,180]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"as the collection of $\\alpha_{\\omega}$ for all arcs of $\\alpha \\cap Y$ . From the construction we see that the diameter of $\\pi_Y(\\alpha)$ is at most two. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,188,795,330]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We now consider the case where $S$ is an annulus $A$ with core curve $\\gamma$ . The Gromov compactification of the annulus cover of $S$ corresponding to $\\gamma \\in \\pi_1(S)$ is well-defined and is independent of the choice of the hyperbolic metrics on $S$ . For any simple closed curve $\\alpha \\in C(S)$ , the projection $\\pi_A(\\alpha)$ is defined to be the lifts of $\\alpha$ to the annulus cover that connects two boundary components of the annulus. Notice that any lift has exactly two well-defined endpoints in the Gromov compactification. The diameter of $\\pi_A(\\alpha)$ is also at most two. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,338,794,375]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The projection of multicurves is defined as the union of the projection of each simple closed curve. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,390,784,409]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7.4. Combinatorial model. Recall that for any $X$ and $Y$ in $\\mathcal{T}(S)$ , ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[379,412,616,454]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nd _ {T h} (X, Y) = \\log \\sup _ {\\alpha} \\frac {\\ell_ {\\alpha} (Y)}{\\ell_ {\\alpha} (X)},\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,455,794,531]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\alpha$ ranges over all essential simple closed curves on $S$ . This implies that there is a simple closed curve $\\alpha$ such that $\\log \\frac{\\ell_{\\alpha}(Y)}{\\ell_{\\alpha}(X)}$ is a good estimate of $d_{Th}$ . Lenzhen, Rafi, and Tao proved that such a curve can be chosen within any short marking $\\mu_{X}$ of $X$ : ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,536,795,571]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 7.1 ([37], Theorem E). There exists a constant $C$ depending on the topology of $S$ such that for any $X$ and $Y$ in $\\mathcal{T}(S)$ , ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[349,575,645,617]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left| d _ {T h} (X, Y) - \\log \\max _ {\\alpha \\in \\mu_ {X}} \\frac {\\ell_ {\\alpha} (Y)}{\\ell_ {\\alpha} (X)} \\right| \\leq C.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,628,794,665]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 7.1 is a consequence of the following estimate of lengths of simple closed curves in terms of short markings. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,670,794,726]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Proposition 7.2 ([37], Proposition 3.1). There exists a positive constant $C$ depending on the topology of $S$ , such that for any $X \\in \\mathcal{T}(S)$ , any simple closed curve $\\gamma$ , and any short marking $\\mu_X$ of $X$ , ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,728,723,768]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nC ^ {- 1} \\sum_ {\\alpha \\in \\mu_ {X}} i (\\gamma , \\alpha) \\ell_ {\\bar {\\alpha}} (X) \\leq \\ell_ {\\alpha} (X) \\leq C \\sum_ {\\alpha \\in \\mu_ {X}} i (\\gamma , \\alpha) \\ell_ {\\bar {\\alpha}} (X).\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,772,792,791]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 7.3. (1) A similar estimate also holds for the extremal length: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[228,795,766,837]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nC ^ {- 1} \\sum_ {\\alpha \\in \\mu_ {X}} i (\\gamma , \\alpha) ^ {2} \\mathrm {E x t} _ {\\bar {\\alpha}} (X) \\leq \\mathrm {E x t} _ {\\alpha} (X) \\leq C \\sum_ {\\alpha \\in \\mu_ {X}} i (\\gamma , \\alpha) ^ {2} \\mathrm {E x t} _ {\\bar {\\alpha}} (X).\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,849,794,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2) For similar estimates using twists with respect to some pants decomposition, see [44]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"28 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"27","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,143,794,251]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7.5. Short curves. One way to understand the behavior of Thurston geodesics in the moduli space of Riemann surfaces is to characterize short curves along the corresponding family of hyperbolic surfaces. Such a characterization is known for Teichmüller geodesics (see [59, Theorem 1.1] or [37, Theorem 2.3]). However, the situation is more involved for Thurston geodesics. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,258,794,295]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Definition 7.4. (1) Let $K$ be a positive constant. Two points $X$ and $Y$ in $\\mathcal{T}(S)$ are said to have $K$ -bounded combinatorics if ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[379,301,616,321]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nd _ {C (\\Sigma)} (\\pi_ {\\Sigma} (\\mu_ {X}), \\pi_ {\\Sigma} (\\mu_ {Y})) \\leq K\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[261,327,792,361]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"for any subsurface $\\Sigma \\subset S$ , where $\\mu_{X}$ and $\\mu_{Y}$ are respectively the short markings of $X$ and $Y$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[230,362,792,398]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(2) A path in $\\mathcal{T}(S)$ is said to be $\\epsilon$ cobounded if it is contained in the $\\epsilon$ thick part of $\\mathcal{T}(S)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,406,795,494]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 7.5 ([37], Theorem A). Let $X$ and $Y$ be two points in the $\\epsilon$ -thick part of $\\mathcal{T}(S)$ . If $X$ and $Y$ have $K$ -bounded combinatorics, then every Thurston geodesic from $X$ to $Y$ fellow travels the Teichmüller geodesic from $X$ to $Y$ , and hence is $\\epsilon'$ -cobounded, where $\\epsilon'$ depends on $\\epsilon$ and $K$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,513,794,549]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This reflects a negative-curvature phenomenon of the Thurston metric. More precisely, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,556,794,628]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 7.6 ([37], Theorem C and Corollary D). Let $\\mathcal{G}$ be a Thurston geodesic in $\\mathcal{T}(S)$ whose endpoints have bounded combinatorics. Then the closed point projection to $\\mathcal{G}$ is strongly contracting. In particular, any quasi-geodesic with the same endpoints as $\\mathcal{G}$ fellow travels $\\mathcal{G}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,637,795,832]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 7.7. From Theorem 7.5, we see bounded combinatorics implies $\\epsilon$ -cobounded. One may wonder whether the inverse still holds or not. For the Teichmüller metric, the converse also holds. In fact, two points $X$ and $Y$ in $\\mathcal{T}(S)$ have bounded combinatorics if and only if the Teichmüller geodesic connecting them is cobounded ([59, Theorem 1.1], see also [37, Theorem 2.2]). However, it is not the case for the Thurston metric. There exists $\\epsilon_0 > 0$ such that for any $\\epsilon > 0$ , there are points $X$ and $Y$ in $\\mathcal{T}(S)$ and a Thurston geodesic from $X$ to $Y$ that stays in the $\\epsilon_0$ thick part of $\\mathcal{T}(S)$ , whereas the associated Teichmüller geodesic from $X$ to $Y$ does not stay in the $\\epsilon$ -thick part of $\\mathcal{T}(S)$ [38, Theorem 1.4]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,849,794,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Recall that the Thuston metric is not uniquely geodesic. If we remove the bounded combinatorics assumption, then the fellow traveling ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,118,792,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"28","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"29 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,143,794,198]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"property fails. In fact, for any $D > 0$ , there are points $X, Y, Z$ in $\\mathcal{T}(S)$ and two Thurston geodesics $\\mathcal{G}_1, \\mathcal{G}_2$ from $X$ to $Y$ with the following properties [38, Theorem 1.1]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[243,210,790,297]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"- Geodesics $\\\\mathcal{G}_1$ and $\\\\mathcal{G}_2$ do not fellow travel each other; the point $Z$ lies in path $\\\\mathcal{G}_1$ but is at least $D$ away from any point in $\\\\mathcal{G}_2$ ; \",\"- The geodesic $\\\\mathcal{G}_1$ parameterized in any way in the reverse direction is not a geodesic. In fact, the point $Z$ is at least $D$ away from any point in any geodesic from $Y$ to $X$ . \"]","page_idx":"29","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[200,313,795,383]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"On the other hand, if we consider the projection to the curve complex, which sends a point in $X \\in \\mathcal{T}(S)$ to the set of shortest simple closed curves, then all Thurston geodesics with common endpoints nearly look the same: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,395,795,431]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 7.8 ([38], Theorem 1.2). The shadow of a Thurston geodesic to the curve graph is a reparameterized quasi-geodesic. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,441,795,512]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 7.9. Since the curve graph is Gromov hyperbolic [42], quasi-geodesics with common endpoints fellow travel each other. Hence, for any two points $X$ and $Y$ in $\\mathcal{T}(S)$ , the shadow to the curve graph of different Thurston geodesics form $X$ to $Y$ fellow travel each other. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,532,795,710]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In [19], the authors provided another characterization of short curves along Thurston geodesics. Before stating the result, let us introduce the notion of absolute twisting $d_{\\alpha}(X,Y)$ of two hyperbolic surfaces $X$ and $Y$ relative to a simple closed curve $\\alpha$ . Let $\\omega$ be a geodesic arc on $X$ which is orthogonal to the geodesic representative of $\\alpha$ on $X$ . Let $\\omega'$ be a geodesic arc on $Y$ which is orthogonal to the geodesic representative of $\\alpha$ on $Y$ . Let $\\widehat{X} \\to X$ be the annulus cover of $X$ corresponding to $\\alpha$ . Let $\\widehat{\\alpha}$ be the core curve of $\\widehat{X}$ . Let $\\widehat{\\omega}$ and $\\widehat{\\omega'}$ be respectively lifts of $\\omega$ and $\\omega'$ intersecting $\\widehat{X}$ . The absolute twisting $d_{\\alpha}(X,Y)$ of $X$ and $Y$ relative to $\\alpha$ is defined to be: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[395,720,596,742]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nd _ {\\alpha} (X, Y) = \\min i (\\widehat {\\omega}, \\widehat {\\omega} ^ {\\prime})\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,750,794,823]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where the minimum ranges over all such $\\omega$ and $\\omega'$ and their lifts. (Notice that $\\widehat{X}$ has a well-defined Gromov compatification, and $i(\\widehat{\\omega},\\widehat{\\omega}')$ is considered the minimum intersection number in the given homotopy class relative to their endpoints.) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,830,794,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Recall that for any pair of distinct points $X$ and $Y$ in $\\mathcal{T}(S)$ , there is a well-defined lamination, the maximally stretched lamination $\\Lambda(X,Y)$ (see Section 2.3). A simple closed curve $\\alpha$ is said to interact with the ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"30 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"29","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,143,792,180]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"maximally stretched lamination $\\Lambda(X, Y)$ if it belongs to the lamination or intersects it essentially. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,188,797,277]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 7.10 ([19], Theorem 1.2). There exists a constant $\\epsilon_0$ such that the following statement holds. Let $X$ and $Y$ be two points in the $\\epsilon_0$ -thick part of $\\mathcal{T}(S)$ and let $\\alpha$ be a simple closed curve on $S$ that interacts with $\\Lambda(X, Y)$ . Then the minimum length $\\ell_{\\alpha}$ of $\\alpha$ along any Thurston geodesic from $X$ to $Y$ satisfies: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[274,281,723,319]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nC ^ {- 1} \\cdot d _ {\\alpha} (X, Y) - C ^ {\\prime} \\leq \\frac {1}{\\ell_ {\\alpha}} \\mathrm {L o g} \\frac {1}{\\ell_ {\\alpha}} \\leq C \\cdot d _ {\\alpha} (X, Y) + C ^ {\\prime}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,321,795,359]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $C$ and $C'$ are two constants that depend only on $\\epsilon_0$ , and where $\\operatorname{Log}(x) := \\max \\{1, \\log(x)\\}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,376,794,412]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For more interesting discussions about short curves, we refer to [19, Section 3]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,420,794,455]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Based on the above characterization of short curves, Telpukhovskiy proved that Masur's criterion does not hold in the Thurston metric: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,464,795,518]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 7.11 ([69]). There are Thurston stretch paths in the Teichmüller space $\\mathcal{T}(S_{0,7})$ with minimal, filling, but not uniquely ergodic horocyclic foliation, that stay in the thick part for the whole time. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,536,795,604]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7.6. Length spectrum metric and the product theorem. Inspired by Minsky's product theorem for the Teichmüller metric, Choi and Rafi proved an analogue for the symmetrized metric $d_{L}$ of the Thurston metric: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[323,613,671,633]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nd _ {L} (X, Y) := \\max \\{d _ {T h} (X, Y), d _ {T h} (Y, X) \\}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,638,635,656]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The metric $d_{L}$ is called the length spectrum metric. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,664,794,700]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For any positive constant $\\epsilon$ , consider the $\\epsilon$ -thick part $\\mathrm{Thick}_{\\epsilon}(S)$ and the $\\epsilon$ -thin part $\\mathrm{Thin}_{\\epsilon}(S)$ defined as below: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,705,812,724]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\operatorname{Thick}_{\\epsilon}(S) \\coloneqq \\{X \\in \\mathcal{T}(S) : \\ell_{\\alpha}(X) \\geq \\epsilon \\text{ for every simple closed curve } \\alpha\\}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[207,728,812,748]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\operatorname{Thin}_{\\epsilon}(S) := \\{X \\in \\mathcal{T}(S) : \\ell_{\\alpha}(X) < \\epsilon \\text{ for some simple closed curve } \\alpha\\}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,753,797,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For a multicurve $\\Gamma$ , we define the subset $\\mathrm{Thin}_{\\epsilon}(\\Gamma; S)$ of the $\\epsilon$ -thin part as the set of points $X \\in \\mathcal{T}(S)$ satisfying $\\ell_{\\alpha}(X) < \\epsilon$ if and only if $\\alpha \\in \\Gamma$ . Let $\\mathcal{T}(S \\backslash \\Gamma)$ be the Teichmüller space of the punctured surface homeomorphic to $S \\backslash \\Gamma$ , let $U_i := \\{(x, y) \\in \\mathbb{R} : y > 1 / \\epsilon\\}$ be the subset of the upper half plane. Then the Fenchel-Nielsen coordinates on $\\mathcal{T}(S)$ provide a natural homeomorphism: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[313,866,679,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\Pi : \\operatorname {T h i n} _ {\\epsilon} (\\Gamma ; S) \\rightarrow \\mathcal {T} (S \\backslash \\Gamma) \\times U _ {1} \\times \\dots \\times U _ {k}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,118,790,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"30","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"31 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,143,794,180]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $d_{L(S\\backslash \\Gamma)}$ be the Lipschitz metric on $\\mathcal{T}(S\\backslash \\Gamma)$ . Let $d_{L(\\gamma_i)}$ be a modified metric of the hyperbolic metric on $U_{i}$ . Let ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[336,188,656,209]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nd _ {L _ {\\Gamma}} := \\sup \\left\\{d _ {L (S \\backslash \\Gamma)}, d _ {L (\\gamma_ {1})}, \\dots , d _ {L (\\gamma_ {k})} \\right\\}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,215,429,233]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Choi and Rafi proved that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,243,795,296]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 7.12 ([15], Theorem C). There exists a constant $c$ depending on $\\epsilon$ and the topology of $S$ such that for any multicurve $\\Gamma$ and for any $X$ and $Y$ in $\\mathrm{Thin}_{\\epsilon}(\\Gamma; S)$ , we have ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[348,305,648,325]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left| d _ {L} (X, Y) - d _ {L _ {\\Gamma}} (\\Pi (X), \\Pi (Y)) \\right| \\leq c.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,343,795,450]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Before closing this subsection, let us mention the comparison between the length spectrum metric and the Teichmüller metric. In the thick part of $\\mathcal{T}(S)$ , these two metrics are almost isometric [15, Theorem B], whereas in the whole Teichmüller space they are not comparable [39, 15]. On the other hand, they are almost isometric in the moduli space [41, 40]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[359,479,635,494]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8. COUNTING LATTICE POINTS ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[200,513,794,565]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this section, we will discuss the lattice counting problem about the Thurston metric. Before stating the counting result precisely, we need several definitions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,574,794,628]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Following Bonahon [9], we can embed the Teichmüller space $\\mathcal{T}(S)$ as a subset of the space $\\mathcal{C}(S)$ of geodesic currents in such a way that for every $Y\\in \\mathcal{T}(S)$ and for every curve $\\gamma$ we have ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[426,637,568,656]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\ni (\\gamma , Y) = \\ell_ {Y} (\\gamma).\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,664,792,700]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"One can also embed $\\mathcal{T}(S)$ into the space of functions on $\\mathcal{C}(S)$ as follows. Let $X\\in \\mathcal{T}(S)$ . Define the function $D_{X}$ : ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[356,708,635,770]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} D _ {X}: \\mathcal {C} (S) \\longrightarrow \\mathbb {R} \\\\ \\eta \\longmapsto \\sup _ {\\lambda \\in \\mathcal {M L} (S)} \\frac {i (\\eta , \\lambda)}{\\ell_ {X} (\\lambda)}. \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,777,794,811]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It is clear that $D_X: \\mathcal{C}(S) \\to \\mathbb{R}$ is positive, homogeneous and continuous. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,821,794,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $\\mu_{Th}$ be the Thurston volume on $\\mathcal{ML}(S)$ . For any positive, homogeneous and continuous function $f$ on $\\mathcal{C}(S)$ , define ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[318,866,676,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nm (f) := \\mu_ {T h} (\\{\\lambda \\in \\mathcal {M L} (S): i (\\alpha , \\lambda) \\leq 1 \\}).\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[202,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"32 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[382,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"31","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,143,480,162]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In particular, for any $Y \\in \\mathcal{T}(S)$ , ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[321,169,676,189]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nm (Y) := \\mu_ {T h} (\\{\\lambda \\in \\mathcal {M L} (S): \\ell_ {Y} (\\lambda) \\leq 1 \\}),\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,196,240,210]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[310,213,686,234]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nm (D _ {Y}) := \\mu_ {T h} (\\{\\lambda \\in \\mathcal {M L} (S): D _ {Y} (\\lambda) \\leq 1 \\}).\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,237,300,253]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, let ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[390,253,607,294]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nm _ {S} := \\int_ {\\mathcal {M} (S)} m (Y) d \\mathrm {v o l} _ {w p}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,296,808,330]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\mathcal{M}(S)$ is the moduli space and $d\\mathrm{vol}_{wp}$ represents the Weil-Petersson volume. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,340,797,378]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 8.1 ([60], Theorem 1.1). Let $S$ be a closed orientable surface of genus at least two. Let $X$ and $Y$ be two points in $\\mathcal{T}(S)$ . Then ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[243,381,751,421]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\lim _ {R \\to \\infty} \\frac {\\# \\{\\phi \\in \\mathrm {M C G} (S) : d _ {T h} (X , \\phi (Y)) \\leq R \\}}{e ^ {(6 g - 6) R}} = \\frac {m (D _ {X}) m (Y)}{m _ {S}}.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,426,797,537]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 8.2. Theorem 8.1 is a consequence of a more general counting result due to [60], where the authors counted the mapping class group orbits of filling currents (for more information about this type of counting problems, we refer to [22, 21] and references therein). The analogue result under the Teichmüller metric was first proved in [5] and improved with an error term in [4]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[372,559,624,575]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"9. SHEARING COORDINATES ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[200,593,795,662]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The shearing coordinates for $\\mathcal{T}(S)$ was introduced by Thurston [74]. The shearing operation is a generalization of the earthquake deformation. In Thurston's preprint, the construction is called cataclysm coordinates. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,672,795,727]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $\\Delta$ be an ideal triangle in the hyperbolic plane. There is a unique circle in $\\Delta$ tangent to each edge of $\\Delta$ . If $\\gamma$ is an edge of $\\Delta$ , then the circle intersects $\\gamma$ at some distinguished point. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,734,795,825]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Consider two ideal triangles $\\Delta_a, \\Delta_b$ , with disjoint interiors and a common edge $\\gamma$ . The shear parameter $s_\\gamma$ is defined to be the signed distance of the two distinguished points on $\\gamma$ . The quantity $s_\\gamma$ measures the magnitude of shift (or twist) when we glue $\\Delta_a$ and $\\Delta_b$ . We refer to [7] for details. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,830,795,886]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Fix a finite ideal triangulation $\\lambda$ of $S$ . For each hyperbolic surface $X \\in \\mathcal{T}(S)$ , $\\lambda$ is represented as a geodesic lamination with finitely many leaves whose complementary components are ideal triangles. We can ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,118,792,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"32","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"33 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[200,143,794,180]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"associate with each edge $\\gamma$ of $\\lambda$ a shear parameter $s_{\\gamma}(X)$ . Then the map ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[388,189,607,233]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} s _ {\\lambda}: \\mathcal {T} (S) \\to \\mathbb {R} ^ {| \\lambda |} \\\\ X \\mapsto (s _ {\\gamma} (X)) _ {\\gamma \\in \\lambda} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,242,795,296]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"is an embedding, which is called a shearing coordinates of $\\mathcal{T}(S)$ . Note that the image of $s_{\\lambda}$ is an open convex cone of a linear subspace of the dimension $6g + 2n - 6$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,303,795,375]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For example, every pants decomposition of $S$ can be completed to be a finite ideal triangulation. Then, the corresponding Fenchel-Nielsen parameters of $\\mathcal{T}(S)$ can be extended (up to linear transformation) to the shearing coordinates. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,385,794,439]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remark 9.1. In Mirzakhani's wrok, random hyperbolic surfaces are defined by gluing random pairs of pants. It is also natural to construct random hyperbolic surfaces by gluing ideal triangles randomly. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,458,795,566]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The above construction works for general maximal geodesic laminations. Fix a maximal geodesic lamination $\\lambda$ . Then each $X \\in \\mathcal{T}(S)$ can be associated with a horocyclic measured foliation $F_{\\lambda}(X)$ and a shearing cocycle. In brief, a shearing cocycle is similar to some transverse weights on a train track carrying $\\lambda$ , and the weights measure the shifts of the shear map when one hyperbolic surface is deformed into another. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,571,794,645]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conversely, for any shearing cocycle, one can construct a measured foliation $F_{\\lambda}$ in a neighborhood of $\\lambda$ , whose leaves are cocycles orthogonal to $\\lambda$ . It turns out that, there is a unique hyperbolic structure $X$ on $S$ such that $F_{\\lambda}$ extends to $F_{\\lambda}(X)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,651,794,688]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $\\mathcal{MF}(\\lambda)$ be the set of measured foliations that is totally transverse to $\\lambda$ (see [74, Proposition 9.4]). Then ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,698,794,733]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 9.2 (Thurston). Let $\\lambda$ be a maximal geodesic lamination on $S$ . Then the shear map ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[400,744,596,782]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} F _ {\\lambda}: \\mathcal {T} (S) \\rightarrow \\mathcal {M F} (\\lambda) \\\\ X \\mapsto F _ {\\lambda} (X) \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,792,563,811]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"is a real analytic parametrization of $\\mathcal{T}(S)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,830,794,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The shearing coordinates can be also interpreted as transverse cycles, as did by Bonahon [10]. There are several nice properties and developments of this notion: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"34 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"33","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[232,143,794,409]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(1) The shear map pulls back the Thurston form on $\\\\mathcal{MF}(S)$ to the Weil-Petersson symplectic form on $\\\\mathcal{T}(S)$ [53, 67]. This has been very useful when Mirzakhani [45] proved that the earthquake flow is measured isomorphic to the horocycle flow on moduli space. \",\"(2) The complexified version of transverse cocycles can be used to measure the bending of pleated surfaces, and thus is used to extend Thurston's parametrization to the quasi-Fuchsian space [10]. Furthermore, Thurston's parametrization can be extended to Hitchin representations into $\\\\mathrm{PSL}_n(\\\\mathbb{R})$ [11, 12]. \",\"(3) There are many related works on decorated Teichmüller spaces, quantum Teichmüller spaces and higher Teichmüller spaces, such as [25, 24, 26], ect. \",\"(4) There is a construction of shearing coordinates on the universal Teichmüller space, see [58, 63, 64] \"]","page_idx":"34","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[199,435,792,506]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"When $\\lambda$ is not a maximal geodesic lamination, the horocyclic foliation is no longer well-defined. Such a difficulty was already encountered in the case of surfaces with boundaries, when Alessandrini-Disarlo [3] constructed geodesics for the arc metric. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[199,513,792,621]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In general, Calderon-Farre [13] defined orthogeodesic foliations associated with $\\lambda$ . The orthogeodesic foliations are constructed on complementary subsurfaces. They showed that the restriction of the orthogeodesic foliation to each component of $S \\setminus \\lambda$ completely determines the hyperbolic structure on that piece. Thus they generalized the shearing coordinates of $\\mathcal{T}(S)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,628,792,666]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We conclude this section with the following result of Théret [71], which improves the result of [7, Theorem 1.3]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,690,795,779]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 9.3 ([71], Theorem 1.1). Let $\\mu$ be a measured geodesic lamination transverse to the complete geodesic lamination $\\lambda$ on $S$ . Then the length function $\\ell_{\\mu}$ is a convex function of the shear coordinates defined over $\\mathcal{T}(S)$ associated with $\\lambda$ , and $\\ell_{\\mu}$ is strictly convex whenever $\\mu$ intersects all leaves of $\\lambda$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[199,813,792,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In particular, lengths functions are convex along stretch lines. An interesting corollary is that the length of the horocyclic foliation is strictly decreasing on a stretch line and converges to zero as $t$ converges to infinity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,118,792,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"34","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"35 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[277,145,718,161]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10. GENERALIZATION OF THE THURSTON METRIC ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[200,180,794,251]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this section, we shall discuss some generalizations of the Thurston metric. As we mentioned earlier, there is a generalization to the setting of hyperbolic surface with geodesic boundary components, the arc metric, see Remark 5.4. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,258,795,401]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Gueritaud-Kassel [28] considered a pair $(j,\\rho)$ of representations of a discrete group $\\Gamma_0$ into $G = \\operatorname{Isom}(\\mathbb{H}^n)$ such that $j$ is injective with $j(\\Gamma_0)$ discrete and geometrically finite. They showed that, when the minimal Lipschitz constant is strictly greater than 1, there exists a geodesic lamination that is \"maximally stretched\" by any extremal $(j,\\rho)$ -equivariant Lipschitz map $f:\\mathbb{H}^n\\to \\mathbb{H}^n$ . As an application, they generalized the two-dimensional results and constructions of Thurston and extend the Thurston metric on Teichmüller space to higher dimension. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,409,794,445]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let us denote the minimal Lipschitz constant of $(j,\\rho)$ -equivariant map by $L(j,\\rho)$ . A related constant is ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[388,467,609,507]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nK (j, \\rho) = \\log \\sup _ {\\gamma} \\frac {\\lambda (\\rho (\\gamma))}{\\lambda (j (\\gamma))},\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,510,794,559]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\lambda$ denotes the translation length of the element, and the supremum is taken over all hyperbolic elements in $\\gamma \\in \\Gamma_0$ . It is obvious that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[423,564,571,584]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nK (j, \\rho) \\leq L (j, \\rho).\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,595,794,667]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $M = \\mathbb{H}^n / \\Gamma_0$ be a geometrically finite hyperbolic manifolds. The Teichmüller space $\\mathcal{T}(M)$ is defined to be the set of conjugacy classes of geometrically finite representations of $\\Gamma_0$ . For $j, \\rho \\in \\mathcal{T}(M)$ , denote the critical exponents of $j$ and $\\rho$ by $\\delta(j)$ and $\\delta(\\rho)$ , respectively. Then ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,676,516,695]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Theorem 10.1 ([28]). The function ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[372,700,620,742]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nd _ {\\mathrm {T h}} (j, \\rho) = \\log \\left(L (j, \\rho) \\frac {\\delta (\\rho)}{\\delta (j)}\\right)\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[202,747,578,766]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"defines an asymmetry metric on $\\mathcal{T}(M)$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,784,794,816]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We call the above metric a generalized Thurston metric. Another version is ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[205,821,625,862]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\overline {{d}} _ {\\mathrm {T h}} (j, \\rho) = \\log \\left(K (j, \\rho) \\frac {\\delta (\\rho)}{\\delta (j)}\\right). \\tag {4}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[200,867,792,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As pointed out by Guéritaud-Kassel, the two metrics differ in general. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[202,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"36 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"35","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[200,143,795,180]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Question 1. Is the generalized Thurston metric $d_{\\mathrm{Th}}$ Finsler? How to construct geodesics of $d_{\\mathrm{Th}}$ ? ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,202,795,292]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Recently, Sapir [62] extended the Thurston metric to the space of projective filling currents; Carvajales-Dai-Pozzetti-Wienhard [14] generalized the Thurston metric and the associated Finsler norm to Anosov representations of surface groups, including the space of Hitchin representations. The distance formula is similar to (4). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,299,795,371]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Thurston metric has an analogue in Outer space, see [75] for a discussion. Just like the Thurston metric on $\\mathcal{T}(S)$ , this metric is not symmetric. It was used by Bestvina [8] to give a Bers-like proof of the train track theorem for fully irreducible automorphisms of $F_{n}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,378,794,398]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Regarding the extremal Lipschitz maps, Thurston [74] suggested that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[258,414,754,484]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"\"I currently think that a characterization of minimal stretch maps should be possible in a considerably more general context (in particular, to include some version for all Riemannian surfaces)...\" ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,501,689,518]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For related results along this line, we refer to [49, 16, 17]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[200,527,794,617]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, let us mention that it is impossible to deform hyperbolic metrics of finite area in $\\mathcal{T}(S)$ such that no length of any closed geodesic is increased. This is a typical example of the (marked) length spectrum rigidity problem, which is extensively studied in geometry and dynamics, see [46, 18, 29] for examples. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[437,662,558,678]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"REFERENCES ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[210,686,795,883]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[1] S.I. Al'ber. On n-dimensional problems in the calculus of variations in the large. In Sov. Math. Dokl, volume 5, page 26, 1964. \",\"[2] D. Alessandrini, L. Liu, A. Papadopoulos, and W. Su. The horofunction compactification of Teichmüller spaces of surfaces with boundary. Topology Appl., 208:160-191, 2016. \",\"[3] Daniele Alessandrini and Valentina Disarlo. Generalizing stretch lines for surfaces with boundary. Int. Math. Res. Not. IMRN, (23):18919-18991, 2022. \",\"[4] Francisco Arana-Herrera. Effective mapping class group dynamics, i: Counting lattice points in teichmüller space. Duke Mathematical Journal, 1(1):1-93, 2023. \",\"[5] Jayadev Athreya, Alexander Bufetov, Alex Eskin, and Maryam Mirzakhani. Lattice point asymptotics and volume growth on Teichmüller space. Duke Math. J., 161(6):1055-1111, 2012. \"]","page_idx":"36","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[271,116,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,118,792,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"36","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"37 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[204,146,795,840]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[6] Assaf Bar-Natan. Geodesic Envelopes in Teichmuller Space Equipped with the Thurston Metric. ProQuest LLC, Ann Arbor, MI, 2022. Thesis (Ph.D.)-University of Toronto (Canada). \",\"[7] M. Bestvina, K. Bromberg, K. Fujiwara, and J. Souto. Shearing coordinates and convexity of length functions on Teichmüller space. Amer. J. Math., 135(6):1449-1476, 2013. \",\"[8] Mladen Bestvina. A Bers-like proof of the existence of train tracks for free group automorphisms. Fund. Math., 214(1):1-12, 2011. \",\"[9] Francis Bonahon. The geometry of Teichmüller space via geodesic currents. Inventiones mathematicae, 92(1):139-162, 1988. \",\"[10] Francis Bonahon. Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form. Toulouse. Faculté des Sciences. Annales Mathématiques. Série 6, 5(2):233-297, 1996. \",\"[11] Francis Bonahon and Guillaume Dreyer. Parameterizing Hitchin components. Duke Mathematical Journal, 163(15):2935-2975, 2014. \",\"[12] Francis Bonahon and Guillaume Dreyer. Hitchin characters and geodesic laminations. Acta Math, 218:201-295, 2017. \",\"[13] Aaron Calderon and James Farre. Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow. arXiv:2102.13124v2, Geometry & Topology, to appear, 2021. \",\"[14] León Carvajales, Xian Dai, Beatrice Pozzetti, and Anna Wienhard. Thurston's asymmetric metrics for Anosov representations. arXiv:2210.05292, 2022. \",\"[15] Young-Eun Choi and Kasra Rafi. Comparison between Teichmüller and Lipschitz metrics. Journal of the London Mathematical Society. Second Series, 76(3):739-756, 2007. \",\"[16] Georgios Daskalopoulos and Karen Uhlenbeck. Transverse Measures and best Lipschitz and Least Gradient maps. October 2020. \",\"[17] Georgios Daskalopoulos and Karen Uhlenbeck. Analytic properties of stretch maps and geodesic laminations. May 2022. \",\"[18] Moon Duchin, Christopher J Leininger, and Kasra Rafi. Length spectra and degeneration of flat metrics. Inventiones mathematicae, 182(2):231-277, 2010. \",\"[19] David Dumas, Anna Lenzhen, Kasra Rafi, and Jing Tao. Coarse and fine geometry of the Thurston metric. Forum of Mathematics. Sigma, 8:Paper No. e28, 58, 2020. \",\"[20] James Eells, Jr. and J. H. Sampson. Harmonic mappings of Riemannian manifolds. Amer. J. Math., 86:109-160, 1964. \",\"[21] Viveka Erlandsson and Juan Souto. Mirzakhani's curve counting and geodesic currents, volume 345 of Progress in Mathematics. Birkhäuser/Springer, Cham, [2022] ©2022. \",\"[22] Viveka Erlandsson and Caglar Uyanik. Length functions on currents and applications to dynamics and counting. In In the tradition of Thurston—geometry and topology, pages 423–458. Springer, Cham, [2020] ©2020. \",\"[23] Albert Fathi, François Laudenbach, and Valentin Poénaru. Thurston's work on surfaces, volume 48 of Mathematical Notes. Princeton University Press, Princeton, NJ, 2012. Translated from the 1979 French original by Djun M. Kim and Dan Margalit. \"]","page_idx":"37","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[202,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"38 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,117,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"37","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[204,146,794,857]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[24] Vladimir Fock and Alexander Goncharov. Moduli spaces of local systems and higher Teichmüller theory. *Publications Mathématiques de l'IHÉS*, 103:1-211, 2006. \",\"[25] Vladimir V Fock and Alexander B Goncharov. Dual Teichmüller and lamination spaces. arXiv preprint math/0510312, 2005. \",\"[26] Vladimir V Fock and Alexander B Goncharov. Moduli spaces of convex projective structures on surfaces. Advances in Mathematics, 208(1):249-273, 2007. \",\"[27] M. Gromov. Hyperbolic manifolds, groups and actions. In Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), volume 97 of Ann. of Math. Stud., pages 183-213. Princeton Univ. Press, Princeton, N.J., 1981. \",\"[28] François Guéritaud and Fanny Kassel. Maximally stretched laminations on geometrically finite hyperbolic manifolds. Geometry & Topology, 21(2):693-840, 2017. \",\"[29] Colin Guillarmou and Thibault Lefeuvre. The marked length spectrum of anosov manifolds. 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Springer-Verlag, Berlin, 1984. \",\"[37] Anna Lenzhen, Kasra Rafi, and Jing Tao. Bounded combinatorics and the Lipschitz metric on Teichmüller space. Geometriae Dedicata, 159:353-371, 2012. \",\"[38] Anna Lenzhen, Kasra Rafi, and Jing Tao. The shadow of a Thurston geodesic to the curve graph. Journal of Topology, 8(4):1085-1118, 2015. \",\"[39] Zhong Li. Length spectrums of Riemann surfaces and the Teichmüller metric. Bull. London Math. Soc., 35(2):247-254, 2003. \",\"[40] L. Liu, H. Shiga, W. Su, and Y. Zhong. Almost-isometry between the Teichmüller metric and the length-spectrum metric on reduced moduli space for surfaces with boundary. Trans. Amer. Math. Soc., 369(9):6429-6464, 2017. \",\"[41] L. Liu and W. Su. Almost-isometry between Teichmüller metric and length-spectrum metric on moduli space. Bull. Lond. Math. Soc., 43(6):1181-1190, 2011. \",\"[42] Howard A. Masur and Yair N. Minsky. Geometry of the complex of curves. I. Hyperbolicity. *Invent. Math.*, 138(1):103-149, 1999. \",\"[43] Yair N Minsky. Harmonic maps, length, and energy in Teichmüller space. Journal of Differential Geometry, 35(1):151-217, 1992. \"]","page_idx":"38","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[272,117,723,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"38","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,118,792,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"38","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"39 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[204,146,795,856]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[44] Yair N. Minsky. Extremal length estimates and product regions in Teichmüller space. Duke Math. J., 83(2):249-286, 1996. \",\"[45] Maryam Mirzakhani. Ergodic theory of the earthquake flow. International Mathematics Research Notices, 2008(9):1073-7928, year=2008, publisher=OUP. \",\"[46] Jean-Pierre Otal. Le spectre marqué des longueurs des surfaces à courbure négative. Annals of Mathematics, 131(1):151-162, 1990. \",\"[47] Huiping Pan. Local Rigidity of the Teichmüller space with the Thurston metric. Science China Mathematics, https://doi.org/10.1007/s11425-021-2020-0, 2023. \",\"[48] Huiping Pan and Michael Wolf. Envelopes of the Thurston metric on Teichmüller space. in preparation. \",\"[49] Huiping Pan and Michael Wolf. Ray structures on Teichmüller space. arXiv:2206.01371, June 2022. \",\"[50] A. Papadopoulos and W. Su. On the Finsler structure of Teichmüller's metric and Thurston's metric. Expo. Math., 33(1):30-47, 2015. \",\"[51] Athanase Papadopoulos. On Thurston's boundary of Teichmüller space and the extension of earthquakes. Topology Appl., 41(3):147-177, 1991. \",\"[52] Athanase Papadopoulos, editor. Handbook of Teichmüller theory. Vol. III, volume 17 of IRMA Lectures in Mathematics and Theoretical Physics. European Mathematical Society (EMS), Zürich, 2012. \",\"[53] Athanase Papadopoulos and Robert C Penner. The Weil-Petersson symplectic structure at Thurston's boundary. Transactions of the American Mathematical Society, 335(2):891-904, 1993. \",\"[54] Athanase Papadopoulos and Guillaume Théret. On Teichmüller's metric and Thurston's asymmetric metric on Teichmüller space. In Handbook of Teichmüller theory. Vol. I, volume 11 of IRMA Lect. Math. Theor. Phys., pages 111-204. Eur. Math. Soc., Zürich, 2007. \",\"[55] Athanase Papadopoulos and Guillaume Théret. Some Lipschitz maps between hyperbolic surfaces with applications to Teichmüller theory. Geometriae Dedicata, 161:63-83, 2012. \",\"[56] Athanase Papadopoulos and Sumio Yamada. Deforming hyperbolic hexagons with applications to the arc and the Thurston metrics on Teichmüller spaces. Monatshefte für Mathematik, 182(4):913-939, 2017. \",\"[57] R. C. Penner and J. L. Harer. Combinatorics of train tracks, volume 125 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, 1992. \",\"[58] Robert C Penner. Universal constructions in Teichmüller theory. Advances in Mathematics, 98(2):143-215, 1993. \",\"[59] Kasra Rafi. A characterization of short curves of a Teichmüller geodesic. Geom. Topol., 9:179-202, 2005. \",\"[60] Kasra Rafi and Juan Souto. Geodesic currents and counting problems. Geom. Funct. Anal., 29(3):871-889, 2019. \",\"[61] J. H. Sampson. Some properties and applications of harmonic mappings. Ann. Sci. École Norm. Sup. (4), 11(2):211-228, 1978. \",\"[62] Jenya Sapir. An extension of the Thurston metric to projective filling currents. arXiv preprint arXiv:2210.08130, 2022. \"]","page_idx":"39","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[204,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"40 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[383,116,612,130]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"39","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN AND WEIXU SU ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[204,145,795,766]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[63] Dragomir Šarić. Circle homeomorphisms and shears. Geometry & Topology, 14(4):2405-2430, 2010. \",\"[64] Dragomir Šaric, Yilin Wang, and Catherine Wolfram. Circle homeomorphisms with square summable diamond shears. arXiv preprint arXiv:2211.11497, 2022. \",\"[65] Richard Schoen and Shing Tung Yau. On univalent harmonic maps between surfaces. Invent. Math., 44(3):265-278, 1978. \",\"[66] Richard M. Schoen. Analytic aspects of the harmonic map problem. In Seminar on nonlinear partial differential equations (Berkeley, Calif., 1983), volume 2 of Math. Sci. Res. Inst. Publ., pages 321-358. Springer, New York, 1984. \",\"[67] Yasar Sozen and Francis Bonahon. The Weil-Petersson and Thurston symplectic forms. Duke Math. J., 108(3):581-597, 2001. \",\"[68] Weixu Su. Problems on the Thurston metric. In Handbook of Teichmüller theory. Vol. V, volume 26 of IRMA Lect. Math. Theor. Phys., pages 55-72. Eur. Math. Soc., Zürich, 2016. \",\"[69] Ivan Telpukhovskiy. Masur's criterion does not hold in the thurston metric. arXiv:1903.00845v2, 2022. \",\"[70] Guillaume Théret. On the negative convergence of Thurston's stretch lines towards the boundary of Teichmüller space. Annales Academiae Scientiarum Fennicae. Mathematica, 32(2):381-408, 2007. \",\"[71] Guillaume Théret. Convexity of length functions and Thurston's shear coordinates. arXiv:1408.5771, 2014. \",\"[72] William P. Thurston. Earthquakes in two-dimensional hyperbolic geometry. In Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984), volume 112 of London Math. Soc. Lecture Note Ser., pages 91-112. Cambridge Univ. Press, Cambridge, 1986. \",\"[73] William P Thurston. The Geometry and Topology of Three-Manifolds: With a Preface by Steven P. Kerckhoff, volume 27. American Mathematical Society, 2022. \",\"[74] William P. Thurston. Minimal stretch maps between hyperbolic surfaces. In Collected works of William P. Thurston with commentary. Vol. I. Foliations, surfaces and differential geometry, pages 533-585. Amer. Math. Soc., Providence, RI, [2022] ©2022. 1986 preprint, 1998 eprint. \",\"[75] Karen Vogtmann. On the geometry of outer space. Bulletin of the American Mathematical Society, 52(1):27-46, 2015. \",\"[76] Cormac Walsh. The horoboundary and isometry group of Thurston's Lipschitz metric. In Handbook of Teichmüller theory. Vol. IV, volume 19 of IRMA Lect. Math. Theor. Phys., pages 327-353. Eur. Math. Soc., Zürich, 2014. \",\"[77] Michael Wolf. The Teichmüller theory of harmonic maps. Journal of Differential Geometry, 29(2):449-479, 1989. \",\"[78] Michael Wolf. Measured foliations and harmonic maps of surfaces. 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","text_format":null,"text_level":null,"type":"text"},{"bbox":"[526,542,686,558]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Thurston metric, 5 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[526,560,676,575]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Thurstonnorm,7 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[526,577,720,594]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Thurston stretch ray, 9 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[526,595,707,611]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"transverse measure, 4 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[204,645,792,675]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"HUIPING PAN, SCHOOL OF MATHEMATICS, SOUTH CHINA UNIVERSITY OF TECHNOLOGY, 510641, GUANGZHOU, CHINA","text_format":null,"text_level":null,"type":"text"},{"bbox":"[223,684,485,699]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Email address: panhp@scut.edu.cn ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[204,718,792,750]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"WEIXU SU, SCHOOL OF MATHEMATICS, SUN YAT-SEN UNIVERSITY, 510275, GUANGZHOU, CHINA ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[223,758,527,773]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Email address: suwx9@mail.sysu.edu.cn ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[204,118,222,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"41","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"42 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[220,183,774,219]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[372,241,620,257]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[259,323,736,443]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABSTRACT. This chapter is a survey about the Thurston metric on the Teichmüller space. The central issue is the constructions of extremal Lipschitz maps between hyperbolic surfaces. We review several constructions, including the original work of Thurston. Coarse geometry and isometry rigidity of the Thurston metric, relation between the Thurston metric and the Thurston compactification are discussed. Some recent generalizations and developments of the Thurston metric are sketched. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,455,702,472]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mathematical classification (2010) 32G15; 30F45; 30F60. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[447,541,549,556]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CONTENTS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[223,575,795,830]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1. Introduction 2 \\\",\\\"2. Background 3 \\\",\\\"3. Extremal Lipschitz maps and geodesic rays 8 \\\",\\\"4. Harmonic stretch lines 19 \\\",\\\"5. Thurston boundary 22 \\\",\\\"6. Isometry Rigidity 24 \\\",\\\"7. Coarse Geometry 26 \\\",\\\"8. Counting lattice points 32 \\\",\\\"9. Shearing coordinates 33 \\\",\\\"10. Generalization of the Thurston metric 36 \\\"]\",\n \"page_idx\": \"0\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[223,840,792,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References 37 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[223,867,792,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Index 41 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[22,238,60,688]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"arXiv:2307.03874v1 [math.GT] 8 Jul 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[493,886,503,896]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[416,145,581,160]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. INTRODUCTION \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,180,794,303]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This survey aims to give a brief exposition of recent results on the Thurston metric. This asymmetric metric, defined by Thurston in his 1986 preprint [74], has a lot of beautiful geometric and analytic properties. Thurston's original investigation, just like his many other masterpieces, are based on first principles. Until now, that preprint [74] together with Chapter 8 and Chapter 9 of [73], are excellent references for learning hyperbolic geometry. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,311,795,383]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Aiming for a geometric understanding of the Teichmüller space from the point of view of hyperbolic surfaces and Lipschitz maps, in parallel with the point of view of Riemann surfaces and quasiconformal maps, Thurston [74] considered the following problem: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[259,398,736,434]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Given any two hyperbolic surfaces $X$ and $Y$ , what is the least possible value of the global Lipschitz constant \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[392,441,607,483]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nL (\\\\phi) := \\\\sup _ {p \\\\neq q} \\\\frac {d (\\\\phi (p)) , \\\\phi (q)}{d (p , q)}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[259,491,736,525]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"for a homeomorphism $\\\\phi : X \\\\to Y$ in a given homotopy class? \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,541,794,612]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Thurston gave a geometric construction of extremal Lipschitz homeomorphisms realizing the extremal Lipschitz constant $\\\\operatorname{Lip}(X, Y)$ in the homotopy class of the identity map, and proved that the extremal Lipschitz constant is the same as another geometric quantity: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[403,621,596,659]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nK (X, Y) := \\\\sup _ {\\\\alpha} \\\\frac {\\\\ell_ {\\\\alpha} (Y)}{\\\\ell_ {\\\\alpha} (X)}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,667,794,720]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\ell_{\\\\alpha}(\\\\cdot)$ is the length of the geodesic representative of $\\\\alpha$ on the corresponding surface and $\\\\alpha$ ranges over all nontrivial homotopy classes of simple closed curves. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,729,795,763]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For any two points $X$ and $Y$ in the Teichmüller space, the Thurston metric is defined as: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[382,777,616,796]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nd _ {T h} (X, Y) := \\\\log \\\\operatorname {L i p} (X, Y).\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,805,794,842]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Among others, Thurston proved that this metric is Finslerian, asymmetric, geodesic but not uniquely geodesic [74]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,849,794,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Through the efforts of many mathematicians, we now have a fairly clear picture of this metric: the horofunction boundary, the isometry \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,118,215,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,145,794,217]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"group, the coarse geometry, the analytic construction of extremal Lipschitz maps and geodesic rays, to name a few. Due to its geometric inspiration, the Thurston metric has been generalized to deformation spaces of other geometric structures and provides new perspectives there. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,223,795,383]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this survey about the Thurston metric, we restrict our attention to recent research. We will look more carefully at several constructions of the extremal Lipschitz maps. Relevant developments will be briefly sketched or summarized without proofs. Other surveys on the Thurston metrics include [54, 50, 68]. In particular, the article [54] contains foundational background material, both on the Teichmüller metric and the Thurston metric. As for prerequisites, the reader is expected to be familiar with hyperbolic geometry and Teichmüller theory. We recommend [23, 35]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,391,795,602]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Here is the outline of this paper. In §2, we review some of the standard facts on Teichmüller space, including the Thurston norm. In §3, we provide various constructions of extremal Lipschitz maps and geodesic rays of the Thurston metric. In §4, we deal with a special type of geodesics, called harmonic stretch lines, and discuss two versions of the Thurston (co-)geodesic flows. In §5, we describe the Thurston boundary and its identification with the horofunction boundary. In §6, we illustrate the isometry rigidity of the Thurston metric, both globally and infinitesimally. In §7 we discuss the coarse geometry of the Thurston metric. In §8, we are concerned with the lattice counting problem. In §9, we discuss the shearing coordinates. In §10, we sketch several generalizations of the Thurston metric. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,611,795,681]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgements. We would like to thank Athanase Papadopoulos for the opportunity of writing this article, for his patience during the preparation of the manuscript, and for suggesting several improvements on the exposition. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[426,709,570,724]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. BACKGROUD \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,743,795,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.1. Teichmüller space. Let $S$ be an orientable closed surface of genus at least two. The Teichmüller space $T(S)$ is the space of equivalence classes of complex structures on $S$ , where two complex structures $X$ and $Y$ are said to be equivalent if there exists a conformal map $X \\\\to Y$ which is homotopic to the identity map. By the Uniformization Theorem, the Teichmüller space $T(S)$ is also the space of equivalence classes of hyperbolic structures on $S$ , where two hyperbolic structures $X$ and $Y$ are said to be equivalent if there exists an isometry $X \\\\to Y$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[782,118,794,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,143,794,181]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"which is homotopic to the identity map. For simplicity, we denote the equivalence class of the complex/hyperbolic structure $X$ by $X$ itself. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,217,792,306]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2. Geodesic laminations and measured geodesic laminations. Let $X \\\\in \\\\mathcal{T}(S)$ be a hyperbolic surface. A geodesic lamination $\\\\lambda$ on $X$ is a closed subset of $X$ which can be decomposed as a disjoint union of simple geodesics. Typical examples are simple closed geodesics. A multicurve is a disjoint union of distinct simple closed geodesics. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,314,542,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $\\\\lambda$ be a geodesic lamination. Then \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[245,349,792,417]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- $\\\\\\\\lambda$ is called maximal if it cuts $X$ into ideal triangles, i.e. $X \\\\\\\\backslash \\\\\\\\lambda$ is a union of ideal triangles; \\\",\\\"- $\\\\\\\\lambda$ is called chain-recurrent if it is the Hausdorff limit of multicurves. \\\"]\",\n \"page_idx\": \"3\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[200,436,794,472]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A chain-recurrent geodesic lamination is said to be maximal if it is not contained in any other chain-recurrent geodesic lamination. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,479,795,551]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"One can equip the set of geodesic laminations on $X$ with the Hausdorff metric and the corresponding Hausdorff topology. With this topology, the set of chain-recurrent geodesic laminations is a closed subset of the space of geodesic laminations [74, Proposition 6.2]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,559,795,664]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Notice that the space of geodesic laminations is independent of the choice of hyperbolic metrics in the following sense. Let $X' \\\\in \\\\mathcal{T}(S)$ be another hyperbolic surface. There is a natural one-to-one correspondence between the space of (resp. chain-recurrent) geodesic laminations on $X$ and the space of (resp. chain-recurrent) geodesic laminations on $X'$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,674,794,728]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $\\\\lambda$ be a geodesic lamination. A transverse measure $\\\\mu$ on $\\\\lambda$ is an assignment of a Radon measure $d\\\\mu_{\\\\tau}$ on each arc $\\\\tau$ transverse to $\\\\lambda$ , subject to the following conditions: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[245,744,792,797]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- if the arc $\\\\\\\\tau'$ is a subarc of $\\\\\\\\tau$ then $d\\\\\\\\mu_{\\\\\\\\tau'} = d\\\\\\\\mu_{\\\\\\\\tau}|_{\\\\\\\\tau'}$ , \\\",\\\"- if two arcs $\\\\\\\\tau$ and $\\\\\\\\tau'$ are homotopic through a family of arcs transverse to $\\\\\\\\lambda$ , then the homotopy sends $d\\\\\\\\mu_{\\\\\\\\tau'}$ to $d\\\\\\\\mu_{\\\\\\\\tau}$ . \\\"]\",\n \"page_idx\": \"3\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[200,813,794,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A geodesic lamination $\\\\lambda$ with a transverse measure $d\\\\mu$ is called a measured geodesic lamination. Typical examples of measured laminations are weighed simple closed curves and weighted multicurves. Usually, we will simply denote a measured geodesic lamination $(\\\\lambda, d\\\\mu)$ by $\\\\lambda$ . For \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,118,215,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,143,794,162]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"any simple closed curve $\\\\gamma$ , the intersection number $i(\\\\lambda, \\\\gamma)$ is defined as: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[415,167,583,208]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\ni (\\\\lambda , \\\\gamma) := \\\\inf \\\\int_ {\\\\gamma^ {\\\\prime}} d \\\\mu\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,212,720,231]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\gamma^\\\\prime$ ranges over all simple closed curves homopotic to $\\\\gamma$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,238,797,417]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As we mentioned above, the space of geodesic laminations is independent of the choice of the hyperbolic metrics. So is the space of measured geodesic laminations. Let $\\\\mathcal{ML}(S)$ be the space of measured geodesic laminations, equipped with the weak- $*$ topology: a sequence of measured laminations $\\\\lambda_{n}$ converges to $\\\\lambda$ if $i(\\\\lambda_n,\\\\gamma)\\\\to i(\\\\lambda ,\\\\gamma)$ for every simple closed curve $\\\\alpha$ . With this topology, $\\\\mathcal{ML}(S)$ is homeomorphic to $\\\\mathbb{R}^{6g - 6 + 2n}$ , where $g$ and $n$ are respectively the genus and the number of punctures of $S$ (see for instance [57]). Let $\\\\mathcal{PML}(S)\\\\coloneqq \\\\mathcal{ML}(S) / _{\\\\mathbb{R}^+}$ be the space of projective classes of measured laminations. The set of weighted simple closed curves is dense in both $\\\\mathcal{ML}(S)$ and $\\\\mathcal{PML}(S)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,434,794,487]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.3. The Thurston metric and the maximally stretched lamination. For any two hyperbolic surfaces $X$ and $Y$ in $\\\\mathcal{T}(S)$ , the extremal Lipschitz constant from $X$ to $Y$ is defined as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[395,493,601,520]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\operatorname {L i p} (X, Y) := \\\\inf _ {f} \\\\{L (f) \\\\}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,526,794,580]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $L(f)$ is the Lipschitz constant of $f$ and where $f$ ranges over all Lipschitz homeomorphsims from $X$ to $Y$ in the homotopy class of the identity map. The Thurston metric $d_{Th}$ is defined as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,585,614,606]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\quad \\\\left. d _ {T h} (X, Y) := \\\\log \\\\operatorname {L i p} (X, Y) \\\\right. \\\\tag {1}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,611,794,646]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Thurston [74, Theorem 8.5] gave another characterization of this metric in terms of simple closed curves: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,651,614,691]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nd _ {T h} (X, Y) = \\\\log \\\\sup _ {\\\\alpha} \\\\frac {\\\\ell_ {\\\\alpha} (Y)}{\\\\ell_ {\\\\alpha} (X)} \\\\tag {2}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,695,794,767]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\ell_{\\\\alpha}(\\\\cdot)$ represents the length of the (unique) geodesic representative of $\\\\alpha$ and where $\\\\alpha$ ranges over all homotopically nontrivial simple closed curves. Since weighted simple closed curves are dense in $\\\\mathcal{ML}(S)$ , one can rewrite the above identity as: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[362,771,635,810]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nd _ {T h} (X, Y) = \\\\log \\\\max _ {\\\\alpha \\\\in \\\\mathcal {M L} (S)} \\\\frac {\\\\ell_ {\\\\alpha} (Y)}{\\\\ell_ {\\\\alpha} (X)}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,813,795,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In general, the measured laminations realizing the maximal ratio of length are not unique. For instance, if $\\\\lambda$ is a non-uniquely ergodic measured lamination which realizes the maximal ratio of length from $X$ to $Y$ , then any measured lamination with the same support as $\\\\lambda$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[782,118,794,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,143,794,217]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"also realizes the maximal ratio from $X$ to $Y$ . Nevertheless, Thurston introduced the notion of maximal ratio-maximizing chain-recurrent geodesic lamination (the maximally stretched lamination for short) from $X$ to $Y$ , which is unique. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[205,222,795,489]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Given $X$ and $Y$ in $\\\\mathcal{T}(S)$ , the maximally stretched lamination $\\\\Lambda(X, Y)$ from $X$ to $Y$ is the largest chain recurrent geodesic lamination $\\\\lambda$ with a following property: there exists an $\\\\exp(d_{Th}(X, Y))$ -Lipschitz map, homotopic to the identity map, from a neighbourhood of $\\\\lambda$ on $X$ to a neighbourhood of $\\\\lambda$ on $Y$ which takes leaves of $\\\\lambda$ on $X$ to corresponding leaves of $\\\\lambda$ on $Y$ by multiplying arc length by a factor of $\\\\exp(d_{Th}(X, Y))$ . It is also the union of all chain recurrent geodesic laminations with the aforementioned property [74, Theorem 8.2]. Equivalently, the maximally stretched lamination is also the union of chain-recurrent laminations to which the restriction of every Lipschitz map from $X$ to $Y$ with the extremal Lipschitz constant, which is homotopic to the identity, takes leaves of $\\\\lambda$ on $X$ to corresponding leaves of $\\\\lambda$ on $Y$ by multiplying arclength by a factor of $\\\\exp(d_{Th}(X, Y))$ . (For the equivalence between these two descriptions, we refer to [28, Section 9], see also [17, Section 5] for a related discussion.) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,497,794,515]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Regarding the behavior of maximally stretched laminations, we have: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,518,795,592]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 2.1 ([74], Theorem 8.4). Let $X, Y \\\\in \\\\mathcal{T}(S)$ be any two distinct hyperbolic surfaces. If $X_{i}$ and $Y_{i}$ are sequences of hyperbolic surfaces converging to $X$ and $Y$ respectively, then $\\\\Lambda(X, Y)$ contains any lamination in the limit set of $\\\\Lambda(X_{i}, Y_{i})$ in the Hausdorff topology. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,604,794,676]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Any Lipschitz map $f$ from $X$ to $Y$ realizing the extremal Lipschitz constant $\\\\operatorname{Lip}(X, Y)$ is called an extremal Lipschitz map. If moreover, $f$ maximally stretches exactly along the maximally stretched lamination $\\\\Lambda(X, Y)$ , then it is called an optimal Lipschitz map from $X$ to $Y$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,684,777,703]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Before closing this subsection, let us mention the following result: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,707,658,728]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 2.2 ([74], Theorem 8.5). Let $X, Y \\\\in \\\\mathcal{T}(S)$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[230,736,790,789]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(1) The extremal Lipschitz constant $\\\\\\\\operatorname{Lip}(X, Y)$ can always be realized by a homeomorphism. \\\",\\\"(2) There exists a Thurston geodesic from $X$ to $Y$ . \\\"]\",\n \"page_idx\": \"5\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[200,796,795,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 2.3. (i) For various constructions of \\\"extremal Lipschitz maps\\\" and Thurston geodesic rays, see Section 3. (ii) In general, there may be more than one geodesic from $X$ to $Y$ . The union of all such geodesics is called the envelope from $X$ to $Y$ . For more information about envelopes, we refer to [19], [6], and [48]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,118,215,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,143,795,181]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.4. The Thurston norm. Let $X \\\\in \\\\mathcal{T}(S)$ . The Thurston norm on the tangent space $T_X\\\\mathcal{T}(S)$ is defined as: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[205,185,725,217]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\| v \\\\| _ {\\\\mathrm {T h}} := \\\\sup _ {\\\\lambda \\\\in \\\\mathcal {P M L} (S)} \\\\left(d _ {X} \\\\log \\\\ell_ {\\\\lambda}\\\\right) [ v ], \\\\quad \\\\forall v \\\\in T _ {X} \\\\mathcal {T} \\\\left(S _ {g, n}\\\\right),\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,220,795,294]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\mathcal{PML}(S) = \\\\mathcal{ML}(S) / _{\\\\mathbb{R}_{>0}}$ is the space of projective measured laminations and $\\\\mathcal{ML}(S)$ is the space of measured laminations on $S$ . The Thurston norm is the infinitesimal norm of the Thurston metric ([74, Page 20], see also [50, Theorem 2.3]). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,301,795,335]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The unit sphere in the cotangent bundle has a very nice description as follows. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,344,797,380]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 2.4 ([74], Theorem 5.1). For any hyperbolic surface $X$ of finite type, the map \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[346,383,645,421]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} d \\\\log \\\\ell : \\\\mathcal {P M L} (S) \\\\longrightarrow T _ {X} ^ {*} \\\\mathcal {T} (S) \\\\\\\\ [ \\\\mu ] \\\\quad \\\\longmapsto d _ {X} \\\\log \\\\ell_ {\\\\mu} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,426,795,481]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"embeds $\\\\mathcal{PM}\\\\mathcal{L}(S)$ as the boundary of a convex neighbourhood of the origin. This convex neighbourhood is dual to the unit ball $\\\\{v\\\\in T_X\\\\mathcal{T}(S):\\\\| v\\\\|_{\\\\mathrm{Th}}\\\\leq 1\\\\}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,496,795,551]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"There are flat places on the unit sphere $T_X^1\\\\mathcal{T}(S)$ of $T_{X}\\\\mathcal{T}(S)$ . A facet is a maximal flat portion of $T_{X}^{1}\\\\mathcal{T}(S)$ which has maximum possible dimension so that it has interior. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,558,797,628]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 2.5 ([74], Theorem 10.1). There is a bijection between the set of facets on the unit sphere $T_X^1 \\\\mathcal{T}(S)$ and the set of simple closed curves. In other words, every facet is contained in a plane $d_X \\\\log \\\\ell_\\\\alpha = 1$ for some simple closed curve $\\\\alpha$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,646,517,662]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For each simple closed curve $\\\\alpha$ , let \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[307,667,687,689]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nF _ {X} (\\\\alpha) := \\\\left\\\\{v \\\\in T _ {X} ^ {1} \\\\mathcal {T} (S): \\\\left(d _ {X} \\\\log \\\\ell_ {\\\\alpha}\\\\right) (v) = 1 \\\\right\\\\}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,694,648,710]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"be the corresponding facet obtained in Theorem 2.5. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,720,795,755]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Lemma 2.6 ([47], Lemma 4.2; [33], Corollary 6.13). Let $\\\\alpha, \\\\beta$ be two simple closed curves. Then \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[325,761,669,781]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\ni (\\\\alpha , \\\\beta) = 0 \\\\iff \\\\partial \\\\mathrm {F} _ {X} (\\\\alpha) \\\\cap \\\\partial \\\\mathrm {F} _ {X} (\\\\beta) \\\\neq \\\\emptyset .\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,796,795,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The unit sphere of the Thurston norm in the tangent space encodes not only the intersection patterns of simple closed curves, but also their hyperbolic lengths. In [19], Dumas-Lenzhen-Rafi-Tao proved that one can recognize lengths and intersection numbers of curves on $X$ from the lengths of facets in the unit sphere in $T_{X}\\\\mathcal{T}(S_{1,1})$ , based on the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[782,118,794,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,145,795,321]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"observation that extremal points of any facet in the unit sphere in $T_X\\\\mathcal{T}(S_{1,1})$ are exactly those vectors tangent to the Thurston stretch lines directed by the two canonical completions of the corresponding simple closed curve. This idea is further exploited and extended to surfaces of higher complexity by Huang-Ohshika-Papadopoulos [33]. Huang-Ohshika-Papadopoulos first observed that stretch vectors with respect to maximal chain-recurrent laminations necessarily arise as the Hausdorff limit of a sequence of shrinking faces of the unit spheres in $T_X\\\\mathcal{T}(S)$ , and then proceeded to prove that one can recognize lengths of simple closed curves on $X$ using such stretch vectors. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,330,797,455]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 2.7. (i) In his thesis, Bar-Natan [6] proved that the set of tangent vectors to the stretch lines corresponding to completions of maximal chain-recurrent laminations is precisely the set of extreme points in the unit sphere of $\\\\mathcal{T}_X\\\\mathcal{T}(S)$ . (ii) For more information about the unit sphere in $T_{X}\\\\mathcal{T}(S)$ , we refer to [33]. (iii) For the comparison of the Thurston norm with the Teichmüller norm, the Weil-Petersson norm, and the earthquake norm, we refer to [32]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[264,481,732,498]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. EXTREMAL LIPSCHITZ MAPS AND GEODESIC RAYS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,516,794,569]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this section, we shall sketch various constructions of extremal Lipschitz maps between hyperbolic surfaces, and the corresponding geodesic rays in the Teichmüller space. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,590,794,662]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1. Deforming polygons via explicit homeomorphisms. One way of constructing extremal Lipschitz maps between surfaces is to consider a pair of orthogonal measured (partial) foliations and to control the effect of the map on the leaves of these foliations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,669,795,792]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Following Thurston's idea, one can deform hyperbolic surfaces by cutting the surface into polygons, deforming each polygon individually, and then gluing the deformed polygons to get new surfaces. One of the advantages of this construction is that the involved deformations/homeomorphisms can be explicitly written down. In the following, we shall introduce this idea with more details, starting with Thurston's original construction. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,813,795,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1.1. Thurston's construction. Let $X$ be a complete hyperbolic surface of finite area. Let $\\\\lambda$ be a maximal geodesic lamination on $X$ , that is, the complementary region $X \\\\backslash \\\\lambda$ is the union of ideal triangles. Suppose further that $\\\\lambda$ admits at least one leaf which does not go to a cusp \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,118,215,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,614,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[233,142,763,324]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"FIGURE 1. In both pictures, the black arcs are leaves of the horocycle foliation $F$ while the red dashed arcs are leaves of $G$ . \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0780/542251631f1c5c4560d1fcb3ec6d6f5e93a84eb9ac7892fd30dd764462548dff.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[200,404,795,633]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"on both sides. Let $\\\\Delta$ be an arbitrary ideal triangle in $X\\\\backslash \\\\lambda$ . Notice that each corner of $\\\\Delta$ can be foliated by horocycles. Extend these foliations until they fill all but the region in the center bounded by three horocycles. Let $F$ be the extended partial foliation, called the horocycle foliation of $\\\\Delta$ . Let $G$ be the partial foliation whose leaves are geodesics rays orthogonal to the leaves of $F$ . Consider the $e^t$ -Lipschitz (self)homeomorphism $f_{t}:\\\\Delta \\\\to \\\\Delta$ which fixes the central region, and maps a horocycle which has distance $r$ from the central region to the horocycle with distance $e^{t}r$ linearly with respect to arc length on the horocycles, see Figure 1. In particular, $f_{t}$ sends leaves of $F$ to (other) leaves of $F$ and keeps each leaf of $G$ invariant (as a set). Thurston proved that the collection of pullback metrics on $X\\\\backslash \\\\lambda$ by all such $\\\\{f_t\\\\}$ extends to a new hyperbolic metric on $X$ , denoted by $\\\\mathbf{stretch}(X,\\\\lambda ,t)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,642,795,715]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 3.1 ([74]). For any complete hyperbolic surface $X$ of finite area, for any maximal geodesic lamination $\\\\lambda$ not all of whose leaves go to a cusp on both sides, there exists a new hyperbolic surface $\\\\operatorname{stretch}(X, \\\\lambda, t)$ depending analytically on $t > 0$ , such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[230,724,794,796]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(1) the identity map $X \\\\\\\\to \\\\\\\\mathbf{stretch}(X, \\\\\\\\lambda, t)$ is Lipschitz with Lipschitz constant $e^t$ , and \\\",\\\"(2) the identity map exactly expands arc length of $\\\\\\\\lambda$ by the constant factor $e^t$ . \\\"]\",\n \"page_idx\": \"8\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[200,813,795,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The family $\\\\{\\\\mathbf{stretch}(X,\\\\lambda ,t):t > 0\\\\}$ is called the Thurston stretch ray directed by $\\\\lambda$ . It is a geodesic under the Thurston metric. For the proof of Theorem 3.1, we refer to [74, Section 4] and [54, Chapter 2, Section 3.5]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[782,118,794,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"9 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,143,794,252]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 3.2. Thurston stretch lines are rare in the sense that at any point $X \\\\in \\\\mathcal{T}(S)$ , the set of unit vectors tangent to Thurston stretch lines through $X$ is of Hausdorff dimension zero [74, Theorem 10.5]. However, for any pair of distinct points in $\\\\mathcal{T}(S)$ , there exists a geodesic from the first point to the second point which a concatenation of finitely many stretch segments [74, Theorem 8.5] \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,285,795,339]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 3.3. Calderon and Farre [13, Lemma 15.11 and Proposition 15.12] generalized Thurston's construction to the case where $X \\\\backslash \\\\lambda$ is a union of regular ideal polygons. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,382,797,664]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1.2. The construction of Papadopoulos-Theret. A right-angled hyperbolic hexagon is said to be symmetric if it has three nonadjacent edges of equal length. Using symmetric right-angled hyperbolic hexagons, Papadopoulos and Theret [55] constructed the first examples of Thurston geodesics which are also geodesics in the reversed direction (up to reparametrization). Their construction starts by constructing extremal Lipschitz homeomorphisms between symmetric right-angled hyperbolic hexagons with controlled Lipschitz constant. By doubling the hexagons, they then obtain extremal Lipschitz homeomorphisms between symmetric hyperbolic pairs of pants, that is, hyperbolic pairs of pants which have three geodesic boundary components of equal length. By gluing pairs of pants along their boundary components without twist and by combining the resulting Lipschitz maps between pairs of pants, they obtain new stretch lines in the Teichmüller space of any hyperbolic surface of finite type which are also geodesics (up to reparametrization) in the opposite direction. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,672,797,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Lipschitz homeomorphisms between symmetric right-angled hyperbolic hexagons is constructed as follows. Consider a symmetric right-angled hyperbolic hexagon $H$ . There are two triples of pairwise non-consecutive edges, one of which is called long with common length $L$ while the other is called short with common length $l$ . Similarly as in the case of ideal triangles, one can equip $H$ with two orthogonal partial measured foliations $(F, G)$ defined as follows. The leaves of $F$ are the loci of equidistant points from the short edges. Those leaves foliate $H$ except a triangle-shaped central region. The transverse measure on $F$ is induced by the arclength of the long edges of $H$ . The leaves of $G$ are geodesics orthogonal to the leaves of $F$ and the transverse measure of $G$ is induced by the arclength of short edges of $H$ (see Figure 2.) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[204,143,795,354]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"FIGURE 2. Each of the hexagons has three long sides of equal length (red) and three short sides of equal length (black). The black arcs are leaves of $F$ , which are loci of equidistant points from the short edges. The red dashed arcs are leaves of $G$ , which are geodesics orthogonal to the leaves of $F$ \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0505/ea803a0bb689ad835e90be706a5c4b6ca77b480a5904512d6dea8f21c3ecdaeb.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[200,511,803,566]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Now Let $H_{t}$ be a family of symmetric right-angled hyperbolic hexagons with long edges being of length $t > 0$ . For any $t > 1$ , Papadopoulos and Théret constructed a homeomorphism $f_{t}: H \\\\to H_{t}$ such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[243,583,792,705]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- $f_{t}$ sends the central region on $H$ to the central region on $H_{t}$ , \\\",\\\"- $f_{t}$ sends affinely the leaves of $F$ at distance $r$ from the central region on $H$ to the leaves at distance $tr$ from the central region on $H_{t}$ , \\\",\\\"- $f_{t}$ sends leaves of $G$ on $H$ to the corresponding leaves of $G$ on $H_{t}$ by multiplying arclength by the factor $t$ , \\\",\\\"- $f_{t}$ is a $t$ -Lipschitz homeomorphism. \\\"]\",\n \"page_idx\": \"10\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[200,726,797,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Doubling the symmetric right-angled hexagons along short edges and then gluing the resulting pairs of pants without twist, Papadopoulos and Thérét constructed a family of hyperbolic surfaces $\\\\{X_{t}\\\\}_{t > 0}$ which is a Thurston geodesic in the forward direction. Notice that the set of short edges of hexagons are glued together to form a pants decomposition of $X_{t}$ while the set of long edges are glued together to form several closed geodesics orthogonal to the aforementioned pants decomposition. Interchanging the role of short edges and long edges, we see that $\\\\{X_{t}\\\\}_{t > 0}$ is also a Thurston geodesic in the backward direction. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,118,790,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"11 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,143,797,409]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1.3. The construction of Papadopoulos-Yamada. Starting with an arbitrary right-angled hyperbolic hexagon, Papadopoulos and Yamada constructed a one-parameter family of right-angled hexagons with a Lipschitz map between any two elements in this family, realizing the smallest Lipschitz constant in the homotopy class of this map relative to the boundary [56]. Let $H$ be an arbitrary right-angled hexagon. Notice that there are two triples of non-consecutive edges on $H$ , one of which called long while the other is called short. Let $\\\\alpha_{1}, \\\\alpha_{2}, \\\\alpha_{3}$ be the three long edges of $H$ . Considering the equidistant curves to the long edges of $H$ and the corresponding orthogonal geodesic arcs, Papadopoulos and Yamada constructed a pair of orthogonal measured (partial) foliations $(F, G)$ on $H$ , which extends the construction in [52]. (The construction here is more involved depending on whether the lengths of short edges satisfy the triangle inequality or not, see [56, Section 2]). Let $H_{t}$ be a family of right-angled hyperbolic hexagons such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[426,412,571,452]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\frac {\\\\cosh \\\\ell_ {H _ {t}} (\\\\alpha_ {i})}{\\\\cosh \\\\ell_ {H} (\\\\alpha_ {i})} = t.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[202,455,235,470]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[328,468,666,507]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nk _ {i} (t) := \\\\frac {\\\\ell_ {H _ {t}} (\\\\alpha_ {i})}{\\\\ell_ {H} (\\\\alpha_ {i})}, \\\\qquad k (t) = \\\\max \\\\{k _ {i} (t) \\\\}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,508,794,544]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For any $t > 1$ , Papadopoulos and Yamada constructed a homeomorphism $f_t: H \\\\to H_t$ such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[245,555,790,660]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- $f_{t}$ sends the central region on $H$ to the central region on $H_{t}$ , \\\",\\\"- $f_{t}$ linearly sends the leaves of $F$ on $H$ to the corresponding leaves on $H_{t}$ , \\\",\\\"- $f_{t}$ (nonlinearly) sends leaves of $G$ on $H$ to the corresponding leaves of $G$ on $H_{t}$ , \\\",\\\"- $f_{t}$ is a $k(t)$ -Lipschitz homeomorphism. \\\"]\",\n \"page_idx\": \"11\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[200,672,794,709]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Notice that each long side $\\\\alpha_{i}$ is a leaf of $F$ , and hence is stretched under $f$ by the factor $k_{i}(t)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,717,795,838]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Unlike the construction of Thurston and Papadopoulos-Theret, where the constructed homeomorphism linearly stretches the leaves of $G$ with a common factor and linearly shrinks the leaves of $F$ , the map here linearly stretches leaves of $F$ with varying factors and non-linearly shrinks leaves of $G$ . In particular, the map $f: H \\\\to H_t$ is linear on each of the three long sides of $H$ but not linear on any of the three short sides of $H$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,849,794,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Now we consider an arbitrary hyperbolic surface $X$ of genus $g$ with $b$ geodesic boundary components. Let $\\\\{\\\\gamma_i\\\\}_{1\\\\leq i\\\\leq 6g - 6 + 3n}$ be a collection \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"12 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,143,794,338]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"of pairwise disjoint geodesic arcs orthogonal to the geodesic boundary components of $X$ , i.e. $\\\\{\\\\gamma_i\\\\}_{1 \\\\leq i \\\\leq 6g - 6 + 3n}$ is a triangulation of $X$ . The complementary region $X \\\\setminus (\\\\cup_{i} \\\\gamma_{i})$ is a union of right-angled hexagons $\\\\{H^i\\\\}$ . Viewing those $\\\\{\\\\gamma_i\\\\}$ as long sides of $H^i$ and applying the previously constructed Lipschitz homeomorphisms to $H^i$ , we arrive at a family of hyperbolic surfaces $X_t$ and a family of Lipschitz homeomorphisms $f_t: X \\\\to X_t$ attaining the optimal Lipschitz constant on some of the $\\\\{\\\\gamma_i\\\\}$ . Doubling $X_t$ along the geodesic boundary components, we get a family of closed hyperbolic surfaces $\\\\{X_t^d\\\\}$ and a family of Lipschitz homeomorphisms $f_t^d: X^d \\\\to X_t^d$ attaining the optimal Lipschitz constant on some of the double of $\\\\{\\\\gamma_i\\\\}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,380,794,468]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1.4. The construction of Huang-Papadopoulos. Since the optimal Lipschitz map is not as rigid outside the maximally stretched loci, one may hope to construct Thurston geodesics which keep some non-trivial subsurface invariant. This is partially done by Huang and Papadopoulos under some conditions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,478,795,585]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Extending the previous constructions to ideal Saccheri quadrilaterals, Huang and Papadopoulos [34, Theorem 3.3 and Theorem 4.7] constructed, for any complete hyperbolic torus $\\\\mathbb{T}$ with one boundary component and any chain-recurrent geodesic lamination $\\\\lambda$ in the convex hull of $\\\\mathbb{T}$ , a family of complete hyperbolic tori $\\\\{\\\\mathbb{T}_t\\\\}_{t\\\\geq 1}$ and a family of Lipschitz homeomorphisms $f_{t}:\\\\mathbb{T}\\\\to \\\\mathbb{T}_{t}$ such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[245,601,818,741]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- the convex hull of $\\\\\\\\mathbb{T}_t$ has the same boundary length as that of $\\\\\\\\mathbb{T}$ , \\\",\\\"- $f_{t}$ is $t$ -Lipschitz and multiplies the arclength of $\\\\\\\\lambda$ by the factor $t$ , \\\",\\\"- $f_{t}$ is an isometry outside a compact neighbourhood of the convex hull of $\\\\\\\\mathbb{T}$ , \\\",\\\"- if the boundary length of the convex hull of $\\\\\\\\mathbb{T}$ is at most $4\\\\\\\\operatorname{arcsinh}(1)$ , $f_{t}$ maps the convex hull of $\\\\\\\\mathbb{T}$ onto the convex hull of $\\\\\\\\mathbb{T}_t$ . \\\"]\",\n \"page_idx\": \"12\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[200,760,794,847]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In particular, for any hyperbolic torus $T$ with one geodesic boundary component of length at most $4\\\\arcsinh(1)$ , the construction above gives a family of hyperbolic tori $\\\\{T_t\\\\}_{t \\\\geq 1}$ , each of which has exactly one geodesic boundary component, and a family of Lipschitz homeomorphisms $f_t: T \\\\to T_t$ such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[245,866,656,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"- $T_{t}$ has the same boundary length as that of $T$ , \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[776,118,790,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"13 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[245,143,794,196]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"- $f_{t}$ is $t$ -Lipschitz, multiplies the arclength of $\\\\lambda$ by the factor $t$ , and maps the boundary of $T$ linearly to the boundary of $T_{t}$ by the factor 1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,210,795,316]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Consider a hyperbolic surface $X$ with punctures or geodesic boundary components. If $X$ contains a hyperbolic torus $T$ with one geodesic boundary component, whose boundary length is at most 4arcsinh(1), then for any chain-recurrent geodesic lamination in $T$ the above construction gives a family of hyperbolic surfaces $X_{t}$ and a family of Lipschitz homeomorphisms $f_{t}: X \\\\to X_{t}$ such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[245,329,691,364]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- $f_{t}$ is $t$ -Lipschitz, and multiplies the arclength of $\\\\\\\\lambda$ ; \\\",\\\"- $f_{t}$ is an isometry on the closure of $X \\\\\\\\backslash T$ . \\\"]\",\n \"page_idx\": \"13\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[200,388,805,493]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2. Deforming crowned surfaces via harmonic diffeomorphisms. Using harmonic maps of high energy, Pan and Wolf constructed piecewise harmonic stretch lines and harmonic stretch lines [49]. Recall that a differentiable map $f: (M, \\\\sigma | dz|^2) \\\\to (N, \\\\rho | dw|^2)$ between Riemannian surfaces is said to be harmonic if it satisfies the Euler-Lagrange equation: \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[401,496,596,516]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nf _ {z \\\\bar {z}} + (\\\\log \\\\rho) _ {w} f _ {z} f _ {\\\\bar {z}} = 0.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,518,794,555]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If $M$ and $N$ are compact, then $f$ is harmonic if and only if it is a critical point of the energy functional \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[401,561,596,599]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nE (f) := \\\\int_ {M} e (f) \\\\sigma | d z | ^ {2}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,607,794,662]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $e(f) \\\\coloneqq \\\\frac{\\\\rho(f(z))}{\\\\sigma(z)} (|f_z|^2 + |f_{\\\\bar{z}}|^2)$ is the energy density of $f$ . Notice that the energy depends on the conformal structure on $M$ and the metric on $N$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,672,795,830]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The basic existence result of harmonic maps was established by Eells and Sampson in [20] and by Hamilton in [30], if the target manifold has nonpositive sectional curvature. The uniqueness was obtained by Al'ber [1] and Hartman [31] if the target manifold has negative sectional curvature and if the image is not contractible to a point or a geodesic. Moreover, Sampson [61] and Schoen-Yau [65] proved that any harmonic map between compact surfaces which is homotopic to a diffeomorphism is a diffeomorphism, provided that the target surface has nonpositive curvature. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[218,839,743,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Suppose that $f$ is harmonic. Consider the pullback of $\\\\rho$ by $f$ : \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[318,864,678,887]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nf ^ {*} (\\\\rho) = \\\\rho f _ {z} \\\\overline {{f _ {\\\\bar {z}}}} d z ^ {2} + e (f) \\\\sigma d z d \\\\bar {z} + \\\\rho \\\\overline {{f _ {z}}} f _ {\\\\bar {z}} d \\\\bar {z} ^ {2}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[202,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"14 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[382,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,143,795,233]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The $(2,0)$ -part of $f^{*}(\\\\rho)$ is called the Hopf differential of $f$ . The harmonicity of $f$ implies that the Hopf differential of $f$ is holomorphic (see [66, 36]). If we choose the coordinate $z = x + iy$ such that the Hopf differential $\\\\Phi = dz^2$ and choose $\\\\sigma$ to be the singular flat metric induced by $|\\\\Phi|$ , then $f^{*}(\\\\rho)$ can be simply expressed as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[367,239,627,262]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nf ^ {*} \\\\rho = (e + 2) d x ^ {2} + (e - 2) d y ^ {2}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,268,795,428]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"By [43, Lemma 3.2 and Lemma 3.3], the energy density satisfies $e(z) = 2 + O(e^{-2r})$ where $r$ represents the distance from $z$ to the zeros of the Hopf differential. In particular, for points far away from the zeros of the Hopf differential, the pullback metric $f^{*}\\\\rho$ is nearly $4dx^{2}$ . Roughly speaking, at regions far away from the zeros of the Hopf differential, the harmonic map $f$ linearly maps horizontal leaves of the Hopf differential to hyperbolic geodesics by a factor of 2 while contracting the vertical leaves exponentially. This observation is the starting point of the construction of Pan and Wolf. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,436,795,526]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 3.4 ([49], Theorem 1.7). Let $Y \\\\in \\\\mathcal{T}(S)$ be any closed hyperbolic surface, and let $\\\\lambda$ be any geodesic lamination. Then for any surjective harmonic diffeomorphism $f: X \\\\to Y \\\\setminus \\\\lambda$ from some (possibly disconnected) punctured surface $X$ , there is a family of new hyperbolic surfaces \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[362,529,633,547]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nY _ {t} := \\\\mathbf {s t r e t c h} (Y, \\\\lambda , f; t) \\\\in \\\\mathcal {T} (S)\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[202,553,573,571]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"depending analytically on $\\\\{t > 0\\\\}$ such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,584,795,680]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(a) the identity map $f_{t}: X \\\\\\\\to Y_{t} \\\\\\\\setminus \\\\\\\\lambda$ is a surjective harmonic map $f_{t}: X \\\\\\\\to Y_{t} \\\\\\\\setminus \\\\\\\\lambda$ with Hopf differential $t\\\\\\\\mathrm{Hopf}(f)$ ; \\\",\\\"(b) for any $0 < s < t$ , the identity map $(f_t \\\\\\\\circ f_s^{-1})$ is $\\\\\\\\sqrt{t / s}$ -Lipschitz with (pointwise) Lipschitz constant strictly less than $\\\\\\\\sqrt{t / s}$ in $S - \\\\\\\\lambda$ , and exactly expands arc length of $\\\\\\\\lambda$ by the constant factor $\\\\\\\\sqrt{t / s}$ . \\\"]\",\n \"page_idx\": \"14\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[200,699,795,808]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A family of hyperbolic structures stretch $(X, \\\\lambda; \\\\widehat{\\\\Phi}, \\\\widehat{f}; t)$ constructed above is called a piecewise harmonic stretch line. It admits a canonical orientation coming from the orientation of the positive real ray $\\\\{t > 0\\\\}$ . With that orientation, a piecewise harmonic stretch line is a (reparametrized) geodesic in the Thurston metric. Whenever we say a piecewise harmonic stretch line, we mean a directed line. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,830,794,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.3. The constructions of Guéritaud-Kassel and Alessandrini-Disarlo. Using a totally different method, Guéritaud and Kassel extended Thurston's construction to a geometrically finite setting and to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[776,118,790,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"15 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,143,794,356]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"higher dimension. Let $\\\\Gamma_0$ be a discrete group. For a pair $(j,\\\\rho)$ of representations of $\\\\Gamma_0$ into $\\\\mathrm{PO}(n,1) = \\\\mathrm{Isom}(\\\\mathbb{H}^n)$ with $j$ geometrically finite. Guéritaud and Kassel investigate the set of $(j,\\\\rho)$ -equivariant Lipschitz maps from $\\\\mathbb{H}^n$ to itself having the minimal Lipschitz constants (such maps do exist if $\\\\rho$ is reductive [28, Lemma 4.10]), establish the existence of maximally stretched locus $E(j,\\\\rho)$ (which is a geodesic lamination if the minimal Lipschitz constant is at least one), and prove the existence of optimal Lipschitz maps whose stretched locus is exactly the maximally stretched locus $E(j,\\\\rho)$ of the representations $(j,\\\\rho)$ [28, Theorem 1.3]. This allows Guéritaud and Kassel to study proper actions of discrete subgroups of $\\\\mathrm{PO}(n,1)\\\\times \\\\mathrm{PO}(n,1)$ on $\\\\mathrm{PO}(n,1)$ by left and right multiplication [28, Theorem 1.8 and Theorem 1.9]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,364,795,436]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"One of the key ideas of Guéritaud and Kassel is to consider the \\\"average of Lipchitz maps\\\". This idea is used by Alessandrini and Disarlo to construct extremal Lipschitz maps between hyperbolic surfaces with geodesic boundary components [3]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,444,795,655]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We now sketch the construction of Alessandrini and Disarlo [3]. Let $X$ be a finite-area hyperbolic surface with geodesic boundary components. A geodesic lamination $\\\\lambda$ on $X$ is called maximal if any connected component of its complementary region $X \\\\backslash \\\\lambda$ is either an ideal triangle, a right-angled quadrilateral with two consecutive ideal vertices, a right-angled pentagon with one ideal vertex, or a right-angled hexagon. These four types of polygons are called geometric pieces. For any maximal geodesic lamination on $X$ , Alessandrini and Disarlo constructed a family of hyperbolic surface $X_{\\\\lambda}^{t}$ homeomorphic to $X$ and a family of generalized stretch maps $\\\\Psi^t: X \\\\to X_{\\\\lambda}^t$ which realizes the minimal Lipschitz constant from $X$ to $X_{\\\\lambda}^{t}$ and maximally stretches along $\\\\lambda$ . Their construction has three steps. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,664,795,806]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Step 1: Generalized stretch map between geometric pieces. Combine Thurston's stretch maps and Guéritaud-Kassel's idea of averaging Lipschitz maps to construct implicit extremal maps between geometric pieces of the same type which stretch along certain sides. However, it is unclear whether the resulting maps between geometric pieces are homeomorphic or not. So one can't simply \\\"glue\\\" these new pieces and the corresponding stretch maps. To overcome this issue, Alessandrini and Disarlo adapted a different idea in the remaining steps. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,813,794,849]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Step 2: Decomposition of $X$ . Let $B \\\\subset X$ be the union of geometric pieces of $X \\\\backslash \\\\lambda$ which are not ideal triangles. The surface $B$ is a crowned \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"16 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,143,795,181]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"hyperbolic surface. Let $C \\\\subset B$ be the union of crown ends of $B$ and set $B_{C} = \\\\overline{B \\\\setminus C} \\\\subset B$ . Finally, let $X_{C} := \\\\overline{X \\\\setminus B_{C}} \\\\subset X$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,188,795,279]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Step 3: Define $X_{\\\\lambda}^{t}$ and the generalized stretch map $\\\\psi^t:X\\\\to X_\\\\lambda^t$ For each $t\\\\geq 0$ , Alessandrini and Disarlo construct hyperbolic surfaces $B^{t},B_{C}^{t},X_{C}^{t}$ homeomorphic to $B,B_{C},X_{C}$ respectively. The new surfaces come with preferred (locally) isometric embeddings $\\\\xi^t:C^t\\\\to B^t$ and $h^t:C^t\\\\to B_C^t$ . The new surface $X_{\\\\lambda}^{t}$ is then defined to be \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[411,285,591,306]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nX _ {\\\\lambda} ^ {t} := \\\\left(B ^ {t} \\\\cup B _ {C} ^ {t}\\\\right) / \\\\sim ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,313,795,404]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\xi^t(z) \\\\sim h^t(z)$ for all $z \\\\in C^t$ . The generalized stretch map $\\\\Psi^t: X \\\\to X_\\\\lambda^t$ is defined by glueing together suitable generalized stretch maps $\\\\beta^t: B \\\\to B^t$ and $\\\\psi^t$ from an open dense subset of $B_C$ to $X_C^t$ . (For the details of the construction, we refer to [3, Section 6.2, 7.4, 8.1 and 8.2]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,412,795,518]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 3.5. (1) It is unclear whether the generalized stretch maps are homeomorphisms or not. (2) Based on the generalized stretch maps and the generalized stretch lines, Alessandrini and Disarlo proved that the Teichmüller space of bordered hyperbolic surfaces with the arc metric is geodesic, and provided new geodesics of the Thurston metric in the Teichmüller space of closed surface. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,537,795,609]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.4. The construction of Daskalopoulos-Uhlenbeck. In [16, 17], Daskalopoulos and Uhlenbeck constructed extremal Lipschitz maps between manifolds using infinity harmonic maps. Here we sketch the construction of [17], which works more generally than hyperbolic surfaces. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,617,795,705]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $(M,g)$ be a compact Riemannian manifold with boundary $\\\\partial M$ (possibly empty) and $\\\\dim(M) = n$ . Let $(N,h)$ be a closed Riemannian manifold of non-positive sectional curvature and let $W^{1,p}(M,N)$ denote the Soblev space of maps $f:M\\\\to N$ such that $f$ and its weak derivative have a finite $L^p$ norm. For any map \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[334,712,665,734]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nf: M \\\\to N \\\\in W ^ {1, p} (M, N) \\\\cap C ^ {0} (M, N),\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,742,470,760]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"define the $J_{p}$ -functional of $f$ as \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[383,768,616,806]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nJ _ {p} (f) := \\\\int_ {M} \\\\mathrm {T r} (Q (d f) ^ {p}) * 1,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,813,795,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $1 \\\\leq p < \\\\infty$ and where $Q(df)^2 = dfdf^T$ is a non-negative symmetric linear map mapping the tangent space $TN$ to itself. The integrand $\\\\mathrm{Tr}(Q(df)^p)$ is essentially the sum of the $p$ -th powers of the singular eigenvalues of $df$ . The Euler-Lagrange equations of the $J_p$ functional \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,118,792,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"17 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[202,147,233,159]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"are \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[405,161,591,181]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nD ^ {*} Q (d f) ^ {q - 2} (d f) ^ {2} = 0,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,184,792,203]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $D = D_{f}$ is the pullback of the Levi-Civita connection on $f^{-1}TN$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,210,795,335]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If the domain manifold $(M,g)$ has nonempty boundary, there are two types minimizing problems: the Dirichlet problem and the Neumann problem. For the Dirichlet problem we fix a continuous map $f:M\\\\to N$ and seek a minimizer in the homotopy class of $f$ relative to the boundary values of $f$ . For the Neumann problem we only fix a homotopy class and no boundary condition at all. Here is the existence theorem concerning the $J_{p}$ functional. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,342,797,467]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 3.6 ([17], Theorem 1.1). Let $(M,g)$ be a compact Riemannian manifold with boundary $\\\\partial M$ (possibly empty) and $\\\\dim(M) = n$ . Let $(N,h)$ be a closed Riemannian manifold of non-positive sectional curvature. Then for each $p > N$ , there exists a minimizer $f$ in $W^{1,p}(M,N)$ of the functional $J_p$ with either the Dirichlet or the Neumann boundary conditions in a homotopy (relative homotopy) class. Furthermore, if $\\\\partial M \\\\neq \\\\emptyset$ , the solution of Dirichlet problem is unique. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,484,795,556]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The next result is about the construction of extremal Lipschitz maps using $J_{p}$ harmonic maps. Recall that a Riemannian manifold $M$ with boundary is said to be convex if it can be isometrically embedded as a convex subset of a manifold of the same dimension without boundary. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,563,797,670]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 3.7 ([17], Theorem 1.4). Let $M, N$ be Riemannian manifolds where $M$ is convex with possibly non-empty boundary and $N$ is closed and has non-positive curvature. Given a sequence $p \\\\to \\\\infty$ , there exists a subsequence (denoted also by $p$ ) and a sequence of $J_p$ minimizers $f_p: M \\\\to N$ in the same homotopy class (either in the absolute sense or relative to the boundary depending on the context) such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[346,675,648,702]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nf = \\\\lim _ {p \\\\to \\\\infty} f _ {p} \\\\in W ^ {1, s} (M, N) f o r a l l s.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,707,794,743]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Furthermore, $f_{p} \\\\to f$ uniformly and $f$ is an extremal Lipschitz map in the (relative) homotopy class. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,760,795,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A critical point of the $J_{p}$ functional (with either the Dirichlet problem or the Neumann problem) is called a Schatten-von Neumann $p$ -harmonic map or simply a $J_{p}$ harmonic map. The limit map obtained in Theorem 3.7 is called infinity harmonic map. About the regularity, Daskalopoulos and Uhlenbeck conjecture that for $p > 2$ , any $J_{p}$ harmonic map between hyperbolic surfaces is of $C^{1,\\\\alpha}$ [17, Conjecture 4.19]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,143,797,321]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We now return to the hyperbolic surface setting. Let $f: M \\\\to N$ be a Lipschitz map between hyperbolic surfaces $M$ and $N$ . Here $M$ and $N$ are not necessary homeomorphic. Suppose further that the minimal Lipschitz constant in the homotopy class of $f$ is at least one. In this setting, the maximally stretched loci of all extremal Lipschitz maps from $M$ to $N$ in the given homotopy class, is a chain recurrent geodesic lamination. In particular, the maximally stretched loci of the infinity harmonic map obtained in Theorem 3.7 contains the maximally stretched lamination. For the inverse direction, they proved: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,330,797,404]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 3.8 ([17], Theorem 1.7). If the maximally stretched lamination $\\\\lambda$ for a homotopy class of maps $M\\\\to N$ consists of a finite number of simple closed geodesics, then the maximally stretched loci of the infinity harmonic map obtained in Theorem 3.7 is exactly $\\\\lambda$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,422,797,532]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Daskalopoulos and Uhlenbeck conjectured that Theorem 3.8 holds in general [17, Conjecture 8.12]: the maximally stretched loci of any infinity harmonic map, whose Lipschitz constant is at least one, is the maximally stretched lamination [17, Conjecture 8.12]. Furthermore, they conjectured that the limit infinity harmonic maps are not homeomorphisms [17, Conjecture 8.5]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,555,816,643]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.5. Concatenations of geodesic segments. In the previous subsections, we discussed the constructions of various geodesic rays. Thurston constructed another type of geodesics, that is, concatenations of Thurston stretch segments [74, Theorem 8.5]. This construction applies to other segments as well. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[362,679,633,696]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. HARMONIC STRETCH LINES \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,713,795,801]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In Section 3, we discussed various constructions of geodesic rays under the Thurston metric. In this section, we will focus on a special type of piecewise harmonic stretch lines, namely, the harmonic stretch lines. Throughout this section, we assume that the underlying topological surface $S$ is a closed orientable surface with genus at least two. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[776,118,790,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"19 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,821,795,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"<sup>1</sup>If the minimal Lipschitz constant is less than one, then the maximally stretched loci may not be a geodesic lamination [28, Section 9.4]. In fact, Guéritaud and Kassel conjectured that in this case the maximally stretched loci is a \\\"grammation\\\" (contraction of \\\"graph\\\" and \\\"lamination\\\") [28, Conjecture 1.4]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[200,143,794,320]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.1. Harmonic stretch lines. Recall that the construction of piecewise harmonic stretch lines through $Y \\\\in \\\\mathcal{T}(S)$ depends on the choice of a geodesic lamination $\\\\lambda$ and a surjective harmonic diffeomorphism $f: X \\\\to Y \\\\backslash \\\\lambda$ from some (possibly disconnected) punctured surface $X$ . If $X$ has several components, the harmonic map $f$ can be prescribed independently on each component. If we impose some additional \\\"compatibility conditions\\\" on the harmonic maps from distinct components, we arrive at the harmonic stretch lines. Originally, the harmonic stretch lines are defined via harmonic map rays, of which we now recall the definition. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,329,795,402]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $X \\\\in \\\\mathcal{T}(S)$ and let $\\\\Phi$ be a holomorphic quadratic differential on $X$ . The harmonic map $ray$ determined by $X$ and $\\\\Phi$ is the set of hyperbolic surfaces $\\\\{Y_t\\\\}_{t > 0}$ such that the Hopf differential of harmonic map from $X$ to $Y_t$ is $t\\\\Phi$ [77]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,409,794,479]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A piecewise harmonic stretch line is said to be a harmonic stretch line if it arises as a limit of some sequence of harmonic map rays in $\\\\mathcal{T}(S)$ . The basic theorem about those harmonic stretch lines is the following. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,484,795,539]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 4.1 ([49], Theorem 1.8). For any two distinct hyperbolic surfaces $Y, Z \\\\in \\\\mathcal{T}(S)$ , there exists a unique harmonic stretch line proceeding from $Y$ to $Z$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,554,795,712]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Actually, one can say more about the relationship between harmonic map rays and Thurston geodesic rays. To that end, we need another definition, the harmonic map dual rays. Let $X \\\\in \\\\mathcal{T}(S)$ and let $\\\\lambda$ be a measured foliation on $X$ . The harmonic map dual ray determined by $X$ and $\\\\lambda$ is the of hyperbolic surfaces such that the horizontal foliation of the Hopf differential of the harmonic map from $X_{t}$ to $X$ is $t\\\\lambda$ (for the existence and uniqueness of such a $X_{t}$ , see [78, Theorem 3.1]). For any two hyperbolic surfaces $X', X$ , we denote by $\\\\mathbf{HR}(X', X)$ the harmonic map which starts at $X'$ and passes through $X$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,719,795,806]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 4.2 ([49], Theorem 1.1). Let $X \\\\in \\\\mathcal{T}(S)$ be a hyperbolic surface and $\\\\lambda$ a measured lamination. Then the family of harmonic map rays $\\\\mathrm{HR}(X_t, X)$ converge to a Thurston geodesic locally uniformly as $X_t$ diverges along the harmonic map dual ray determined by $X$ and $\\\\lambda$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,813,794,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 4.3. The conclusion still holds if we replace the harmonic map dual ray by a Teichmüller ray [49, Theorem 1.2]. Similar results also hold for harmonic map dual rays. We fixed $X \\\\in \\\\mathcal{T}(S)$ and a holomorphic quadratic differential $\\\\Phi$ on $X$ . Suppose that $Y_{t}$ diverges along \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"20 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,143,795,217]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the harmonic map ray determined by $X$ and $\\\\Phi$ . Then the family of harmonic map dual rays, each of which starts at $Y_{t}$ and passes through $X$ , converges to the Teichmüller geodesic determined by $X$ and $\\\\Phi$ locally uniformly [49, Theorem 1.4]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,232,795,268]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If we remove the assumption that $X_{t}$ diverges along a harmonic map ray, then we have the following sub-convergence result: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,275,797,348]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 4.4 ([49], Theorem 1.3). For any fixed $X \\\\in \\\\mathcal{T}(S)$ , let $X_{n} \\\\in \\\\mathcal{T}(S)$ be an arbitrary divergent sequence. with $X_{n} \\\\to \\\\infty$ . Then the sequence of harmonic map rays $\\\\mathbf{HR}(X_n, X)$ contains a subsequence which converges to some Thurston geodesic locally uniformly. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,363,795,436]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Next, we extend the existence/ uniqueness theory of harmonic stretch lines to rays whose terminal point is a projective measured lamination, representing a point on the boundary of the Thurston compactification of the Teichmüller space $\\\\mathcal{T}(S)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,441,795,497]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 4.5 ([49], Theorem 1.11). For any $Y \\\\in \\\\mathcal{T}(S)$ and any $[\\\\eta] \\\\in \\\\mathcal{PML}(S)$ , there exists a unique harmonic stretch ray starting at $Y$ , which converges to $[\\\\eta] \\\\in \\\\mathcal{PML}(S)$ in the Thurston compactification. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,503,795,540]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Moreover, these rays foliate $\\\\mathcal{T}(S)$ if we fix $Y$ and let $[\\\\eta]$ vary in $\\\\mathcal{PML}(S)$ , or if we fix $[\\\\eta]$ and let $Y$ vary in $\\\\mathcal{T}(S)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,556,843,609]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, let us mention the following continuity property, where $\\\\mathrm{HSL}(X,X^{\\\\prime})$ represents the harmonic stretch line proceeding from $X\\\\in \\\\mathcal{T}(S)$ to $X^{\\\\prime}\\\\in \\\\mathcal{T}(S)\\\\cup \\\\mathcal{PM}\\\\mathcal{L}(S)$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,617,797,655]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proposition 4.6 ([49], Proposition 12.14 and Proposition 13.8). Let $Y$ and $Z$ be two distinct points in $\\\\mathcal{T}(S)$ . Let $[\\\\eta] \\\\in \\\\mathcal{PML}(S)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[210,662,795,771]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(i) Suppose that $Y_{n} \\\\\\\\to Y$ and $Z_{n} \\\\\\\\to Z$ in $\\\\\\\\mathcal{T}(S)$ , then the sequence of harmonic stretch lines $\\\\\\\\mathrm{HSL}(Y_n,Z_n)$ locally uniformly converges to the harmonic stretch line $\\\\\\\\mathrm{HSL}(Y,Z)$ . \\\",\\\"(ii) Suppose that $Y_{n} \\\\\\\\to Y$ in $\\\\\\\\mathcal{T}(S)$ and $[\\\\\\\\eta_n] \\\\\\\\to [\\\\\\\\eta]$ in $\\\\\\\\mathcal{PM}\\\\\\\\mathcal{L}(S)$ , then the sequence of harmonic stretch lines $\\\\\\\\mathrm{HSL}(Y_n, [\\\\\\\\eta]_n)$ locally uniformly converges to the harmonic stretch line $\\\\\\\\mathrm{HSL}(Y, [\\\\\\\\eta])$ . \\\"]\",\n \"page_idx\": \"20\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[200,777,795,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 4.7. Using the identification between $\\\\mathcal{ML}(S)$ and $T_{Y}^{*}\\\\mathcal{T}(S)$ , Theorem 4.5 induces a bijection from $T_{Y}^{*}\\\\mathcal{T}(S)$ to $\\\\mathcal{T}(S)$ which sends rays through the origin in $T_{Y}^{*}\\\\mathcal{T}(S)$ to harmonic stretch rays in $\\\\mathcal{T}(S)$ . (By Proposition 4.6 such a bijection is a homeomorphism.) A natural question is to improve Theorem 4.5 to an exponential map from $T_{Y}\\\\mathcal{T}(S)$ to $\\\\mathcal{T}(S)$ . Since the Thurston norm is not strictly convex, this does not \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,118,790,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"20\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"21 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,143,794,198]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"follow directly from Theorem 4.5. The existence part of the exponential map is clear, see [49, Remark 1.12]. However, the uniqueness part is unknown yet. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,217,792,233]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.2. Two versions of the geodesic flow for the Thurston metric. \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,234,702,252]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 4.5 allows us to define the Thurston geodesic flow \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[308,260,684,280]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\psi_ {t}: \\\\mathcal {T} (S) \\\\times \\\\mathcal {P M L} (S) \\\\longrightarrow \\\\mathcal {T} (S) \\\\times \\\\mathcal {P M L} (S)\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,287,795,342]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"such that the orbit through $(Y, [\\\\eta]) \\\\in \\\\mathcal{T}(S) \\\\times \\\\mathcal{PML}(S)$ is the harmonic stretch line determined by $Y$ and $[\\\\eta]$ via Theorem 4.5. Moreover, every harmonic stretch line appears as a (forward) orbit. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,349,683,367]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"There is another version of the Thurston geodesic flow \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[313,376,679,396]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\phi_ {t}: \\\\mathcal {T} (S) \\\\times \\\\mathcal {P M L} (S) \\\\rightarrow \\\\mathcal {T} (S) \\\\times \\\\mathcal {P M L} (S)\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,402,794,439]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"such that the orbit through $(Y, [\\\\eta]) \\\\in \\\\mathcal{T}(S) \\\\times \\\\mathcal{PML}(S)$ is the stretch line obtained from Theorem 4.2. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,446,720,467]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For a further discussion about those flows, we refer to [49]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[383,496,611,513]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5. THURSTON BOUNDARY \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,531,794,604]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Teichmüller space $\\\\mathcal{T}(S)$ parametrizes hyperbolic structures on the topological surface $S$ . A sequence of hyperbolic surfaces $X_{n}\\\\in \\\\mathcal{T}(S)$ which tends to infinity has the property that some closed curve $\\\\gamma$ on $S$ becomes infinitely long, that is, the hyperbolic length $\\\\ell_{\\\\gamma}(X_n)\\\\to \\\\infty$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,611,795,681]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The length of long curves can be measured quantitatively by looking at their transverse measures with respect to measured foliations. This observation of Thurston [72] resulted in a natural compactification of $\\\\mathcal{T}(S)$ , which is called the Thurston compactification. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,689,794,779]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Recall that a measured foliation $(F, \\\\mu)$ is a foliation $F$ on $S$ equipped with an invariant transverse measure $\\\\mu$ . We require that the singularities of $F$ are similar to the singularities of holomorphic quadratic differentials (or meromorphic quadratic differentials with at most simple pole at the punctures, when $S$ is a punctured surface). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,786,794,823]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For simplicity, we denote $(F,\\\\mu)$ by $\\\\mu$ . For any simple closed curve $\\\\gamma$ , the intersection number $i(\\\\gamma ,\\\\mu)$ is defined by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[415,845,583,887]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\ni (\\\\gamma , \\\\mu) = \\\\inf _ {\\\\gamma^ {\\\\prime}} \\\\int_ {\\\\gamma^ {\\\\prime}} d \\\\mu ,\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[202,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"22 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"21\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,143,794,233]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\gamma'$ is taken over all simple closed curves homotopic to $\\\\gamma$ . Two measured foliations $\\\\mu_1, \\\\mu_2$ are said to be equivalent if $i(\\\\gamma, \\\\mu_1) = i(\\\\gamma, \\\\mu_2)$ for all simple closed curves $\\\\gamma$ on $S$ . Let $\\\\mathcal{MF}$ be the set of equivalence classes of measured foliations on $S$ . The set of projective equivalence classes of measured foliations is denoted by $\\\\mathcal{PMF}(S)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,241,795,313]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As shown by Thurston (see [23]), $\\\\mathcal{PMF}(S)$ is topologically a sphere of dimension $6g - 7 + 2n$ . Moreover, $\\\\mathcal{PMF}(S)$ is the Thurston boundary of $\\\\mathcal{T}(S)$ . By definition, a sequence of hyperbolic surfaces $X_{n}\\\\in \\\\mathcal{T}(S)$ converges to the projective class of $\\\\mu$ if there is some $c_{n} > 0$ such that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[415,318,580,339]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nc _ {n} \\\\ell_ {\\\\gamma} (X _ {n}) \\\\rightarrow i (\\\\gamma , \\\\mu)\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,344,794,380]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"for all simple closed curves $\\\\gamma$ on $S$ . To glue $\\\\mathcal{T}(S)$ together with $\\\\mathcal{PMF}(S)$ , we can embed both $\\\\mathcal{T}(S)$ and $\\\\mathcal{PMF}(S)$ into $\\\\mathbb{P}\\\\mathbb{R}^{\\\\infty}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,388,794,441]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"There are many applications of Thurston's theory of measured foliations. Below, we will limit ourselves to illustrating some of the results related to the Thurston metric. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,449,794,503]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The following result, first proved by Papadopoulos [51, Theorem 5.1], implies there is direct relation between the Thurston metric and the Thurston boundary: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,511,795,583]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 5.1. Let $\\\\lambda$ be a maximal geodesic lamination on $X \\\\in \\\\mathcal{T}(S)$ with $\\\\mu = F_{\\\\lambda}(X)$ being the transverse horocycle foliation. Then the corresponding Thurston stretch ray converges to the projective class $[\\\\mu] \\\\in \\\\mathcal{PMF}(S)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,590,795,715]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 5.2. The problem of the convergence of anti-stretch lines (stretch lines in backward direction) towards the Thurston boundary was studied by Théret [70]. If the anti-stretch line is directed by a complete geodesic lamination $\\\\lambda$ which is the completion of a uniquely ergodic measured lamination $\\\\mu$ , then it converges to the projective class of $\\\\mu$ . For general stretch lines, the problem of the convergence or non-convergence remains open. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,733,794,787]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It is true that every geodesic ray of the Thurston metric has a unique limit in the Thurston boundary. This is a corollary of the following result by Walsh [76, Theorem 3.6]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,795,794,830]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 5.3. The horofunction boundary of $\\\\mathcal{T}(S)$ , endowed with the Thurston metric, is homeomorphic to the Thurston boundary. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,849,794,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The horofunction compactification and the corresponding boundary of a proper metric space are introduced by Gromov [27]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,118,792,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"22\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,143,794,303]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 5.4. An asymmetric metric, called arc metric, is defined on the Teichmüller space of compact hyperbolic surfaces with boundary. It is an analogue of the Thurston metric defined on the Teichmüller space of complete finite area hyperbolic surfaces without boundary. Theorem 5.3 was generalized to the arc metric by [2]. Geodesics for the arc metric, which are analogues of Thurston's stretch lines, were constructed by [3]. By [49, Theorem 14.1], the arc metric coincides with the Lipschitz metric, which is defined using Lipschitz maps similarly as (1). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,324,794,378]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let us briefly mention the work of Bonahon [9] on geodesic currents. Let us endow the surface $S$ with a hyperbolic metric. For simplicity, we assume that $S$ is a closed hyperbolic surface. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,386,795,476]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A geodesic current is a locally finite Radon (positive) measure on the space of geodesics on $S$ . Alternatively, a geodesic current is a finite Radon measure on the unique tangent bundle of $S$ that is invariant under the geodesic flow. Closed geodesics or weighted sums of closed geodesics on $S$ are examples of geodesic currents. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,483,795,608]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Denote the space of geodesic currents on $S$ by $\\\\mathcal{C}(S)$ , endowed with the weak* topology. We can embed $\\\\mathcal{MF}(S)$ into $\\\\mathcal{C}(S)$ , by representing each measured foliation as a geodesic lamination with an invariant transverse measure. On the other hand, every hyperbolic structure $X \\\\in \\\\mathcal{T}(S)$ corresponds to a Liouville current. By taking projective classes, the Teichmüller space embeds into $\\\\mathrm{PC}(S)$ , and Bonahon [9] proved that the boundary of the image is exactly $\\\\mathcal{PMF}(S)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[393,647,602,664]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6. ISOMETRY RIGIDITY\",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,681,794,719]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this section, we will discuss the rigidity of the Thurston metric, especially the isometry rigidity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,747,812,801]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6.1. Global rigidity. We start with the global rigidity due to Walsh [76]. Using an identification of the horofunction boundary of the Thurston metric with the Thurston boundary (Theorem 5.3), Walsh proved that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,813,797,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 6.1 ([76], Theorem 7.8). If $S$ is not a sphere with four or less punctures, nor a torus with two or fewer punctures, then every isometry of $(\\\\mathcal{T}(S), d_{Th})$ is an element of the extended mapping class group. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"24 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"23\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,143,795,215]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 6.1 is an analogue of Royden's theorem for the Teichmüller metric. Note that the proof of Walsh is geometric. An important step consists of reducing the problem into showing that every isometry of the Thurston metric induces an automorphism of the curve complex. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,223,795,242]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Furthermore, distinct surfaces give rise to distinct Teichmüller spaces: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,250,795,305]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 6.2 ([76], Theorem 7.8). Let $S_{g,n}$ and $S_{g',n'}$ be orientable surfaces of finite type with negative Euler characteristics. Assume that $\\\\{(g,n),(g',n')\\\\}$ is not one of the three sets: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[305,309,687,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\{(1, 1), (0, 4) \\\\}, \\\\{(1, 2), (0, 5) \\\\}, \\\\{(2, 0), (0, 6) \\\\}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,334,794,369]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If $(g,n)\\\\neq (g^{\\\\prime},n^{\\\\prime})$ , then $(\\\\mathcal{T}(S),d_{Th})$ and $(\\\\mathcal{T}(S_{g^{\\\\prime},n^{\\\\prime}}),d_{Th})$ are not isometric. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,387,794,460]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6.2. Infinitesimal rigidity. The infinitesimal rigidity of the Thurston metric was first studied by Dumas-Lenzhen-Rafi-Tao [19] for once-punctured tori, then independently by Pan [47] and Huang-Ohshika-Papadopoulos [33] for surfaces of higher complexity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,467,795,521]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 6.3 ([19, 47, 33]). Let $S$ be a surface of finite type with negative characteristic. Let $X, Y \\\\in \\\\mathcal{T}(S)$ . Then there exists an isometry of normed vector spaces \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[331,526,663,547]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left(T _ {X} \\\\mathcal {T} (S), \\\\| \\\\bullet \\\\| _ {\\\\mathrm {T h}}\\\\right)\\\\rightarrow \\\\left(T _ {Y} \\\\mathcal {T} (S), \\\\| \\\\bullet \\\\| _ {\\\\mathrm {T h}}\\\\right)\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,551,794,585]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"if and only $X$ and $Y$ are in the same extended mapping class group orbit. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,604,795,642]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We can also use the Thurston norm to distinguish the topology of the underlying hyperbolic surfaces. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,648,795,702]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 6.4 ([47]). Let $S$ and $S'$ be two surfaces of finite type with negative Euler characteristics. Then there exists an isometry of normed vector spaces \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[330,708,665,729]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left(T _ {X} \\\\mathcal {T} (S), \\\\| \\\\bullet \\\\| _ {\\\\mathrm {T h}}\\\\right)\\\\rightarrow \\\\left(T _ {Y} \\\\mathcal {T} \\\\left(S ^ {\\\\prime}\\\\right), \\\\| \\\\bullet \\\\| _ {\\\\mathrm {T h}}\\\\right)\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,733,794,770]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"for some $X \\\\in \\\\mathcal{T}(S)$ and $Y \\\\in \\\\mathcal{T}(S')$ if and only if and only if $S$ and $S'$ are homeomorphic. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,777,795,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 6.5. The original statement of Theorem 6.4 is slightly differently from the statement here. In [47, Theorem 1.6], the isometry is assumed to be $\\\\mathbb{R}$ -linear. As pointed out in [33, Remark 1.16], this assumption is unnecessary, as isometries of the Thurston norm are also isometries of its (additive) symmetrisation, and the Mazur-Ulam theorem ensures that any isometry of the Thurston norm must be affine, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,118,792,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"24\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"25 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,143,794,181]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and hence there exists an isometric translate of the affine isometry which is a linear map. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,196,709,214]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Using the infinitesimal rigidity, we have the local rigidity: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,222,797,313]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 6.6 ([19, 47, 33]). Let $S$ be a surface of finite type with negative Euler characteristic. Let $U \\\\subset \\\\mathcal{T}(S)$ be a connected open subset, considered as a metric space with the restriction of the Thurston metric. Then any isometric embedding $(U, d_{Th}) \\\\to (\\\\mathcal{T}(S), d_{Th})$ is the restriction to $U$ of an element of the extended mapping class group. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,327,794,398]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Intuitively, this says that the quotient of $\\\\mathcal{T}(S)$ by the mapping class group is \\\"totally unsymmetric\\\": each ball fits into the space isometrically in only one place. As a direct consequence of Theorem 6.6, this proves Theorem 6.1 and extends it to the exceptional surfaces: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,406,797,460]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 6.7 ([76, 19, 47, 33]). Let $S$ be a surface of finite type with negative characteristic. Then every isometry of $\\\\mathcal{T}(S), d_{Th}$ is induced by an element of the extended mapping class group. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,476,794,512]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To pass from the infinitesimal rigidity to the local rigidity, one needs the following regularity result about the Thurston norm: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,518,797,574]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 6.8 ([19], Theorem 6.1). Let $S$ be a surface of finite type with negative characteristic. Then the Thurston norm function $T\\\\mathcal{T}(S) \\\\to \\\\mathbb{R}$ is locally Lipschitz. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[393,594,604,611]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7. COARSE GEOMETRY \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,628,794,664]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this section, we will discuss the coarse geometry of the Thurston metric. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,681,797,824]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7.1. Short markings. A pants decomposition on $S$ is a collection of mutually disjoint curves which cut $S$ into pairs of pants. A marking $\\\\mu$ on $S$ is a pants curve system $P$ with additionally a set of transverse curves $Q$ satisfying the following properties. We require each curve $\\\\alpha \\\\in P$ to have a unique transverse curve $\\\\beta \\\\in Q$ that intersects $\\\\alpha$ minimally (once or twice) and is disjoint from all other curves in $P$ . We will often say $\\\\alpha$ and $\\\\beta$ are dual to each other, and write $\\\\bar{\\\\alpha} = \\\\beta$ or $\\\\bar{\\\\beta} = \\\\alpha$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,830,797,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Given $X \\\\in \\\\mathcal{T}(S)$ , a short marking $\\\\mu_{X}$ on $X$ is a marking where the pants curve system is constructed using the algorithm that picks the shortest curve on $X$ , then the second shortest disjoint from the first, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"26 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"25\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,145,795,233]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and so on. Once the pants curve system is complete, the transverse curves are then chosen to be as short as possible. Note that a short marking on $X$ may not be unique, but all short markings on $X$ form a bounded set in the curve complex. Thus, we will refer to $\\\\mu_{X}$ as the associated short marking on $X$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,260,795,367]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7.2. Curve graphs. Given two curves $\\\\alpha$ and $\\\\beta$ on $S$ , we define their intersection numberi $(\\\\alpha, \\\\beta)$ to be the minimal number of intersections between any representatives of homotopy classes of $\\\\alpha$ and $\\\\beta$ . Notice that the minimum of intersection numbers for any two distinct (homotopy classes of) simple closed curves is 1 for the once-punctured torus, 2 for the four-holed sphere, and 0 for all other surfaces. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,375,795,465]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The curve graph $C(S)$ is defined as follows: the vertices are homotopy classes of nontrivial simple closed curves and two vertices are connected by an edge if the corresponding curves can be realized to have minimal possible intersection numbers. We equip $C(S)$ with a metric by assigning length one to every edge. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,472,795,667]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"If $S$ is an annulus, the above definition does not give interesting objects since there is only one homotopy class of simple closed curves on any annulus. We need a different definition. To emphasize the difference, we denote by $A$ the (topological) annulus. By an arc on $A$ we always mean a homotopy class of a simple arc $\\\\omega$ connecting the two boundary components of $A$ where the homotopy is taken relative to the endpoints of $\\\\omega$ . The intersection $i(\\\\omega, \\\\omega')$ of two arcs is the minimal number of intersections between any representatives of homotopy classes of $\\\\omega$ and $\\\\omega'$ . The vertices of the curve graph $C(A)$ are arcs on $A$ and the edges are pairs of arcs with zero intersection. We also equip $C(A)$ with a metric as above. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,694,794,729]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7.3. Subsurface projection. For any subsurface $Y$ of $S$ , the subsurface projection \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[403,734,594,753]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\pi_ {Y}: C (S) \\\\to \\\\mathcal {P} (C (Y))\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,760,795,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"from $C(S)$ to the set of subsets of the vertices of $C(Y)$ is defined as follows. Suppose first that $Y$ is not an annulus. If $\\\\alpha$ is disjoint from $Y$ , then $\\\\pi_Y(\\\\alpha) = \\\\emptyset$ . If $\\\\alpha$ is contained in $Y$ , then $\\\\pi_Y(\\\\alpha) = \\\\alpha$ . If $\\\\alpha$ intersects $Y$ , then $\\\\alpha \\\\cap Y$ is a union of arcs. Let $\\\\omega$ be such an arc. Let $\\\\delta$ and $\\\\delta'$ be the boundary components of $Y$ intersecting $\\\\omega$ . Let $\\\\alpha_{\\\\omega}$ be the collection of boundary components of the $\\\\epsilon$ -regular neighbourhood of $\\\\delta \\\\cup \\\\omega \\\\cup \\\\delta'$ for sufficiently small $\\\\epsilon$ . The projection $\\\\pi_Y(\\\\alpha)$ is then defined \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,118,792,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"26\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"27 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,143,794,180]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"as the collection of $\\\\alpha_{\\\\omega}$ for all arcs of $\\\\alpha \\\\cap Y$ . From the construction we see that the diameter of $\\\\pi_Y(\\\\alpha)$ is at most two. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,188,795,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We now consider the case where $S$ is an annulus $A$ with core curve $\\\\gamma$ . The Gromov compactification of the annulus cover of $S$ corresponding to $\\\\gamma \\\\in \\\\pi_1(S)$ is well-defined and is independent of the choice of the hyperbolic metrics on $S$ . For any simple closed curve $\\\\alpha \\\\in C(S)$ , the projection $\\\\pi_A(\\\\alpha)$ is defined to be the lifts of $\\\\alpha$ to the annulus cover that connects two boundary components of the annulus. Notice that any lift has exactly two well-defined endpoints in the Gromov compactification. The diameter of $\\\\pi_A(\\\\alpha)$ is also at most two. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,338,794,375]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The projection of multicurves is defined as the union of the projection of each simple closed curve. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,390,784,409]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7.4. Combinatorial model. Recall that for any $X$ and $Y$ in $\\\\mathcal{T}(S)$ , \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[379,412,616,454]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nd _ {T h} (X, Y) = \\\\log \\\\sup _ {\\\\alpha} \\\\frac {\\\\ell_ {\\\\alpha} (Y)}{\\\\ell_ {\\\\alpha} (X)},\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,455,794,531]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\alpha$ ranges over all essential simple closed curves on $S$ . This implies that there is a simple closed curve $\\\\alpha$ such that $\\\\log \\\\frac{\\\\ell_{\\\\alpha}(Y)}{\\\\ell_{\\\\alpha}(X)}$ is a good estimate of $d_{Th}$ . Lenzhen, Rafi, and Tao proved that such a curve can be chosen within any short marking $\\\\mu_{X}$ of $X$ : \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,536,795,571]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 7.1 ([37], Theorem E). There exists a constant $C$ depending on the topology of $S$ such that for any $X$ and $Y$ in $\\\\mathcal{T}(S)$ , \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[349,575,645,617]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left| d _ {T h} (X, Y) - \\\\log \\\\max _ {\\\\alpha \\\\in \\\\mu_ {X}} \\\\frac {\\\\ell_ {\\\\alpha} (Y)}{\\\\ell_ {\\\\alpha} (X)} \\\\right| \\\\leq C.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,628,794,665]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 7.1 is a consequence of the following estimate of lengths of simple closed curves in terms of short markings. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,670,794,726]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Proposition 7.2 ([37], Proposition 3.1). There exists a positive constant $C$ depending on the topology of $S$ , such that for any $X \\\\in \\\\mathcal{T}(S)$ , any simple closed curve $\\\\gamma$ , and any short marking $\\\\mu_X$ of $X$ , \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,728,723,768]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nC ^ {- 1} \\\\sum_ {\\\\alpha \\\\in \\\\mu_ {X}} i (\\\\gamma , \\\\alpha) \\\\ell_ {\\\\bar {\\\\alpha}} (X) \\\\leq \\\\ell_ {\\\\alpha} (X) \\\\leq C \\\\sum_ {\\\\alpha \\\\in \\\\mu_ {X}} i (\\\\gamma , \\\\alpha) \\\\ell_ {\\\\bar {\\\\alpha}} (X).\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,772,792,791]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 7.3. (1) A similar estimate also holds for the extremal length: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[228,795,766,837]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nC ^ {- 1} \\\\sum_ {\\\\alpha \\\\in \\\\mu_ {X}} i (\\\\gamma , \\\\alpha) ^ {2} \\\\mathrm {E x t} _ {\\\\bar {\\\\alpha}} (X) \\\\leq \\\\mathrm {E x t} _ {\\\\alpha} (X) \\\\leq C \\\\sum_ {\\\\alpha \\\\in \\\\mu_ {X}} i (\\\\gamma , \\\\alpha) ^ {2} \\\\mathrm {E x t} _ {\\\\bar {\\\\alpha}} (X).\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,849,794,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2) For similar estimates using twists with respect to some pants decomposition, see [44]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"28 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"27\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,143,794,251]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7.5. Short curves. One way to understand the behavior of Thurston geodesics in the moduli space of Riemann surfaces is to characterize short curves along the corresponding family of hyperbolic surfaces. Such a characterization is known for Teichmüller geodesics (see [59, Theorem 1.1] or [37, Theorem 2.3]). However, the situation is more involved for Thurston geodesics. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,258,794,295]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Definition 7.4. (1) Let $K$ be a positive constant. Two points $X$ and $Y$ in $\\\\mathcal{T}(S)$ are said to have $K$ -bounded combinatorics if \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[379,301,616,321]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nd _ {C (\\\\Sigma)} (\\\\pi_ {\\\\Sigma} (\\\\mu_ {X}), \\\\pi_ {\\\\Sigma} (\\\\mu_ {Y})) \\\\leq K\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[261,327,792,361]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"for any subsurface $\\\\Sigma \\\\subset S$ , where $\\\\mu_{X}$ and $\\\\mu_{Y}$ are respectively the short markings of $X$ and $Y$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[230,362,792,398]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(2) A path in $\\\\mathcal{T}(S)$ is said to be $\\\\epsilon$ cobounded if it is contained in the $\\\\epsilon$ thick part of $\\\\mathcal{T}(S)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,406,795,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 7.5 ([37], Theorem A). Let $X$ and $Y$ be two points in the $\\\\epsilon$ -thick part of $\\\\mathcal{T}(S)$ . If $X$ and $Y$ have $K$ -bounded combinatorics, then every Thurston geodesic from $X$ to $Y$ fellow travels the Teichmüller geodesic from $X$ to $Y$ , and hence is $\\\\epsilon'$ -cobounded, where $\\\\epsilon'$ depends on $\\\\epsilon$ and $K$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,513,794,549]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This reflects a negative-curvature phenomenon of the Thurston metric. More precisely, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,556,794,628]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 7.6 ([37], Theorem C and Corollary D). Let $\\\\mathcal{G}$ be a Thurston geodesic in $\\\\mathcal{T}(S)$ whose endpoints have bounded combinatorics. Then the closed point projection to $\\\\mathcal{G}$ is strongly contracting. In particular, any quasi-geodesic with the same endpoints as $\\\\mathcal{G}$ fellow travels $\\\\mathcal{G}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,637,795,832]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 7.7. From Theorem 7.5, we see bounded combinatorics implies $\\\\epsilon$ -cobounded. One may wonder whether the inverse still holds or not. For the Teichmüller metric, the converse also holds. In fact, two points $X$ and $Y$ in $\\\\mathcal{T}(S)$ have bounded combinatorics if and only if the Teichmüller geodesic connecting them is cobounded ([59, Theorem 1.1], see also [37, Theorem 2.2]). However, it is not the case for the Thurston metric. There exists $\\\\epsilon_0 > 0$ such that for any $\\\\epsilon > 0$ , there are points $X$ and $Y$ in $\\\\mathcal{T}(S)$ and a Thurston geodesic from $X$ to $Y$ that stays in the $\\\\epsilon_0$ thick part of $\\\\mathcal{T}(S)$ , whereas the associated Teichmüller geodesic from $X$ to $Y$ does not stay in the $\\\\epsilon$ -thick part of $\\\\mathcal{T}(S)$ [38, Theorem 1.4]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,849,794,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Recall that the Thuston metric is not uniquely geodesic. If we remove the bounded combinatorics assumption, then the fellow traveling \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,118,792,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"28\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"29 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,143,794,198]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"property fails. In fact, for any $D > 0$ , there are points $X, Y, Z$ in $\\\\mathcal{T}(S)$ and two Thurston geodesics $\\\\mathcal{G}_1, \\\\mathcal{G}_2$ from $X$ to $Y$ with the following properties [38, Theorem 1.1]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[243,210,790,297]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"- Geodesics $\\\\\\\\mathcal{G}_1$ and $\\\\\\\\mathcal{G}_2$ do not fellow travel each other; the point $Z$ lies in path $\\\\\\\\mathcal{G}_1$ but is at least $D$ away from any point in $\\\\\\\\mathcal{G}_2$ ; \\\",\\\"- The geodesic $\\\\\\\\mathcal{G}_1$ parameterized in any way in the reverse direction is not a geodesic. In fact, the point $Z$ is at least $D$ away from any point in any geodesic from $Y$ to $X$ . \\\"]\",\n \"page_idx\": \"29\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[200,313,795,383]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"On the other hand, if we consider the projection to the curve complex, which sends a point in $X \\\\in \\\\mathcal{T}(S)$ to the set of shortest simple closed curves, then all Thurston geodesics with common endpoints nearly look the same: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,395,795,431]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 7.8 ([38], Theorem 1.2). The shadow of a Thurston geodesic to the curve graph is a reparameterized quasi-geodesic. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,441,795,512]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 7.9. Since the curve graph is Gromov hyperbolic [42], quasi-geodesics with common endpoints fellow travel each other. Hence, for any two points $X$ and $Y$ in $\\\\mathcal{T}(S)$ , the shadow to the curve graph of different Thurston geodesics form $X$ to $Y$ fellow travel each other. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,532,795,710]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In [19], the authors provided another characterization of short curves along Thurston geodesics. Before stating the result, let us introduce the notion of absolute twisting $d_{\\\\alpha}(X,Y)$ of two hyperbolic surfaces $X$ and $Y$ relative to a simple closed curve $\\\\alpha$ . Let $\\\\omega$ be a geodesic arc on $X$ which is orthogonal to the geodesic representative of $\\\\alpha$ on $X$ . Let $\\\\omega'$ be a geodesic arc on $Y$ which is orthogonal to the geodesic representative of $\\\\alpha$ on $Y$ . Let $\\\\widehat{X} \\\\to X$ be the annulus cover of $X$ corresponding to $\\\\alpha$ . Let $\\\\widehat{\\\\alpha}$ be the core curve of $\\\\widehat{X}$ . Let $\\\\widehat{\\\\omega}$ and $\\\\widehat{\\\\omega'}$ be respectively lifts of $\\\\omega$ and $\\\\omega'$ intersecting $\\\\widehat{X}$ . The absolute twisting $d_{\\\\alpha}(X,Y)$ of $X$ and $Y$ relative to $\\\\alpha$ is defined to be: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[395,720,596,742]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nd _ {\\\\alpha} (X, Y) = \\\\min i (\\\\widehat {\\\\omega}, \\\\widehat {\\\\omega} ^ {\\\\prime})\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,750,794,823]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where the minimum ranges over all such $\\\\omega$ and $\\\\omega'$ and their lifts. (Notice that $\\\\widehat{X}$ has a well-defined Gromov compatification, and $i(\\\\widehat{\\\\omega},\\\\widehat{\\\\omega}')$ is considered the minimum intersection number in the given homotopy class relative to their endpoints.) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,830,794,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Recall that for any pair of distinct points $X$ and $Y$ in $\\\\mathcal{T}(S)$ , there is a well-defined lamination, the maximally stretched lamination $\\\\Lambda(X,Y)$ (see Section 2.3). A simple closed curve $\\\\alpha$ is said to interact with the \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"30 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"29\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,143,792,180]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"maximally stretched lamination $\\\\Lambda(X, Y)$ if it belongs to the lamination or intersects it essentially. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,188,797,277]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 7.10 ([19], Theorem 1.2). There exists a constant $\\\\epsilon_0$ such that the following statement holds. Let $X$ and $Y$ be two points in the $\\\\epsilon_0$ -thick part of $\\\\mathcal{T}(S)$ and let $\\\\alpha$ be a simple closed curve on $S$ that interacts with $\\\\Lambda(X, Y)$ . Then the minimum length $\\\\ell_{\\\\alpha}$ of $\\\\alpha$ along any Thurston geodesic from $X$ to $Y$ satisfies: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[274,281,723,319]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nC ^ {- 1} \\\\cdot d _ {\\\\alpha} (X, Y) - C ^ {\\\\prime} \\\\leq \\\\frac {1}{\\\\ell_ {\\\\alpha}} \\\\mathrm {L o g} \\\\frac {1}{\\\\ell_ {\\\\alpha}} \\\\leq C \\\\cdot d _ {\\\\alpha} (X, Y) + C ^ {\\\\prime}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,321,795,359]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $C$ and $C'$ are two constants that depend only on $\\\\epsilon_0$ , and where $\\\\operatorname{Log}(x) := \\\\max \\\\{1, \\\\log(x)\\\\}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,376,794,412]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For more interesting discussions about short curves, we refer to [19, Section 3]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,420,794,455]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Based on the above characterization of short curves, Telpukhovskiy proved that Masur's criterion does not hold in the Thurston metric: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,464,795,518]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 7.11 ([69]). There are Thurston stretch paths in the Teichmüller space $\\\\mathcal{T}(S_{0,7})$ with minimal, filling, but not uniquely ergodic horocyclic foliation, that stay in the thick part for the whole time. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,536,795,604]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7.6. Length spectrum metric and the product theorem. Inspired by Minsky's product theorem for the Teichmüller metric, Choi and Rafi proved an analogue for the symmetrized metric $d_{L}$ of the Thurston metric: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[323,613,671,633]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nd _ {L} (X, Y) := \\\\max \\\\{d _ {T h} (X, Y), d _ {T h} (Y, X) \\\\}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,638,635,656]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The metric $d_{L}$ is called the length spectrum metric. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,664,794,700]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For any positive constant $\\\\epsilon$ , consider the $\\\\epsilon$ -thick part $\\\\mathrm{Thick}_{\\\\epsilon}(S)$ and the $\\\\epsilon$ -thin part $\\\\mathrm{Thin}_{\\\\epsilon}(S)$ defined as below: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,705,812,724]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\operatorname{Thick}_{\\\\epsilon}(S) \\\\coloneqq \\\\{X \\\\in \\\\mathcal{T}(S) : \\\\ell_{\\\\alpha}(X) \\\\geq \\\\epsilon \\\\text{ for every simple closed curve } \\\\alpha\\\\}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[207,728,812,748]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\operatorname{Thin}_{\\\\epsilon}(S) := \\\\{X \\\\in \\\\mathcal{T}(S) : \\\\ell_{\\\\alpha}(X) < \\\\epsilon \\\\text{ for some simple closed curve } \\\\alpha\\\\}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,753,797,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For a multicurve $\\\\Gamma$ , we define the subset $\\\\mathrm{Thin}_{\\\\epsilon}(\\\\Gamma; S)$ of the $\\\\epsilon$ -thin part as the set of points $X \\\\in \\\\mathcal{T}(S)$ satisfying $\\\\ell_{\\\\alpha}(X) < \\\\epsilon$ if and only if $\\\\alpha \\\\in \\\\Gamma$ . Let $\\\\mathcal{T}(S \\\\backslash \\\\Gamma)$ be the Teichmüller space of the punctured surface homeomorphic to $S \\\\backslash \\\\Gamma$ , let $U_i := \\\\{(x, y) \\\\in \\\\mathbb{R} : y > 1 / \\\\epsilon\\\\}$ be the subset of the upper half plane. Then the Fenchel-Nielsen coordinates on $\\\\mathcal{T}(S)$ provide a natural homeomorphism: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[313,866,679,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\Pi : \\\\operatorname {T h i n} _ {\\\\epsilon} (\\\\Gamma ; S) \\\\rightarrow \\\\mathcal {T} (S \\\\backslash \\\\Gamma) \\\\times U _ {1} \\\\times \\\\dots \\\\times U _ {k}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,118,790,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"30\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"31 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,143,794,180]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $d_{L(S\\\\backslash \\\\Gamma)}$ be the Lipschitz metric on $\\\\mathcal{T}(S\\\\backslash \\\\Gamma)$ . Let $d_{L(\\\\gamma_i)}$ be a modified metric of the hyperbolic metric on $U_{i}$ . Let \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[336,188,656,209]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nd _ {L _ {\\\\Gamma}} := \\\\sup \\\\left\\\\{d _ {L (S \\\\backslash \\\\Gamma)}, d _ {L (\\\\gamma_ {1})}, \\\\dots , d _ {L (\\\\gamma_ {k})} \\\\right\\\\}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,215,429,233]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Choi and Rafi proved that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,243,795,296]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 7.12 ([15], Theorem C). There exists a constant $c$ depending on $\\\\epsilon$ and the topology of $S$ such that for any multicurve $\\\\Gamma$ and for any $X$ and $Y$ in $\\\\mathrm{Thin}_{\\\\epsilon}(\\\\Gamma; S)$ , we have \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[348,305,648,325]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left| d _ {L} (X, Y) - d _ {L _ {\\\\Gamma}} (\\\\Pi (X), \\\\Pi (Y)) \\\\right| \\\\leq c.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,343,795,450]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Before closing this subsection, let us mention the comparison between the length spectrum metric and the Teichmüller metric. In the thick part of $\\\\mathcal{T}(S)$ , these two metrics are almost isometric [15, Theorem B], whereas in the whole Teichmüller space they are not comparable [39, 15]. On the other hand, they are almost isometric in the moduli space [41, 40]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[359,479,635,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8. COUNTING LATTICE POINTS \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,513,794,565]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this section, we will discuss the lattice counting problem about the Thurston metric. Before stating the counting result precisely, we need several definitions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,574,794,628]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Following Bonahon [9], we can embed the Teichmüller space $\\\\mathcal{T}(S)$ as a subset of the space $\\\\mathcal{C}(S)$ of geodesic currents in such a way that for every $Y\\\\in \\\\mathcal{T}(S)$ and for every curve $\\\\gamma$ we have \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[426,637,568,656]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\ni (\\\\gamma , Y) = \\\\ell_ {Y} (\\\\gamma).\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,664,792,700]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"One can also embed $\\\\mathcal{T}(S)$ into the space of functions on $\\\\mathcal{C}(S)$ as follows. Let $X\\\\in \\\\mathcal{T}(S)$ . Define the function $D_{X}$ : \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[356,708,635,770]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} D _ {X}: \\\\mathcal {C} (S) \\\\longrightarrow \\\\mathbb {R} \\\\\\\\ \\\\eta \\\\longmapsto \\\\sup _ {\\\\lambda \\\\in \\\\mathcal {M L} (S)} \\\\frac {i (\\\\eta , \\\\lambda)}{\\\\ell_ {X} (\\\\lambda)}. \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,777,794,811]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It is clear that $D_X: \\\\mathcal{C}(S) \\\\to \\\\mathbb{R}$ is positive, homogeneous and continuous. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,821,794,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $\\\\mu_{Th}$ be the Thurston volume on $\\\\mathcal{ML}(S)$ . For any positive, homogeneous and continuous function $f$ on $\\\\mathcal{C}(S)$ , define \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[318,866,676,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nm (f) := \\\\mu_ {T h} (\\\\{\\\\lambda \\\\in \\\\mathcal {M L} (S): i (\\\\alpha , \\\\lambda) \\\\leq 1 \\\\}).\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[202,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"32 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[382,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"31\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,143,480,162]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In particular, for any $Y \\\\in \\\\mathcal{T}(S)$ , \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[321,169,676,189]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nm (Y) := \\\\mu_ {T h} (\\\\{\\\\lambda \\\\in \\\\mathcal {M L} (S): \\\\ell_ {Y} (\\\\lambda) \\\\leq 1 \\\\}),\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,196,240,210]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[310,213,686,234]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nm (D _ {Y}) := \\\\mu_ {T h} (\\\\{\\\\lambda \\\\in \\\\mathcal {M L} (S): D _ {Y} (\\\\lambda) \\\\leq 1 \\\\}).\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,237,300,253]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, let \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[390,253,607,294]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nm _ {S} := \\\\int_ {\\\\mathcal {M} (S)} m (Y) d \\\\mathrm {v o l} _ {w p}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,296,808,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\mathcal{M}(S)$ is the moduli space and $d\\\\mathrm{vol}_{wp}$ represents the Weil-Petersson volume. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,340,797,378]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 8.1 ([60], Theorem 1.1). Let $S$ be a closed orientable surface of genus at least two. Let $X$ and $Y$ be two points in $\\\\mathcal{T}(S)$ . Then \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[243,381,751,421]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\lim _ {R \\\\to \\\\infty} \\\\frac {\\\\# \\\\{\\\\phi \\\\in \\\\mathrm {M C G} (S) : d _ {T h} (X , \\\\phi (Y)) \\\\leq R \\\\}}{e ^ {(6 g - 6) R}} = \\\\frac {m (D _ {X}) m (Y)}{m _ {S}}.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,426,797,537]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 8.2. Theorem 8.1 is a consequence of a more general counting result due to [60], where the authors counted the mapping class group orbits of filling currents (for more information about this type of counting problems, we refer to [22, 21] and references therein). The analogue result under the Teichmüller metric was first proved in [5] and improved with an error term in [4]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[372,559,624,575]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"9. SHEARING COORDINATES \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,593,795,662]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The shearing coordinates for $\\\\mathcal{T}(S)$ was introduced by Thurston [74]. The shearing operation is a generalization of the earthquake deformation. In Thurston's preprint, the construction is called cataclysm coordinates. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,672,795,727]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $\\\\Delta$ be an ideal triangle in the hyperbolic plane. There is a unique circle in $\\\\Delta$ tangent to each edge of $\\\\Delta$ . If $\\\\gamma$ is an edge of $\\\\Delta$ , then the circle intersects $\\\\gamma$ at some distinguished point. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,734,795,825]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Consider two ideal triangles $\\\\Delta_a, \\\\Delta_b$ , with disjoint interiors and a common edge $\\\\gamma$ . The shear parameter $s_\\\\gamma$ is defined to be the signed distance of the two distinguished points on $\\\\gamma$ . The quantity $s_\\\\gamma$ measures the magnitude of shift (or twist) when we glue $\\\\Delta_a$ and $\\\\Delta_b$ . We refer to [7] for details. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,830,795,886]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Fix a finite ideal triangulation $\\\\lambda$ of $S$ . For each hyperbolic surface $X \\\\in \\\\mathcal{T}(S)$ , $\\\\lambda$ is represented as a geodesic lamination with finitely many leaves whose complementary components are ideal triangles. We can \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,118,792,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"32\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"33 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[200,143,794,180]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"associate with each edge $\\\\gamma$ of $\\\\lambda$ a shear parameter $s_{\\\\gamma}(X)$ . Then the map \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[388,189,607,233]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} s _ {\\\\lambda}: \\\\mathcal {T} (S) \\\\to \\\\mathbb {R} ^ {| \\\\lambda |} \\\\\\\\ X \\\\mapsto (s _ {\\\\gamma} (X)) _ {\\\\gamma \\\\in \\\\lambda} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,242,795,296]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"is an embedding, which is called a shearing coordinates of $\\\\mathcal{T}(S)$ . Note that the image of $s_{\\\\lambda}$ is an open convex cone of a linear subspace of the dimension $6g + 2n - 6$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,303,795,375]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For example, every pants decomposition of $S$ can be completed to be a finite ideal triangulation. Then, the corresponding Fenchel-Nielsen parameters of $\\\\mathcal{T}(S)$ can be extended (up to linear transformation) to the shearing coordinates. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,385,794,439]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remark 9.1. In Mirzakhani's wrok, random hyperbolic surfaces are defined by gluing random pairs of pants. It is also natural to construct random hyperbolic surfaces by gluing ideal triangles randomly. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,458,795,566]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The above construction works for general maximal geodesic laminations. Fix a maximal geodesic lamination $\\\\lambda$ . Then each $X \\\\in \\\\mathcal{T}(S)$ can be associated with a horocyclic measured foliation $F_{\\\\lambda}(X)$ and a shearing cocycle. In brief, a shearing cocycle is similar to some transverse weights on a train track carrying $\\\\lambda$ , and the weights measure the shifts of the shear map when one hyperbolic surface is deformed into another. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,571,794,645]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conversely, for any shearing cocycle, one can construct a measured foliation $F_{\\\\lambda}$ in a neighborhood of $\\\\lambda$ , whose leaves are cocycles orthogonal to $\\\\lambda$ . It turns out that, there is a unique hyperbolic structure $X$ on $S$ such that $F_{\\\\lambda}$ extends to $F_{\\\\lambda}(X)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,651,794,688]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $\\\\mathcal{MF}(\\\\lambda)$ be the set of measured foliations that is totally transverse to $\\\\lambda$ (see [74, Proposition 9.4]). Then \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,698,794,733]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 9.2 (Thurston). Let $\\\\lambda$ be a maximal geodesic lamination on $S$ . Then the shear map \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[400,744,596,782]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} F _ {\\\\lambda}: \\\\mathcal {T} (S) \\\\rightarrow \\\\mathcal {M F} (\\\\lambda) \\\\\\\\ X \\\\mapsto F _ {\\\\lambda} (X) \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,792,563,811]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"is a real analytic parametrization of $\\\\mathcal{T}(S)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,830,794,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The shearing coordinates can be also interpreted as transverse cycles, as did by Bonahon [10]. There are several nice properties and developments of this notion: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"34 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"33\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[232,143,794,409]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(1) The shear map pulls back the Thurston form on $\\\\\\\\mathcal{MF}(S)$ to the Weil-Petersson symplectic form on $\\\\\\\\mathcal{T}(S)$ [53, 67]. This has been very useful when Mirzakhani [45] proved that the earthquake flow is measured isomorphic to the horocycle flow on moduli space. \\\",\\\"(2) The complexified version of transverse cocycles can be used to measure the bending of pleated surfaces, and thus is used to extend Thurston's parametrization to the quasi-Fuchsian space [10]. Furthermore, Thurston's parametrization can be extended to Hitchin representations into $\\\\\\\\mathrm{PSL}_n(\\\\\\\\mathbb{R})$ [11, 12]. \\\",\\\"(3) There are many related works on decorated Teichmüller spaces, quantum Teichmüller spaces and higher Teichmüller spaces, such as [25, 24, 26], ect. \\\",\\\"(4) There is a construction of shearing coordinates on the universal Teichmüller space, see [58, 63, 64] \\\"]\",\n \"page_idx\": \"34\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[199,435,792,506]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"When $\\\\lambda$ is not a maximal geodesic lamination, the horocyclic foliation is no longer well-defined. Such a difficulty was already encountered in the case of surfaces with boundaries, when Alessandrini-Disarlo [3] constructed geodesics for the arc metric. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[199,513,792,621]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In general, Calderon-Farre [13] defined orthogeodesic foliations associated with $\\\\lambda$ . The orthogeodesic foliations are constructed on complementary subsurfaces. They showed that the restriction of the orthogeodesic foliation to each component of $S \\\\setminus \\\\lambda$ completely determines the hyperbolic structure on that piece. Thus they generalized the shearing coordinates of $\\\\mathcal{T}(S)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,628,792,666]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We conclude this section with the following result of Théret [71], which improves the result of [7, Theorem 1.3]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,690,795,779]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 9.3 ([71], Theorem 1.1). Let $\\\\mu$ be a measured geodesic lamination transverse to the complete geodesic lamination $\\\\lambda$ on $S$ . Then the length function $\\\\ell_{\\\\mu}$ is a convex function of the shear coordinates defined over $\\\\mathcal{T}(S)$ associated with $\\\\lambda$ , and $\\\\ell_{\\\\mu}$ is strictly convex whenever $\\\\mu$ intersects all leaves of $\\\\lambda$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[199,813,792,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In particular, lengths functions are convex along stretch lines. An interesting corollary is that the length of the horocyclic foliation is strictly decreasing on a stretch line and converges to zero as $t$ converges to infinity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[271,116,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,118,792,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"34\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"35 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[277,145,718,161]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10. GENERALIZATION OF THE THURSTON METRIC \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,180,794,251]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this section, we shall discuss some generalizations of the Thurston metric. As we mentioned earlier, there is a generalization to the setting of hyperbolic surface with geodesic boundary components, the arc metric, see Remark 5.4. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,258,795,401]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Gueritaud-Kassel [28] considered a pair $(j,\\\\rho)$ of representations of a discrete group $\\\\Gamma_0$ into $G = \\\\operatorname{Isom}(\\\\mathbb{H}^n)$ such that $j$ is injective with $j(\\\\Gamma_0)$ discrete and geometrically finite. They showed that, when the minimal Lipschitz constant is strictly greater than 1, there exists a geodesic lamination that is \\\"maximally stretched\\\" by any extremal $(j,\\\\rho)$ -equivariant Lipschitz map $f:\\\\mathbb{H}^n\\\\to \\\\mathbb{H}^n$ . As an application, they generalized the two-dimensional results and constructions of Thurston and extend the Thurston metric on Teichmüller space to higher dimension. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,409,794,445]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let us denote the minimal Lipschitz constant of $(j,\\\\rho)$ -equivariant map by $L(j,\\\\rho)$ . A related constant is \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[388,467,609,507]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nK (j, \\\\rho) = \\\\log \\\\sup _ {\\\\gamma} \\\\frac {\\\\lambda (\\\\rho (\\\\gamma))}{\\\\lambda (j (\\\\gamma))},\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,510,794,559]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\lambda$ denotes the translation length of the element, and the supremum is taken over all hyperbolic elements in $\\\\gamma \\\\in \\\\Gamma_0$ . It is obvious that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[423,564,571,584]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nK (j, \\\\rho) \\\\leq L (j, \\\\rho).\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,595,794,667]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $M = \\\\mathbb{H}^n / \\\\Gamma_0$ be a geometrically finite hyperbolic manifolds. The Teichmüller space $\\\\mathcal{T}(M)$ is defined to be the set of conjugacy classes of geometrically finite representations of $\\\\Gamma_0$ . For $j, \\\\rho \\\\in \\\\mathcal{T}(M)$ , denote the critical exponents of $j$ and $\\\\rho$ by $\\\\delta(j)$ and $\\\\delta(\\\\rho)$ , respectively. Then \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,676,516,695]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Theorem 10.1 ([28]). The function \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[372,700,620,742]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nd _ {\\\\mathrm {T h}} (j, \\\\rho) = \\\\log \\\\left(L (j, \\\\rho) \\\\frac {\\\\delta (\\\\rho)}{\\\\delta (j)}\\\\right)\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[202,747,578,766]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"defines an asymmetry metric on $\\\\mathcal{T}(M)$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,784,794,816]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We call the above metric a generalized Thurston metric. Another version is \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[205,821,625,862]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\overline {{d}} _ {\\\\mathrm {T h}} (j, \\\\rho) = \\\\log \\\\left(K (j, \\\\rho) \\\\frac {\\\\delta (\\\\rho)}{\\\\delta (j)}\\\\right). \\\\tag {4}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[200,867,792,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As pointed out by Guéritaud-Kassel, the two metrics differ in general. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[202,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"36 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"35\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[200,143,795,180]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Question 1. Is the generalized Thurston metric $d_{\\\\mathrm{Th}}$ Finsler? How to construct geodesics of $d_{\\\\mathrm{Th}}$ ? \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,202,795,292]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Recently, Sapir [62] extended the Thurston metric to the space of projective filling currents; Carvajales-Dai-Pozzetti-Wienhard [14] generalized the Thurston metric and the associated Finsler norm to Anosov representations of surface groups, including the space of Hitchin representations. The distance formula is similar to (4). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,299,795,371]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Thurston metric has an analogue in Outer space, see [75] for a discussion. Just like the Thurston metric on $\\\\mathcal{T}(S)$ , this metric is not symmetric. It was used by Bestvina [8] to give a Bers-like proof of the train track theorem for fully irreducible automorphisms of $F_{n}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,378,794,398]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Regarding the extremal Lipschitz maps, Thurston [74] suggested that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[258,414,754,484]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"\\\"I currently think that a characterization of minimal stretch maps should be possible in a considerably more general context (in particular, to include some version for all Riemannian surfaces)...\\\" \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,501,689,518]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For related results along this line, we refer to [49, 16, 17]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[200,527,794,617]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, let us mention that it is impossible to deform hyperbolic metrics of finite area in $\\\\mathcal{T}(S)$ such that no length of any closed geodesic is increased. This is a typical example of the (marked) length spectrum rigidity problem, which is extensively studied in geometry and dynamics, see [46, 18, 29] for examples. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[437,662,558,678]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"36\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"REFERENCES \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[210,686,795,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[1] S.I. Al'ber. On n-dimensional problems in the calculus of variations in the large. In Sov. Math. Dokl, volume 5, page 26, 1964. \\\",\\\"[2] D. 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May 2022. \\\",\\\"[18] Moon Duchin, Christopher J Leininger, and Kasra Rafi. Length spectra and degeneration of flat metrics. Inventiones mathematicae, 182(2):231-277, 2010. \\\",\\\"[19] David Dumas, Anna Lenzhen, Kasra Rafi, and Jing Tao. Coarse and fine geometry of the Thurston metric. Forum of Mathematics. Sigma, 8:Paper No. e28, 58, 2020. \\\",\\\"[20] James Eells, Jr. and J. H. Sampson. Harmonic mappings of Riemannian manifolds. Amer. J. Math., 86:109-160, 1964. \\\",\\\"[21] Viveka Erlandsson and Juan Souto. Mirzakhani's curve counting and geodesic currents, volume 345 of Progress in Mathematics. Birkhäuser/Springer, Cham, [2022] ©2022. \\\",\\\"[22] Viveka Erlandsson and Caglar Uyanik. Length functions on currents and applications to dynamics and counting. In In the tradition of Thurston—geometry and topology, pages 423–458. Springer, Cham, [2020] ©2020. \\\",\\\"[23] Albert Fathi, François Laudenbach, and Valentin Poénaru. Thurston's work on surfaces, volume 48 of Mathematical Notes. Princeton University Press, Princeton, NJ, 2012. Translated from the 1979 French original by Djun M. Kim and Dan Margalit. \\\"]\",\n \"page_idx\": \"37\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[202,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"38 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,117,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"37\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[204,146,794,857]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[24] Vladimir Fock and Alexander Goncharov. Moduli spaces of local systems and higher Teichmüller theory. *Publications Mathématiques de l'IHÉS*, 103:1-211, 2006. \\\",\\\"[25] Vladimir V Fock and Alexander B Goncharov. Dual Teichmüller and lamination spaces. arXiv preprint math/0510312, 2005. \\\",\\\"[26] Vladimir V Fock and Alexander B Goncharov. Moduli spaces of convex projective structures on surfaces. Advances in Mathematics, 208(1):249-273, 2007. \\\",\\\"[27] M. Gromov. Hyperbolic manifolds, groups and actions. In Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), volume 97 of Ann. of Math. Stud., pages 183-213. Princeton Univ. Press, Princeton, N.J., 1981. \\\",\\\"[28] François Guéritaud and Fanny Kassel. Maximally stretched laminations on geometrically finite hyperbolic manifolds. Geometry & Topology, 21(2):693-840, 2017. \\\",\\\"[29] Colin Guillarmou and Thibault Lefeuvre. The marked length spectrum of anosov manifolds. Annals of Mathematics, 190(1):321-344, 2019. \\\",\\\"[30] Richard S. Hamilton. Harmonic maps of manifolds with boundary. Lecture Notes in Mathematics, Vol. 471. Springer-Verlag, Berlin-New York, 1975. \\\",\\\"[31] Philip Hartman. On homotopic harmonic maps. Canadian J. Math., 19:673-687, 1967. \\\",\\\"[32] Yi Huang, Ken'ichi Ohshika, Huiping Pan, and Athanase Papadopoulos. The earthquake metric on Teichmüller space. in preparation. \\\",\\\"[33] Yi Huang, Ken'Ichi Ohshika, and Athanase Papadopoulos. The infinitesimal and global thurston geometry of Teichmüller space. November 2021. \\\",\\\"[34] Yi Huang and Athanase Papadopoulos. Optimal lipschitz maps on one-holed Tori and the Thurston metric theory of Teichmüeller space. arXiv:1909.03639, 2019. \\\",\\\"[35] John H. Hubbard. Teichmüller theory and applications to geometry, topology, and dynamics, volume 2. Matrix Editions, 2016. \\\",\\\"[36] Jürgen Jost. Harmonic maps between surfaces, volume 1062 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1984. \\\",\\\"[37] Anna Lenzhen, Kasra Rafi, and Jing Tao. Bounded combinatorics and the Lipschitz metric on Teichmüller space. Geometriae Dedicata, 159:353-371, 2012. \\\",\\\"[38] Anna Lenzhen, Kasra Rafi, and Jing Tao. The shadow of a Thurston geodesic to the curve graph. Journal of Topology, 8(4):1085-1118, 2015. \\\",\\\"[39] Zhong Li. Length spectrums of Riemann surfaces and the Teichmüller metric. Bull. London Math. Soc., 35(2):247-254, 2003. \\\",\\\"[40] L. Liu, H. Shiga, W. Su, and Y. Zhong. Almost-isometry between the Teichmüller metric and the length-spectrum metric on reduced moduli space for surfaces with boundary. Trans. Amer. Math. Soc., 369(9):6429-6464, 2017. \\\",\\\"[41] L. Liu and W. Su. Almost-isometry between Teichmüller metric and length-spectrum metric on moduli space. Bull. Lond. Math. Soc., 43(6):1181-1190, 2011. \\\",\\\"[42] Howard A. Masur and Yair N. Minsky. Geometry of the complex of curves. I. Hyperbolicity. *Invent. Math.*, 138(1):103-149, 1999. \\\",\\\"[43] Yair N Minsky. Harmonic maps, length, and energy in Teichmüller space. Journal of Differential Geometry, 35(1):151-217, 1992. \\\"]\",\n \"page_idx\": \"38\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[272,117,723,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"38\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"THE GEOMETRY OF THE THURSTON METRIC: A SURVEY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,118,792,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"38\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"39 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[204,146,795,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[44] Yair N. Minsky. Extremal length estimates and product regions in Teichmüller space. Duke Math. J., 83(2):249-286, 1996. \\\",\\\"[45] Maryam Mirzakhani. Ergodic theory of the earthquake flow. International Mathematics Research Notices, 2008(9):1073-7928, year=2008, publisher=OUP. \\\",\\\"[46] Jean-Pierre Otal. Le spectre marqué des longueurs des surfaces à courbure négative. Annals of Mathematics, 131(1):151-162, 1990. \\\",\\\"[47] Huiping Pan. Local Rigidity of the Teichmüller space with the Thurston metric. Science China Mathematics, https://doi.org/10.1007/s11425-021-2020-0, 2023. \\\",\\\"[48] Huiping Pan and Michael Wolf. Envelopes of the Thurston metric on Teichmüller space. in preparation. \\\",\\\"[49] Huiping Pan and Michael Wolf. Ray structures on Teichmüller space. arXiv:2206.01371, June 2022. \\\",\\\"[50] A. Papadopoulos and W. Su. On the Finsler structure of Teichmüller's metric and Thurston's metric. Expo. Math., 33(1):30-47, 2015. \\\",\\\"[51] Athanase Papadopoulos. On Thurston's boundary of Teichmüller space and the extension of earthquakes. Topology Appl., 41(3):147-177, 1991. \\\",\\\"[52] Athanase Papadopoulos, editor. Handbook of Teichmüller theory. Vol. III, volume 17 of IRMA Lectures in Mathematics and Theoretical Physics. European Mathematical Society (EMS), Zürich, 2012. \\\",\\\"[53] Athanase Papadopoulos and Robert C Penner. The Weil-Petersson symplectic structure at Thurston's boundary. Transactions of the American Mathematical Society, 335(2):891-904, 1993. \\\",\\\"[54] Athanase Papadopoulos and Guillaume Théret. On Teichmüller's metric and Thurston's asymmetric metric on Teichmüller space. In Handbook of Teichmüller theory. Vol. I, volume 11 of IRMA Lect. Math. Theor. Phys., pages 111-204. Eur. Math. Soc., Zürich, 2007. \\\",\\\"[55] Athanase Papadopoulos and Guillaume Théret. Some Lipschitz maps between hyperbolic surfaces with applications to Teichmüller theory. Geometriae Dedicata, 161:63-83, 2012. \\\",\\\"[56] Athanase Papadopoulos and Sumio Yamada. Deforming hyperbolic hexagons with applications to the arc and the Thurston metrics on Teichmüller spaces. Monatshefte für Mathematik, 182(4):913-939, 2017. \\\",\\\"[57] R. C. Penner and J. L. Harer. Combinatorics of train tracks, volume 125 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, 1992. \\\",\\\"[58] Robert C Penner. Universal constructions in Teichmüller theory. Advances in Mathematics, 98(2):143-215, 1993. \\\",\\\"[59] Kasra Rafi. A characterization of short curves of a Teichmüller geodesic. Geom. Topol., 9:179-202, 2005. \\\",\\\"[60] Kasra Rafi and Juan Souto. Geodesic currents and counting problems. Geom. Funct. Anal., 29(3):871-889, 2019. \\\",\\\"[61] J. H. Sampson. Some properties and applications of harmonic mappings. Ann. Sci. École Norm. Sup. (4), 11(2):211-228, 1978. \\\",\\\"[62] Jenya Sapir. An extension of the Thurston metric to projective filling currents. arXiv preprint arXiv:2210.08130, 2022. \\\"]\",\n \"page_idx\": \"39\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[204,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"40 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[383,116,612,130]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"39\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN AND WEIXU SU \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[204,145,795,766]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"[63] Dragomir Šarić. Circle homeomorphisms and shears. Geometry & Topology, 14(4):2405-2430, 2010. \\\",\\\"[64] Dragomir Šaric, Yilin Wang, and Catherine Wolfram. Circle homeomorphisms with square summable diamond shears. arXiv preprint arXiv:2211.11497, 2022. \\\",\\\"[65] Richard Schoen and Shing Tung Yau. On univalent harmonic maps between surfaces. Invent. Math., 44(3):265-278, 1978. \\\",\\\"[66] Richard M. Schoen. Analytic aspects of the harmonic map problem. In Seminar on nonlinear partial differential equations (Berkeley, Calif., 1983), volume 2 of Math. Sci. Res. Inst. Publ., pages 321-358. Springer, New York, 1984. \\\",\\\"[67] Yasar Sozen and Francis Bonahon. The Weil-Petersson and Thurston symplectic forms. Duke Math. J., 108(3):581-597, 2001. \\\",\\\"[68] Weixu Su. Problems on the Thurston metric. In Handbook of Teichmüller theory. Vol. V, volume 26 of IRMA Lect. Math. Theor. Phys., pages 55-72. Eur. Math. Soc., Zürich, 2016. \\\",\\\"[69] Ivan Telpukhovskiy. Masur's criterion does not hold in the thurston metric. arXiv:1903.00845v2, 2022. \\\",\\\"[70] Guillaume Théret. On the negative convergence of Thurston's stretch lines towards the boundary of Teichmüller space. Annales Academiae Scientiarum Fennicae. Mathematica, 32(2):381-408, 2007. \\\",\\\"[71] Guillaume Théret. Convexity of length functions and Thurston's shear coordinates. arXiv:1408.5771, 2014. \\\",\\\"[72] William P. Thurston. Earthquakes in two-dimensional hyperbolic geometry. In Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984), volume 112 of London Math. Soc. Lecture Note Ser., pages 91-112. Cambridge Univ. Press, Cambridge, 1986. \\\",\\\"[73] William P Thurston. The Geometry and Topology of Three-Manifolds: With a Preface by Steven P. Kerckhoff, volume 27. American Mathematical Society, 2022. \\\",\\\"[74] William P. Thurston. Minimal stretch maps between hyperbolic surfaces. In Collected works of William P. Thurston with commentary. Vol. I. Foliations, surfaces and differential geometry, pages 533-585. Amer. Math. Soc., Providence, RI, [2022] ©2022. 1986 preprint, 1998 eprint. \\\",\\\"[75] Karen Vogtmann. On the geometry of outer space. Bulletin of the American Mathematical Society, 52(1):27-46, 2015. \\\",\\\"[76] Cormac Walsh. The horoboundary and isometry group of Thurston's Lipschitz metric. In Handbook of Teichmüller theory. Vol. IV, volume 19 of IRMA Lect. Math. Theor. Phys., pages 327-353. Eur. Math. Soc., Zürich, 2014. \\\",\\\"[77] Michael Wolf. The Teichmüller theory of harmonic maps. Journal of Differential Geometry, 29(2):449-479, 1989. \\\",\\\"[78] Michael Wolf. Measured foliations and harmonic maps of surfaces. Journal of Differential Geometry, 49(3):437-467, 1998. \\\"]\",\n \"page_idx\": \"40\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[468,787,527,803]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"INDEX \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,829,380,847]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"absolute twisting, 30 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,829,648,845]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"cobounded, 29 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,867,431,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"boundedcombinatorics,29 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,868,656,883]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"curve graph, 27 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[490,886,506,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"40\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"41 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[470,117,524,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"INDEX \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,145,426,162]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"extremal Lipschitz map, 6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,176,434,195]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"generalized stretch map, 16 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,196,372,212]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"geodesic current, 24 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,214,392,229]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"geodesiclamination,4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[223,232,426,265]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"chain-recurrent geodesic lamination, 4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[223,267,429,301]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"maximal chain-recurrent geodesic lamination, 4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[223,303,372,335]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"maximal geodesic lamination, 4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[223,337,379,371]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"measured geodesic lamination, 4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,145,697,161]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Liouville current, 24 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,175,627,191]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"marking, 26 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[545,193,694,210]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"short marking, 26 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,210,697,244]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"maximally stretchedlamination, 6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,246,710,262]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"measuredfoliation,22 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,263,638,279]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"multicurve, 4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,292,738,311]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"optimal Lipschitz map, 6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,323,730,340]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"pants decomposition, 26 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,340,792,373]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"piecewise harmonic stretch line, 15 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,387,357,404]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"harmonic map, 14 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[225,406,401,422]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$J_{p}$ harmonic map, 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[223,424,408,440]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"harmonic map ray, 20 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[223,441,442,458]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"infinity harmonic map, 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[223,459,421,493]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Schatten-von Neumann $p$ -harmonic map, 18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,494,413,508]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"harmonic stretch line, 20 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,511,372,527]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Hopdfifferential,15 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,529,426,545]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"horofunction boundary, 23 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,561,455,577]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"intersection number, 5, 22, 27 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,594,431,611]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"length spectrum metric, 31 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,388,728,405]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"shearing coordinates, 34 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,406,694,422]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"shearing cocycle, 34 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,424,730,440]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"shearing coordinates, 33 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,441,735,458]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"subsurface projection, 27 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,459,759,494]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"symmetric right-angled hyperbolic hexagon, 10 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,506,697,523]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Teichmüller space, 3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,523,751,541]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Thurston geodesic flow, 22 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,542,686,558]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Thurston metric, 5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,560,676,575]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Thurstonnorm,7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[526,577,720,594]\",\n \"code_body\": null,\n \"code_caption\": null,\n 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null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"HUIPING PAN, SCHOOL OF MATHEMATICS, SOUTH CHINA UNIVERSITY OF TECHNOLOGY, 510641, GUANGZHOU, CHINA\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[223,684,485,699]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Email address: panhp@scut.edu.cn \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,718,792,750]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"WEIXU SU, SCHOOL OF MATHEMATICS, SUN YAT-SEN UNIVERSITY, 510275, GUANGZHOU, CHINA \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[223,758,527,773]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Email address: suwx9@mail.sysu.edu.cn \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[204,118,222,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"41\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"42 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.48550/arxiv.2307.03874"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Physics/Mathematics and Computational Science"},"sha256":{"kind":"string","value":"d006d739a75b434d4718d2ef2e1cc11a9e8ebffc847bc54b6d013444a52c79a7"},"title":{"kind":"string","value":"The geometry of the Thurston metric: a survey"}}},{"rowIdx":271,"cells":{"abstract":{"kind":"string","value":"Heavy metals have non-biodegradable, toxic and accumulative properties in the environment. Heavy metals that enter water bodies will be carried by the flow towards the coast. Zinc (Zn) is one of the metals found polluting the waters in the city of Surabaya, Indonesia. One of the efforts to overcome this problem is the use of mangroves as phytoremediation agents. The purpose of the study was to determine the ability of Avicennia marina (Forssk.) Vierh in the Wonorejo Ecoforest to accumulate Zn by determining the bioconcentration factor (BCF) and the translocation factor (TF). Determination of the sampling points of this study using the transect method. Samples were taken in the form roots, stems, and leaves of mangrove plants and those were analyzed for Zn concentration using an atomic absorption spectrophotometer (AAS). Based on the result, A. marina showed the immobilized of Zn in root due to the BCF value was higher than 1. In conclusion, A. marina have potential to be phytoremediation plants in coastal area."},"author":{"kind":"string","value":"Sulistiyaning Titah Harmin|Pratikno Herman|Marwah Luthansa Uridna"},"content_list":{"kind":"list like","value":[{"bbox":"[114,182,846,262]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Uptake and Accumulation of Zinc by Grey Mangrove at Wonorejo Mangrove Forest, Surabaya, Indonesia ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[116,283,750,300]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Harmin Sulistiyaning Titah $^{1*}$ , Herman Pratikno $^{2}$ , Uridna Marwah Luthansa $^{1}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[116,312,881,372]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{1}$ Department of Environmental Engineering, Faculty of Civil, Planning and Geo Engineering, Institut Teknologi Sepuluh Nopember, Keputih, Sukolilo, 60111 Surabaya, Indonesia $^{2}$ Department of Ocean Engineering, Faculty of Marine Technology, Institut Teknologi Sepuluh Nopember, Keputih, Sukolilo, 60111 Surabaya, Indonesia ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[216,403,783,622]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract. Heavy metals have non-biodegradable, toxic and accumulative properties in the environment. Heavy metals that enter water bodies will be carried by the flow towards the coast. Zinc $(\\mathrm{Zn})$ is one of the metals found polluting the waters in the city of Surabaya, Indonesia. One of the efforts to overcome this problem is the use of mangroves as phytoremediation agents. The purpose of the study was to determine the ability of Avicennia marina (Forssk.) Vierh in the Wonorejo Ecoforest to accumulate $\\mathrm{Zn}$ by determining the bioconcentration factor (BCF) and the translocation factor (TF). Determination of the sampling points of this study using the transect method. Samples were taken in the form roots, stems, and leaves of mangrove plants and those were analyzed for $\\mathrm{Zn}$ concentration using an atomic absorption spectrophotometer (AAS). Based on the result, A. marina showed the immobilized of $\\mathrm{Zn}$ in root due to the BCF value was higher than 1. In conclusion, A. marina have potential to be phytoremediation plants in coastal area. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[216,663,783,692]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: Avicennia marina (Forssk.) Vierh, heavy metal polution, phytoremediation, white mangrove ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[116,731,282,750]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[116,762,883,894]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The increasing of industries has both positive and negative impacts. The positive impact resulting from industrial activities is the creation of many jobs, while the negative impact is a decreasing of environmental quality due to waste disposal. Industrial waste is a serious problem in the era of industrial industrialization [1]. Every industrial activity will produce various kinds of waste. The type of waste varies depend on the type of activity. According to Nasir and Saputro [2], industrial waste treatment must start from the beginning of the process until the end, because if it is not conducted properly, it will have a fatal impact on the environment and human survival. According to Yudo [3], industrial waste is generally ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[66,48,399,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"E3S Web of Conferences 432, 00012 (2023) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[64,62,222,74]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$2^{nd}ICoN$ -BEAT 2021 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[571,48,927,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1051/e3sconf/202343200012 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[116,913,525,930]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"* Coresponding Author: harminsulis@gmail.com ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[64,954,925,980]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (https://creativecommons.org/licenses/by/4.0/). ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[114,94,879,125]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"disposed of into rivers without any treatment, so that it can cause a decreasing in the quality of water bodies. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,128,883,387]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The coastal zone has a high potential for heavy metal accumulation because it is directly adjacent to land and sea [1]. Heavy metal pollution in coastal areas is caused by agricultural runoff, industrial and domestic waste, chemical spills, ship fuel, WWTP effluent, mining and domestic waste [4]. According to Tchounwou et al., heavy metals such as mercury (Hg), lead (Pb), arsenic (As), cadmium (Cd), chromium (Cr), zinc (Zn) and nickel (Ni) are inorganic materials that often cause serious water problems. The heavy metal waste enters water bodies and then settles in river estuary sediments [6]. The continuous deposition of heavy metals will cause environmental pollution because of the accumulative and toxic properties of metals [6]. One of the efforts to overcome heavy metal pollution in estuary dan coastal areas is phytoremediation using mangrove plants. Mangroves are plants that can live in areas with high salinity [7]. Several studies have proven that mangrove plants can accumulate heavy metals that pollute the environment [8]. The estuary of the Wonorejo river has the potential to accumulate heavy metals due to this location is passed by industries and domestic areas [9]. The aim of this study was to determine the ability of Avicennia marina (Forssk.) Vierh that grown at Wonorejo Mangrove Forest to uptake and accumulate of Zn. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[116,411,415,429]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 Materials and methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[116,454,334,471]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.1 Location sampling ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[114,483,883,645]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The location of the study was at the Wonorejo Mangrove Ecoforest area, in Surabaya, Indonesia. Based on the consideration of mangrove thickness, the determination of sampling stations was observed visually, using the google earth application, with easy road access and safety to reach the study location. The research station was divided into three regions, namely A Station (7° 18'19.75\" South Latitude and $112^{\\circ}50'39.4''$ East Longitude), B Station (7° 18'20.19\" South Latitude and $112^{\\circ}50'40.0''$ East Longitude), and C Station (7° 18'21.90\" South Latitude and $112^{\\circ}50'40.56''$ East Longitude). The location of this research was also shown in Figure 1. Based on observation, A. marina was founded at B dan C station. The codes of sampling locations of A. marina were SBP3 A. marina, SCP1 A. marina, SCP2 A. marina and SCP3 A. marina. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[195,659,829,853]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 1. Location of study. \"]","image_footnote":"[]","img_path":"images/0572/9905750e76ab67980084513c27c35606a266ccd1cd17e5dfffc5cac1b47fd6df.jpg","list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[64,48,399,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"E3S Web of Conferences 432, 00012 (2023) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[64,62,220,74]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$2^{nd}ICoN$ -BEAT 2021 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[571,48,927,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1051/e3sconf/202343200012 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,966,501,977]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[110,94,883,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2.2 Determination of BCF (bioconcentration factor) and TF (translocation factor) ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[110,139,885,252]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The results of the analysis of the concentrations contained in the environment and mangrove plants, were used to calculate the values of BCF (bioconcentration factor) and TF (translocation factor). The BCF and TF were used to determine the heavy metals' accumulation and translocation abilities, in parts of the mangroves. The Bio-concentration factor (BCF) or biological accumulation coefficient (BAC) calculation [10] was used to determine the plants' ability to extract metal from the substrate [11]. Equation (1) shows BAC determination ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[397,251,848,288]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nB C F = \\frac {\\left| Z n i n r o o t s \\right|}{\\left[ Z n i n m e d i a \\right]} \\tag {1}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[110,306,883,338]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The BCF determination results were used to classify plants that are in hyperaccumulator, as shown in Table 1 based on Bini et al. [10]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[187,381,810,463]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0281/007a79adba5741ba69dd2c414feacccd257031a2740f3b7f93dca5dd146ad14b.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":"<table><tr><td>Category</td><td>Range</td></tr><tr><td>High accumulator / hyperaccumulator plants</td><td>1 to10</td></tr><tr><td>Moderate accumulator plants</td><td>0.1 to 1</td></tr><tr><td>Low accumulator plants</td><td>0.01 to 0.1</td></tr><tr><td>Non accumulator plants</td><td>< 0.01</td></tr></table>","table_caption":"[\"Table 1. Category of BCF value \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[110,488,586,505]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The TF value was determined using Equation 2 [11, 12]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[395,519,848,556]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nT F = \\frac {\\left| Z n i n S t e m s \\right|}{\\left[ Z n i n r o o t s \\right]} \\tag {2}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[110,584,440,603]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 Results and discussions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[110,627,523,644]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1 The concentration of Zn in sediments ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[110,656,885,885]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The results of the analysis of Zn in sediments was shown in Figure 2. The concentration of Zn were $56.7\\mathrm{mgkg^{-1}}$ , $45.8\\mathrm{mgkg^{-1}}$ , $62.5\\mathrm{mgkg^{-1}}$ and $59.6\\mathrm{mgkg^{-1}}$ at code location of SBP3 A. marina, SCP1 A. marina, SCP2 A. marina and SCP3 A. marina, respective. Indonesia does not have quality stones for sediments in coastal areas, so the sediment quality standards used in this study refer to the Environmental Protection Agency (EPA) Sediment Quality, Australian and New Zealand Environment and Conservation Council (Anzecc/Armcanz Guidelines) and the Canadian Council of Ministers. of Environment (CCME). The quality standards used in this study for Zn sediments came from America, Australia and Canada. The American quality standard for Zn sediment is $>2\\mathrm{mgkg^{-1}}$ , Australia $410\\mathrm{mgkg^{-1}}$ and Canada $315\\mathrm{mgkg^{-1}}$ . Based on Figure 2, all sediments in this study have exceeded the quality standard threshold according to the sediment quality reference from America due to concentrations of Zn in the sediment were greater than $2\\mathrm{mgkg^{-1}}$ . However, based on the Australian and Canadian quality standards, concentration of Zn in the sediment in the estuary were still below the quality standard. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,46,399,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"E3S Web of Conferences 432, 00012 (2023) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[62,60,222,74]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$2^{nd}ICoN-BEAT$ 2021 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[569,46,929,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1051/e3sconf/202343200012 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,964,501,977]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[228,108,771,350]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 2. Zn concentration in sediment. \"]","image_footnote":"[]","img_path":"images/0210/d7339ea406ada467f3f5a41e9c06f81f0486589a5e09083198d4ea3d5f892098.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[110,394,879,413]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2 Mangrove ability to remediate heavy metal Zn by determining BCF and TF ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[110,423,883,505]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mangrove plants were used as phytoremediation agents, due to being able to accumulate heavy metals around them naturally, which was also referred to as biosorption. Mangroves also filter, catch, and bind pollution within the environment, in the form of excess sediment, garbage, and other household wastes, which contributed greatly to improving water quality [14]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[110,505,883,683]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 2 showed concentration of Zn in mangrove roots, stems and leaves of A. marina at B and C Station. The Zn concentration in the roots of A. marina at B Station was high $(82.3\\mathrm{mgkg}^{-1})$ . The results showed that Zn in mangrove roots at station of C had a range of $52.2\\mathrm{mgkg}^{-1}$ to $93.3\\mathrm{mgkg}^{-1}$ . The highest average Zn concentration in the mangrove roots of station C was found in the mangrove type of A. marina. A. marina was able to absorb the highest Zn metal compared to other types of mangroves. Concentration of Zn in stems of A. marina were $51.2\\mathrm{mgkg}^{-1}$ till $101.3\\mathrm{mgkg}^{-1}$ at B dan C Station. Concentration of Zn in leaves of A. marina were $37.6\\mathrm{mgkg}^{-1}$ till $138.3\\mathrm{mgkg}^{-1}$ . According to research by Amin [7], Avicennia mangroves have a higher accumulation capacity than other mangrove species. A. marina prevents the entry of heavy metals into other tissues so that the concentration of heavy metals in the roots is higher. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[226,697,771,911]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 3. Concentration of Zn in mangrove roots, stems and leaves of A. marina \"]","image_footnote":"[]","img_path":"images/0191/cd8b0b427cf6f78860559fd0231f15d797efe7771d49df135fb9a28a16fbf99f.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[62,46,399,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"E3S Web of Conferences 432, 00012 (2023) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[62,60,222,74]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$2^{nd}ICoN-BEAT$ 2021 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[569,46,927,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1051/e3sconf/202343200012 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,964,501,977]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[110,94,885,225]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The BCF value were calculated using equation 1. The BCF value in $A$ . marina were 1.14 till 1.49. Figure 4 showed the BCF value of $A$ . marina. Based on the classify which plants [10], $A$ . marina showed potential as a hyperaccumulator for Zn. This result indicates that A. marina was taken up Zn from sediment and $A$ . marina was included as a hyperaccumulator plant for Zn. It considered that $A$ . marina was an efficient hyperaccumulator plants. However, according to Meeinkuirt et al. [15], $A$ . marina was a phytoremediator plants for Zn, Cr, and Pb; and Rhizophora mucronata Lam. for Cu and Zn. $A$ . marina showed the immobilized of Zn in root due to the BCF value was higher than 1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[110,225,883,307]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 5 showed the TF value of $A$ . marina. The TF showed the all of value did not exceed 1, it indicated that the process of phytoremediation was phytostabilization. Some species accumulated metals in shoots; however, they cannot be classified as hyperaccumulators since metal concentrations were not sufficiently high to fit the criteria for plants in a phytoextraction strategy, even those with TF > 1 and BCF > 1. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[230,320,767,526]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 4. BCF Value or Bioconcentration Factor on A. marina \"]","image_footnote":"[]","img_path":"images/0952/29d98b2ff9731a2c94f6beb7efee7dc3226861fb4bd1477d22f74b7928c91a68.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[230,557,765,772]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 5. TF value or translocation factor on $A$ marina \"]","image_footnote":"[]","img_path":"images/0127/f6fb840082b7cb4a8f71ad186202e327f2965fdd9cac3d7eae2fb74f70cec721.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[110,823,295,841]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 Conclusions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[110,853,885,919]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Zn accumulation by roots of $A$ marina reached $52.2\\mathrm{mgkg^{-1}}$ till $93.0\\mathrm{mgkg^{-1}}$ . The BCF value in $A$ marina were 1.14 till 1.49 with the concentration Zn in sediment were 52.2 $\\mathrm{mgkg^{-1}}$ to $93.3\\mathrm{mgkg^{-1}}$ . $A$ marina showed potential as a hyperaccumulator for Zn. However, the TF showed the most of value did not excess 1, it indicated that the process of ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[62,46,399,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"E3S Web of Conferences 432, 00012 (2023) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[62,60,222,74]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$2^{nd}ICoN-BEAT$ 2021 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[569,46,929,62]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1051/e3sconf/202343200012 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,964,501,977]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[114,94,881,128]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"phytoremediation was phytostabilization. In conclusion, $A$ . marina can be considered for use in phytomonitoring and phytoremediation of $\\mathrm{Zn}$ in coastal areas. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,153,881,197]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The author is grateful to the Ministry of Education, Culture, Research, and Technology, Directorate General of Higher Education for funding this study with Contract No. 008/E5/PG.0200.PT/2022 and No. 1527/PKS/ITS/2022 for third year research. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,221,249,240]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[118,269,879,920]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1. H. Setiawan, Jurnal Ilmu Kehutanan, 7, 1: 12-24 (2013) [in Bahasa Indonesia] https://doi.org/10.22146/jik.6134 \",\"2. M. Nasir, E.P. Saputro, and S. Handayani, benefit, 19, 2: 143-149 (2015) [in Bahasa Indonesia] https://doi.org/10.23917/benefit.v19i2.2313 \",\"3. S. Yudo. J. Air. Indones., 2, 1: 1-15 (2006) [in Bahasa Indonesia] https://doi.org/10.29122/jai.v2i1.2275 \",\"4. B.R.D. Harnani, Kemampuan Avicennia marina dan Avicennia alba Untuk Menurunkan Konsentrasi Tembaga (Cu) Di Muara Sungai Wonorejo, Surabaya [Ability of Avicennia marina and Avicennia alba to reduce copper (Cu) concentrations at the Wonorejo River estuary, Surabaya]. [Undergraduate Thesis] Faculty of Civil Engineering and Planning, Institut Teknologi Sepuluh Nopember (2017) [in Bahasa Indonesia] https://core.ac.uk/download/pdf/291464221.pdf \",\"5. P.B. Tchounwou, C.G. Yedjou, A.K. Patlolla, and D.J. Sutton. Heavy Metal Toxicity and the Environment, in: A. Luch (Eds.), Molecular, Clinical and Environmental Toxicology: Experientia Supplementum, Vol 101. Basel: Springer (2012) https://doi.org/10.1007/978-3-7643-8340-4_6 \",\"6. R.F. Febriana. 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Sci. and Manag., 19, 1: 27-36 (2016) https://doi.org/10.47125/jesam/2016_1/04 \"]","page_idx":"5","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[66,48,399,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"E3S Web of Conferences 432, 00012 (2023) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[64,62,222,74]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$2^{nd}ICoN$ -BEAT 2021 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[571,46,927,63]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1051/e3sconf/202343200012 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,966,501,977]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[120,94,875,324]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"12. E.E.C. Melo, E.T.S. Costa, L.R.G. Guilherme, V. Faquin, C.W.A. Nascimento, J. Hazard. Mater. 168, 1: 479-483 (2009) https://doi.org/10.1016/j.jhazmat.2009.02.048 \",\"13. H.S. Titah, S.R.S Abdullah, M. Idris, N. Anuar, H. Basri, M. Mukhlisin. Ecolog. Eng., 58: 303-313 (2013) https://doi.org/10.1016/j.ecoleng.2013.07.018 \",\"14. R. Utami, W. Rismawati, K. Sapanli. Pemanfaatan Mangrove Untuk Mengurangi Logam Berat Di Perairan [Utilization of Mangroves to Reduce Heavy Metals In The Waters]. in: Proceedings of the National Seminar on World Water Day (Palembang, Indonesia, 2018) [in Bahasa Indonesia] http://conference.unsri.ac.id/index.php/semnashas/article/view/799/428 \",\"15. W. Meeinkuirt, P. Kaewtubtim, S. Seepom, J. Pichtel. Metal Uptake and Accumulation by Mangrove Plant Species in Pattani Bay, Thailand. in: Proceedings of the 3rd World Congress on New Technologies (NewTech'17) (Rome, Italy, 2017) https://doi.org/10.11159/icepr17.158 \"]","page_idx":"6","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[64,46,399,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"E3S Web of Conferences 432, 00012 (2023) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[64,60,222,74]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$2^{nd}ICoN$ -BEAT 2021 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[571,46,927,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"https://doi.org/10.1051/e3sconf/202343200012 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[488,964,501,977]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[114,182,846,262]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Uptake and Accumulation of Zinc by Grey Mangrove at Wonorejo Mangrove Forest, Surabaya, Indonesia \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[116,283,750,300]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Harmin Sulistiyaning Titah $^{1*}$ , Herman Pratikno $^{2}$ , Uridna Marwah Luthansa $^{1}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[116,312,881,372]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{1}$ Department of Environmental Engineering, Faculty of Civil, Planning and Geo Engineering, Institut Teknologi Sepuluh Nopember, Keputih, Sukolilo, 60111 Surabaya, Indonesia $^{2}$ Department of Ocean Engineering, Faculty of Marine Technology, Institut Teknologi Sepuluh Nopember, Keputih, Sukolilo, 60111 Surabaya, Indonesia \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[216,403,783,622]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract. Heavy metals have non-biodegradable, toxic and accumulative properties in the environment. Heavy metals that enter water bodies will be carried by the flow towards the coast. Zinc $(\\\\mathrm{Zn})$ is one of the metals found polluting the waters in the city of Surabaya, Indonesia. One of the efforts to overcome this problem is the use of mangroves as phytoremediation agents. The purpose of the study was to determine the ability of Avicennia marina (Forssk.) Vierh in the Wonorejo Ecoforest to accumulate $\\\\mathrm{Zn}$ by determining the bioconcentration factor (BCF) and the translocation factor (TF). Determination of the sampling points of this study using the transect method. Samples were taken in the form roots, stems, and leaves of mangrove plants and those were analyzed for $\\\\mathrm{Zn}$ concentration using an atomic absorption spectrophotometer (AAS). Based on the result, A. marina showed the immobilized of $\\\\mathrm{Zn}$ in root due to the BCF value was higher than 1. In conclusion, A. marina have potential to be phytoremediation plants in coastal area. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[216,663,783,692]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: Avicennia marina (Forssk.) Vierh, heavy metal polution, phytoremediation, white mangrove \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[116,731,282,750]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[116,762,883,894]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The increasing of industries has both positive and negative impacts. The positive impact resulting from industrial activities is the creation of many jobs, while the negative impact is a decreasing of environmental quality due to waste disposal. Industrial waste is a serious problem in the era of industrial industrialization [1]. Every industrial activity will produce various kinds of waste. The type of waste varies depend on the type of activity. According to Nasir and Saputro [2], industrial waste treatment must start from the beginning of the process until the end, because if it is not conducted properly, it will have a fatal impact on the environment and human survival. According to Yudo [3], industrial waste is generally \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[66,48,399,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"E3S Web of Conferences 432, 00012 (2023) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[64,62,222,74]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$2^{nd}ICoN$ -BEAT 2021 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[571,48,927,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1051/e3sconf/202343200012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[116,913,525,930]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"* Coresponding Author: harminsulis@gmail.com \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[64,954,925,980]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (https://creativecommons.org/licenses/by/4.0/). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[114,94,879,125]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"disposed of into rivers without any treatment, so that it can cause a decreasing in the quality of water bodies. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,128,883,387]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The coastal zone has a high potential for heavy metal accumulation because it is directly adjacent to land and sea [1]. Heavy metal pollution in coastal areas is caused by agricultural runoff, industrial and domestic waste, chemical spills, ship fuel, WWTP effluent, mining and domestic waste [4]. According to Tchounwou et al., heavy metals such as mercury (Hg), lead (Pb), arsenic (As), cadmium (Cd), chromium (Cr), zinc (Zn) and nickel (Ni) are inorganic materials that often cause serious water problems. The heavy metal waste enters water bodies and then settles in river estuary sediments [6]. The continuous deposition of heavy metals will cause environmental pollution because of the accumulative and toxic properties of metals [6]. One of the efforts to overcome heavy metal pollution in estuary dan coastal areas is phytoremediation using mangrove plants. Mangroves are plants that can live in areas with high salinity [7]. Several studies have proven that mangrove plants can accumulate heavy metals that pollute the environment [8]. The estuary of the Wonorejo river has the potential to accumulate heavy metals due to this location is passed by industries and domestic areas [9]. The aim of this study was to determine the ability of Avicennia marina (Forssk.) Vierh that grown at Wonorejo Mangrove Forest to uptake and accumulate of Zn. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[116,411,415,429]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 Materials and methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[116,454,334,471]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.1 Location sampling \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,483,883,645]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The location of the study was at the Wonorejo Mangrove Ecoforest area, in Surabaya, Indonesia. Based on the consideration of mangrove thickness, the determination of sampling stations was observed visually, using the google earth application, with easy road access and safety to reach the study location. The research station was divided into three regions, namely A Station (7° 18'19.75\\\" South Latitude and $112^{\\\\circ}50'39.4''$ East Longitude), B Station (7° 18'20.19\\\" South Latitude and $112^{\\\\circ}50'40.0''$ East Longitude), and C Station (7° 18'21.90\\\" South Latitude and $112^{\\\\circ}50'40.56''$ East Longitude). The location of this research was also shown in Figure 1. Based on observation, A. marina was founded at B dan C station. The codes of sampling locations of A. marina were SBP3 A. marina, SCP1 A. marina, SCP2 A. marina and SCP3 A. marina. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[195,659,829,853]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 1. Location of study. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0572/9905750e76ab67980084513c27c35606a266ccd1cd17e5dfffc5cac1b47fd6df.jpg\",\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[64,48,399,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"E3S Web of Conferences 432, 00012 (2023) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[64,62,220,74]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$2^{nd}ICoN$ -BEAT 2021 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[571,48,927,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1051/e3sconf/202343200012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,966,501,977]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[110,94,883,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2.2 Determination of BCF (bioconcentration factor) and TF (translocation factor) \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,139,885,252]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The results of the analysis of the concentrations contained in the environment and mangrove plants, were used to calculate the values of BCF (bioconcentration factor) and TF (translocation factor). The BCF and TF were used to determine the heavy metals' accumulation and translocation abilities, in parts of the mangroves. The Bio-concentration factor (BCF) or biological accumulation coefficient (BAC) calculation [10] was used to determine the plants' ability to extract metal from the substrate [11]. Equation (1) shows BAC determination \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[397,251,848,288]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nB C F = \\\\frac {\\\\left| Z n i n r o o t s \\\\right|}{\\\\left[ Z n i n m e d i a \\\\right]} \\\\tag {1}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[110,306,883,338]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The BCF determination results were used to classify plants that are in hyperaccumulator, as shown in Table 1 based on Bini et al. [10]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[187,381,810,463]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0281/007a79adba5741ba69dd2c414feacccd257031a2740f3b7f93dca5dd146ad14b.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Category</td><td>Range</td></tr><tr><td>High accumulator / hyperaccumulator plants</td><td>1 to10</td></tr><tr><td>Moderate accumulator plants</td><td>0.1 to 1</td></tr><tr><td>Low accumulator plants</td><td>0.01 to 0.1</td></tr><tr><td>Non accumulator plants</td><td>< 0.01</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1. Category of BCF value \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[110,488,586,505]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The TF value was determined using Equation 2 [11, 12]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[395,519,848,556]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nT F = \\\\frac {\\\\left| Z n i n S t e m s \\\\right|}{\\\\left[ Z n i n r o o t s \\\\right]} \\\\tag {2}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[110,584,440,603]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 Results and discussions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,627,523,644]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1 The concentration of Zn in sediments \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,656,885,885]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The results of the analysis of Zn in sediments was shown in Figure 2. The concentration of Zn were $56.7\\\\mathrm{mgkg^{-1}}$ , $45.8\\\\mathrm{mgkg^{-1}}$ , $62.5\\\\mathrm{mgkg^{-1}}$ and $59.6\\\\mathrm{mgkg^{-1}}$ at code location of SBP3 A. marina, SCP1 A. marina, SCP2 A. marina and SCP3 A. marina, respective. Indonesia does not have quality stones for sediments in coastal areas, so the sediment quality standards used in this study refer to the Environmental Protection Agency (EPA) Sediment Quality, Australian and New Zealand Environment and Conservation Council (Anzecc/Armcanz Guidelines) and the Canadian Council of Ministers. of Environment (CCME). The quality standards used in this study for Zn sediments came from America, Australia and Canada. The American quality standard for Zn sediment is $>2\\\\mathrm{mgkg^{-1}}$ , Australia $410\\\\mathrm{mgkg^{-1}}$ and Canada $315\\\\mathrm{mgkg^{-1}}$ . Based on Figure 2, all sediments in this study have exceeded the quality standard threshold according to the sediment quality reference from America due to concentrations of Zn in the sediment were greater than $2\\\\mathrm{mgkg^{-1}}$ . However, based on the Australian and Canadian quality standards, concentration of Zn in the sediment in the estuary were still below the quality standard. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,46,399,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"E3S Web of Conferences 432, 00012 (2023) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[62,60,222,74]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$2^{nd}ICoN-BEAT$ 2021 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[569,46,929,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1051/e3sconf/202343200012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,964,501,977]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[228,108,771,350]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 2. Zn concentration in sediment. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0210/d7339ea406ada467f3f5a41e9c06f81f0486589a5e09083198d4ea3d5f892098.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[110,394,879,413]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2 Mangrove ability to remediate heavy metal Zn by determining BCF and TF \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,423,883,505]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mangrove plants were used as phytoremediation agents, due to being able to accumulate heavy metals around them naturally, which was also referred to as biosorption. Mangroves also filter, catch, and bind pollution within the environment, in the form of excess sediment, garbage, and other household wastes, which contributed greatly to improving water quality [14]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,505,883,683]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 2 showed concentration of Zn in mangrove roots, stems and leaves of A. marina at B and C Station. The Zn concentration in the roots of A. marina at B Station was high $(82.3\\\\mathrm{mgkg}^{-1})$ . The results showed that Zn in mangrove roots at station of C had a range of $52.2\\\\mathrm{mgkg}^{-1}$ to $93.3\\\\mathrm{mgkg}^{-1}$ . The highest average Zn concentration in the mangrove roots of station C was found in the mangrove type of A. marina. A. marina was able to absorb the highest Zn metal compared to other types of mangroves. Concentration of Zn in stems of A. marina were $51.2\\\\mathrm{mgkg}^{-1}$ till $101.3\\\\mathrm{mgkg}^{-1}$ at B dan C Station. Concentration of Zn in leaves of A. marina were $37.6\\\\mathrm{mgkg}^{-1}$ till $138.3\\\\mathrm{mgkg}^{-1}$ . According to research by Amin [7], Avicennia mangroves have a higher accumulation capacity than other mangrove species. A. marina prevents the entry of heavy metals into other tissues so that the concentration of heavy metals in the roots is higher. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[226,697,771,911]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 3. Concentration of Zn in mangrove roots, stems and leaves of A. marina \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0191/cd8b0b427cf6f78860559fd0231f15d797efe7771d49df135fb9a28a16fbf99f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[62,46,399,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"E3S Web of Conferences 432, 00012 (2023) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[62,60,222,74]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$2^{nd}ICoN-BEAT$ 2021 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[569,46,927,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1051/e3sconf/202343200012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,964,501,977]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[110,94,885,225]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The BCF value were calculated using equation 1. The BCF value in $A$ . marina were 1.14 till 1.49. Figure 4 showed the BCF value of $A$ . marina. Based on the classify which plants [10], $A$ . marina showed potential as a hyperaccumulator for Zn. This result indicates that A. marina was taken up Zn from sediment and $A$ . marina was included as a hyperaccumulator plant for Zn. It considered that $A$ . marina was an efficient hyperaccumulator plants. However, according to Meeinkuirt et al. [15], $A$ . marina was a phytoremediator plants for Zn, Cr, and Pb; and Rhizophora mucronata Lam. for Cu and Zn. $A$ . marina showed the immobilized of Zn in root due to the BCF value was higher than 1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,225,883,307]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Figure 5 showed the TF value of $A$ . marina. The TF showed the all of value did not exceed 1, it indicated that the process of phytoremediation was phytostabilization. Some species accumulated metals in shoots; however, they cannot be classified as hyperaccumulators since metal concentrations were not sufficiently high to fit the criteria for plants in a phytoextraction strategy, even those with TF > 1 and BCF > 1. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[230,320,767,526]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 4. BCF Value or Bioconcentration Factor on A. marina \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0952/29d98b2ff9731a2c94f6beb7efee7dc3226861fb4bd1477d22f74b7928c91a68.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[230,557,765,772]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 5. TF value or translocation factor on $A$ marina \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0127/f6fb840082b7cb4a8f71ad186202e327f2965fdd9cac3d7eae2fb74f70cec721.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[110,823,295,841]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 Conclusions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,853,885,919]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Zn accumulation by roots of $A$ marina reached $52.2\\\\mathrm{mgkg^{-1}}$ till $93.0\\\\mathrm{mgkg^{-1}}$ . The BCF value in $A$ marina were 1.14 till 1.49 with the concentration Zn in sediment were 52.2 $\\\\mathrm{mgkg^{-1}}$ to $93.3\\\\mathrm{mgkg^{-1}}$ . $A$ marina showed potential as a hyperaccumulator for Zn. However, the TF showed the most of value did not excess 1, it indicated that the process of \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[62,46,399,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"E3S Web of Conferences 432, 00012 (2023) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[62,60,222,74]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$2^{nd}ICoN-BEAT$ 2021 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[569,46,929,62]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1051/e3sconf/202343200012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,964,501,977]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[114,94,881,128]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"phytoremediation was phytostabilization. In conclusion, $A$ . marina can be considered for use in phytomonitoring and phytoremediation of $\\\\mathrm{Zn}$ in coastal areas. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,153,881,197]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The author is grateful to the Ministry of Education, Culture, Research, and Technology, Directorate General of Higher Education for funding this study with Contract No. 008/E5/PG.0200.PT/2022 and No. 1527/PKS/ITS/2022 for third year research. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,221,249,240]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[118,269,879,920]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1. H. Setiawan, Jurnal Ilmu Kehutanan, 7, 1: 12-24 (2013) [in Bahasa Indonesia] https://doi.org/10.22146/jik.6134 \\\",\\\"2. M. Nasir, E.P. Saputro, and S. Handayani, benefit, 19, 2: 143-149 (2015) [in Bahasa Indonesia] https://doi.org/10.23917/benefit.v19i2.2313 \\\",\\\"3. S. Yudo. J. Air. Indones., 2, 1: 1-15 (2006) [in Bahasa Indonesia] https://doi.org/10.29122/jai.v2i1.2275 \\\",\\\"4. B.R.D. Harnani, Kemampuan Avicennia marina dan Avicennia alba Untuk Menurunkan Konsentrasi Tembaga (Cu) Di Muara Sungai Wonorejo, Surabaya [Ability of Avicennia marina and Avicennia alba to reduce copper (Cu) concentrations at the Wonorejo River estuary, Surabaya]. [Undergraduate Thesis] Faculty of Civil Engineering and Planning, Institut Teknologi Sepuluh Nopember (2017) [in Bahasa Indonesia] https://core.ac.uk/download/pdf/291464221.pdf \\\",\\\"5. P.B. Tchounwou, C.G. Yedjou, A.K. Patlolla, and D.J. Sutton. Heavy Metal Toxicity and the Environment, in: A. Luch (Eds.), Molecular, Clinical and Environmental Toxicology: Experientia Supplementum, Vol 101. Basel: Springer (2012) https://doi.org/10.1007/978-3-7643-8340-4_6 \\\",\\\"6. R.F. Febriana. Penerapan Komunikasi Terapentik oleh Tenaga Kesehatan untuk Mengurangi Tingkat Stres Narapidana di Lembaga Permasyarakatan Mojokerto Klas IIB [Application of Therapeutic Communication by Health Workers to Reduce the Stress Level of Prisoners in Class IIB Mojokerto Penitentiary]. [Undergraduate Thesis] School of Social and Political Sciences, Universitas Brawijaya, Indonesia (2018) [in Bahasa Indonesia] http://repository.ub.ac.id/165116/1/Rizki%20Ffitrie%20Febriana.pdf \\\",\\\"7. A.A. Amin, V.K. Baihaqi, R. Prawitma, and A. Kurniawan, Analysis Daya Serap Mangrove Avicennia marina dan Rhizophora mucronata Terhadap Logam Berat (Zn) di Kawasan Mangrove Wonorejo, Surabaya, Jawa Timur [Analysis of Absorption of Avicennia marina and Rhizophora mucronata Mangrove on Heavy Metals (Zn) in Wonorejo Mangrove Area, Surabaya, East Java], Proceedings SEMINAKEL 14: 7-15 (2019) [in Bahasa Indonesia] https://prosidingseminakelHangtuah.ac.id/index.php/jurnal/article/view/38 \\\",\\\"8. M. Yamin, B. Burhanudin, J. Jamaludin, and N. Nasruddin, J. biol. tropis, 18, 1 (2018) [in Bahasa Indonesia] https://doi.org/10.29303/jbt.v18i1.560 \\\",\\\"9. S.H.J. Sari, J.F.A. Kirana, and G. Guntur, J. Pend. Geo., 22, 1: 1-9 (2017) [inBahasa Indonesia] http://dx.doi.org/10.17977/um017v22i12017p001 \\\",\\\"10. C.L., Bini, L., Gentili, B., Maleci, O., Vaselli, Trace elements in plant and soils of urban parks, in: Annexed tocontaminated soil prost., INRA, Paris (1995) \\\",\\\"11. M. Idris, S.R.S. Abdullah, H.S. Titah, M.T. Latif, A.R. Abasa, A.K. Husin, et al., J. Environ. Sci. and Manag., 19, 1: 27-36 (2016) https://doi.org/10.47125/jesam/2016_1/04 \\\"]\",\n \"page_idx\": \"5\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[66,48,399,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"E3S Web of Conferences 432, 00012 (2023) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[64,62,222,74]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$2^{nd}ICoN$ -BEAT 2021 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[571,46,927,63]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1051/e3sconf/202343200012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,966,501,977]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[120,94,875,324]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"12. E.E.C. Melo, E.T.S. Costa, L.R.G. Guilherme, V. Faquin, C.W.A. Nascimento, J. Hazard. Mater. 168, 1: 479-483 (2009) https://doi.org/10.1016/j.jhazmat.2009.02.048 \\\",\\\"13. H.S. Titah, S.R.S Abdullah, M. Idris, N. Anuar, H. Basri, M. Mukhlisin. Ecolog. Eng., 58: 303-313 (2013) https://doi.org/10.1016/j.ecoleng.2013.07.018 \\\",\\\"14. R. Utami, W. Rismawati, K. Sapanli. Pemanfaatan Mangrove Untuk Mengurangi Logam Berat Di Perairan [Utilization of Mangroves to Reduce Heavy Metals In The Waters]. in: Proceedings of the National Seminar on World Water Day (Palembang, Indonesia, 2018) [in Bahasa Indonesia] http://conference.unsri.ac.id/index.php/semnashas/article/view/799/428 \\\",\\\"15. W. Meeinkuirt, P. Kaewtubtim, S. Seepom, J. Pichtel. Metal Uptake and Accumulation by Mangrove Plant Species in Pattani Bay, Thailand. in: Proceedings of the 3rd World Congress on New Technologies (NewTech'17) (Rome, Italy, 2017) https://doi.org/10.11159/icepr17.158 \\\"]\",\n \"page_idx\": \"6\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[64,46,399,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"E3S Web of Conferences 432, 00012 (2023) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[64,60,222,74]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$2^{nd}ICoN$ -BEAT 2021 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[571,46,927,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://doi.org/10.1051/e3sconf/202343200012 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[488,964,501,977]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1051/e3sconf/202343200012"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Earth and Atmospheric Sciences"},"sha256":{"kind":"string","value":"69de2805cf6d78dbb2ac4175c51e0ac09ef616b36f0f1d9e2f24ca5ebac97e5a"},"title":{"kind":"string","value":"Uptake and Accumulation of Zinc by Grey Mangrove at Wonorejo Mangrove Forest, Surabaya, Indonesia"}}},{"rowIdx":272,"cells":{"abstract":{"kind":"string","value":"\n \nThe purpose of this paper is to extend standard finite mixture models in the context of multinomial mixtures for spatial data, in order to cluster geographical units according to demographic characteristics. The spatial information is incorporated on the model through the mixing probabilities of each component. To be more specific, a Gibbs distribution is assumed for prior probabilities. In this way, assignment of each observation is affected by neighbors' cluster and spatial dependence is included in the model. Estimation is based on a modified EM algorithm which is enriched by an extra, initial step for approximating the field. The simulated field algorithm is used in this initial step. The presented model will be used for clustering municipalities of Attica with respect to age distribution of residents.\n "},"author":{"kind":"string","value":"Panagiotis Papastamoulis|Anna Nalpantidi|Dimitris Karlis"},"content_list":{"kind":"list like","value":[{"bbox":"[240,165,754,189]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Multinomial mixture for spatial data ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[228,207,767,241]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Anna Nalpantidi, Dimitris Karlis and Panagiotis Papastamoulis \nDepartment of Statistics ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[305,243,691,258]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Athens University of Economics and Business ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[419,272,576,289]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"February 16, 2024 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[462,320,532,333]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[184,340,813,465]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The purpose of this paper is to extend standard finite mixture models in the context of multinomial mixtures for spatial data, in order to cluster geographical units according to demographic characteristics. The spatial information is incorporated on the model through the mixing probabilities of each component. To be more specific, a Gibbs distribution is assumed for prior probabilities. In this way, assignment of each observation is affected by neighbors' cluster and spatial dependence is included in the model. Estimation is based on a modified EM algorithm which is enriched by an extra, initial step for approximating the field. The simulated field algorithm is used in this initial step. The presented model will be used for clustering municipalities of Attica with respect to age distribution of residents. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[169,472,800,488]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: demography; mixture models; spatial correlation; mean field approximation; ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[145,510,334,527]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,541,849,708]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Clustering regions according to demographic traits is a convenient way to summarize all the available information for an area and reveal hidden subgroups of regions that share common characteristics. More specifically, demographic traits and especially age and sex (Poston et al., 2010) are the most important elements for describing a population. Consequently, dividing an area into groups according to demographics can provide a better insight for the population structure of the area, rather than examining each region individually. However, a plausible assumption is that adjacent areas are affected by common social and environmental conditions and as a result they tend to have similar demographic traits. This implies that data are spatially dependent taking into consideration the first law of geography (Tobler, 1970). As a consequence, standard clustering methods may not be adequate for analyzing these data, since they assume independent observations and ignore the extra variation due to spatial heterogeneity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,708,849,814]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Spatially constrained clustering is rapidly evolving in the last decades, as it is embedded in a wide range of fields like epidemiology, image processing criminology, geospatial economics and others. Constrained clustering was defined by Legendre (1987) who was interested in including spatial, temporal or spatio-temporal restrictions. Since then, many popular clustering algorithms have been modified to adapt spatial information. Pappas (1992) presented a generalization of $k$ -means in the context of image segmentation. He introduced a generalization of $k$ -means, by using a Gibbs random field (Geman and Geman, 1984; Besag, 1986; Derin and Elliott, 1987) for inserting ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[22,258,57,717]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"arXiv:2402.09888v1 [stat.ME] 15 Feb 2024 ","text_format":null,"text_level":null,"type":"aside_text"},{"bbox":"[493,847,503,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,851,210]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the spatial constraints. As hierarchical clustering is concerned, Carvalho et al. (2009) provided a modification of the classical hierarchical agglomerative method. More specifically, neighborhood restriction was imposed on the proximity matrix, which now refers to pairs of adjacent areas and not all possible pairs of observations. Due to the popularity of the field, an excessive number of algorithms have been proposed in the literature (Liu et al., 2012; Ng and Han, 2002; Kumar et al., 2012; Patil et al., 2006). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,210,851,316]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the context of finite mixture models, Green and Richardson (2002) proposed a general approach for modelling spatial heterogeneity of count data instead of the model proposed by Besag, York, Molliè (known as the BYM model) (Besag et al., 1991) and other similar models for the same purpose which use multivariate Gaussian distribution and incorporate spatial structure on covariance matrix. They proposed modelling allocation variables as Hidden Markov Random Fields (HMRF) that follows Potts model, with the purpose of facing local discontinuities and oversmoothed maps that may occur with the other methods. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,316,851,513]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A few years later, Alfo et al. (2008), based on the work of Green and Richardson (2002), introduced an extension of this model, in the context of image-segmentation. They proposed a Gaussian mixture model where allocation variables are modelled using a discrete HMRF. Then, due to the Hammersley-Clifford theorem, it is proved that component labels follow a Gibbs distribution. The difference with the previous work lies on the root of adopting a Gibbs distribution with cluster-specific parameters in prior probabilities. While interaction parameter was constant for all the regions, in the work of Alfo et al. (2008) it is allowed to vary across the image/region. However, the concept of inhomogeneous HMRF with spatially varying interaction parameter wasn't new since, Aykroyd and Zimeras (1999) had proposed approaches on this framework. Forbes et al. (2013), followed the idea of discrete HMRF model for disease mapping, but proposed a more complex structure on the interactions. On the work of Green and Richardson (2002) and Alfo et al. (2008) adjacent areas are penalized equally. Forbes et al. (2013) proposed taking into consideration, not only the adjacency of regions but also the adjacency of clusters. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,512,851,632]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In 2009, Alfo et al. (2009) extended their work (Alfo et al., 2008) for mapping spatially dependent disease counts with special focus on multivariate disease counts. Based on these works, we propose a finite multinomial mixture model for spatial data. The presented model takes into account spatial dependence that leads to an extra source of variation, except for the common heterogeneity. In contrary to standard multinomial mixture model, this methodology let spatial dependence influence the component in which each observation will be assigned. The spatial information is adapted on prior probability of each component, which is let to be affected by the cluster of adjacent areas for each observation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,633,851,755]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The paper consists of five sections. In Section 2, we will present standard multinomial mixture, a brief discussion upon its estimation method and the definition of number of clusters. In Section 3 we will define the proposed model and we will focus on theoretical elements to support it. In addition, there are details provided about model selection procedure and the estimation, since common computational methods are not adequate for the proposed model. Some simulation results to support the new model are provided in Section 4. A real data application of the model on data from Greek census of 2001 is included in Section 5. Finally, Section 6 summarizes all remarkable conclusions of the survey. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[493,847,504,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,116,851,136]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 Multinomial mixture model for independent observations ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,147,849,223]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It is assumed that a surrounding area can be partitioned in $K$ groups of sub-regions that share common demographic traits. More specifically, we would like to find clusters where area units have similar proportion of residents in each age group. For this purpose we will use finite mixture models and especially mixtures of multinomial distributions, which is a plausible assumption for this purpose. A brief description of the model is presented. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,223,849,287]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Let $J$ be the number of categories (age groups) and $\\lambda = (\\lambda_1, \\lambda_2, \\dots, \\lambda_J)$ be the vector of probabilities of success for each category. It is obvious that $\\sum_{j=1}^{J} \\lambda_j = 1$ and $0 \\leq \\lambda_j \\leq 1$ . Let $\\mathbf{y} = (y_1, \\ldots, y_J)'$ be an observation from multinomial distribution. Then $m$ denotes the total number of records of $\\mathbf{y}$ : $m = \\sum_{j=1}^{J} y_j$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,287,849,333]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Considering K clusters, there are $K$ multinomial distributions with corresponding probability vectors $\\pmb{\\lambda}_{\\pmb{k}} = (\\lambda_{k1},\\lambda_{k2},\\dots,\\lambda_{kj})$ , $k = 1,\\dots,K$ . Then $\\pmb{y}$ is distributed according to the following probability distribution: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[241,343,851,386]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP (\\boldsymbol {Y}) = \\sum_ {k = 1} ^ {K} p _ {k} \\frac {m !}{y _ {1} ! y _ {2} ! \\cdots y _ {J} !} \\lambda_ {k 1} ^ {y _ {1}} \\lambda_ {k 2} ^ {y _ {2}} \\dots \\lambda_ {k J} ^ {y _ {J}} = \\sum_ {k = 1} ^ {K} p _ {k} \\frac {m !}{y _ {1} ! y _ {2} ! \\cdots y _ {J} !} \\prod_ {j = 1} ^ {J} \\lambda_ {k j} ^ {y _ {j}} \\tag {1}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[143,391,852,421]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Taking into consideration the unobserved labels $(\\mathbf{Z})$ that specify from which component each observation comes from we can write that ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[395,431,602,448]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nZ \\sim \\text {M u l t i n o m i a l} (1, p) \\text {a n d}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[377,455,849,473]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\mathbf {Y} \\mid \\mathbf {Z} = \\mathbf {z} \\sim \\text {M u l t i n o m i a l} (m, \\lambda_ {z}) \\tag {2}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[143,478,849,551]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A necessary and sufficient condition for the generic identifiability of finite mixtures of multinomial distributions is the restriction $m \\geqslant 2K - 1$ (Teicher, 1963; Blischke, 1964; Titterington et al., 1985; Grün and Leisch, 2008). The reader is referred to Papastamoulis (2023) for estimation of finite mixtures of multinomial distributions under a maximum likelihood as well as a Bayesian point of view. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,575,849,595]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 Multinomial mixture for spatially dependent observations ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,608,295,625]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.1 Definition ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,633,849,723]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finite mixture models is an appropriate tool for capturing the heterogeneity of a population since, they divide it into subgroups in a way that observations of the same cluster are homogeneous, while observations from different clusters are different. However, the model of Section 2 does not capture the spatial heterogeneity that exists when spatial data is the case. This means that there is an extra source of variation that is not taken into consideration and as a result the model is inadequate. Therefore, we have to incorporate spatial information in the model. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,724,849,785]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the same concept, it is assumed that there is an area, which consists of $n$ sub-regions. For each sub-region, the number of residents in each age group is recorded and it is denoted by $\\pmb{y}_i = (y_{i1}, y_{i2}, \\dots, y_{iJ})'$ . Let $m_i$ denote the total counts of $i$ -th region. In addition, an adjacency matrix $(\\mathbf{A}_{nxn})$ which reflects the spatial dependence, is defined as follows: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[359,792,620,825]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nA _ {i j} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f i a n d j a r e a d j a c e n t} \\\\ 0, & \\text {e l s e}, \\end{array} \\right.\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[493,847,504,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,852,196]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where, $A_{ij}$ denotes the element of $i$ -th row and $j$ -th column of matrix $\\mathbf{A}$ . The adjacency can be considered in different ways, like using the distance between two area units. However, we consider that two regions are adjacent if they are spatially contiguous. Let $N_i$ , $i = 1, \\dots, n$ denote the number of neighbors of $i$ -th region or else the neighborhood system. In order to assume $N_i$ as a neighbor system of $i$ -th region it must be valid that: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[165,204,308,247]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1. $i\\\\notin N_i,\\\\forall i\\\\in N$ \",\"2. $j\\\\in N_{j}\\\\leftrightarrow i\\\\in N_{j}$ \"]","page_idx":"3","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[143,253,852,314]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Moreover, no further features have been recorded for each region. A general approach for modelling spatial dependence in FMMs was introduced by Green and Richardson (2002) and extended by Alfo et al. (2008). This approach will be adopted in this work but in the framework of multinomial mixture. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,315,851,390]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Geman and Geman (1984) proposed modelling the class process $z_{ik}$ , $i = 1, \\dots, n$ , $k = 1, \\dots, K$ by a Markov Random Field (MRF). Recalling the Hammersley-Clifford theorem, modelling indicator variables as a MRF is equivalent of using a Gibbs distribution for prior probabilities. Based on the Hammersley-Clifford theorem the process $\\{Z_i : i \\in N\\}$ is a MRF, if and only if its joint distribution is a Gibbs distribution (Besag, 1974). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[169,390,539,406]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Then the joint distribution of the MRF is given by ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[377,419,620,450]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP _ {G} (\\boldsymbol {z}) = W ^ {- 1} \\exp \\{- \\sum_ {c} V _ {c} (\\boldsymbol {z} _ {c}) \\},\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[143,460,852,535]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $W = \\sum_{z} \\exp \\{-\\sum_{c} V_{c}(z_{c})\\}$ is the normalizing constant or partitioning function, a sum over all possible values of $z$ . The sum on the $V(\\cdot)$ function (also known as the potential function) is over the set of cliques. The term clique refers to the set of nodes in which every pair is connected by an edge if MRF is seen as a graph. In simple words, a clique is a pair of regions that are spatially contiguous. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,536,852,583]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In that case, the common prior probabilities of the mixture model $p_k = P(z_{ik} = 1)$ are replaced by the conditional prior probabilities: $t_{ik} = P(z_{ik} = 1 | \\mathbf{z}_j, j \\in N_i)$ . Given the assigned neighborhood system, the Gibbs distribution is defined by: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[285,595,851,630]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nt _ {i j} = P \\left(z _ {i k} = 1 \\mid \\boldsymbol {z} _ {j}, j \\in N _ {i}\\right) \\propto \\exp \\left\\{\\alpha_ {k} - \\beta_ {k} \\sum_ {j \\in N _ {i}} V \\left(z _ {i k} z _ {j k}\\right) \\right\\}, \\tag {3}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[143,638,542,656]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"for $i = 1,\\dots ,n$ ， $k = 1,\\ldots ,K$ .Then (1) isreformedas:","text_format":null,"text_level":null,"type":"text"},{"bbox":"[212,665,851,710]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP (\\mathbf {Y} _ {i}) = \\sum_ {k = 1} ^ {K} t _ {i k} \\frac {m _ {i} !}{y _ {i 1} ! , y _ {i 2} ! \\cdots y _ {i J} !} \\lambda_ {k 1} ^ {y _ {i 1}} \\lambda_ {k 2} ^ {y _ {i 2}} \\dots \\lambda_ {k J} ^ {y _ {i J}} = \\sum_ {k = 1} ^ {K} t _ {i k} \\frac {m _ {i} !}{y _ {i 1} ! , y _ {i 2} ! \\cdots y _ {i J} !} \\prod_ {j = 1} ^ {J} \\lambda_ {k j} ^ {y _ {i j}} \\tag {4}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[143,719,851,795]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Equation (3) is a Gibbs distribution with cluster specific parameters. It is supported that the standard model of Green and Richardson (2002), where intercept $(\\alpha)$ and interaction term $(\\beta)$ are constant to the whole area, is restrictive and in many physical systems this assumption is violated, thus the cluster-specific Gibbs is preferred. We follow the suggested potential function of Alfò et al. (2008), namely ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[370,794,851,828]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nV (z _ {i k} z _ {j k}) = \\left\\{ \\begin{array}{l l} - 1, & \\text {i f} z _ {i k} z _ {j k} = 1 \\\\ + 1, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[493,847,504,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,852,165]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This structure implies that neighbors of $i$ -th region that belong to other cluster than $k$ are penalized. Then prior probability of $k$ -th component for $i$ -th observation is increased when its neighbors belong there. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,166,852,198]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Adopting the above potential function and posing first cluster as the reference category, the rior conditional probabilities in (3) are equivalent to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[284,208,851,226]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nt _ {i k} \\propto \\exp [ \\alpha_ {k} + \\beta_ {k} (n _ {i k} - n _ {i k} ^ {c}) ], \\quad i = 1, \\dots , n, \\quad k = 1, \\dots , K, \\tag {6}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[143,234,854,356]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"with $\\alpha_{1} = \\beta_{1} = 0$ for ensuring identifiability. Parameter $\\alpha_{k}$ , $k = 1,\\dots ,K$ accounts for the prior probability of $k$ -th cluster without taking into consideration the neighbors. On the other hand, parameter $\\beta_{k}$ , $k = 1,\\ldots ,K$ expresses how the cluster assignment of each observations is affected by the cluster of the neighbors. This means that in case of $\\beta = (0,\\dots,0)'$ , then standard multinomial mixture given in (1) occurs. $n_{ik}$ and $n_{ik}^{c}$ denote the number of neighbors of $i$ -th region that belong and not belong to $k$ -th cluster respectively. The expression (6) corresponds to a multinomial logit model for the prior conditional probabilities of cluster membership; it is also called as Strauss automodel (Strauss, 1977). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,357,852,388]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this point, it is important to mention that prior probabilities $p_k$ , $k = 1, \\dots, K$ , which have very natural and useful interpretation, are difficult to be calculated under this approach. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,405,614,422]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3.2 Parameter Estimation and Model selection ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,430,852,580]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Selecting maximum likelihood approach for the estimation of parameters, due to the unobserved labels, EM algorithm is the appropriate tool. However, spatial dependence increase the complexity of the model and as a consequence it is necessary to apply approximations for making the algorithm tractable. For this reason, instead of defining the common likelihood, an approximation has been proposed by Besag (1975) which is a pseudolikelihood. Pseudolikelihood allows defining the joint distribution of the MRF by taking the product of conditional probabilities of observing $z_{i}$ , given the values of all the other regions ( $z_{j}, j \\neq i$ ). In this way, the calculation of normalizing constant of joint Gibbs distribution, which demands all possible realizations of MRF can be avoided. Then, assuming also that $Y_{i}|Z_{i}$ are independent for $i = 1, \\dots, n$ , the observed likelihood is approximated by: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[326,580,851,622]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nL _ {o b s} (\\boldsymbol {\\theta} | \\boldsymbol {y}) = \\prod_ {i = 1} ^ {n} \\sum_ {k = 1} ^ {K} t _ {i k} \\frac {m _ {i} !}{y _ {i 1} ! y _ {i 2} ! \\cdots y _ {i J} !} \\lambda_ {k 1} ^ {y _ {i 1}} \\dots \\lambda_ {k J} ^ {y _ {i J}} \\tag {7}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[143,626,640,643]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and the complete likelihood and log-likelihood are approximated by: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[307,654,851,694]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nL _ {c} (\\boldsymbol {\\theta} | \\boldsymbol {y}, \\boldsymbol {z}) = \\prod_ {i = 1} ^ {n} \\sum_ {k = 1} ^ {K} \\left[ t _ {i k} \\frac {m _ {i} !}{y _ {i 1} ! y _ {i 2} ! \\cdots y _ {i J} !} \\lambda_ {k 1} ^ {y _ {i 1}} \\dots \\lambda_ {k J} ^ {y _ {i J}} \\right] ^ {z _ {i k}} \\tag {8}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[143,705,179,719]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[235,729,849,821]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\begin{array}{l} l _ {c} (\\boldsymbol {\\theta} | \\boldsymbol {y}, \\boldsymbol {z}) = \\sum_ {i = 1} ^ {n} \\sum_ {k = 1} ^ {K} \\left[ z _ {i k} \\log (t _ {i k}) + z _ {i k} \\log \\left(\\frac {m _ {i} !}{y _ {i 1} ! y _ {i 2} ! \\dots y _ {i J} !} \\lambda_ {k 1} ^ {y _ {i 1}} \\dots \\lambda_ {k J} ^ {y _ {i J}}\\right) \\right] = \\\\ = \\sum_ {i = 1} ^ {n} \\sum_ {k = 1} ^ {K} \\left[ z _ {i k} \\log \\left(t _ {i k}\\right) + z _ {i k} \\sum_ {j = 1} ^ {J} y _ {i j} \\log \\left(\\lambda_ {k j}\\right) \\right] + c o n s t a n t \\tag {9} \\\\ \\end{array}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[493,845,504,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,852,179]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The above form of likelihoods includes the conditional distributions of $z_{i} | z_{j}, i \\neq j$ instead of the marginal distribution $z_{i}$ . In case of complete independence of $z_{i}$ , pseudolikelihoods coincide with true likelihoods. Having approximated the quantities we need, EM algorithm can be applied as common: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[163,189,852,233]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"- $\\pmb{E}$ -step: Taking the expectation of approximated log-likelihood with respect to unobserved data $\\pmb{z}_i$ , the approximated posterior probability of $i$ -th observation belongs to $k$ -th cluster is estimated by: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[366,234,851,268]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\hat {z _ {i k}} = w _ {i k} = E \\left[ z _ {i k} \\mid \\boldsymbol {\\theta}, \\boldsymbol {y} \\right] = \\frac {t _ {i k} f \\left(\\boldsymbol {y} _ {i} \\mid \\boldsymbol {\\lambda} _ {k}\\right)}{\\sum_ {\\ell = 1} ^ {K} t _ {i \\ell} f \\left(\\boldsymbol {y} _ {i} \\mid \\boldsymbol {\\lambda} _ {\\ell}\\right)} \\tag {10}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[183,273,851,319]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $\\pmb{\\lambda}_{k} = (\\lambda_{k1},\\dots,\\lambda_{kJ})'$ and $f(\\pmb{y}_i|\\pmb{\\lambda}_k)$ the probability mass function of multinomial distribution for $i$ -th observation and $k$ -th component. Now, the approximated expected complete log-likelihood is calculated by: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[348,329,851,378]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nQ = \\sum_ {i = 1} ^ {n} \\sum_ {k = 1} ^ {K} \\left[ w _ {i k} \\log \\left(t _ {i k}\\right) + w _ {i _ {k}} \\sum_ {j = 1} ^ {J} y _ {i j} \\log \\left(\\lambda_ {k j}\\right) \\right] \\tag {11}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[165,391,854,436]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"- $M$ -step: In this step approximated maximum likelihood estimators are provided, by maximizing (11) with respect to $\\pmb{\\theta} = (\\pmb{\\theta}_1, \\dots, \\pmb{\\theta}_K)$ , where $\\pmb{\\theta}_k = (\\pmb{\\theta}_{k,mult}, \\pmb{\\theta}_{k,Gibbs})$ and $\\pmb{\\theta}_{k,Gibbs} = (\\alpha_k, \\beta_k)$ and $\\pmb{\\theta}_{k,mult} = (\\lambda_{k1}, \\dots, \\lambda_{kj})$ for $k = 1, \\dots, K$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[186,441,745,455]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Parameters of Gibbs distribution: We have to solve the equation system ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[303,467,851,507]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\frac {\\partial Q}{\\partial \\left(\\alpha_ {k} , \\beta_ {k}\\right)} = \\frac {\\partial}{\\partial \\left(\\alpha_ {k} , \\beta_ {k}\\right)} \\sum_ {i = 1} ^ {n} \\sum_ {k = 1} ^ {K} w _ {i k} \\log \\left(t _ {i k}\\right) = 0, \\quad k = 2, \\dots , K \\tag {12}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[184,517,849,546]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, this equation is extremely complex and numerical methods are suggested for its solution. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[184,551,851,609]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Parameters of multinomial distributions: The maximization of Q under the constraint $\\sum_{j=1}^{J} \\lambda_{kj} = 1$ is needed for finding the estimators of $\\lambda_{kj}$ . Thus, the maximum pseudolikelihood estimates for parameters of each multinomial and every category are given by the formula: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[450,609,849,643]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\hat {\\lambda_ {k j}} = \\frac {\\sum_ {i = 1} ^ {n} w _ {i k} y _ {i j}}{\\sum_ {i = 1} ^ {n} w _ {i k} m _ {i}} \\tag {13}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[184,647,395,662]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"for $k = 1,\\ldots ,K,j = 1,\\ldots ,J$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,671,852,821]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The parameter estimation in this model is not a trivial issue due to Gibbs distribution. In order to facilitate the procedure, pseudolikelihood was proposed. Then, conditional probabilities can be approximated by MCMC simulations. However, it has been proved that this approach is restrictive since it is inappropriate when strong dependence between regions is present. In addition, it is computationally demanding. For this reason, another approximation of complex complete likelihood was introduced by Qian and Titterington (1991) and extended by Celeux et al. (2003). This, method uses Mean field theory, from the domain of statistical mechanics, in order to approximate the HMRF and then apply EM. Mean field approximation means that the value of $i$ -th area is independent to values of other areas while these are set to be fixed an irrelevant to $i$ -th value. Based on this idea, intractable distributions like Gibbs distribution can be faced. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[493,847,504,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,852,181]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"According to this, Celeux et al. (2003) suggested a class of algorithms that consists of two steps. In the first stage, the hidden field $(\\mathbf{z})$ is approximated given the observed data $(\\pmb{y})$ and the current parameters $(\\pmb{\\theta}^{(t)})$ , thus an approximation of Gibbs distribution is achieved as follows: Denoting $\\tilde{\\pmb{z}}$ the configuration of HMRF, ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[344,191,655,231]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nP _ {\\tilde {\\boldsymbol {z}}} (\\boldsymbol {z} | \\boldsymbol {\\theta} _ {G i b b s}) = \\prod_ {i = 1} ^ {n} P _ {G} (\\boldsymbol {z} _ {i} | \\tilde {\\boldsymbol {z}} _ {j}, j \\in N _ {i}, \\boldsymbol {\\theta} _ {G i b b s} ^ {(t)})\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[143,239,849,330]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the second step, given the corresponding approximated field, the approximated posterior probabilities can be estimated (E-step) and then M-step follows for providing estimations of the parameters of interest. They proposed three algorithms for approximating the hidden field: mean field, mode field and simulated field algorithm. The concept of simulated field algorithm will be used in this work as it has been proved that it provides better results. This is the counterpart of the Stochastic EM algorithm in a spatial framework. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,330,849,361]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The modified classification EM (CEM) algorithm that used for estimating the proposed model can be sketched as follows. At the $t$ -th iteration we have: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[163,368,746,411]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"1. Simulate $\\\\tilde{z}_i$ from $P_G(\\\\pmb {z}_i|\\\\tilde{\\\\pmb{z}}_j^{(t - 1)},j\\\\in N_i,\\\\pmb{\\\\theta}_{Gibbs}^{(t)})$ for $i = 1,\\\\ldots ,n$ \",\"2. Using the field approximation $\\\\tilde{z}$ from the previous step apply CEM algorithm \"]","page_idx":"6","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[192,420,511,435]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(a) $E$ -step: Estimate posterior probabilities: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[375,448,851,501]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\tilde {w} _ {i k} ^ {(t)} = \\frac {t _ {i k} \\left(\\tilde {\\boldsymbol {z}} _ {\\boldsymbol {i}} ^ {(t)} \\mid \\boldsymbol {\\alpha} ^ {(t - 1)} , \\boldsymbol {\\beta} ^ {(t - 1)}\\right) f \\left(\\boldsymbol {y} _ {\\boldsymbol {i}} \\mid \\boldsymbol {\\lambda} _ {\\boldsymbol {k}} ^ {(t - 1)}\\right)}{\\sum_ {l = 1} ^ {K} t _ {i l} \\left(\\tilde {\\boldsymbol {z}} _ {\\boldsymbol {i}} ^ {(t)} \\mid \\boldsymbol {\\alpha} ^ {(t - 1)} , \\boldsymbol {\\beta} ^ {(t - 1)}\\right) f \\left(\\boldsymbol {y} _ {\\boldsymbol {i}} \\mid \\boldsymbol {\\lambda} _ {l} ^ {(t - 1)}\\right)} \\tag {14}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[220,513,715,529]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Then, approximated expected complete log-likelihood is modified as: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[339,540,851,589]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nQ ^ {M F} = \\sum_ {i = 1} ^ {n} \\sum_ {k = 1} ^ {K} \\left[ \\tilde {w} _ {i k} ^ {(t)} \\log (t _ {i k}) + \\tilde {w} _ {i k} ^ {(t)} \\sum_ {j = 1} ^ {J} y _ {i j} \\log \\left(\\lambda_ {k j} ^ {(t - 1)}\\right) \\right] \\tag {15}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[191,601,849,646]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"(b) $C$ -step: Set $z_{ik}^{(t)} = 1$ and all other $0$ , if $\\\\tilde{w}_{ik}^{(t)} = \\\\max_{\\\\ell}\\\\tilde{w}_{i\\\\ell}^{(t)}$ , $\\\\ell = 1,\\\\ldots ,K$ \",\"(c) $M$ -step: Estimate $\\\\alpha_{k}^{(t)}, \\\\beta_{k}^{(t)}$ and $\\\\lambda_{kj}^{(t)}$ given $z_{ik}^{(t)}$ and $\\\\tilde{\\\\boldsymbol{w}}_{\\\\boldsymbol{i}}^{(t)}$ , $k = 1, \\\\ldots, K$ and $j = 1, \\\\ldots, J$ . \"]","page_idx":"6","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[143,652,849,683]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The above procedure is repeated for a significant number of iterations, until convergence to maximum observed approximated likelihood is achieved. The approximated observed likelihood is: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[269,694,851,734]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nL _ {o b s, a p p r o x} (\\boldsymbol {\\theta}) = \\prod_ {i = 1} ^ {n} \\sum_ {k = 1} ^ {K} f \\left(y _ {i} \\mid z _ {i k}, \\boldsymbol {\\lambda} _ {k}\\right) P \\left(z _ {i k} = 1 \\mid \\tilde {\\boldsymbol {z}} _ {j}, j \\in N _ {i}, \\alpha_ {k}, \\beta_ {k}\\right) \\tag {16}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[143,744,849,792]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Up to this approximation of observed likelihood, Forbes and Peyrard (2003) displayed an approximation of BIC in case of mean field approximations. Denoting $\\hat{\\pmb{\\theta}}$ as the approximation of true MLE then, the approximation of BIC is: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[346,806,849,824]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\nB I C ^ {\\tilde {z}} (\\hat {\\boldsymbol {\\theta}}) = 2 \\log \\left(L _ {o b s, a p p r o x} (\\hat {\\boldsymbol {\\theta}})\\right) - d \\log (n) \\tag {17}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[493,847,503,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[385,116,612,296]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0733/e6b2ee9dbd13799a71babd45ccd789c5a6384ae3ed29a5f1df152755ac0bfc5a.jpg","list_items":null,"page_idx":"7","sub_type":null,"table_body":"<table><tr><td></td><td>Cluster 1</td><td>Cluster 2</td></tr><tr><td>λk1</td><td>0.12</td><td>0.08</td></tr><tr><td>λk2</td><td>0.12</td><td>0.08</td></tr><tr><td>λk3</td><td>0.12</td><td>0.08</td></tr><tr><td>λk4</td><td>0.12</td><td>0.08</td></tr><tr><td>λk5</td><td>0.12</td><td>0.08</td></tr><tr><td>λk6</td><td>0.08</td><td>0.12</td></tr><tr><td>λk7</td><td>0.08</td><td>0.12</td></tr><tr><td>λk8</td><td>0.08</td><td>0.12</td></tr><tr><td>λk9</td><td>0.08</td><td>0.12</td></tr><tr><td>λk10</td><td>0.08</td><td>0.12</td></tr></table>","table_caption":"[\"Table 1: Parameters of the multinomial distributions \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[143,343,849,373]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"where $d$ is the number of free parameters in the model, in our case $d = 2(K - 1) + K(J - 1)$ . The approximation of observed likelihood is given by the equation (16). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,375,852,481]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Initialization of EM is a crucial issue, since it is possible to find a local maximum instead of the global maximum which is the case. For this reason, we propose the strategy of Biernacki et al. (2003). More specifically, we used different initial values and ran the EM algorithm. For each set of initial values the maximum likelihood was recorded. The solution that corresponds to the highest approximated observed likelihood was used as initial value for the final EM. Finally as far as the convergence of the algorithm and because of the stochastic nature of the algorithm, we stopped when we failed to find a larger log-likelihood for 50 successive iterations. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[145,502,387,523]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 Simulation study ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,534,851,669]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this section we examine the performance of the proposed model under different conditions. More specifically, we focus on different lattice sizes and various parameters of the Gibbs distribution, which measures how interaction of neighbors affects the assignment of each observation in each cluster. We assumed that we have a $N$ -dimensional square lattice $(N = 8,10,20)$ . The points of each lattice come from a mixture of two multinomial distributions. For each multinomial distribution we have assumed 10 categories, and size equal to 100 while the parameters are presented in Table 1. According to the presented model, the prior probabilities of the mixture follow the Gibbs distribution, so we have three different scenarios for this distribution namely $\\beta = (0,0.01)'$ , $(0,0.1)'$ and $(0,0.2)'$ respectively. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,670,849,729]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To evaluate the performance of the model we used the Adjusted Rand Index (ARI) (Hubert and Arabie, 1985). The index measures the agreement between two partitions. Values close to 1 indicate complete agreement. In this case, we compared the cluster labels estimated by the proposed model with the true labels. True labels have been simulated by a Gibbs sampler. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,729,849,820]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For all scenarios we have simulated 100 samples. Figure 1 depicts the results of the simulations. More specifically, we conclude that Gibbs distribution does not affect essentially the model's performance. To be more specific, ARI values are similar for each combination of $\\beta$ parameter and sample size. On the other hand, comparing results with respect to different lattice size, it seems that there are significant differences: as sample size increases, the variability of the ARI decreases. When $N = 8$ , there are cases where ARI is less than 0.70, while in case of $N = 20$ , ARI is never ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[493,847,504,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,851,179]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"less than 0.80. So, for small sample sizes it is possible not to have such a good partition as in higher sample sizes. We also see a slight improvement on ARI as lattice size increases. However, the general conclusion is that model clusters adequately the observations, since, in each case the median ARI is higher than 0.80. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,180,849,210]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally note that initialisation of the algorithm as well as convergence were used as described in Section 3. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[292,223,707,539]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 1: Boxplots of ARI for different lattices and different values of $\\\\beta$ . \"]","image_footnote":"[]","img_path":"images/0174/24706650b70b4a789b9f19629c3ff31789ad8b4d632f12cb28574c73bac39913.jpg","list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[143,625,715,645]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 Application: Data from Greek census of 2001 ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,655,852,776]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Attica is one of the thirteen administrative regions of Greece which encompasses the capital of Greece, Athens, and the biggest port of the country, Piraeus. Except for Athens and surrounding cities, Saronic islands, Cythera and a small part of Peloponnese mainland pertain to Attica region. As it is expected, the extension of the region, in combination with the wave of urbanization, has led Attica to encompass a significant percentage of Greek population. To be more specific, according to Greek census of 2001, more than the one third of total Greek population lives in Athens, with the percentage estimated around $35\\%$ . With the purpose of a better administration of Attica, it has been partition into 66 municipalities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,777,851,824]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It is common that people choose living in areas that service their needs and usually, their needs depend on their age. For example, young people prefer living in big cities instead of villages, in order to study or work. This, in combination with the fact that municipalities of Attica not only ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[491,847,504,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"8","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"9 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[143,119,849,224]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"do they correspond to urban cities and small towns, but also islands and suburbs, motivates in believing that sub-regions of Attica present heterogeneity with respect to the age distribution of their inhabitants. In other words, it seems plausible assuming that all municipalities of Attica do not present the same percentage of people in each age group, but some of them tend to be similar and described as a cluster. Furthermore, another hypothesis is that adjacent sub-regions are affected by similar environmental and social factors, so they attract people of the same age and consequently, this may encourage clustering on the same group. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,226,849,376]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The purpose of this section is to present a clustering of municipalities of Attica region according to age distribution of their residents. Use of similar data has been treated in Jorgensen (2013) where the spatial aspect was ignored. Nevertheless, special interest is given to spatial dependence of the sub-regions of Attica. It is assumed that two regions are adjacent if they are spatially contiguous. For this reason, six area units that are far away from the main part of Attica (Cythera, Hydra, Spetses, Poros, Troezen, Agistri) have been excluded, since the main assumption of common characteristics due to adjacency is not plausible. The islands of Salamina and Aegina have been kept and as adjacency is concerned, it has been considered that Salamina is neighbor of Perama and Aegina is neighbor of Pireus, as long as the communication of the mainland of Attica with these islands becomes through the ports of the correspond municipalities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,377,849,421]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The clustering was conducted by applying the multinomial mixture with Gibbs prior, that was presented in section 3. The results were compared to the results of standard multinomial mixture. The analysis was conducted with R package. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,422,849,496]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The clustering refers to 60 of 66 municipalities of Attica. For each of them the number of inhabitants per age group is recorded. There are 18 age groups: from 0 to 84. Each group contains five ages and the final group refers to people whose age is 85 and over. An example of the form of the data is presented in Table 2. The data comes from Greek census of 2001 and data were taken from the National Statistical Office website. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,497,849,617]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Before starting clustering, it would be interesting examining whether the hypothesis of heterogeneity and spatial dependence are plausible for this data. In Figure 2, a small number of municipalities have been chosen in order to indicate the heterogeneity of the regions. As it is obvious, not all regions have the same age profile. More specifically, Zografos presents an excess of records in ages 20-29. Furthermore, Aegina have high percentages of residents in ages $60+$ , compared to the other regions. On the other hand, Aspropyrgos dominate in younger ages of 0-19, while it presents the lower percentages on older age groups. Egaleo seems to represent an intermediate situation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,618,849,723]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"After that, we examine the second assumption that regions are spatially correlated. For this purpose Moran's Index $I$ (Moran, 1950) was used. The above index was used for examining spatial autocorrelation on univariate observations. However, in this study, observations are multivariate. For overcoming this problem, the mean age of each municipality is computed and used for the Moran index. Using mean age as variable of interest and the adjacency matrix as the weight matrix, the results shown that $I = 0.33$ and there is evidence that municipalities of Attica are shown spatial correlation (permutation test pvalue $< 0.001$ ). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,724,849,814]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The above study indicated that data presents heterogeneity so clustering is meaningful. First, standard multinomial mixture was applied for clustering data. The estimation of both models was based on the spatial counterpart of stochastic EM that was described in section 3. Especially for the case of standard multinomial mixture, the vector of spatial parameters $(\\pmb{b}_{k\\times k})$ were set equal to zero. The two models are nested and this justify the usage of the same algorithm. Furthermore, the estimation of Gibbs parameters was based on simulated annealing algorithm. Variant of Newton-","text_format":null,"text_level":null,"type":"text"},{"bbox":"[488,845,508,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"9","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"10 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[359,116,637,416]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0473/7e3b0ab505cdc23ac6396055f9f43b93820fddcda74dbfd8f501609f9daac834.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":"<table><tr><td>Age group</td><td>Records</td><td>Proportions</td></tr><tr><td>0-4</td><td>3132</td><td>0.038</td></tr><tr><td>5-9</td><td>3128</td><td>0.038</td></tr><tr><td>10-14</td><td>3387</td><td>0.042</td></tr><tr><td>15-19</td><td>6069</td><td>0.075</td></tr><tr><td>20-24</td><td>9304</td><td>0.114</td></tr><tr><td>25-29</td><td>7368</td><td>0.090</td></tr><tr><td>30-34</td><td>6770</td><td>0.083</td></tr><tr><td>35-39</td><td>5587</td><td>0.069</td></tr><tr><td>40-44</td><td>5595</td><td>0.069</td></tr><tr><td>45-49</td><td>5538</td><td>0.068</td></tr><tr><td>50-54</td><td>5244</td><td>0.064</td></tr><tr><td>55-59</td><td>4150</td><td>0.051</td></tr><tr><td>60-64</td><td>4400</td><td>0.054</td></tr><tr><td>65-69</td><td>3924</td><td>0.048</td></tr><tr><td>70-74</td><td>3429</td><td>0.042</td></tr><tr><td>75-79</td><td>2166</td><td>0.027</td></tr><tr><td>80-84</td><td>1253</td><td>0.015</td></tr><tr><td>85+</td><td>970</td><td>0.012</td></tr></table>","table_caption":"[\"Table 2: Number and rounded proportion of residents by age in Zografos from census of 2001 \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[143,465,852,542]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Raphson was also used, but in terms of maximum log-likelihood simulated annealing was slightly better. The algorithm applied for adequate number of iterations for each case, until convergence was achieved. Initialization process was based on the strategy described in Section 3 for $k = 2$ while for $K = 3,\\ldots ,9$ , initialization was based on the solutions of previous model plus a random vector for the new component. Convergence was detected as described at the end of Section 3. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,542,852,604]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The maximum log-likelihood values as well as BIC for models with different number of components, from the application of standard multinomial mixture are provided in Table 3. Maximum value of BIC indicates the optimal model. According to Table 3, BIC suggests the model with eight components as the best choice. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[370,614,624,782]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0200/39c2eda1079fe108c5a1332ad6b5258c15b1c98524b1fc76f270e2b3bc013837.jpg","list_items":null,"page_idx":"10","sub_type":null,"table_body":"<table><tr><td>K</td><td>log-likelihood</td><td>BIC</td></tr><tr><td>1</td><td>-28590.73</td><td>-57251.07</td></tr><tr><td>2</td><td>-18303.01</td><td>-36749.32</td></tr><tr><td>3</td><td>-15971.25</td><td>-32159.50</td></tr><tr><td>4</td><td>-13096.92</td><td>-26484.54</td></tr><tr><td>5</td><td>-11878.35</td><td>-24121.10</td></tr><tr><td>6</td><td>-11537.93</td><td>-23513.95</td></tr><tr><td>7</td><td>-10730.52</td><td>-21972.83</td></tr><tr><td>8</td><td>-10670.59</td><td>-21926.79</td></tr><tr><td>9</td><td>-10658.97</td><td>-21977.13</td></tr></table>","table_caption":"[\"Table 3: Maximized log-likelihood and BIC for standard multinomial finite mixture \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[488,845,508,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"10","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"11 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[282,119,709,455]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 2: Percentage of residents in each age group for four municipalities \"]","image_footnote":"[]","img_path":"images/0114/55aa81a50119c9a5e56103acbd5e4d19b44f56869c06d866f66143660c70cfaf.jpg","list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[143,523,849,553]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The correspond results of the proposed model of multinomial mixture that takes into consideration the spatial information are presented in Tables 4 and 5. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,554,849,718]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It occurs that both models proposed the same number of clusters, while the estimated parameters of multinomial distributions are close. This is something expected, since this model is proposed for capturing the extra variation from spatial information that it is not explained by the standard model. In Celeux et al. (2003), a simulation study indicates similar superior behavior of the spatial model, namely an improved misclassification rate, while the parameters estimates are similar. They conclude that standard EM provides the same estimations of parameters with the modified EM that includes an extra step of field's simulation, but the second method presents lower error rate than the first. As it has been discussed, the two models are nested, so likelihood ratio test (LRT) can be used for comparing them. The results showed that the there is statistically significant difference between the two models which means that spatial term is statistically significant (LRT pvalue $< 0.05$ ). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,720,849,809]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The two models propose the same clusters that can be seen in Figure 7, while the parameters of each cluster are depicted in Figure 3. Table 6 includes the mean age of each group. Based on the mean age, clusters with similar value have been grouped in order to present the proportion of residents in each age group, for every cluster. The results are presented in Figures 4, 5 and 6. It seems that there is an interesting structure of municipalities of Attica with respect to age of the residents. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[488,845,508,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"11","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"12 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[83,290,356,398]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0175/05968f226f514d5421f96e0c80e6e4e95efdbd142920e8246cfb9942accb22b4.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[359,292,630,398]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0305/4311e9e98c32879f44e4f34bd4b00d65a1040a039754f095c4d6fd663312a292.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[633,292,903,398]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0850/488a33210e70c8519ecbb2d94ba65cf473551564f84baa30722920867097650f.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[84,401,354,506]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0935/b4f2a2ca3373fb5566ba1b8d9128a8e7f9cdfc47c92024be8d48178361638d5f.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[359,401,629,506]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0796/0510e615fba4b9dc60b70d6b3fdc786e8ca2379ef617fe0061cddfffbb844c09.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[633,401,903,506]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0260/0016b7a7319750402cb439004764beef756d4b427d474cf7617ade18fb1cc4c1.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[83,508,354,614]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0072/554db8e925362607786c8f9e4b2657755e7f921aba2a5902116e1c60f45f5c24.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[359,508,629,614]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 3: Percentage of residents in each age group for each cluster \"]","image_footnote":"[]","img_path":"images/0576/3da70d81b72e0ba97a1520e286300d38f9c49d2702e2179550f2a73bcb6c7c3a.jpg","list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[490,847,508,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"12","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"13 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[349,116,648,284]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0907/1a7171413b12e5d5b077ab83ac8387b0128b39256f5677c08f7ef5ae30c7439a.jpg","list_items":null,"page_idx":"13","sub_type":null,"table_body":"<table><tr><td>K</td><td>log-likelihoodapprox</td><td>BICapprox</td></tr><tr><td>1</td><td>-28590.73</td><td>-57251.07</td></tr><tr><td>2</td><td>-18298.02</td><td>-36743.44</td></tr><tr><td>3</td><td>-15963.93</td><td>-32153.05</td></tr><tr><td>4</td><td>-13099.68</td><td>-26502.34</td></tr><tr><td>5</td><td>-11873.5</td><td>-24127.77</td></tr><tr><td>6</td><td>-11525.79</td><td>-23510.15</td></tr><tr><td>7</td><td>-10718.53</td><td>-21973.42</td></tr><tr><td>8</td><td>-10659.71</td><td>-21933.57</td></tr><tr><td>9</td><td>-10627.76</td><td>-21947.46</td></tr></table>","table_caption":"[\"Table 4: Approximated maximized log-likelihood and BIC for multinomial finite mixture with Gibbs prior \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[143,349,849,530]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Clusters 1,3,4: Clusters 1,3 and 4 represent municipalities that have an intermediate structure compared to the regions of the other clusters. Clusters 1 and 3 seems to have similar structure for the ages 0-25 when cluster 4 has lower proportions on ages 0-10. For ages 20-30, there is a peak for cluster 4. Looking at the map (7), cluster 4 includes centre of Attica (Athens) with two other adjacent areas. In these municipalities, there are universities and as a consequence it is plausible to have significant number of young people, especially of these ages. Based on Figure 3, the peak in these ages is the highest among all clusters. For the ages 30-70, cluster 1 and 4 have similar behaviour. According to the map, municipalities of cluster 4 are closer to municipalities of cluster 1. Given that cluster 1 is the central part of Attica and that the referred age groups imply the workforce of each region, the similarity is plausible, providing that work opportunities are better in the center than in the suburbs. As ages of $70+$ are concerned, the differences are meaningful for the three clusters. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,531,849,622]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Clusters 2,5,6: Clusters 2,5 and 6 consists of municipalities with the youngest population among municipalities of Atttica. Although the three clusters have similar population structure, the interesting is in cluster 5. As it is obvious from Figure 5, cluster five has the highest proportions in ages 0-25 and the lowest values in ages $50+$ . In fact, the above annotations can be generalized as a comparison of cluster 5 with all the other clusters of the analysis (Figure 3). The essential difference of this cluster is attributed to the excess presence of Roma in these regions. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,622,849,729]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Clusters 7,8: Clusters 7 and 8 constitute a very small part of Attica since they consists of three and one municipalities respectively. These clusters presents slightly lower percentages in younger population and higher records on elderly, compared with the rest clusters. As a result, mean age of these clusters is somewhat higher from the rest. Cluster 7 is close to centre (cluster 4) and this explains the high percentage of residents in ages correspond to workforce. As cluster 8 is concerned it refers to Aegina island. The chances for educational or work improvement is difficult to an island, so the excess of elderly population can be explained as it is known destination fro retired people. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,750,316,768]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 Conclusion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[143,782,849,813]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In this paper, we proposed an extension of the work by Alfo et al. (2008) and Alfo et al. (2009) in the context of multinomial mixture. The aim is to find an appropriate way to cluster geographical ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[488,845,508,858]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"13","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"14 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[220,116,777,460]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0112/df0ee50477d53a78dfe8e470864f98c47113262f2f1a9ec28d12b2ab95eac41e.jpg","list_items":null,"page_idx":"14","sub_type":null,"table_body":"<table><tr><td>Parameter</td><td>1st</td><td>2nd</td><td>3rd</td><td>4th</td><td>5th</td><td>6th</td><td>7th</td><td>8th</td></tr><tr><td>λk1</td><td>0.044</td><td>0.051</td><td>0.045</td><td>0.038</td><td>0.060</td><td>0.051</td><td>0.043</td><td>0.042</td></tr><tr><td>λk2</td><td>0.046</td><td>0.052</td><td>0.049</td><td>0.037</td><td>0.062</td><td>0.052</td><td>0.044</td><td>0.050</td></tr><tr><td>λk3</td><td>0.050</td><td>0.056</td><td>0.051</td><td>0.040</td><td>0.066</td><td>0.055</td><td>0.045</td><td>0.055</td></tr><tr><td>λk4</td><td>0.062</td><td>0.067</td><td>0.066</td><td>0.060</td><td>0.081</td><td>0.067</td><td>0.055</td><td>0.059</td></tr><tr><td>λk5</td><td>0.076</td><td>0.073</td><td>0.079</td><td>0.090</td><td>0.088</td><td>0.080</td><td>0.065</td><td>0.066</td></tr><tr><td>λk6</td><td>0.080</td><td>0.074</td><td>0.080</td><td>0.092</td><td>0.089</td><td>0.085</td><td>0.068</td><td>0.075</td></tr><tr><td>λk7</td><td>0.083</td><td>0.083</td><td>0.079</td><td>0.088</td><td>0.085</td><td>0.091</td><td>0.076</td><td>0.075</td></tr><tr><td>λk8</td><td>0.075</td><td>0.078</td><td>0.069</td><td>0.073</td><td>0.077</td><td>0.08</td><td>0.074</td><td>0.071</td></tr><tr><td>λk9</td><td>0.076</td><td>0.081</td><td>0.067</td><td>0.074</td><td>0.075</td><td>0.078</td><td>0.078</td><td>0.069</td></tr><tr><td>λk10</td><td>0.071</td><td>0.078</td><td>0.063</td><td>0.069</td><td>0.067</td><td>0.068</td><td>0.075</td><td>0.065</td></tr><tr><td>λk11</td><td>0.071</td><td>0.075</td><td>0.068</td><td>0.067</td><td>0.059</td><td>0.064</td><td>0.076</td><td>0.065</td></tr><tr><td>λk12</td><td>0.054</td><td>0.056</td><td>0.058</td><td>0.051</td><td>0.045</td><td>0.048</td><td>0.058</td><td>0.058</td></tr><tr><td>λk13</td><td>0.056</td><td>0.052</td><td>0.064</td><td>0.054</td><td>0.046</td><td>0.051</td><td>0.059</td><td>0.061</td></tr><tr><td>λk14</td><td>0.052</td><td>0.043</td><td>0.060</td><td>0.051</td><td>0.038</td><td>0.048</td><td>0.055</td><td>0.064</td></tr><tr><td>λk15</td><td>0.047</td><td>0.035</td><td>0.049</td><td>0.048</td><td>0.030</td><td>0.039</td><td>0.053</td><td>0.059</td></tr><tr><td>λk16</td><td>0.029</td><td>0.022</td><td>0.028</td><td>0.033</td><td>0.017</td><td>0.022</td><td>0.037</td><td>0.036</td></tr><tr><td>λk17</td><td>0.016</td><td>0.013</td><td>0.015</td><td>0.020</td><td>0.009</td><td>0.012</td><td>0.022</td><td>0.020</td></tr><tr><td>λk18</td><td>0.012</td><td>0.010</td><td>0.010</td><td>0.015</td><td>0.006</td><td>0.009</td><td>0.016</td><td>0.014</td></tr><tr><td>αk</td><td>0</td><td>2.048</td><td>1.572</td><td>0.600</td><td>1.074</td><td>0.938</td><td>0.408</td><td>-0.642</td></tr><tr><td>βk</td><td>0</td><td>0.781</td><td>0.786</td><td>0.429</td><td>0.678</td><td>0.265</td><td>0.404</td><td>0.426</td></tr><tr><td>nk</td><td>15</td><td>8</td><td>8</td><td>3</td><td>5</td><td>17</td><td>3</td><td>1</td></tr></table>","table_caption":"[\"Table 5: Parameter estimates for multinomial finite mixture with Gibbs prior (rounded on 3 digits) \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[143,525,849,585]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"regions according to demographic traits and especially the age. It seems that in this way population structure of an area can be described and be studied in a more efficient way. The proposed model not only does it account for the common heterogeneity, but also for spatial heterogeneity that exists due to the nature of the data. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,585,849,646]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The spatial information is incorporated by prior probabilities. More specifically, allocation variables are modelled as MRF. Then, model estimation is based on a modification of CEM, where a step for approximating the field is preceded before common steps of CEM. Simulated field algorithm has been selected rather than mean field or mode field, since literature supports that it is better. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,647,849,720]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Although the usefulness of this model, there are issues to be concerned. The initialization process is extremely demanding because of the excess of parameters to be estimated and as a result the algorithm is possible to be trapped in local maximum. Moreover, in case of large records in each category of the multinomial distributions, as in the examined example, computational problems may arise due to very small probabilities. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[143,722,849,782]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, the presented model can be enriched by the usage of more than one demographics. For example, it would be interesting using not only age but also sex, with the purpose of gaining more information about the population structure. In addition, prior probabilities can also be improved by inserting extra explanatory variables except for neighbors' behavior. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[488,845,508,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"14","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"15 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[416,116,581,266]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0805/d0e06c7a75c85eef9f809250b76f78de34e2d3dcb6b859bb15e2c2656b3c49b8.jpg","list_items":null,"page_idx":"15","sub_type":null,"table_body":"<table><tr><td>Cluster</td><td>Mean age</td></tr><tr><td>1</td><td>37.57</td></tr><tr><td>2</td><td>35.87</td></tr><tr><td>3</td><td>37.60</td></tr><tr><td>4</td><td>38.22</td></tr><tr><td>5</td><td>32.69</td></tr><tr><td>6</td><td>35.40</td></tr><tr><td>7</td><td>39.64</td></tr><tr><td>8</td><td>39.04</td></tr></table>","table_caption":"[\"Table 6: Mean age of residents in each cluster. \"]","table_footnote":"[]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[145,311,274,330]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"15","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[145,343,852,792]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Alfo, M., L. 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Elliott (1987). Modeling and segmentation of noisy and textured images using Gibbs random fields. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-9(1), 39-55. \",\"Forbes, F., M. Charras-Garrido, L. Azizi, S. Doyle, and D. Abrial (2013). Spatial risk mapping for rare disease with hidden Markov fields and variational EM. The Annals of Applied Statistics 7, 1192-1216. \",\"Forbes, F. and N. Peyrard (2003). Hidden Markov random field model selection criteria based on mean field-like approximations. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(9), 1089-1101. \",\"Geman, S. and D. Geman (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-6(6), 721-741. \",\"Green, P. J. and S. Richardson (2002). Hidden Markov models and disease mapping. Journal of the American Statistical Association 97(460), 1055-1070. \",\"Grün, B. and F. Leisch (2008). 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N. and Jayant, N. S. (1992). An adaptive clustering algorithm for image segmentation. IEEE Transaction Signal Process 40(4), 901-914. \",\"Patil, G. P., R. Modarres, W. L. Myers, and P. Patankar (2006). Spatially constrained clustering and upper level set scan hotspot detection in surveillance geoinformatics. *Environmental and Ecological Statistics* 13(4), 365-377. \",\"Poston, J., L. Dudley, and L. F. Bouvier (2010). Population and Society: An Introduction to Demography. Cambridge University Press. \",\"Qian, W. and D. Titterington (1991). Estimation of parameters in hidden Markov models. *Philosophical Transactions of the Royal Society of London*. Series A: Physical and Engineering Sciences 337(1647), 407-428. \",\"Strauss, D. J. (1977). Clustering on coloured lattices. Journal of Applied Probability 14 (1), 135-143. \",\"Teicher, H. (1963, 12). Identifiability of finite mixtures. Annals of Mathematical Statistics 34(4), 1265-1269. \",\"Titterington, D. M., A. F. Smith, and U. E. Makov (1985). Statistical analysis of finite mixture distributions. Wiley. \"]","page_idx":"18","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[488,845,508,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"18","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"19 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[328,164,647,406]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 7: Map of clusters according to eight component models \"]","image_footnote":"[]","img_path":"images/0597/d9a891ae4b4cea5725098ba3fa1a177cbc96787df45f8619275442dba0d42ca8.jpg","list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[145,523,852,555]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Tobler, W. R. (1970). A computer movie simulating urban growth in the Detroit region. *Economic Geography* 46(sup1), 234-240. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[488,845,509,859]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"19","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"20 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[240,165,754,189]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Multinomial mixture for spatial data \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[228,207,767,241]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Anna Nalpantidi, Dimitris Karlis and Panagiotis Papastamoulis \\nDepartment of Statistics \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[305,243,691,258]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Athens University of Economics and Business \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[419,272,576,289]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"February 16, 2024 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[462,320,532,333]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[184,340,813,465]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The purpose of this paper is to extend standard finite mixture models in the context of multinomial mixtures for spatial data, in order to cluster geographical units according to demographic characteristics. The spatial information is incorporated on the model through the mixing probabilities of each component. To be more specific, a Gibbs distribution is assumed for prior probabilities. In this way, assignment of each observation is affected by neighbors' cluster and spatial dependence is included in the model. Estimation is based on a modified EM algorithm which is enriched by an extra, initial step for approximating the field. The simulated field algorithm is used in this initial step. The presented model will be used for clustering municipalities of Attica with respect to age distribution of residents. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[169,472,800,488]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: demography; mixture models; spatial correlation; mean field approximation; \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,510,334,527]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,541,849,708]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Clustering regions according to demographic traits is a convenient way to summarize all the available information for an area and reveal hidden subgroups of regions that share common characteristics. More specifically, demographic traits and especially age and sex (Poston et al., 2010) are the most important elements for describing a population. Consequently, dividing an area into groups according to demographics can provide a better insight for the population structure of the area, rather than examining each region individually. However, a plausible assumption is that adjacent areas are affected by common social and environmental conditions and as a result they tend to have similar demographic traits. This implies that data are spatially dependent taking into consideration the first law of geography (Tobler, 1970). As a consequence, standard clustering methods may not be adequate for analyzing these data, since they assume independent observations and ignore the extra variation due to spatial heterogeneity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,708,849,814]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Spatially constrained clustering is rapidly evolving in the last decades, as it is embedded in a wide range of fields like epidemiology, image processing criminology, geospatial economics and others. Constrained clustering was defined by Legendre (1987) who was interested in including spatial, temporal or spatio-temporal restrictions. Since then, many popular clustering algorithms have been modified to adapt spatial information. Pappas (1992) presented a generalization of $k$ -means in the context of image segmentation. He introduced a generalization of $k$ -means, by using a Gibbs random field (Geman and Geman, 1984; Besag, 1986; Derin and Elliott, 1987) for inserting \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[22,258,57,717]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"arXiv:2402.09888v1 [stat.ME] 15 Feb 2024 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"aside_text\"\n },\n {\n \"bbox\": \"[493,847,503,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,851,210]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the spatial constraints. As hierarchical clustering is concerned, Carvalho et al. (2009) provided a modification of the classical hierarchical agglomerative method. More specifically, neighborhood restriction was imposed on the proximity matrix, which now refers to pairs of adjacent areas and not all possible pairs of observations. Due to the popularity of the field, an excessive number of algorithms have been proposed in the literature (Liu et al., 2012; Ng and Han, 2002; Kumar et al., 2012; Patil et al., 2006). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,210,851,316]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the context of finite mixture models, Green and Richardson (2002) proposed a general approach for modelling spatial heterogeneity of count data instead of the model proposed by Besag, York, Molliè (known as the BYM model) (Besag et al., 1991) and other similar models for the same purpose which use multivariate Gaussian distribution and incorporate spatial structure on covariance matrix. They proposed modelling allocation variables as Hidden Markov Random Fields (HMRF) that follows Potts model, with the purpose of facing local discontinuities and oversmoothed maps that may occur with the other methods. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,316,851,513]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A few years later, Alfo et al. (2008), based on the work of Green and Richardson (2002), introduced an extension of this model, in the context of image-segmentation. They proposed a Gaussian mixture model where allocation variables are modelled using a discrete HMRF. Then, due to the Hammersley-Clifford theorem, it is proved that component labels follow a Gibbs distribution. The difference with the previous work lies on the root of adopting a Gibbs distribution with cluster-specific parameters in prior probabilities. While interaction parameter was constant for all the regions, in the work of Alfo et al. (2008) it is allowed to vary across the image/region. However, the concept of inhomogeneous HMRF with spatially varying interaction parameter wasn't new since, Aykroyd and Zimeras (1999) had proposed approaches on this framework. Forbes et al. (2013), followed the idea of discrete HMRF model for disease mapping, but proposed a more complex structure on the interactions. On the work of Green and Richardson (2002) and Alfo et al. (2008) adjacent areas are penalized equally. Forbes et al. (2013) proposed taking into consideration, not only the adjacency of regions but also the adjacency of clusters. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,512,851,632]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In 2009, Alfo et al. (2009) extended their work (Alfo et al., 2008) for mapping spatially dependent disease counts with special focus on multivariate disease counts. Based on these works, we propose a finite multinomial mixture model for spatial data. The presented model takes into account spatial dependence that leads to an extra source of variation, except for the common heterogeneity. In contrary to standard multinomial mixture model, this methodology let spatial dependence influence the component in which each observation will be assigned. The spatial information is adapted on prior probability of each component, which is let to be affected by the cluster of adjacent areas for each observation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,633,851,755]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The paper consists of five sections. In Section 2, we will present standard multinomial mixture, a brief discussion upon its estimation method and the definition of number of clusters. In Section 3 we will define the proposed model and we will focus on theoretical elements to support it. In addition, there are details provided about model selection procedure and the estimation, since common computational methods are not adequate for the proposed model. Some simulation results to support the new model are provided in Section 4. A real data application of the model on data from Greek census of 2001 is included in Section 5. Finally, Section 6 summarizes all remarkable conclusions of the survey. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[493,847,504,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,116,851,136]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 Multinomial mixture model for independent observations \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,147,849,223]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It is assumed that a surrounding area can be partitioned in $K$ groups of sub-regions that share common demographic traits. More specifically, we would like to find clusters where area units have similar proportion of residents in each age group. For this purpose we will use finite mixture models and especially mixtures of multinomial distributions, which is a plausible assumption for this purpose. A brief description of the model is presented. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,223,849,287]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Let $J$ be the number of categories (age groups) and $\\\\lambda = (\\\\lambda_1, \\\\lambda_2, \\\\dots, \\\\lambda_J)$ be the vector of probabilities of success for each category. It is obvious that $\\\\sum_{j=1}^{J} \\\\lambda_j = 1$ and $0 \\\\leq \\\\lambda_j \\\\leq 1$ . Let $\\\\mathbf{y} = (y_1, \\\\ldots, y_J)'$ be an observation from multinomial distribution. Then $m$ denotes the total number of records of $\\\\mathbf{y}$ : $m = \\\\sum_{j=1}^{J} y_j$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,287,849,333]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Considering K clusters, there are $K$ multinomial distributions with corresponding probability vectors $\\\\pmb{\\\\lambda}_{\\\\pmb{k}} = (\\\\lambda_{k1},\\\\lambda_{k2},\\\\dots,\\\\lambda_{kj})$ , $k = 1,\\\\dots,K$ . Then $\\\\pmb{y}$ is distributed according to the following probability distribution: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[241,343,851,386]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP (\\\\boldsymbol {Y}) = \\\\sum_ {k = 1} ^ {K} p _ {k} \\\\frac {m !}{y _ {1} ! y _ {2} ! \\\\cdots y _ {J} !} \\\\lambda_ {k 1} ^ {y _ {1}} \\\\lambda_ {k 2} ^ {y _ {2}} \\\\dots \\\\lambda_ {k J} ^ {y _ {J}} = \\\\sum_ {k = 1} ^ {K} p _ {k} \\\\frac {m !}{y _ {1} ! y _ {2} ! \\\\cdots y _ {J} !} \\\\prod_ {j = 1} ^ {J} \\\\lambda_ {k j} ^ {y _ {j}} \\\\tag {1}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[143,391,852,421]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Taking into consideration the unobserved labels $(\\\\mathbf{Z})$ that specify from which component each observation comes from we can write that \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[395,431,602,448]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nZ \\\\sim \\\\text {M u l t i n o m i a l} (1, p) \\\\text {a n d}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[377,455,849,473]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\mathbf {Y} \\\\mid \\\\mathbf {Z} = \\\\mathbf {z} \\\\sim \\\\text {M u l t i n o m i a l} (m, \\\\lambda_ {z}) \\\\tag {2}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[143,478,849,551]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A necessary and sufficient condition for the generic identifiability of finite mixtures of multinomial distributions is the restriction $m \\\\geqslant 2K - 1$ (Teicher, 1963; Blischke, 1964; Titterington et al., 1985; Grün and Leisch, 2008). The reader is referred to Papastamoulis (2023) for estimation of finite mixtures of multinomial distributions under a maximum likelihood as well as a Bayesian point of view. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,575,849,595]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 Multinomial mixture for spatially dependent observations \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,608,295,625]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.1 Definition \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,633,849,723]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finite mixture models is an appropriate tool for capturing the heterogeneity of a population since, they divide it into subgroups in a way that observations of the same cluster are homogeneous, while observations from different clusters are different. However, the model of Section 2 does not capture the spatial heterogeneity that exists when spatial data is the case. This means that there is an extra source of variation that is not taken into consideration and as a result the model is inadequate. Therefore, we have to incorporate spatial information in the model. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,724,849,785]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the same concept, it is assumed that there is an area, which consists of $n$ sub-regions. For each sub-region, the number of residents in each age group is recorded and it is denoted by $\\\\pmb{y}_i = (y_{i1}, y_{i2}, \\\\dots, y_{iJ})'$ . Let $m_i$ denote the total counts of $i$ -th region. In addition, an adjacency matrix $(\\\\mathbf{A}_{nxn})$ which reflects the spatial dependence, is defined as follows: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[359,792,620,825]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nA _ {i j} = \\\\left\\\\{ \\\\begin{array}{l l} 1, & \\\\text {i f i a n d j a r e a d j a c e n t} \\\\\\\\ 0, & \\\\text {e l s e}, \\\\end{array} \\\\right.\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[493,847,504,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,852,196]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where, $A_{ij}$ denotes the element of $i$ -th row and $j$ -th column of matrix $\\\\mathbf{A}$ . The adjacency can be considered in different ways, like using the distance between two area units. However, we consider that two regions are adjacent if they are spatially contiguous. Let $N_i$ , $i = 1, \\\\dots, n$ denote the number of neighbors of $i$ -th region or else the neighborhood system. In order to assume $N_i$ as a neighbor system of $i$ -th region it must be valid that: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[165,204,308,247]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1. $i\\\\\\\\notin N_i,\\\\\\\\forall i\\\\\\\\in N$ \\\",\\\"2. $j\\\\\\\\in N_{j}\\\\\\\\leftrightarrow i\\\\\\\\in N_{j}$ \\\"]\",\n \"page_idx\": \"3\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[143,253,852,314]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Moreover, no further features have been recorded for each region. A general approach for modelling spatial dependence in FMMs was introduced by Green and Richardson (2002) and extended by Alfo et al. (2008). This approach will be adopted in this work but in the framework of multinomial mixture. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,315,851,390]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Geman and Geman (1984) proposed modelling the class process $z_{ik}$ , $i = 1, \\\\dots, n$ , $k = 1, \\\\dots, K$ by a Markov Random Field (MRF). Recalling the Hammersley-Clifford theorem, modelling indicator variables as a MRF is equivalent of using a Gibbs distribution for prior probabilities. Based on the Hammersley-Clifford theorem the process $\\\\{Z_i : i \\\\in N\\\\}$ is a MRF, if and only if its joint distribution is a Gibbs distribution (Besag, 1974). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[169,390,539,406]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Then the joint distribution of the MRF is given by \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[377,419,620,450]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP _ {G} (\\\\boldsymbol {z}) = W ^ {- 1} \\\\exp \\\\{- \\\\sum_ {c} V _ {c} (\\\\boldsymbol {z} _ {c}) \\\\},\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[143,460,852,535]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $W = \\\\sum_{z} \\\\exp \\\\{-\\\\sum_{c} V_{c}(z_{c})\\\\}$ is the normalizing constant or partitioning function, a sum over all possible values of $z$ . The sum on the $V(\\\\cdot)$ function (also known as the potential function) is over the set of cliques. The term clique refers to the set of nodes in which every pair is connected by an edge if MRF is seen as a graph. In simple words, a clique is a pair of regions that are spatially contiguous. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,536,852,583]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In that case, the common prior probabilities of the mixture model $p_k = P(z_{ik} = 1)$ are replaced by the conditional prior probabilities: $t_{ik} = P(z_{ik} = 1 | \\\\mathbf{z}_j, j \\\\in N_i)$ . Given the assigned neighborhood system, the Gibbs distribution is defined by: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[285,595,851,630]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nt _ {i j} = P \\\\left(z _ {i k} = 1 \\\\mid \\\\boldsymbol {z} _ {j}, j \\\\in N _ {i}\\\\right) \\\\propto \\\\exp \\\\left\\\\{\\\\alpha_ {k} - \\\\beta_ {k} \\\\sum_ {j \\\\in N _ {i}} V \\\\left(z _ {i k} z _ {j k}\\\\right) \\\\right\\\\}, \\\\tag {3}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[143,638,542,656]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"for $i = 1,\\\\dots ,n$ ， $k = 1,\\\\ldots ,K$ .Then (1) isreformedas:\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[212,665,851,710]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP (\\\\mathbf {Y} _ {i}) = \\\\sum_ {k = 1} ^ {K} t _ {i k} \\\\frac {m _ {i} !}{y _ {i 1} ! , y _ {i 2} ! \\\\cdots y _ {i J} !} \\\\lambda_ {k 1} ^ {y _ {i 1}} \\\\lambda_ {k 2} ^ {y _ {i 2}} \\\\dots \\\\lambda_ {k J} ^ {y _ {i J}} = \\\\sum_ {k = 1} ^ {K} t _ {i k} \\\\frac {m _ {i} !}{y _ {i 1} ! , y _ {i 2} ! \\\\cdots y _ {i J} !} \\\\prod_ {j = 1} ^ {J} \\\\lambda_ {k j} ^ {y _ {i j}} \\\\tag {4}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[143,719,851,795]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Equation (3) is a Gibbs distribution with cluster specific parameters. It is supported that the standard model of Green and Richardson (2002), where intercept $(\\\\alpha)$ and interaction term $(\\\\beta)$ are constant to the whole area, is restrictive and in many physical systems this assumption is violated, thus the cluster-specific Gibbs is preferred. We follow the suggested potential function of Alfò et al. (2008), namely \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[370,794,851,828]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nV (z _ {i k} z _ {j k}) = \\\\left\\\\{ \\\\begin{array}{l l} - 1, & \\\\text {i f} z _ {i k} z _ {j k} = 1 \\\\\\\\ + 1, & \\\\text {o t h e r w i s e} \\\\end{array} \\\\right. \\\\tag {5}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[493,847,504,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,852,165]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This structure implies that neighbors of $i$ -th region that belong to other cluster than $k$ are penalized. Then prior probability of $k$ -th component for $i$ -th observation is increased when its neighbors belong there. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,166,852,198]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Adopting the above potential function and posing first cluster as the reference category, the rior conditional probabilities in (3) are equivalent to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[284,208,851,226]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nt _ {i k} \\\\propto \\\\exp [ \\\\alpha_ {k} + \\\\beta_ {k} (n _ {i k} - n _ {i k} ^ {c}) ], \\\\quad i = 1, \\\\dots , n, \\\\quad k = 1, \\\\dots , K, \\\\tag {6}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[143,234,854,356]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"with $\\\\alpha_{1} = \\\\beta_{1} = 0$ for ensuring identifiability. Parameter $\\\\alpha_{k}$ , $k = 1,\\\\dots ,K$ accounts for the prior probability of $k$ -th cluster without taking into consideration the neighbors. On the other hand, parameter $\\\\beta_{k}$ , $k = 1,\\\\ldots ,K$ expresses how the cluster assignment of each observations is affected by the cluster of the neighbors. This means that in case of $\\\\beta = (0,\\\\dots,0)'$ , then standard multinomial mixture given in (1) occurs. $n_{ik}$ and $n_{ik}^{c}$ denote the number of neighbors of $i$ -th region that belong and not belong to $k$ -th cluster respectively. The expression (6) corresponds to a multinomial logit model for the prior conditional probabilities of cluster membership; it is also called as Strauss automodel (Strauss, 1977). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,357,852,388]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this point, it is important to mention that prior probabilities $p_k$ , $k = 1, \\\\dots, K$ , which have very natural and useful interpretation, are difficult to be calculated under this approach. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,405,614,422]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3.2 Parameter Estimation and Model selection \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,430,852,580]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Selecting maximum likelihood approach for the estimation of parameters, due to the unobserved labels, EM algorithm is the appropriate tool. However, spatial dependence increase the complexity of the model and as a consequence it is necessary to apply approximations for making the algorithm tractable. For this reason, instead of defining the common likelihood, an approximation has been proposed by Besag (1975) which is a pseudolikelihood. Pseudolikelihood allows defining the joint distribution of the MRF by taking the product of conditional probabilities of observing $z_{i}$ , given the values of all the other regions ( $z_{j}, j \\\\neq i$ ). In this way, the calculation of normalizing constant of joint Gibbs distribution, which demands all possible realizations of MRF can be avoided. Then, assuming also that $Y_{i}|Z_{i}$ are independent for $i = 1, \\\\dots, n$ , the observed likelihood is approximated by: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[326,580,851,622]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nL _ {o b s} (\\\\boldsymbol {\\\\theta} | \\\\boldsymbol {y}) = \\\\prod_ {i = 1} ^ {n} \\\\sum_ {k = 1} ^ {K} t _ {i k} \\\\frac {m _ {i} !}{y _ {i 1} ! y _ {i 2} ! \\\\cdots y _ {i J} !} \\\\lambda_ {k 1} ^ {y _ {i 1}} \\\\dots \\\\lambda_ {k J} ^ {y _ {i J}} \\\\tag {7}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[143,626,640,643]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and the complete likelihood and log-likelihood are approximated by: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[307,654,851,694]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nL _ {c} (\\\\boldsymbol {\\\\theta} | \\\\boldsymbol {y}, \\\\boldsymbol {z}) = \\\\prod_ {i = 1} ^ {n} \\\\sum_ {k = 1} ^ {K} \\\\left[ t _ {i k} \\\\frac {m _ {i} !}{y _ {i 1} ! y _ {i 2} ! \\\\cdots y _ {i J} !} \\\\lambda_ {k 1} ^ {y _ {i 1}} \\\\dots \\\\lambda_ {k J} ^ {y _ {i J}} \\\\right] ^ {z _ {i k}} \\\\tag {8}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[143,705,179,719]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[235,729,849,821]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\begin{array}{l} l _ {c} (\\\\boldsymbol {\\\\theta} | \\\\boldsymbol {y}, \\\\boldsymbol {z}) = \\\\sum_ {i = 1} ^ {n} \\\\sum_ {k = 1} ^ {K} \\\\left[ z _ {i k} \\\\log (t _ {i k}) + z _ {i k} \\\\log \\\\left(\\\\frac {m _ {i} !}{y _ {i 1} ! y _ {i 2} ! \\\\dots y _ {i J} !} \\\\lambda_ {k 1} ^ {y _ {i 1}} \\\\dots \\\\lambda_ {k J} ^ {y _ {i J}}\\\\right) \\\\right] = \\\\\\\\ = \\\\sum_ {i = 1} ^ {n} \\\\sum_ {k = 1} ^ {K} \\\\left[ z _ {i k} \\\\log \\\\left(t _ {i k}\\\\right) + z _ {i k} \\\\sum_ {j = 1} ^ {J} y _ {i j} \\\\log \\\\left(\\\\lambda_ {k j}\\\\right) \\\\right] + c o n s t a n t \\\\tag {9} \\\\\\\\ \\\\end{array}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[493,845,504,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,852,179]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The above form of likelihoods includes the conditional distributions of $z_{i} | z_{j}, i \\\\neq j$ instead of the marginal distribution $z_{i}$ . In case of complete independence of $z_{i}$ , pseudolikelihoods coincide with true likelihoods. Having approximated the quantities we need, EM algorithm can be applied as common: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[163,189,852,233]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"- $\\\\pmb{E}$ -step: Taking the expectation of approximated log-likelihood with respect to unobserved data $\\\\pmb{z}_i$ , the approximated posterior probability of $i$ -th observation belongs to $k$ -th cluster is estimated by: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[366,234,851,268]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\hat {z _ {i k}} = w _ {i k} = E \\\\left[ z _ {i k} \\\\mid \\\\boldsymbol {\\\\theta}, \\\\boldsymbol {y} \\\\right] = \\\\frac {t _ {i k} f \\\\left(\\\\boldsymbol {y} _ {i} \\\\mid \\\\boldsymbol {\\\\lambda} _ {k}\\\\right)}{\\\\sum_ {\\\\ell = 1} ^ {K} t _ {i \\\\ell} f \\\\left(\\\\boldsymbol {y} _ {i} \\\\mid \\\\boldsymbol {\\\\lambda} _ {\\\\ell}\\\\right)} \\\\tag {10}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[183,273,851,319]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $\\\\pmb{\\\\lambda}_{k} = (\\\\lambda_{k1},\\\\dots,\\\\lambda_{kJ})'$ and $f(\\\\pmb{y}_i|\\\\pmb{\\\\lambda}_k)$ the probability mass function of multinomial distribution for $i$ -th observation and $k$ -th component. Now, the approximated expected complete log-likelihood is calculated by: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[348,329,851,378]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nQ = \\\\sum_ {i = 1} ^ {n} \\\\sum_ {k = 1} ^ {K} \\\\left[ w _ {i k} \\\\log \\\\left(t _ {i k}\\\\right) + w _ {i _ {k}} \\\\sum_ {j = 1} ^ {J} y _ {i j} \\\\log \\\\left(\\\\lambda_ {k j}\\\\right) \\\\right] \\\\tag {11}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[165,391,854,436]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"- $M$ -step: In this step approximated maximum likelihood estimators are provided, by maximizing (11) with respect to $\\\\pmb{\\\\theta} = (\\\\pmb{\\\\theta}_1, \\\\dots, \\\\pmb{\\\\theta}_K)$ , where $\\\\pmb{\\\\theta}_k = (\\\\pmb{\\\\theta}_{k,mult}, \\\\pmb{\\\\theta}_{k,Gibbs})$ and $\\\\pmb{\\\\theta}_{k,Gibbs} = (\\\\alpha_k, \\\\beta_k)$ and $\\\\pmb{\\\\theta}_{k,mult} = (\\\\lambda_{k1}, \\\\dots, \\\\lambda_{kj})$ for $k = 1, \\\\dots, K$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[186,441,745,455]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Parameters of Gibbs distribution: We have to solve the equation system \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[303,467,851,507]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\frac {\\\\partial Q}{\\\\partial \\\\left(\\\\alpha_ {k} , \\\\beta_ {k}\\\\right)} = \\\\frac {\\\\partial}{\\\\partial \\\\left(\\\\alpha_ {k} , \\\\beta_ {k}\\\\right)} \\\\sum_ {i = 1} ^ {n} \\\\sum_ {k = 1} ^ {K} w _ {i k} \\\\log \\\\left(t _ {i k}\\\\right) = 0, \\\\quad k = 2, \\\\dots , K \\\\tag {12}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[184,517,849,546]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, this equation is extremely complex and numerical methods are suggested for its solution. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[184,551,851,609]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Parameters of multinomial distributions: The maximization of Q under the constraint $\\\\sum_{j=1}^{J} \\\\lambda_{kj} = 1$ is needed for finding the estimators of $\\\\lambda_{kj}$ . Thus, the maximum pseudolikelihood estimates for parameters of each multinomial and every category are given by the formula: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[450,609,849,643]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\hat {\\\\lambda_ {k j}} = \\\\frac {\\\\sum_ {i = 1} ^ {n} w _ {i k} y _ {i j}}{\\\\sum_ {i = 1} ^ {n} w _ {i k} m _ {i}} \\\\tag {13}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[184,647,395,662]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"for $k = 1,\\\\ldots ,K,j = 1,\\\\ldots ,J$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,671,852,821]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The parameter estimation in this model is not a trivial issue due to Gibbs distribution. In order to facilitate the procedure, pseudolikelihood was proposed. Then, conditional probabilities can be approximated by MCMC simulations. However, it has been proved that this approach is restrictive since it is inappropriate when strong dependence between regions is present. In addition, it is computationally demanding. For this reason, another approximation of complex complete likelihood was introduced by Qian and Titterington (1991) and extended by Celeux et al. (2003). This, method uses Mean field theory, from the domain of statistical mechanics, in order to approximate the HMRF and then apply EM. Mean field approximation means that the value of $i$ -th area is independent to values of other areas while these are set to be fixed an irrelevant to $i$ -th value. Based on this idea, intractable distributions like Gibbs distribution can be faced. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[493,847,504,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,852,181]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"According to this, Celeux et al. (2003) suggested a class of algorithms that consists of two steps. In the first stage, the hidden field $(\\\\mathbf{z})$ is approximated given the observed data $(\\\\pmb{y})$ and the current parameters $(\\\\pmb{\\\\theta}^{(t)})$ , thus an approximation of Gibbs distribution is achieved as follows: Denoting $\\\\tilde{\\\\pmb{z}}$ the configuration of HMRF, \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[344,191,655,231]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nP _ {\\\\tilde {\\\\boldsymbol {z}}} (\\\\boldsymbol {z} | \\\\boldsymbol {\\\\theta} _ {G i b b s}) = \\\\prod_ {i = 1} ^ {n} P _ {G} (\\\\boldsymbol {z} _ {i} | \\\\tilde {\\\\boldsymbol {z}} _ {j}, j \\\\in N _ {i}, \\\\boldsymbol {\\\\theta} _ {G i b b s} ^ {(t)})\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[143,239,849,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the second step, given the corresponding approximated field, the approximated posterior probabilities can be estimated (E-step) and then M-step follows for providing estimations of the parameters of interest. They proposed three algorithms for approximating the hidden field: mean field, mode field and simulated field algorithm. The concept of simulated field algorithm will be used in this work as it has been proved that it provides better results. This is the counterpart of the Stochastic EM algorithm in a spatial framework. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,330,849,361]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The modified classification EM (CEM) algorithm that used for estimating the proposed model can be sketched as follows. At the $t$ -th iteration we have: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[163,368,746,411]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"1. Simulate $\\\\\\\\tilde{z}_i$ from $P_G(\\\\\\\\pmb {z}_i|\\\\\\\\tilde{\\\\\\\\pmb{z}}_j^{(t - 1)},j\\\\\\\\in N_i,\\\\\\\\pmb{\\\\\\\\theta}_{Gibbs}^{(t)})$ for $i = 1,\\\\\\\\ldots ,n$ \\\",\\\"2. Using the field approximation $\\\\\\\\tilde{z}$ from the previous step apply CEM algorithm \\\"]\",\n \"page_idx\": \"6\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[192,420,511,435]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(a) $E$ -step: Estimate posterior probabilities: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[375,448,851,501]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\tilde {w} _ {i k} ^ {(t)} = \\\\frac {t _ {i k} \\\\left(\\\\tilde {\\\\boldsymbol {z}} _ {\\\\boldsymbol {i}} ^ {(t)} \\\\mid \\\\boldsymbol {\\\\alpha} ^ {(t - 1)} , \\\\boldsymbol {\\\\beta} ^ {(t - 1)}\\\\right) f \\\\left(\\\\boldsymbol {y} _ {\\\\boldsymbol {i}} \\\\mid \\\\boldsymbol {\\\\lambda} _ {\\\\boldsymbol {k}} ^ {(t - 1)}\\\\right)}{\\\\sum_ {l = 1} ^ {K} t _ {i l} \\\\left(\\\\tilde {\\\\boldsymbol {z}} _ {\\\\boldsymbol {i}} ^ {(t)} \\\\mid \\\\boldsymbol {\\\\alpha} ^ {(t - 1)} , \\\\boldsymbol {\\\\beta} ^ {(t - 1)}\\\\right) f \\\\left(\\\\boldsymbol {y} _ {\\\\boldsymbol {i}} \\\\mid \\\\boldsymbol {\\\\lambda} _ {l} ^ {(t - 1)}\\\\right)} \\\\tag {14}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[220,513,715,529]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Then, approximated expected complete log-likelihood is modified as: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[339,540,851,589]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nQ ^ {M F} = \\\\sum_ {i = 1} ^ {n} \\\\sum_ {k = 1} ^ {K} \\\\left[ \\\\tilde {w} _ {i k} ^ {(t)} \\\\log (t _ {i k}) + \\\\tilde {w} _ {i k} ^ {(t)} \\\\sum_ {j = 1} ^ {J} y _ {i j} \\\\log \\\\left(\\\\lambda_ {k j} ^ {(t - 1)}\\\\right) \\\\right] \\\\tag {15}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[191,601,849,646]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"(b) $C$ -step: Set $z_{ik}^{(t)} = 1$ and all other $0$ , if $\\\\\\\\tilde{w}_{ik}^{(t)} = \\\\\\\\max_{\\\\\\\\ell}\\\\\\\\tilde{w}_{i\\\\\\\\ell}^{(t)}$ , $\\\\\\\\ell = 1,\\\\\\\\ldots ,K$ \\\",\\\"(c) $M$ -step: Estimate $\\\\\\\\alpha_{k}^{(t)}, \\\\\\\\beta_{k}^{(t)}$ and $\\\\\\\\lambda_{kj}^{(t)}$ given $z_{ik}^{(t)}$ and $\\\\\\\\tilde{\\\\\\\\boldsymbol{w}}_{\\\\\\\\boldsymbol{i}}^{(t)}$ , $k = 1, \\\\\\\\ldots, K$ and $j = 1, \\\\\\\\ldots, J$ . \\\"]\",\n \"page_idx\": \"6\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[143,652,849,683]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The above procedure is repeated for a significant number of iterations, until convergence to maximum observed approximated likelihood is achieved. The approximated observed likelihood is: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[269,694,851,734]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nL _ {o b s, a p p r o x} (\\\\boldsymbol {\\\\theta}) = \\\\prod_ {i = 1} ^ {n} \\\\sum_ {k = 1} ^ {K} f \\\\left(y _ {i} \\\\mid z _ {i k}, \\\\boldsymbol {\\\\lambda} _ {k}\\\\right) P \\\\left(z _ {i k} = 1 \\\\mid \\\\tilde {\\\\boldsymbol {z}} _ {j}, j \\\\in N _ {i}, \\\\alpha_ {k}, \\\\beta_ {k}\\\\right) \\\\tag {16}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[143,744,849,792]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Up to this approximation of observed likelihood, Forbes and Peyrard (2003) displayed an approximation of BIC in case of mean field approximations. Denoting $\\\\hat{\\\\pmb{\\\\theta}}$ as the approximation of true MLE then, the approximation of BIC is: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[346,806,849,824]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\nB I C ^ {\\\\tilde {z}} (\\\\hat {\\\\boldsymbol {\\\\theta}}) = 2 \\\\log \\\\left(L _ {o b s, a p p r o x} (\\\\hat {\\\\boldsymbol {\\\\theta}})\\\\right) - d \\\\log (n) \\\\tag {17}\\n$$\",\n \"text_format\": \"latex\",\n \"text_level\": null,\n \"type\": \"equation\"\n },\n {\n \"bbox\": \"[493,847,503,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[385,116,612,296]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0733/e6b2ee9dbd13799a71babd45ccd789c5a6384ae3ed29a5f1df152755ac0bfc5a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td></td><td>Cluster 1</td><td>Cluster 2</td></tr><tr><td>λk1</td><td>0.12</td><td>0.08</td></tr><tr><td>λk2</td><td>0.12</td><td>0.08</td></tr><tr><td>λk3</td><td>0.12</td><td>0.08</td></tr><tr><td>λk4</td><td>0.12</td><td>0.08</td></tr><tr><td>λk5</td><td>0.12</td><td>0.08</td></tr><tr><td>λk6</td><td>0.08</td><td>0.12</td></tr><tr><td>λk7</td><td>0.08</td><td>0.12</td></tr><tr><td>λk8</td><td>0.08</td><td>0.12</td></tr><tr><td>λk9</td><td>0.08</td><td>0.12</td></tr><tr><td>λk10</td><td>0.08</td><td>0.12</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 1: Parameters of the multinomial distributions \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[143,343,849,373]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"where $d$ is the number of free parameters in the model, in our case $d = 2(K - 1) + K(J - 1)$ . The approximation of observed likelihood is given by the equation (16). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,375,852,481]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Initialization of EM is a crucial issue, since it is possible to find a local maximum instead of the global maximum which is the case. For this reason, we propose the strategy of Biernacki et al. (2003). More specifically, we used different initial values and ran the EM algorithm. For each set of initial values the maximum likelihood was recorded. The solution that corresponds to the highest approximated observed likelihood was used as initial value for the final EM. Finally as far as the convergence of the algorithm and because of the stochastic nature of the algorithm, we stopped when we failed to find a larger log-likelihood for 50 successive iterations. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,502,387,523]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 Simulation study \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,534,851,669]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this section we examine the performance of the proposed model under different conditions. More specifically, we focus on different lattice sizes and various parameters of the Gibbs distribution, which measures how interaction of neighbors affects the assignment of each observation in each cluster. We assumed that we have a $N$ -dimensional square lattice $(N = 8,10,20)$ . The points of each lattice come from a mixture of two multinomial distributions. For each multinomial distribution we have assumed 10 categories, and size equal to 100 while the parameters are presented in Table 1. According to the presented model, the prior probabilities of the mixture follow the Gibbs distribution, so we have three different scenarios for this distribution namely $\\\\beta = (0,0.01)'$ , $(0,0.1)'$ and $(0,0.2)'$ respectively. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,670,849,729]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To evaluate the performance of the model we used the Adjusted Rand Index (ARI) (Hubert and Arabie, 1985). The index measures the agreement between two partitions. Values close to 1 indicate complete agreement. In this case, we compared the cluster labels estimated by the proposed model with the true labels. True labels have been simulated by a Gibbs sampler. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,729,849,820]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For all scenarios we have simulated 100 samples. Figure 1 depicts the results of the simulations. More specifically, we conclude that Gibbs distribution does not affect essentially the model's performance. To be more specific, ARI values are similar for each combination of $\\\\beta$ parameter and sample size. On the other hand, comparing results with respect to different lattice size, it seems that there are significant differences: as sample size increases, the variability of the ARI decreases. When $N = 8$ , there are cases where ARI is less than 0.70, while in case of $N = 20$ , ARI is never \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[493,847,504,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,851,179]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"less than 0.80. So, for small sample sizes it is possible not to have such a good partition as in higher sample sizes. We also see a slight improvement on ARI as lattice size increases. However, the general conclusion is that model clusters adequately the observations, since, in each case the median ARI is higher than 0.80. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,180,849,210]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally note that initialisation of the algorithm as well as convergence were used as described in Section 3. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[292,223,707,539]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 1: Boxplots of ARI for different lattices and different values of $\\\\\\\\beta$ . \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0174/24706650b70b4a789b9f19629c3ff31789ad8b4d632f12cb28574c73bac39913.jpg\",\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[143,625,715,645]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 Application: Data from Greek census of 2001 \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,655,852,776]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Attica is one of the thirteen administrative regions of Greece which encompasses the capital of Greece, Athens, and the biggest port of the country, Piraeus. Except for Athens and surrounding cities, Saronic islands, Cythera and a small part of Peloponnese mainland pertain to Attica region. As it is expected, the extension of the region, in combination with the wave of urbanization, has led Attica to encompass a significant percentage of Greek population. To be more specific, according to Greek census of 2001, more than the one third of total Greek population lives in Athens, with the percentage estimated around $35\\\\%$ . With the purpose of a better administration of Attica, it has been partition into 66 municipalities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,777,851,824]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It is common that people choose living in areas that service their needs and usually, their needs depend on their age. For example, young people prefer living in big cities instead of villages, in order to study or work. This, in combination with the fact that municipalities of Attica not only \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[491,847,504,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"8\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"9 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[143,119,849,224]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"do they correspond to urban cities and small towns, but also islands and suburbs, motivates in believing that sub-regions of Attica present heterogeneity with respect to the age distribution of their inhabitants. In other words, it seems plausible assuming that all municipalities of Attica do not present the same percentage of people in each age group, but some of them tend to be similar and described as a cluster. Furthermore, another hypothesis is that adjacent sub-regions are affected by similar environmental and social factors, so they attract people of the same age and consequently, this may encourage clustering on the same group. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,226,849,376]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The purpose of this section is to present a clustering of municipalities of Attica region according to age distribution of their residents. Use of similar data has been treated in Jorgensen (2013) where the spatial aspect was ignored. Nevertheless, special interest is given to spatial dependence of the sub-regions of Attica. It is assumed that two regions are adjacent if they are spatially contiguous. For this reason, six area units that are far away from the main part of Attica (Cythera, Hydra, Spetses, Poros, Troezen, Agistri) have been excluded, since the main assumption of common characteristics due to adjacency is not plausible. The islands of Salamina and Aegina have been kept and as adjacency is concerned, it has been considered that Salamina is neighbor of Perama and Aegina is neighbor of Pireus, as long as the communication of the mainland of Attica with these islands becomes through the ports of the correspond municipalities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,377,849,421]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The clustering was conducted by applying the multinomial mixture with Gibbs prior, that was presented in section 3. The results were compared to the results of standard multinomial mixture. The analysis was conducted with R package. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,422,849,496]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The clustering refers to 60 of 66 municipalities of Attica. For each of them the number of inhabitants per age group is recorded. There are 18 age groups: from 0 to 84. Each group contains five ages and the final group refers to people whose age is 85 and over. An example of the form of the data is presented in Table 2. The data comes from Greek census of 2001 and data were taken from the National Statistical Office website. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,497,849,617]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Before starting clustering, it would be interesting examining whether the hypothesis of heterogeneity and spatial dependence are plausible for this data. In Figure 2, a small number of municipalities have been chosen in order to indicate the heterogeneity of the regions. As it is obvious, not all regions have the same age profile. More specifically, Zografos presents an excess of records in ages 20-29. Furthermore, Aegina have high percentages of residents in ages $60+$ , compared to the other regions. On the other hand, Aspropyrgos dominate in younger ages of 0-19, while it presents the lower percentages on older age groups. Egaleo seems to represent an intermediate situation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,618,849,723]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"After that, we examine the second assumption that regions are spatially correlated. For this purpose Moran's Index $I$ (Moran, 1950) was used. The above index was used for examining spatial autocorrelation on univariate observations. However, in this study, observations are multivariate. For overcoming this problem, the mean age of each municipality is computed and used for the Moran index. Using mean age as variable of interest and the adjacency matrix as the weight matrix, the results shown that $I = 0.33$ and there is evidence that municipalities of Attica are shown spatial correlation (permutation test pvalue $< 0.001$ ). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,724,849,814]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The above study indicated that data presents heterogeneity so clustering is meaningful. First, standard multinomial mixture was applied for clustering data. The estimation of both models was based on the spatial counterpart of stochastic EM that was described in section 3. Especially for the case of standard multinomial mixture, the vector of spatial parameters $(\\\\pmb{b}_{k\\\\times k})$ were set equal to zero. The two models are nested and this justify the usage of the same algorithm. Furthermore, the estimation of Gibbs parameters was based on simulated annealing algorithm. Variant of Newton-\",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[488,845,508,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"9\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"10 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[359,116,637,416]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0473/7e3b0ab505cdc23ac6396055f9f43b93820fddcda74dbfd8f501609f9daac834.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Age group</td><td>Records</td><td>Proportions</td></tr><tr><td>0-4</td><td>3132</td><td>0.038</td></tr><tr><td>5-9</td><td>3128</td><td>0.038</td></tr><tr><td>10-14</td><td>3387</td><td>0.042</td></tr><tr><td>15-19</td><td>6069</td><td>0.075</td></tr><tr><td>20-24</td><td>9304</td><td>0.114</td></tr><tr><td>25-29</td><td>7368</td><td>0.090</td></tr><tr><td>30-34</td><td>6770</td><td>0.083</td></tr><tr><td>35-39</td><td>5587</td><td>0.069</td></tr><tr><td>40-44</td><td>5595</td><td>0.069</td></tr><tr><td>45-49</td><td>5538</td><td>0.068</td></tr><tr><td>50-54</td><td>5244</td><td>0.064</td></tr><tr><td>55-59</td><td>4150</td><td>0.051</td></tr><tr><td>60-64</td><td>4400</td><td>0.054</td></tr><tr><td>65-69</td><td>3924</td><td>0.048</td></tr><tr><td>70-74</td><td>3429</td><td>0.042</td></tr><tr><td>75-79</td><td>2166</td><td>0.027</td></tr><tr><td>80-84</td><td>1253</td><td>0.015</td></tr><tr><td>85+</td><td>970</td><td>0.012</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 2: Number and rounded proportion of residents by age in Zografos from census of 2001 \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[143,465,852,542]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Raphson was also used, but in terms of maximum log-likelihood simulated annealing was slightly better. The algorithm applied for adequate number of iterations for each case, until convergence was achieved. Initialization process was based on the strategy described in Section 3 for $k = 2$ while for $K = 3,\\\\ldots ,9$ , initialization was based on the solutions of previous model plus a random vector for the new component. Convergence was detected as described at the end of Section 3. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,542,852,604]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The maximum log-likelihood values as well as BIC for models with different number of components, from the application of standard multinomial mixture are provided in Table 3. Maximum value of BIC indicates the optimal model. According to Table 3, BIC suggests the model with eight components as the best choice. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[370,614,624,782]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0200/39c2eda1079fe108c5a1332ad6b5258c15b1c98524b1fc76f270e2b3bc013837.jpg\",\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>K</td><td>log-likelihood</td><td>BIC</td></tr><tr><td>1</td><td>-28590.73</td><td>-57251.07</td></tr><tr><td>2</td><td>-18303.01</td><td>-36749.32</td></tr><tr><td>3</td><td>-15971.25</td><td>-32159.50</td></tr><tr><td>4</td><td>-13096.92</td><td>-26484.54</td></tr><tr><td>5</td><td>-11878.35</td><td>-24121.10</td></tr><tr><td>6</td><td>-11537.93</td><td>-23513.95</td></tr><tr><td>7</td><td>-10730.52</td><td>-21972.83</td></tr><tr><td>8</td><td>-10670.59</td><td>-21926.79</td></tr><tr><td>9</td><td>-10658.97</td><td>-21977.13</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 3: Maximized log-likelihood and BIC for standard multinomial finite mixture \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[488,845,508,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"10\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"11 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[282,119,709,455]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 2: Percentage of residents in each age group for four municipalities \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0114/55aa81a50119c9a5e56103acbd5e4d19b44f56869c06d866f66143660c70cfaf.jpg\",\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[143,523,849,553]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The correspond results of the proposed model of multinomial mixture that takes into consideration the spatial information are presented in Tables 4 and 5. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,554,849,718]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It occurs that both models proposed the same number of clusters, while the estimated parameters of multinomial distributions are close. This is something expected, since this model is proposed for capturing the extra variation from spatial information that it is not explained by the standard model. In Celeux et al. (2003), a simulation study indicates similar superior behavior of the spatial model, namely an improved misclassification rate, while the parameters estimates are similar. They conclude that standard EM provides the same estimations of parameters with the modified EM that includes an extra step of field's simulation, but the second method presents lower error rate than the first. As it has been discussed, the two models are nested, so likelihood ratio test (LRT) can be used for comparing them. The results showed that the there is statistically significant difference between the two models which means that spatial term is statistically significant (LRT pvalue $< 0.05$ ). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,720,849,809]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The two models propose the same clusters that can be seen in Figure 7, while the parameters of each cluster are depicted in Figure 3. Table 6 includes the mean age of each group. Based on the mean age, clusters with similar value have been grouped in order to present the proportion of residents in each age group, for every cluster. The results are presented in Figures 4, 5 and 6. It seems that there is an interesting structure of municipalities of Attica with respect to age of the residents. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[488,845,508,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"11\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"12 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[83,290,356,398]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0175/05968f226f514d5421f96e0c80e6e4e95efdbd142920e8246cfb9942accb22b4.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[359,292,630,398]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0305/4311e9e98c32879f44e4f34bd4b00d65a1040a039754f095c4d6fd663312a292.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[633,292,903,398]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0850/488a33210e70c8519ecbb2d94ba65cf473551564f84baa30722920867097650f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[84,401,354,506]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0935/b4f2a2ca3373fb5566ba1b8d9128a8e7f9cdfc47c92024be8d48178361638d5f.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[359,401,629,506]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0796/0510e615fba4b9dc60b70d6b3fdc786e8ca2379ef617fe0061cddfffbb844c09.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[633,401,903,506]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0260/0016b7a7319750402cb439004764beef756d4b427d474cf7617ade18fb1cc4c1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[83,508,354,614]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0072/554db8e925362607786c8f9e4b2657755e7f921aba2a5902116e1c60f45f5c24.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[359,508,629,614]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 3: Percentage of residents in each age group for each cluster \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0576/3da70d81b72e0ba97a1520e286300d38f9c49d2702e2179550f2a73bcb6c7c3a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[490,847,508,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"12\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"13 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[349,116,648,284]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0907/1a7171413b12e5d5b077ab83ac8387b0128b39256f5677c08f7ef5ae30c7439a.jpg\",\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>K</td><td>log-likelihoodapprox</td><td>BICapprox</td></tr><tr><td>1</td><td>-28590.73</td><td>-57251.07</td></tr><tr><td>2</td><td>-18298.02</td><td>-36743.44</td></tr><tr><td>3</td><td>-15963.93</td><td>-32153.05</td></tr><tr><td>4</td><td>-13099.68</td><td>-26502.34</td></tr><tr><td>5</td><td>-11873.5</td><td>-24127.77</td></tr><tr><td>6</td><td>-11525.79</td><td>-23510.15</td></tr><tr><td>7</td><td>-10718.53</td><td>-21973.42</td></tr><tr><td>8</td><td>-10659.71</td><td>-21933.57</td></tr><tr><td>9</td><td>-10627.76</td><td>-21947.46</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 4: Approximated maximized log-likelihood and BIC for multinomial finite mixture with Gibbs prior \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[143,349,849,530]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Clusters 1,3,4: Clusters 1,3 and 4 represent municipalities that have an intermediate structure compared to the regions of the other clusters. Clusters 1 and 3 seems to have similar structure for the ages 0-25 when cluster 4 has lower proportions on ages 0-10. For ages 20-30, there is a peak for cluster 4. Looking at the map (7), cluster 4 includes centre of Attica (Athens) with two other adjacent areas. In these municipalities, there are universities and as a consequence it is plausible to have significant number of young people, especially of these ages. Based on Figure 3, the peak in these ages is the highest among all clusters. For the ages 30-70, cluster 1 and 4 have similar behaviour. According to the map, municipalities of cluster 4 are closer to municipalities of cluster 1. Given that cluster 1 is the central part of Attica and that the referred age groups imply the workforce of each region, the similarity is plausible, providing that work opportunities are better in the center than in the suburbs. As ages of $70+$ are concerned, the differences are meaningful for the three clusters. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,531,849,622]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Clusters 2,5,6: Clusters 2,5 and 6 consists of municipalities with the youngest population among municipalities of Atttica. Although the three clusters have similar population structure, the interesting is in cluster 5. As it is obvious from Figure 5, cluster five has the highest proportions in ages 0-25 and the lowest values in ages $50+$ . In fact, the above annotations can be generalized as a comparison of cluster 5 with all the other clusters of the analysis (Figure 3). The essential difference of this cluster is attributed to the excess presence of Roma in these regions. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,622,849,729]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Clusters 7,8: Clusters 7 and 8 constitute a very small part of Attica since they consists of three and one municipalities respectively. These clusters presents slightly lower percentages in younger population and higher records on elderly, compared with the rest clusters. As a result, mean age of these clusters is somewhat higher from the rest. Cluster 7 is close to centre (cluster 4) and this explains the high percentage of residents in ages correspond to workforce. As cluster 8 is concerned it refers to Aegina island. The chances for educational or work improvement is difficult to an island, so the excess of elderly population can be explained as it is known destination fro retired people. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,750,316,768]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6 Conclusion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,782,849,813]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In this paper, we proposed an extension of the work by Alfo et al. (2008) and Alfo et al. (2009) in the context of multinomial mixture. The aim is to find an appropriate way to cluster geographical \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[488,845,508,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"13\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"14 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[220,116,777,460]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0112/df0ee50477d53a78dfe8e470864f98c47113262f2f1a9ec28d12b2ab95eac41e.jpg\",\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Parameter</td><td>1st</td><td>2nd</td><td>3rd</td><td>4th</td><td>5th</td><td>6th</td><td>7th</td><td>8th</td></tr><tr><td>λk1</td><td>0.044</td><td>0.051</td><td>0.045</td><td>0.038</td><td>0.060</td><td>0.051</td><td>0.043</td><td>0.042</td></tr><tr><td>λk2</td><td>0.046</td><td>0.052</td><td>0.049</td><td>0.037</td><td>0.062</td><td>0.052</td><td>0.044</td><td>0.050</td></tr><tr><td>λk3</td><td>0.050</td><td>0.056</td><td>0.051</td><td>0.040</td><td>0.066</td><td>0.055</td><td>0.045</td><td>0.055</td></tr><tr><td>λk4</td><td>0.062</td><td>0.067</td><td>0.066</td><td>0.060</td><td>0.081</td><td>0.067</td><td>0.055</td><td>0.059</td></tr><tr><td>λk5</td><td>0.076</td><td>0.073</td><td>0.079</td><td>0.090</td><td>0.088</td><td>0.080</td><td>0.065</td><td>0.066</td></tr><tr><td>λk6</td><td>0.080</td><td>0.074</td><td>0.080</td><td>0.092</td><td>0.089</td><td>0.085</td><td>0.068</td><td>0.075</td></tr><tr><td>λk7</td><td>0.083</td><td>0.083</td><td>0.079</td><td>0.088</td><td>0.085</td><td>0.091</td><td>0.076</td><td>0.075</td></tr><tr><td>λk8</td><td>0.075</td><td>0.078</td><td>0.069</td><td>0.073</td><td>0.077</td><td>0.08</td><td>0.074</td><td>0.071</td></tr><tr><td>λk9</td><td>0.076</td><td>0.081</td><td>0.067</td><td>0.074</td><td>0.075</td><td>0.078</td><td>0.078</td><td>0.069</td></tr><tr><td>λk10</td><td>0.071</td><td>0.078</td><td>0.063</td><td>0.069</td><td>0.067</td><td>0.068</td><td>0.075</td><td>0.065</td></tr><tr><td>λk11</td><td>0.071</td><td>0.075</td><td>0.068</td><td>0.067</td><td>0.059</td><td>0.064</td><td>0.076</td><td>0.065</td></tr><tr><td>λk12</td><td>0.054</td><td>0.056</td><td>0.058</td><td>0.051</td><td>0.045</td><td>0.048</td><td>0.058</td><td>0.058</td></tr><tr><td>λk13</td><td>0.056</td><td>0.052</td><td>0.064</td><td>0.054</td><td>0.046</td><td>0.051</td><td>0.059</td><td>0.061</td></tr><tr><td>λk14</td><td>0.052</td><td>0.043</td><td>0.060</td><td>0.051</td><td>0.038</td><td>0.048</td><td>0.055</td><td>0.064</td></tr><tr><td>λk15</td><td>0.047</td><td>0.035</td><td>0.049</td><td>0.048</td><td>0.030</td><td>0.039</td><td>0.053</td><td>0.059</td></tr><tr><td>λk16</td><td>0.029</td><td>0.022</td><td>0.028</td><td>0.033</td><td>0.017</td><td>0.022</td><td>0.037</td><td>0.036</td></tr><tr><td>λk17</td><td>0.016</td><td>0.013</td><td>0.015</td><td>0.020</td><td>0.009</td><td>0.012</td><td>0.022</td><td>0.020</td></tr><tr><td>λk18</td><td>0.012</td><td>0.010</td><td>0.010</td><td>0.015</td><td>0.006</td><td>0.009</td><td>0.016</td><td>0.014</td></tr><tr><td>αk</td><td>0</td><td>2.048</td><td>1.572</td><td>0.600</td><td>1.074</td><td>0.938</td><td>0.408</td><td>-0.642</td></tr><tr><td>βk</td><td>0</td><td>0.781</td><td>0.786</td><td>0.429</td><td>0.678</td><td>0.265</td><td>0.404</td><td>0.426</td></tr><tr><td>nk</td><td>15</td><td>8</td><td>8</td><td>3</td><td>5</td><td>17</td><td>3</td><td>1</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 5: Parameter estimates for multinomial finite mixture with Gibbs prior (rounded on 3 digits) \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[143,525,849,585]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"regions according to demographic traits and especially the age. It seems that in this way population structure of an area can be described and be studied in a more efficient way. The proposed model not only does it account for the common heterogeneity, but also for spatial heterogeneity that exists due to the nature of the data. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,585,849,646]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The spatial information is incorporated by prior probabilities. More specifically, allocation variables are modelled as MRF. Then, model estimation is based on a modification of CEM, where a step for approximating the field is preceded before common steps of CEM. Simulated field algorithm has been selected rather than mean field or mode field, since literature supports that it is better. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,647,849,720]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Although the usefulness of this model, there are issues to be concerned. The initialization process is extremely demanding because of the excess of parameters to be estimated and as a result the algorithm is possible to be trapped in local maximum. Moreover, in case of large records in each category of the multinomial distributions, as in the examined example, computational problems may arise due to very small probabilities. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[143,722,849,782]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, the presented model can be enriched by the usage of more than one demographics. For example, it would be interesting using not only age but also sex, with the purpose of gaining more information about the population structure. In addition, prior probabilities can also be improved by inserting extra explanatory variables except for neighbors' behavior. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[488,845,508,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"14\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"15 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[416,116,581,266]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0805/d0e06c7a75c85eef9f809250b76f78de34e2d3dcb6b859bb15e2c2656b3c49b8.jpg\",\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Cluster</td><td>Mean age</td></tr><tr><td>1</td><td>37.57</td></tr><tr><td>2</td><td>35.87</td></tr><tr><td>3</td><td>37.60</td></tr><tr><td>4</td><td>38.22</td></tr><tr><td>5</td><td>32.69</td></tr><tr><td>6</td><td>35.40</td></tr><tr><td>7</td><td>39.64</td></tr><tr><td>8</td><td>39.04</td></tr></table>\",\n \"table_caption\": \"[\\\"Table 6: Mean age of residents in each cluster. \\\"]\",\n \"table_footnote\": \"[]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[145,311,274,330]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[145,343,852,792]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Alfo, M., L. Nieddu, and D. Vicari (2008). A finite mixture model for image segmentation. Statistics and Computing 18(2), 137-150. \\\",\\\"Alfo, M., L. Nieddu, and D. Vicari (2009). Finite mixture models for mapping spatially dependent disease counts. Biometrical Journal 51(1), 84-97. \\\",\\\"Aykroyd, R. and S. Zimeras (1999). Inhomogeneous prior models for image reconstruction. Journal of the American Statistical Association 94(447), 934-946. \\\",\\\"Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society: Series B (Methodology) 36(2), 192-225. \\\",\\\"Besag, J. (1975). Statistical analysis of non-lattice data. Journal of the Royal Statistical Society: Series D (The Statistician) 24(3), 179-195. \\\",\\\"Besag, J. (1986). On the statistical analysis of dirty pictures. Journal of the Royal Statistical Society: Series B (Methodology) 48(3), 259-279. \\\",\\\"Besag, J., J. York, and A. Mollier (1991). Bayesian image restoration, with two applications in spatial statistics. Annals of the Institute of Statistical Mathematics 43(1), 1-20. \\\",\\\"Biernacki, C., G. Celeux, and G. Govaert (2003). Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models. Computational Statistics & Data Analysis 41(3-4), 561-575. \\\",\\\"Blischke, W. R. (1964). Estimating the parameters of mixtures of binomial distributions. Journal of the American Statistical Association 59(306), 510-528. \\\",\\\"Carvalho, A. X. Y., P. H. M. Albuquerque, G. R. de Almeida Junior, and R. D. Guimaraes (2009). Spatial hierarchical clustering. Revista Brasileira de Biometria 27(3), 411-442. \\\",\\\"Celeux, G., F. Forbes, and N. Peyrard (2003). EM procedures using mean field-like approximations for Markov model-based image segmentation. Pattern Recognition 36(1), 131-144. \\\"]\",\n \"page_idx\": \"15\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[488,847,508,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"15\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"16 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[282,119,709,452]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 4: Percentage of residents in each age group for three clusters \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0582/5f0a749301ae397aee240461987499ecf072bc22582f029670b1cf029c373027.jpg\",\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[145,522,854,816]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Derin, H. and H. Elliott (1987). Modeling and segmentation of noisy and textured images using Gibbs random fields. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-9(1), 39-55. \\\",\\\"Forbes, F., M. Charras-Garrido, L. Azizi, S. Doyle, and D. Abrial (2013). Spatial risk mapping for rare disease with hidden Markov fields and variational EM. The Annals of Applied Statistics 7, 1192-1216. \\\",\\\"Forbes, F. and N. Peyrard (2003). Hidden Markov random field model selection criteria based on mean field-like approximations. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(9), 1089-1101. \\\",\\\"Geman, S. and D. Geman (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-6(6), 721-741. \\\",\\\"Green, P. J. and S. Richardson (2002). Hidden Markov models and disease mapping. Journal of the American Statistical Association 97(460), 1055-1070. \\\",\\\"Grün, B. and F. Leisch (2008). Identifiability of finite mixtures of multinomial logit models with varying and fixed effects. Journal of Classification 25(2), 225-247. \\\"]\",\n \"page_idx\": \"16\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[490,845,508,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"16\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"17 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[282,119,709,452]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 5: Percentage of residents in each age group for three clusters \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0336/0c8c845d0e94b1655f9ce0810156c8b24ebe3352a0c7ede3b6fdb2461f911a77.jpg\",\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[143,518,851,823]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Hubert, L. and P. Arabie (1985). Comparing partitions. Journal of Classification 2, 193-218. \\\",\\\"Jorgensen, M. A. (2013). Forming clusters from census areas with similar tabular statistics. *Communications in Statistics-Theory and Methods* 42(12), 2136-2151. \\\",\\\"Kumar, C. N. S., V. S. Ramulu, K. S. Reddy, S. Kotha, and C. M. Kumar (2012). Spatial data mining using cluster analysis. International Journal of Computer Science & Information Technology 4(4), 71. \\\",\\\"Legendre, P. (1987). Constrained clustering. In P. Legendre and L. Legendre (Eds.), *Developments in Numerical Ecology*, Berlin, Heidelberg, pp. 289-307. Springer Berlin Heidelberg. \\\",\\\"Liu, Q., M. Deng, Y. Shi, and J. Wang (2012). A density-based spatial clustering algorithm considering both spatial proximity and attribute similarity. Computers & Geosciences 46, 269-309. \\\",\\\"Moran, P. A. (1950). Notes on continuous stochastic phenomena. Biometrika 37(1/2), 17-23. \\\",\\\"Ng, R. T. and J. Han (2002). CLARANS: A method for clustering objects for spatial data mining. IEEE Transactions on Knowledge and Data Engineering 14(5), 1003-1016. \\\",\\\"Papastamoulis, P. (2023). Model based clustering of multinomial count data. Advances in Data Analysis and Classification ( ), (to appear). \\\"]\",\n \"page_idx\": \"17\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[488,845,508,858]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"17\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"18 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[282,118,709,452]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 6: Percentage of residents in each age group for two clusters \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0613/a50f22156eedce15babc54ad17c9dc81c78337547d8430f55e81a8277614b974.jpg\",\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[143,522,852,811]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Pappas, T. N. and Jayant, N. S. (1992). An adaptive clustering algorithm for image segmentation. IEEE Transaction Signal Process 40(4), 901-914. \\\",\\\"Patil, G. P., R. Modarres, W. L. Myers, and P. Patankar (2006). Spatially constrained clustering and upper level set scan hotspot detection in surveillance geoinformatics. *Environmental and Ecological Statistics* 13(4), 365-377. \\\",\\\"Poston, J., L. Dudley, and L. F. Bouvier (2010). Population and Society: An Introduction to Demography. Cambridge University Press. \\\",\\\"Qian, W. and D. Titterington (1991). Estimation of parameters in hidden Markov models. *Philosophical Transactions of the Royal Society of London*. Series A: Physical and Engineering Sciences 337(1647), 407-428. \\\",\\\"Strauss, D. J. (1977). Clustering on coloured lattices. Journal of Applied Probability 14 (1), 135-143. \\\",\\\"Teicher, H. (1963, 12). Identifiability of finite mixtures. Annals of Mathematical Statistics 34(4), 1265-1269. \\\",\\\"Titterington, D. M., A. F. Smith, and U. E. Makov (1985). Statistical analysis of finite mixture distributions. Wiley. \\\"]\",\n \"page_idx\": \"18\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[488,845,508,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"18\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"19 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[328,164,647,406]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 7: Map of clusters according to eight component models \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0597/d9a891ae4b4cea5725098ba3fa1a177cbc96787df45f8619275442dba0d42ca8.jpg\",\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[145,523,852,555]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Tobler, W. R. (1970). A computer movie simulating urban growth in the Detroit region. *Economic Geography* 46(sup1), 234-240. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[488,845,509,859]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"19\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"20 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.48550/arxiv.2402.09888"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Medicine and Health Sciences"},"sha256":{"kind":"string","value":"04971f4383784505554a8808ca85e1551fa91ec3cf77af77d5137bce209aed3a"},"title":{"kind":"string","value":"Multinomial mixture for spatial data"}}},{"rowIdx":273,"cells":{"abstract":{"kind":"string","value":"Context. Some metal-poor stars have abundance patterns, which are midway between the slow (s) and rapid (r) neutron capture processes. Aims. We show that the helium shell of a fast rotating massive star experiencing a jet-like explosion undergoes two efficient neutron capture processes: one during stellar evolution and one during the explosion. It eventually provides a material whose chemical composition is midway between the s- and r-process. Methods. A low metallicity 40 M-circle dot model with an initial rotational velocity of similar to 700 km s(-1) was computed from birth to pre-supernova with an extended nuclear network following the slow neutron capture process. A two-dimensional hydrodynamic relativistic code was used to model a E = 10(52) erg relativistic jet-like explosion hitting the stellar mantle. The jet-induced nucleosynthesis was calculated in post-processing with an optimised network of 1812 nuclei. Results. During the star's life, heavy elements from 30 less than or similar to Z less than or similar to 82 are produced thanks to an efficient s-process, which is boosted by rotation. At the end of evolution, the helium shell is largely enriched in trans-iron elements and in (unburnt) Ne-22, whose abundance is similar to 20 times higher than in a non-rotating model. During the explosion, the jet heats the helium shell up to similar to 1.5 GK. It efficiently activates (alpha, n) reactions, such as Ne-22(alpha, n), and leads to a strong n-process with neutron densities of similar to 10(19)-10(20) cm(-3) during 0.1 s. This has the effect of shifting the s-process pattern, which was built during stellar evolution, towards heavier elements (e.g. Eu). The resulting chemical pattern is consistent with the abundances of the carbon-enhanced metal-poor r/s star CS29528-028, provided the ejecta of the jet model is not homogeneously mixed. Conclusions. The helium burning zones of rotating massive stars experience an efficient s-process during the evolution followed by an efficient n-process during a jet-like explosion. This is a new astrophysical site which can explain at least some of the metal-poor stars showing abundance patterns midway between the s- and r-process."},"author":{"kind":"string","value":"Choplin, Arthur|Tominaga, Nozomu|Meyer, Bradley S."},"content_list":{"kind":"list like","value":[{"bbox":"[122,156,875,181]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A strong neutron burst in jet-like supernovae of spinstars ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[253,187,742,206]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Arthur Choplin $^{1,2}$ , Nozomu Tominaga $^{1,3}$ , and Bradley S. Meyer $^{4}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,222,900,294]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"$^{1}$ Department of Physics, Faculty of Science and Engineering, Konan University, 8-9-1 Okamoto, Kobe, Hyogo 658-8501, Japan e-mail: arthur.choplin@konan-u.ac.jp \",\"2 Geneva Observatory, University of Geneva, Maillettes 51, 1290 Sauverny, Switzerland \",\"3 Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan \",\"$^{4}$ Department of Physics and Astronomy, Clemson University, Clemson, SC 29634-0978, USA \"]","page_idx":"0","sub_type":"text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[94,303,405,316]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received 16 March 2020 / Accepted 28 May 2020 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[455,326,541,338]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABSTRACT ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,350,900,374]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Context. Some metal-poor stars have abundance patterns, which are midway between the slow $(s)$ and rapid $(r)$ neutron capture processes. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,374,900,409]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Aims. We show that the helium shell of a fast rotating massive star experiencing a jet-like explosion undergoes two efficient neutron capture processes: one during stellar evolution and one during the explosion. It eventually provides a material whose chemical composition is midway between the $s$ - and $r$ -process. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,409,900,458]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Methods. A low metallicity $40M_{\\odot}$ model with an initial rotational velocity of $\\sim 700\\mathrm{km~s^{-1}}$ was computed from birth to pre-supernova with an extended nuclear network following the slow neutron capture process. A two-dimensional hydrodynamic relativistic code was used to model a $E = 10^{52}$ erg relativistic jet-like explosion hitting the stellar mantle. The jet-induced nucleosynthesis was calculated in post-processing with an optimised network of 1812 nuclei. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,457,900,539]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Results. During the star's life, heavy elements from $30 \\lesssim Z \\lesssim 82$ are produced thanks to an efficient $s$ -process, which is boosted by rotation. At the end of evolution, the helium shell is largely enriched in trans-iron elements and in (unburnt) ${}^{22}\\mathrm{Ne}$ , whose abundance is $\\sim 20$ times higher than in a non-rotating model. During the explosion, the jet heats the helium shell up to $\\sim 1.5\\mathrm{GK}$ . It efficiently activates $(\\alpha, n)$ reactions, such as ${}^{22}\\mathrm{Ne}(\\alpha, n)$ , and leads to a strong $n$ -process with neutron densities of $\\sim 10^{19} - 10^{20}\\mathrm{cm}^{-3}$ during $0.1\\mathrm{s}$ . This has the effect of shifting the $s$ -process pattern, which was built during stellar evolution, towards heavier elements (e.g. Eu). The resulting chemical pattern is consistent with the abundances of the carbon-enhanced metal-poor $r/s$ star CS29528-028, provided the ejecta of the jet model is not homogeneously mixed. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,539,900,576]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Conclusions. The helium burning zones of rotating massive stars experience an efficient $s$ -process during the evolution followed by an efficient $n$ -process during a jet-like explosion. This is a new astrophysical site which can explain at least some of the metal-poor stars showing abundance patterns midway between the $s$ - and $r$ -process. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,582,836,595]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Key words. stars: massive - stars: rotation - stars: jets - stars: interiors - nuclear reactions, nucleosynthesis, abundances ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,614,184,627]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[55,640,490,835]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Understanding the origin of the elements is among the very topical challenges of modern astrophysics (e.g. the reviews of Meyer 1994; Arnould et al. 2007; Thielemann et al. 2017; Cowan et al. 2019; Arnould & Goriely 2020). The solar abundances first revealed the existence of a slow $(s)$ and a rapid $(r)$ neutron capture process (Suess & Urey 1956; Burbidge et al. 1957). The $s$ -process operates during the life of asymptotic giant branch (AGB, main $s$ -process, e.g. Busso et al. 1999; Herwig 2005; Lugaro et al. 2012; Karakas & Lattanzio 2014) and massive stars (weak $s$ -process, e.g. Langer et al. 1989; Prantzos et al. 1990; Kappeler et al. 2011). Promising sites for the $r$ -process include neutron star mergers (e.g. Wanajo et al. 2014; Thielemann et al. 2017) as well as magneto-rotational supernovae and collapsars from massive stars (e.g. Winteler et al. 2012; Nishimura et al. 2015; Halevi & Mosta 2018; Siegel et al. 2019). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,835,492,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Besides the Sun, metal-poor (MP) stars (e.g. the review of Beers & Christlieb 2005; Frebel & Norris 2015) are prime targets to investigate the origin of elements since they likely formed from a material that was enriched by just one or a few previous sources. Thus their abundances only reflect one or a few previous nucleosynthetic events. A zoo of MP stars was progressively constituted based on the chemical composition of these objects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,614,939,835]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Numerous MP stars have supersolar $\\mathrm{[C / Fe]}$ ratios and are called carbon-enhanced metal-poor (CEMP) stars. At $[\\mathrm{Fe / H}]\\lesssim -3$ , most MP stars are CEMP stars and generally do not show clear enhancements in heavy elements (CEMP-no stars, e.g. Yong et al. 2013; Norris et al. 2013; Bonifacio et al. 2015; Yoon et al. 2016). In addition to carbon, most CEMP-no stars have supersolar $\\mathrm{[N / Fe]}$ , $\\mathrm{[O / Fe]}$ , $\\mathrm{[Na / Fe]}$ , $\\mathrm{[Mg / Fe]}$ , and $\\mathrm{[Al / Fe]}$ ratios. The most discussed scenarios to explain these nearly pristine objects that are enriched in light elements rely on massive stellar models experiencing significant mixing at the time of the supernova and possibly strong fallback (e.g. Umeda & Nomoto 2003; Limongi et al. 2003; Nomoto et al. 2003; Iwamoto et al. 2005; Heger & Woosley 2010; Tominaga et al. 2007b, 2014; Ishigaki et al. 2018) and models experiencing mid to fast rotation during their lives (e.g. Meynet et al. 2006, 2010; Hirschi 2007; Joggerst et al. 2010; Maeder et al. 2015; Takahashi et al. 2014; Choplin et al. 2017a, 2019). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,835,939,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"At $[\\mathrm{Fe / H}]\\gtrsim -3$ , many CEMP stars with clear enhancement of heavy elements were found. This includes CEMP stars with clear $s$ -process signatures (CEMP- $s$ stars, e.g. Burris et al. 2000; Simmerer et al. 2004; Sivarani et al. 2004; Placco et al. 2013) and $r$ -process signatures (CEMP- $r$ stars, e.g. Sneden et al. 2003; Ji et al. 2016; Hansen et al. 2018; Sakari et al. 2018). The origin of the CEMP- $r$ stars is tightly linked to the $r$ -process site (cf. first ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,67,371,105]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A&A 639, A126 (2020) \nhttps://doi.org/10.1051/0004-6361/202037966 \n© ESO 2020 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[754,71,937,118]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Astronomy & Astrophysics ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[389,941,606,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Article published by EDP Sciences ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[826,941,939,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A126, page 1 of 8 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[55,93,492,445]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"paragraph). Most of the CEMP- $s$ stars are found in binary systems (Hansen et al. 2016) and are thought to have acquired their $s$ -processed material, from a now extinct AGB companion, during a (wind) mass transfer episode (e.g. Stancliffe & Glebbeek 2008; Bisterzo et al. 2010; Masseron et al. 2010; Lugaro et al. 2012; Hollek et al. 2015; Abate et al. 2015). An efficient $s$ -process is also expected in rotating massive stars (cf. Sect. 2) and therefore these objects could explain at least a part of the CEMP- $s$ sample (Choplin et al. 2017b; Banerjee et al. 2019). In addition to CEMP- $s$ and CEMP- $r$ stars, one also finds $r + s$ CEMP stars, which are likely made of a combination of $s$ - and $r$ -process patterns (Gull et al. 2018), and CEMP- $r/s$ stars (also named CEMP- $i$ stars, e.g. Roederer et al. 2016). This last class shows intermediate abundance patterns for which neither an $s$ -process nor an $r$ -process pattern, and likely nor a combination of both, can reasonably reproduce the abundances (Jonsell et al. 2006; Lugaro et al. 2012; Bisterzo et al. 2012; Abate et al. 2016). An intermediate neutron capture process, that is, an $i$ -process operating at neutron densities in between the $s$ - and $r$ -process (first named by Cowan & Rose 1977), may be a solution to explain these stars<sup>1</sup> (Dardelet et al. 2014; Roederer et al. 2016; Hampel et al. 2016, 2019). The $i$ -process may operate in AGB or super-AGB stars (Herwig et al. 2011; Jones et al. 2017) in rapidly accreting white dwarfs (Denissenkov et al. 2017, 2019) or in the helium shell of very low (or zero) metallicity massive stars experiencing proton ingestion events during late evolutionary stages (Banerjee et al. 2018; Clarkson et al. 2018). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,445,490,563]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In addition to the $s$ -, $r$ -, and $i$ -processes, one finds the $n$ -process. It consists in a short neutron burst in the helium shell of massive stars when the supernova shock wave passes through it (Blake & Schramm 1976; Truran et al. 1978; Thielemann et al. 1979; Blake et al. 1981; Hillebrandt et al. 1981; Rauscher et al. 2002; Meyer et al. 2004). Most of the neutron are provided by the ${}^{22}\\mathrm{Ne}(\\alpha,\\mathrm{n})$ reaction. It has been shown that the $n$ -process could explain some anomalous isotopic signatures in meteorites (Meyer et al. 2000; Pignatari et al. 2015, 2018). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,564,492,708]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Here, we propose a new scenario providing abundance patterns midway between the $s$ - and $r$ -process and which can possibly explain the metal-poor stars having these types of intermediate abundance patterns. This scenario relies on two successive neutron capture processes in the same source: an efficient $s$ -process followed by a strong $n$ -process. The basic working of it is explained in Sect. 2. The codes used and methods are presented in Sect. 3, the results and comparisons with the metal-poor star C29528-028 are presented in Sects. 4 and 5, respectively, followed by discussions in Sect. 6. A summary and the main conclusions are given in Sect. 7. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,727,485,759]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. The helium shell of a rotating massive star hit by a jet ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[55,764,492,896]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This section describes the basic working of the scenario discussed throughout this paper. By progressively transporting chemical elements from a burning region to another rotational mixing impacts the nucleosynthesis during stellar evolution (e.g. Meynet & Maeder 2000; Heger et al. 2000; Brott et al. 2011; Chieffi & Limongi 2013; Choplin et al. 2016). Especially, rotation has been found to increase the production of $^{13}\\mathrm{C}$ and $^{22}\\mathrm{Ne}$ , which release neutrons by $(\\alpha, n)$ reactions. It boosts the efficiency of the $s$ -process in massive stars, mainly during the core helium burning stage (Pignatari et al. 2008; Frischknecht ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,93,937,120]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"et al. 2012, 2016; Limongi & Chieffi 2018; Choplin et al. 2018; Banerjee et al. 2019, see also Sect. 4.1). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,120,937,288]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As mentioned in Sect. 1, at the time of the supernova, the shock wave passing through the helium shell can trigger the $n$ -process. Its efficiency very much depends on the pre-supernova amount of ${}^{22}\\mathrm{Ne}$ and the ability of the explosion to burn it during the shock passage. In case of a rotating progenitor, the $n$ -process can be particularly efficient. On the one hand, rotation produces more ${}^{22}\\mathrm{Ne}$ during the evolution and allows for a higher amount of unburnt ${}^{22}\\mathrm{Ne}$ in the helium shell at the pre-supernova stage. On the other hand, rotation may trigger energetic jet-like explosions (e.g. Woosley 1993; MacFadyen & Woosley 1999; Woosley & Heger 2006), thus leading to high temperatures in the helium shell and therefore an efficient activation of the ${}^{22}\\mathrm{Ne}(\\alpha, n)$ reaction. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,288,939,341]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The combined effect of fast rotation and jet-like explosion can induce an efficient $s$ -process during evolution and an efficient $n$ -process during explosion. In this paper we examine the combination of these two effects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,359,601,373]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. Methods ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[502,380,937,524]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We modelled the evolution and explosion of a $40M_{\\odot}$ star by combining a one-dimensional stellar evolution code with a two-dimensional explosion code. The Geneva stellar evolution code (Eggenberger et al. 2008) was used to compute a pre-supernova $40M_{\\odot}$ model at a metallicity of $Z = 10^{-3}$ with an initial rotation rate on the zero-age main sequence of $\\upsilon_{\\mathrm{ini}} / \\upsilon_{\\mathrm{crit}} = 0.8^2$ . This corresponds to an initial equatorial velocity of $704\\mathrm{km s^{-1}}$ . The nuclear network was coupled to the evolution and used throughout the entire process. It comprises 737 isotopes from hydrogen to polonium. We refer to Choplin & Hirschi (2020) for more details on the initial set up of the model. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,524,939,760]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The jet-like explosion was modelled with a two-dimensional relativistic hydrodynamical code (Tominaga et al. 2007a; Tominaga 2009). At $t = 0$ , a jet was launched at the mass coordinate $1.93M_{\\odot}$ , lasting for 10 seconds with a constant energy deposition rate of $10^{51}\\mathrm{erg s^{-1}}$ . The total energy deposited is then $10^{52}\\mathrm{erg}$ which corresponds to the typical energy of a hypernova (e.g. Nomoto et al. 2004, 2006). The opening angle is 5 degrees and the Lorentz factor is $\\Gamma = 100$ . The hydrodynamics is followed for $5\\times 10^{5}\\mathrm{s}$ . The thermodynamic histories are recorded by $2.5\\times 10^{4}$ mass particles representing Lagrangian mass elements of the stellar mantle. The initial grid is linear with a resolution of 100 along the $\\theta$ -direction and logarithmic with a resolution of 250 in the $r$ -direction. The nucleosynthesis of mass particles initially located in the helium shell was calculated in post-processing with a neutron-rich nuclear network of 1812 isotopes. Nucleosynthesis tests with different network sizes were carried out in order to reduce the network size as much as possible without missing isotopes. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,776,591,789]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. Results ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[502,797,937,865]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"During its life, this rotating $40M_{\\odot}$ model loses $16M_{\\odot}$ through stellar winds: $8\\%$ of the mass is lost during the main sequence, $82\\%$ during core helium burning, and $10\\%$ after core helium burning. The final mass of the model is then $M_{\\mathrm{fin}} = 24M_{\\odot}$ with a hydrogen envelope that is mainly composed of helium ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[423,65,574,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A&A 639,A126 (2020) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[502,872,937,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 The initial equatorial velocity is $\\upsilon_{\\mathrm{ini}}$ and $\\upsilon_{\\mathrm{crit}}$ is the initial equatorial velocity at which the gravitational acceleration is balanced by the centrifugal force. It is defined as $\\upsilon_{\\mathrm{crit}} = \\sqrt{\\frac{2GM}{3R_{\\mathrm{pb}}}}$ , where $R_{\\mathrm{pb}}$ is the polar radius at the break-up velocity (see Maeder & Meynet 2000). ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[57,904,492,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"<sup>1</sup> Such a process has also been proposed to explain the isotopic signature of presolar grains (Jadhav et al. 2013; Liu et al. 2014). ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[57,940,171,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A126, page 2 of 8 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[72,97,475,311]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 1. Pre-supernova abundance profile of the rotating $40M_{\\\\odot}$ progenitor model. The outer layers are shown. The shaded areas show the convective zones. \"]","image_footnote":"[]","img_path":"images/0985/cfaa0eb3f8daf78e98f664f80adeaeb0852240d77ac4a55180eb65f55e686044.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[55,376,490,468]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"(71% in mass). The final surface hydrogen mass fraction is 0.3 (Fig. 1) and the total hydrogen mass left in the star is $1.4M_{\\odot}$ . For comparison purposes, the same model without rotation loses $6.42M_{\\odot}$ , has a final hydrogen envelope of $18.29M_{\\odot}$ (composed of $\\sim 45\\%$ hydrogen and $\\sim 55\\%$ helium), has a final surface hydrogen mass fraction of 0.73, and the total hydrogen mass that is left in the star is $8.2M_{\\odot}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,483,428,510]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.1. Rotation-induced nucleosynthesis during stellar evolution ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[55,517,490,714]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We recall below how rotation boosts the $s$ -process during the evolution of massive stars (cf. discussions in Pignatari et al. 2008; Frischknecht et al. 2016; Limongi & Chieffi 2018; Choplin et al. 2018; Banerjee et al. 2019). During the core helium burning phase, ${}^{12}\\mathrm{C}$ and ${}^{16}\\mathrm{O}$ are transported by rotation-induced mixing from the helium core to the hydrogen shell, which boosts the CNO cycle in the hydrogen shell and synthesises primary ${}^{13}\\mathrm{C}$ and ${}^{14}\\mathrm{N}$ . Due to the growth of the convective helium core combined with the backward diffusion of hydrogen burning products, the extra ${}^{13}\\mathrm{C}$ and ${}^{14}\\mathrm{N}$ are engulfed in the helium core The ${}^{14}\\mathrm{N}$ is quickly transformed into ${}^{22}\\mathrm{Ne}$ through ${}^{14}\\mathrm{N}(\\alpha ,\\gamma)^{18}\\mathrm{F}(\\beta^{+})^{18}\\mathrm{O}(\\alpha ,\\gamma)^{22}\\mathrm{Ne}$ . Neutrons, which are mainly released by ${}^{13}\\mathrm{C}(\\alpha ,n)$ and ${}^{22}\\mathrm{Ne}(\\alpha ,n)$ , trigger the $s$ -process provided any heavy seed (e.g. ${}^{56}\\mathrm{Fe}$ ) is present in the helium burning core. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,713,490,806]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the present model, this effect boosts the $s$ -process by a factor of $\\sim 10 - 1000$ for elements with $35 < Z < 82$ (Fig. 2). The same model without rotation only experiences a modest enhancement of elements with $Z < 45$ (Fig. 2, black line). At the pre-supernova stage, the mass fraction of $^{22}\\mathrm{Ne}$ that is left (unburnt) in the helium shell is $2.2 \\times 10^{-2}$ (Fig. 1), which is $\\sim 20$ times higher than for the same model but without rotation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,820,406,834]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.2. Jet-induced nucleosynthesis: Light elements ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[55,841,490,895]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The jet penetrates into the helium shell after $2\\mathrm{s}$ . The mass particles located at the bottom of the helium shell have pre-jet temperatures of $0.3 - 0.4\\mathrm{GK}$ . Those with $\\theta_{\\mathrm{ini}} \\leq 10^{\\circ}$ reach $1 < T < 1.5\\mathrm{GK}$ during the passage of the jet (Fig. 3). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[517,96,924,311]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 2. Integrated mass fractions of the material above the bottom of the helium shell (after beta decays) at the pre-supernova stage. The red (black) solid line shows a low metallicity $40M_{\\\\odot}$ model computed with (without) rotation. The black dashed line shows the initial chemical composition of the models. The vertical dotted lines show the location of Sr, Ba, and Pb. \"]","image_footnote":"[]","img_path":"images/0139/85910a95400dd22877d30f3461cc5d5ac9f54d3f28457ddc440d4425f6da30ce.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[502,417,939,601]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Close to the jet axis, the high temperature activates $^{22}\\mathrm{Ne}(\\alpha ,n)$ , but also $^{13}\\mathrm{C}(\\alpha ,n)$ and $^{17}\\mathrm{O}(\\alpha ,n)$ , the isotopes $^{13}\\mathrm{C}$ and $^{17}\\mathrm{O}$ being produced by $^{12}\\mathrm{C}(n,\\gamma)$ and $^{16}\\mathrm{O}(n,\\gamma)$ (Fig. 4). Even closer to the jet axis and deeper in the helium shell, the higher temperature efficiently produces $^{24}\\mathrm{Mg}$ , $^{28}\\mathrm{Si}$ , and $^{32}\\mathrm{S}$ (Fig. 5) through $(\\alpha ,\\gamma)$ reactions. Some $(\\alpha ,p)$ reactions, such as $^{24}\\mathrm{Mg}(\\alpha ,p)^{27}\\mathrm{Al}$ and $^{27}\\mathrm{Mg}(\\alpha ,p)^{30}\\mathrm{Si}$ , also become strong and, therefore, they release protons, which activate some $(p,\\gamma)$ reactions. For instance, $^{31}\\mathrm{P}$ is enhanced (Fig. 5) through $^{30}\\mathrm{Si}(p,\\gamma)^{31}\\mathrm{P}$ . The high $^{35}\\mathrm{Cl}$ abundance comes from the chain $^{24}\\mathrm{Mg}(\\alpha ,p)^{27}\\mathrm{Al}(\\alpha ,p)^{30}\\mathrm{Si}(\\alpha ,\\gamma)^{34}\\mathrm{S}(p,\\gamma)^{35}\\mathrm{Cl}$ . The high $^{36}\\mathrm{Ar}$ and $^{39}\\mathrm{K}$ mainly come from $^{34}\\mathrm{S}(p,\\gamma)^{35}\\mathrm{Cl}(p,\\gamma)^{36}\\mathrm{Ar}$ and $^{34}\\mathrm{S}(\\alpha ,\\gamma)^{38}\\mathrm{Ar}(p,\\gamma)^{39}\\mathrm{K}$ , respectively. Some Ti is also formed thanks to $^{44}\\mathrm{Ca}(p,\\gamma)^{45}\\mathrm{Sc}(p,\\gamma)^{46}\\mathrm{Ti}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,615,865,630]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.3. Jet-induced nucleosynthesis: Heavy elements ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[502,637,937,871]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"During the jet explosion, the $(\\alpha ,n)$ reactions lead to a burst of neutrons. For mass particles that are initially along the jet axis $(\\theta_{\\mathrm{ini}}\\lesssim 5^{\\circ})$ and with initial mass coordinates of $M_{\\mathrm{r,in i}}\\sim$ $15.5 - 18M_{\\odot}$ , the neutron density reaches $n_{\\mathrm{n}} > 10^{19}\\mathrm{cm}^{-3}$ during $\\sim 0.1\\mathrm{s}$ (Fig. 7, left panel). The neutron exposure4 of these mass particles goes up to $1.35\\mathrm{mbarn^{-1}}$ (Fig. 7). Despite $n_{\\mathrm{n}}$ values being close to $r$ -process values, the abundant light elements in the helium shell (especially $^{12}\\mathrm{C}$ and $^{16}\\mathrm{O}$ ) act as strong neutron poisons. This reduces the amount of available neutron for heavy seeds and does not lead to $r$ -process nucleosynthesis. Nevertheless, during the burst, isotopes that are far from the valley of stability are produced (Fig. 8, bottom panel). The pre-jet abundance pattern is therefore shifted towards higher mass numbers compared to the initial pattern (Fig. 9). In particular, the first $(A\\sim 80 - 90)$ and second $(A\\sim 130 - 140)$ s-process peaks that were built during stellar evolution are shifted to higher atomic masses (see also Fig. 6). Details on the nucleosynthesis are given below. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[270,65,724,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A. Choplin et al.: A strong neutron burst in jet-like supernovae of spinstars ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[55,904,489,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 Produced from the initial hydrogen and helium content of the star, but not from the initial metals. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[502,892,937,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 The neutron exposure was computed as $\\tau = \\int n_{\\mathrm{n}}\\sqrt{2k_{\\mathrm{B}}T / m_{\\mathrm{n}}}\\mathrm{d}t$ with $n_{\\mathrm{n}}$ the neutron density, $k_{\\mathrm{B}}$ the Boltzmann constant, $T$ the temperature, and $m_{\\mathrm{n}}$ the neutron mass. ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[826,941,937,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A126, page 3 of 8 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,96,480,337]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0109/e4502ea7b9c9cd8ef6bdcab6c8340bf5d599ecf15bf6c4fb7eec02d70cb86176.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[517,96,917,336]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 3. Location of the mass particles after $2.8\\\\mathrm{s}$ (left panel) and $5.4\\\\mathrm{s}$ (right panel). The colour shows the temperature of the mass particles. The inner grey circle shows the central remnant. The black circle with a radius of $\\\\sim 0.7\\\\times 10^{10}\\\\mathrm{cm}$ shows the location of the bottom of the helium shell. \"]","image_footnote":"[]","img_path":"images/0337/5364749ec6329a225efe98b4ec4e4e49941984900b245d018730ef8f92c28dd7.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[72,392,478,598]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 4. Flowchart of a mass particle with $M_{\\\\mathrm{r,ini}} = 16.53M_{\\\\odot}$ (i.e. originally in the helium shell, cf. Fig. 1) and $\\\\theta_{\\\\mathrm{ini}} = 3.15^{\\\\circ}$ at its temperature peak. Mass fractions of isotopes are shown by the red colourmap. Black squares denote stable isotopes. Net reaction rates, considering forward and reverse reactions, are shown by arrows. Arrows are coloured as a function of the reaction type: yellow for $(\\\\alpha, \\\\gamma)$ , cyan for $(n, \\\\gamma)$ , green for $(\\\\alpha, n)$ , and blue for $(\\\\gamma, \\\\alpha)$ and $(n, \\\\alpha)$ . Rates below $7\\\\times 10^{22}\\\\mathrm{cm s^{-1}}$ are not shown. \"]","image_footnote":"[]","img_path":"images/0654/50ccb3ad5ed8152e83c626c866d2bcc041eb33fd2d16487a383eff6857043922.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[55,720,492,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"During the jet explosion, $^{56,57,58,60}\\mathrm{Fe}$ are mostly transformed into $^{60-64}\\mathrm{Fe}$ by neutron captures. After the explosion, $^{60-64}\\mathrm{Fe}$ eventually decay to the stable $^{60,61,62,64}\\mathrm{Ni}$ and $^{63}\\mathrm{Cu}$ isotopes. This has the overall effect of destroying Fe and somewhat increasing Ni and Cu (Figs. 6 and 10). The $^{59}\\mathrm{Co}$ isotope, which is the only stable isotope of Co, is mainly transformed into $^{62-69}\\mathrm{Co}$ isotopes which decay to Ni, Cu, Zn, and $^{69}\\mathrm{Ga}$ . The production of $^{59}\\mathrm{Fe}$ , $^{59}\\mathrm{Mn}$ , and $^{59}\\mathrm{Cr}$ , which will decay to $^{59}\\mathrm{Co}$ , is too small to replenish $^{59}\\mathrm{Co}$ and therefore the final Co abundance stays low (Fig. 10). The higher final Zn abundance is mainly due to the decay of $^{66,67,68}\\mathrm{Ni}$ to $^{66,67,68}\\mathrm{Zn}$ isotopes. The final Mo is also enhanced, mainly thanks to the decay of neutron-rich $\\mathrm{Zr}^{(96-100)\\mathrm{Zr}}$ isotopes to stable Mo isotopes. The final Ru is enhanced thanks to the decay of the neutron-rich $\\mathrm{Zr}^{(101,102,104)\\mathrm{Zr}}$ , Nb, and Mo isotopes to stable Ru isotopes. We note that $^{103}\\mathrm{Rh}$ , which is the only stable isotope of Rh, is largely ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[519,392,926,545]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 5. Effect of the jet on C-Ti elements for a mass particle with $M_{\\\\mathrm{r,ini}} = 15.78M_{\\\\odot}$ and $\\\\theta_{\\\\mathrm{ini}} = 0.45^{\\\\circ}$ . We note that $X_{\\\\mathrm{jet}}$ are the post-jet mass fractions and $X_{\\\\mathrm{nojet}}$ are the mass fractions of the same mass particle that would not have experienced a jet explosion. In both cases, elements are beta decayed. \"]","image_footnote":"[]","img_path":"images/0143/5f4be77868e8e22aea142ab895bfaeb45fac5fef900342184b3f14ecea538902.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[514,627,934,785]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 6. Same as Fig. 5, but for Fe-Ho elements and for a mass particle with $M_{\\\\mathrm{r,ini}} = 16.53M_{\\\\odot}$ and $\\\\theta_{\\\\mathrm{ini}} = 3.15^{\\\\circ}$ (same mass particle as in Fig. 4). \"]","image_footnote":"[]","img_path":"images/0515/b559dcb295d99bcd7b524de7268252ec994067b1a29f08612dc2bf082e628ed2.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[502,837,939,932]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"enhanced by the decay of $^{103}\\mathrm{Zr}$ , $^{103}\\mathrm{Nb}$ , and $^{103}\\mathrm{Mo}$ . It is similar for Nd, Sm, Eu, Gd, Tb, and Dy ( $Z = 60 - 66$ ) elements whose final abundances are raised (Figs. 6 and 10) because of the decays of the neutron-rich isotopes of Cs, Ba, La, Ce, and Pr ( $Z = 55 - 59$ ). The final Tm, Lu, and Ta abundances are lower because they experience efficient neutron captures until the neutron magic number 126 (Fig. 8), and they are not ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[423,65,574,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A&A 639,A126 (2020) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[58,941,171,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A126, page 4 of 8 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[87,98,467,297]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0356/c6fbef3dd3b9aa207ce157387a86e0b27ca6b7c4483b414effa39a15612d45f5.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[97,309,465,511]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 7. Maximum neutron density (top) and neutron exposure (bottom) during the jet explosion as a function of the initial mass coordinate. Coloured lines show different initial angles. Each point represents a mass particle with initial coordinates $\\\\theta_{\\\\mathrm{ini}}$ and $M_{\\\\mathrm{r,ini}}$ . The two dashed lines show the initial location of the bottom of helium and hydrogen shells. The shaded areas show the convective zone at the pre-jet stage (see also Fig. 1). \"]","image_footnote":"[]","img_path":"images/0885/dd8297e1d384dfd4ffe85a0c8e104793e5a843c3898ac0e1213b3f02666478da.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[55,619,492,789]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"efficiently replenished by neutron-rich isotopes for elements with a lower atomic mass. For instance, most of the initial $^{169-173}\\mathrm{Tm}$ are transformed into $^{195}\\mathrm{Tm}$ , which eventually decay to $^{195}\\mathrm{Pt}$ , and $\\mathrm{Tm}$ is only slightly replenished by the decay of $^{169}\\mathrm{Sm}$ , $^{169}\\mathrm{Eu}$ , and $^{169}\\mathrm{Gd}$ , whose post-jet mass fractions are small (about $10^{-11}$ ). The abundance of $^{209}\\mathrm{Bi}$ also increases (Fig. 10) because of the decay of the unstable $^{209}\\mathrm{Tl}$ and $^{209}\\mathrm{Pb}$ isotopes, which are produced during the jet explosion. Furthermore, $\\mathrm{Pb}$ is not affected by the jet explosion because of a closed loop of beta and alpha decays leading back to $\\mathrm{Pb}$ (or possibly $^{209}\\mathrm{Bi}$ ). For instance, any unstable $^{210}\\mathrm{Pb}$ produced during the explosion experiences double beta decay to $^{210}\\mathrm{Po}$ , and then alpha decay to the stable $^{206}\\mathrm{Pb}$ isotope. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,789,492,869]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The stable isotopes, which are shielded by isotopes with the same mass and a lower atomic number, are not replenished by beta decays and are therefore completely destroyed by the jet. This is the case for $^{136}\\mathrm{Ba}$ or $^{148}\\mathrm{Sm}$ (Fig. 6) whose final mass fractions are nearly zero because they are shielded by the stable $^{136}\\mathrm{Xe}$ and $^{148}\\mathrm{Nd}$ isotopes, respectively. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[57,883,304,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4.4. Case of a spherical explosion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[55,903,490,932]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As a test, we ran two spherical explosions: one with the same total energy ( $E_{\\mathrm{TOT}} = 10^{52}$ erg) and one with $E_{\\mathrm{TOT}} = 10^{53}$ erg. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,97,934,271]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0058/8e11e6f024e6e277a4e23158f126179397eabfe59bf699adb3b35694bbbf51de.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[507,273,934,448]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 8. Pre-jet mass fractions (top panel) and post-jet mass fractions (before beta decays, bottom panel) for a mass particle at $M_{\\\\mathrm{r,inii}} = 16.53M_{\\\\odot}$ and $\\\\theta_{\\\\mathrm{ini}} = 3.15^{\\\\circ}$ (same mass particle as in Fig. 4). Black squares denote stable isotopes. The light blue line shows a typical $r$ -process flow for comparison purposes (taken from Arnould & Goriely 2020, their Fig. 5). The grey line shows the neutron drip line. Thin dotted lines show the location of the magic numbers. \"]","image_footnote":"[]","img_path":"images/0260/40274f8b541638baee974a0b4639b098160560550162ed4dfc52e8eb25308e15.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[502,561,939,799]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For the $10^{52}$ erg spherical explosion, the bottom of the helium shell is heated up to $\\sim 0.6$ GK. In this case, the $(\\alpha, n)$ reactions are weaker and the neutron density goes up to $\\sim 10^{15} \\mathrm{~cm}^{-3}$ . It leads to a much smaller neutron exposure that slightly affects the distribution of heavy elements. For a $10^{53}$ erg spherical explosion, the bottom of the helium shell is heated up to $\\sim 1$ GK, which leads to a maximal neutron density of about $\\sim 10^{19-20} \\mathrm{~cm}^{-3}$ , that is, similar to the jet-explosion discussed throughout this paper. In this case, the abundances of heavy elements are significantly affected in the same way as in Figs. 9 and 10. This means that $\\gtrsim 10$ times more energetic spherical explosions could lead to a similar nucleosynthesis as the $10^{52}$ erg jet-like explosion considered in this work. We note that a $10^{53}$ erg explosion corresponds to an extreme case which may not be realistic. Consequently, the nucleosynthetic signature of a boosted $n$ -process (as discussed throughout this paper) very likely points towards jet-like, or at least aspherical, explosions. We plan to explore the effect of various opening angles and explosion energies in a future work. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,820,907,835]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5. Signature in the metal-poor star CS29528-028 ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[502,841,939,895]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The chemical signature of jet-like explosions from rotating stars may be seen at the surface of observed metal-poor stars that have formed with the material ejected by previous sources. Here, we focus on CS29528-028 which has $\\mathrm{[Fe / H] - 2.12}$ $T_{\\mathrm{eff}} = 7100\\mathrm{K}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[270,65,724,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A. Choplin et al.: A strong neutron burst in jet-like supernovae of spinstars ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[502,904,937,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 The strongest explosions detected have $10^{52} < E < 10^{53}$ erg (see e.g. Fig. 2 in Nomoto et al. 2013). ","text_format":null,"text_level":null,"type":"page_footnote"},{"bbox":"[826,941,937,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A126, page 5 of 8 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[67,96,480,249]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 9. Pre-jet and post-jet mass fractions for the mass particle at $M_{\\\\mathrm{r,ini}} = 16.53M_{\\\\odot}$ and $\\\\theta_{\\\\mathrm{ini}} = 3.15^{\\\\circ}$ (the same mass particle as in Figs. 1, 4, and 8). The vertical dotted lines show the location of $^{88}\\\\mathrm{Sr}$ , $^{138}\\\\mathrm{Ba}$ , and $^{208}\\\\mathrm{Pb}$ . \"]","image_footnote":"[]","img_path":"images/0440/b88a7d8fb98afa0690863773bd7f6b8e9b52ec31a1ceb14eb911a43b05bdafe1.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[70,309,478,463]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 10. Effect of the jet on heavy elements for the mass particle at $M_{\\\\mathrm{r,ini}} = 16.53M_{\\\\odot}$ and $\\\\theta_{\\\\mathrm{ini}} = 3.15^{\\\\circ}$ (the same mass particle as in Figs. 1, 4, 8, and 9). The solid red line shows the composition after the jet explosion and after beta decays. The solid black line shows the composition if no jet explosion occurred (still after beta decays). Dashed lines show the patterns before beta decays. \"]","image_footnote":"[]","img_path":"images/0825/511444d483db14ffcbd532aaf45380416e4f083d0082902ebb9ea9ca08886501.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[55,564,490,669]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"and $\\log g = 4.27$ (Allen et al. 2012). It was classified as a carbon-enhanced metal-poor star with heavy abundances midway between the $s$ - and $r$ -process (CEMP- $r/s$ Beers & Christlieb 2005) because of its high $[\\mathrm{C / Fe}] = 2.76$ , enrichment in trans-Fe elements, and intermediate $[\\mathrm{Ba / Eu}] = 0.33$ (Aoki et al. 2007; Allen et al. 2012). Aoki et al. (2007) reported a $[\\mathrm{Na / Fe}]$ ratio of 2.68, but with a suggested NLTE correction of $-0.7$ , thus giving $[\\mathrm{Na / Fe}]_{\\mathrm{NLTE}} = 1.98$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,670,492,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We compared the abundances of CS29528-028 with four models. The first and second ones are $40M_{\\odot}$ non-rotating and rotating models, respectively, which did not experience jet-induced nucleosynthesis (orange and black lines in Fig. 11). The mass cut was set at a mass coordinate of $1.93M_{\\odot}$ (just as the jet model, cf. Sect. 3). The ejecta of the non-rotating (rotating) model was mixed with 150 $(400)M_{\\odot}$ of ISM material to produce the fits shown in Fig. 11. The third model (rot+jet_A, blue pattern) shows the integrated chemical composition of all ejected mass particles after the jet. For the fourth model, we searched for the best fit by considering the dependence of the yields in the final angle $\\theta_{\\mathrm{fin}}$ and final velocity $v_{\\mathrm{fin}}$ of the ejected material. Indeed, a neighbouring halo hosting a future star may not be enriched by the full ejecta, but only by a part of it, having a certain angle range. Also, the higher velocity material is more likely to reach and enrich a neighbouring halo. The rot+jet_B model (red pattern in Fig. 11) shows the best fit when the final angle range and the velocity threshold $v_{\\mathrm{th}}$ are left as free parameters; it is important to specify that only the mass particles with $v_{\\mathrm{fin}} > v_{\\mathrm{th}}$ were considered in this case. This model corresponds to ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[514,96,929,227]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0348/13cfe466b2d2fa5c9aaa4bf2a0fba76f10e2982942acb61e22c35367b7a9197d.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[512,229,929,282]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 11. Best fits (top panel) and their residuals (bottom panel) for the metal-poor star CS29528-028. The squares are the abundances from Aoki et al. (2007), and the circles are from Allen et al. (2012). Only an upper limit was derived for nitrogen. When two measurements were available for one element, the most recent one (Allen et al. 2012) was selected to calculate $\\\\chi^2$ and used to plot the residuals. The four patterns show the best fits and their $\\\\chi^2$ value for four models (cf. text for details). All models were considered after beta decay. \"]","image_footnote":"[]","img_path":"images/0669/3457e2d9bde6380891b18f536a9e5e056d47a6ba87d37f9a4411950c95de27c9.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[502,413,937,478]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"the integration of the mass particles with $7 < \\theta_{\\mathrm{fin}} < 17^{\\circ}$ and with $v_{\\mathrm{fin}} > 0.04\\mathrm{c}$ . The mass particles in this angle range are located in between the two dashed lines shown in Fig. 12. The mass particles with $v_{\\mathrm{fin}} > 0.04\\mathrm{c}$ are enclosed by the outermost contour shown in Fig. 12. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,479,937,621]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Without rotation, the enrichment in elements with $Z > 40$ cannot be reproduced. Rotation provides elements from the second $s$ -process peak but lacks Nd and Eu. Jet-induced nucleosynthesis boosts the production of the elements beyond the first and second $s$ -process peaks (cf. Sect. 4.3) and, therefore, can provide the required Nd and Eu (rot+jet_B model). However, if the ejecta is fully mixed (rot+jet_A model), Nd and Eu are underproduced. This is because in this case the material processed by the jet is diluted with a large amount of unprocessed (or slightly processed) material, which blurs the nucleosynthesis signature of the jet. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,621,937,674]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The rot+jet_B model requires that the fastest ejecta in a given angle range reaches a nearby halo hosting the future CS29528-028 star. The requirements of this scenario are stringent, meaning that it may be a rare event. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,705,623,719]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6. Discussion ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[504,726,759,741]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6.1. The efficiency of the $n$ -process ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[502,747,937,931]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"First, the strength of the $n$ -process very much depends on the amount of ${}^{22}\\mathrm{Ne}$ in the helium-shell at the pre-SN stage. In a non-rotating model, this amount is directly linked to the initial amount of CNO elements: During the main-sequence, the CNO cycle transforms most of the initial CNO into ${}^{14}\\mathrm{N}$ and the ${}^{14}\\mathrm{N}$ is converted into ${}^{22}\\mathrm{Ne}$ during helium burning by the chain ${}^{14}\\mathrm{N}(\\alpha,\\gamma)^{18}\\mathrm{F}(\\beta^{+})^{18}\\mathrm{O}(\\alpha,\\gamma)^{22}\\mathrm{Ne}$ . Therefore, higher metallicity stars, which contain more CNO at birth, are more likely to experience a more efficient $n$ -process. At solar metallicity, the initial sum of CNO elements in a mass fraction is about $10^{-2}$ , which leads to a ${}^{22}\\mathrm{Ne}$ mass fraction at the pre-SN stage of about $10^{-2}$ at maximum. This is similar to the case discussed here (Fig. 1), meaning that an energetic explosion at solar metallicity should also lead to an efficient $n$ -process. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[423,65,574,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A&A 639,A126 (2020) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[58,941,171,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A126, page 6 of 8 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[80,98,467,464]","code_body":null,"code_caption":null,"image_caption":"[\"Fig. 12. Location of the mass particles at $t = 5 \\\\times 10^{5}$ s. The coloured particles represent the particles originally in the helium shell. The colourmap shows the initial angles of these particles. The two dashed lines show $\\\\theta = 7$ and $17^{\\\\circ}$ . Iso-velocity contours are shown for particles that have the highest velocities $(v_{\\\\mathrm{fin}} > 0.04c)$ . Lighter contours correspond to higher velocities. \"]","image_footnote":"[]","img_path":"images/0771/1eea3ce9c2acc2cb0464bd865d9d7d85c348f16d46550a16de15a95a41bf7726.jpg","list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[55,565,489,669]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Rotation-induced mixing syntheses additional primary $^{22}\\mathrm{Ne}$ during the core-helium burning phase (cf. Sect. 4.1). Some of it is burnt during the evolution, thus boosting the $s$ -process, and some of it is left at the pre-SN stage. If the leftover $^{22}\\mathrm{Ne}$ is burnt during the explosion, that boosts the $n$ -process. Rotation can therefore provide a significant amount of $^{22}\\mathrm{Ne}$ at the pre-SN stage, even at low metallicity, and thus leads to a boosted $n$ -process at low metallicity. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,670,492,760]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Nevertheless, the $n$ -process scales with the abundances of existing heavy seeds (e.g. Fe, Sr, Ba) in the helium shell at the pre-SN stage. This process merely redistributes the abundances of heavy elements in the helium shell. If the abundances of the heavy seed are very small in the shell at the pre-SN stage, the $n$ -process continues to operate but the absolute abundances of heavy elements stay very small. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,760,490,851]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Finally, the strength of the $n$ -process is highly dependent on the peak temperature reached in the helium-shell during the explosion. It the peak temperature is too low, the ${}^{22}\\mathrm{Ne}(\\alpha ,n)$ reaction is not efficiently activated and the $n$ -process stays weak, regardless of the pre-SN ${}^{22}\\mathrm{Ne}$ abundance. For a given energy, an aspherical explosion allows for a higher peak temperature to be reached in the helium shell (cf. Sect. 4.4). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,851,490,932]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"For instance, Rauscher et al. (2002) reported that for non-rotating solar metallicity $\\sim 20M_{\\odot}$ stars exploding as spherical type II SNe with $10^{51} \\lesssim E \\lesssim 2 \\times 10^{51}$ erg, the $n$ -process only slightly redistributes the heavy elements at the bottom of the helium shell (cf. their section 5.4). These models contain $^{22}\\mathrm{Ne}$ , but it is likely not significantly burnt during the explosion. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,93,717,108]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6.2. The $n$ - and the $i$ -process ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[502,114,939,311]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the nuclear chart, the boosted $n$ -process that is studied here populates a region midway between the $s$ -process and $r$ -process regions (Fig. 8). However, this process differs from the $i$ -process. The latter is associated with hydrogen ingestion in a convective helium burning region, which triggers the chain ${}^{12}\\mathrm{C}(p,\\gamma)^{13}\\mathrm{N}(\\beta^{+})^{13}\\mathrm{C}(\\alpha ,n)$ and leads to neutron densities in between the $s-$ and $r$ -process (typically $n_{n}\\sim 10^{13}\\mathrm{cm}^{-3}-$ $10^{15}\\mathrm{cm}^{-3}$ , Cowan & Rose 1977; Malaney 1986; Dardelet et al. 2014; Clarkson et al. 2018; Denissenkov et al. 2019; Hampel et al. 2019). Typical neutron exposures are $1\\lesssim \\tau \\lesssim 20\\mathrm{mbarn}^{-1}$ and the timescale involved is $\\gtrsim 1$ day. By contrast, in the case of the $n$ -process, the neutrons are mainly provided by the ${}^{22}\\mathrm{Ne}(\\alpha ,n)$ reaction; the timescale is shorter ( $\\sim 1$ s) because of the explosive nature of the event. Also, the neutron density is higher and the neutron exposure is similar or lower (Fig. 7). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,330,828,344]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6.3. On the production of Pb in massive stars ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[502,350,939,414]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The abundance of $\\mathrm{Pb}$ is challenging to determine in metal-poor stars because it generally relies on a single line, which may be blended by a CH line. Although $\\mathrm{Pb}$ is not detected in CS29528-028, some CEMP- $r/s$ stars have a high $\\mathrm{Pb}$ abundance (e.g. Placco et al. 2013). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,416,937,651]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We recall that any Pb that is synthesised during the massive star evolution in the helium shell should not be affected by the passage of the jet (cf. Sect. 4.3). Thus, if any Pb is synthesised in massive stars, it should occur during stellar evolution. The rotating massive stellar models of Limongi & Chieffi (2018) and Banerjee et al. (2019) produce a significant amount of Pb during their lives, while only small or modest amounts are synthesised in similar models from Frischknecht et al. (2012, 2016), Choplin et al. (2018), Choplin & Hirschchi (2020), and from this work (cf. Fig 2). Among the important parameters impacting the production of Pb is the treatment of rotation in the stellar interior, which varies from code to code. An efficient internal rotational mixing during stellar evolution favours the production of Pb: It provides more $^{22}\\mathrm{Ne}$ and $^{13}\\mathrm{C}$ (cf. Sect. 2) and thus increases the neutron source ( $^{13}\\mathrm{C},$ $^{22}\\mathrm{Ne}$ ) over seed (e.g. $^{56}\\mathrm{Fe}$ ) ratio, thus boosting the production of heavier $s$ -elements, such as Pb. Unfortunately, the physics of rotation still suffers from important uncertainties and therefore a firm answer cannot be given now. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,674,752,688]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"7. Summary and conclusions ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[502,695,937,903]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We inspected the combined effect of fast rotation and jet-like explosion on the helium shell nucleosynthesis of a low metallicity $40M_{\\odot}$ star. As has already been found, rotation boosts the $s$ -process during the evolution and leaves a high amount of unprocessed ${}^{22}\\mathrm{Ne}$ in the helium shell at the pre-supernova stage. An energetic jet-like explosion heats the helium shell up to $\\sim 1.5\\mathrm{GK}$ . It efficiently activates $(\\alpha ,n)$ reactions (especially ${}^{22}\\mathrm{Ne}(\\alpha ,n)$ ) and leads to neutron densities of $10^{19} - 10^{20}\\mathrm{cm}^{-3}$ for $\\sim 0.1$ s. This neutron burst shifts the $s$ -process pattern towards heavier elements. In particular, the production of Mo, Ru, and Rh (right after the first $s$ -process peak) and Nd, Sm, Eu, and Gb (right after the second $s$ -process peaks) is significantly boosted. A spherical explosion, with the energy equally distributed to all angles, does not heat the helium shell sufficiently enough to produce these types of high neutron densities unless the explosion energies is extremely high, about $10^{53}$ erg. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[502,904,937,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Overall we have shown that the helium shell of a rotating massive star experiences two successive efficient neutron ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[270,65,724,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A. Choplin et al.: A strong neutron burst in jet-like supernovae of spinstars ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[826,941,937,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A126, page 7 of 8 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[55,93,490,198]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"capture processes: an efficient $s$ -process during the evolution and an efficient $n$ -process during a jet-like explosion. It gives a material whose chemical composition is midway between the $s$ - and $r$ -process. Such a scenario may explain the metal-poor stars showing these types of intermediate abundance patterns. In particular, the abundances of the CEMP- $r/s$ star CS29528-028 are compatible with the yields of our jet model, provided a non-homogeneous mixing of the ejecta. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,199,490,288]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"We also note that the $r$ -process may occur in the jet or accretion disc of jet-like explosions (e.g. Winteler et al. 2012; Nishimura et al. 2015; Siegel et al. 2019). Depending on the degree of mixing between the jet, disc, and stellar mantle material, combinations of $s-$ , $n-$ , and $r$ -process patterns may result and produce a variety of chemical signatures in the interstellar medium. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[55,313,490,357]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Acknowledgements. The authors thank an anonymous referee for constructive comments that improved the manuscript. A.C. acknowledges funding from the Swiss National Science Foundation under grant P2GEP2_184492. B.S.M. acknowledges funding from NASA Grant NNX17AE32G. 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J., & Glebbeek, E. 2008, MNRAS, 389, 1828 \",\"Suess,H.E.,& Urey,H.C.1956,Rev.Mod.Phys.,28,53\",\"Takahashi, K., Umeda, H., & Yoshida, T. 2014, ApJ, 794, 40 \",\"Thielemann, F.-K., Arnould, M., & Hillebrandt, W. 1979, A&A, 74, 175 \",\"Thielemann, F.-K., Eichler, M., Panov, I. V., & Wehmeyer, B. 2017, Ann. Rev. Nucl. Part. Sci., 67, 253 \",\"Tominaga,N.2009,ApJ,690,526 \",\"Tominaga,N.,Iwamoto,N.,&Nomoto,K.2014,ApJ,785,98 \",\"Tominaga,N.,Umeda,H.,& Nomoto,K.2007a,ApJ,660,516 \",\"Tominaga, N., Maeda, K., Umeda, H., et al. 2007b, ApJ, 657, L77 \",\"Truran, J. W., Cowan, J. J., & Cameron, A. G. W. 1978, ApJ, 222, L63 \",\"Umeda,H.,&Nomoto,K.2003,Nature,422,871 \",\"Wanajo, S., Sekiguchi, Y., Nishimura, N., et al. 2014, ApJ, 789, L39 \",\"Winteler, C., Kappeli, R., Perego, A., et al. 2012, ApJ, 750, L22 \",\"Woosley, S. E. 1993, ApJ, 405, 273 \",\"Woosley, S. E., & Heger, A. 2006, ApJ, 637, 914 \",\"Yong, D., Norris, J. E., Bessell, M. S., et al. 2013, ApJ, 762, 26 \",\"Yoon, J., Beers, T. C., Placco, V. M., et al. 2016, ApJ, 833, 20 \"]","page_idx":"7","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[423,65,574,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A&A 639,A126 (2020) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[57,941,171,954]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"7","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A126, page 8 of 8 ","text_format":null,"text_level":null,"type":"footer"}],"string":"[\n {\n \"bbox\": \"[122,156,875,181]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A strong neutron burst in jet-like supernovae of spinstars \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[253,187,742,206]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Arthur Choplin $^{1,2}$ , Nozomu Tominaga $^{1,3}$ , and Bradley S. Meyer $^{4}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,222,900,294]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"$^{1}$ Department of Physics, Faculty of Science and Engineering, Konan University, 8-9-1 Okamoto, Kobe, Hyogo 658-8501, Japan e-mail: arthur.choplin@konan-u.ac.jp \\\",\\\"2 Geneva Observatory, University of Geneva, Maillettes 51, 1290 Sauverny, Switzerland \\\",\\\"3 Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan \\\",\\\"$^{4}$ Department of Physics and Astronomy, Clemson University, Clemson, SC 29634-0978, USA \\\"]\",\n \"page_idx\": \"0\",\n \"sub_type\": \"text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[94,303,405,316]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received 16 March 2020 / Accepted 28 May 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[455,326,541,338]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABSTRACT \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,350,900,374]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Context. Some metal-poor stars have abundance patterns, which are midway between the slow $(s)$ and rapid $(r)$ neutron capture processes. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,374,900,409]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Aims. We show that the helium shell of a fast rotating massive star experiencing a jet-like explosion undergoes two efficient neutron capture processes: one during stellar evolution and one during the explosion. It eventually provides a material whose chemical composition is midway between the $s$ - and $r$ -process. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,409,900,458]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Methods. A low metallicity $40M_{\\\\odot}$ model with an initial rotational velocity of $\\\\sim 700\\\\mathrm{km~s^{-1}}$ was computed from birth to pre-supernova with an extended nuclear network following the slow neutron capture process. A two-dimensional hydrodynamic relativistic code was used to model a $E = 10^{52}$ erg relativistic jet-like explosion hitting the stellar mantle. The jet-induced nucleosynthesis was calculated in post-processing with an optimised network of 1812 nuclei. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,457,900,539]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Results. During the star's life, heavy elements from $30 \\\\lesssim Z \\\\lesssim 82$ are produced thanks to an efficient $s$ -process, which is boosted by rotation. At the end of evolution, the helium shell is largely enriched in trans-iron elements and in (unburnt) ${}^{22}\\\\mathrm{Ne}$ , whose abundance is $\\\\sim 20$ times higher than in a non-rotating model. During the explosion, the jet heats the helium shell up to $\\\\sim 1.5\\\\mathrm{GK}$ . It efficiently activates $(\\\\alpha, n)$ reactions, such as ${}^{22}\\\\mathrm{Ne}(\\\\alpha, n)$ , and leads to a strong $n$ -process with neutron densities of $\\\\sim 10^{19} - 10^{20}\\\\mathrm{cm}^{-3}$ during $0.1\\\\mathrm{s}$ . This has the effect of shifting the $s$ -process pattern, which was built during stellar evolution, towards heavier elements (e.g. Eu). The resulting chemical pattern is consistent with the abundances of the carbon-enhanced metal-poor $r/s$ star CS29528-028, provided the ejecta of the jet model is not homogeneously mixed. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,539,900,576]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Conclusions. The helium burning zones of rotating massive stars experience an efficient $s$ -process during the evolution followed by an efficient $n$ -process during a jet-like explosion. This is a new astrophysical site which can explain at least some of the metal-poor stars showing abundance patterns midway between the $s$ - and $r$ -process. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,582,836,595]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Key words. stars: massive - stars: rotation - stars: jets - stars: interiors - nuclear reactions, nucleosynthesis, abundances \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,614,184,627]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,640,490,835]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Understanding the origin of the elements is among the very topical challenges of modern astrophysics (e.g. the reviews of Meyer 1994; Arnould et al. 2007; Thielemann et al. 2017; Cowan et al. 2019; Arnould & Goriely 2020). The solar abundances first revealed the existence of a slow $(s)$ and a rapid $(r)$ neutron capture process (Suess & Urey 1956; Burbidge et al. 1957). The $s$ -process operates during the life of asymptotic giant branch (AGB, main $s$ -process, e.g. Busso et al. 1999; Herwig 2005; Lugaro et al. 2012; Karakas & Lattanzio 2014) and massive stars (weak $s$ -process, e.g. Langer et al. 1989; Prantzos et al. 1990; Kappeler et al. 2011). Promising sites for the $r$ -process include neutron star mergers (e.g. Wanajo et al. 2014; Thielemann et al. 2017) as well as magneto-rotational supernovae and collapsars from massive stars (e.g. Winteler et al. 2012; Nishimura et al. 2015; Halevi & Mosta 2018; Siegel et al. 2019). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,835,492,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Besides the Sun, metal-poor (MP) stars (e.g. the review of Beers & Christlieb 2005; Frebel & Norris 2015) are prime targets to investigate the origin of elements since they likely formed from a material that was enriched by just one or a few previous sources. Thus their abundances only reflect one or a few previous nucleosynthetic events. A zoo of MP stars was progressively constituted based on the chemical composition of these objects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,614,939,835]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Numerous MP stars have supersolar $\\\\mathrm{[C / Fe]}$ ratios and are called carbon-enhanced metal-poor (CEMP) stars. At $[\\\\mathrm{Fe / H}]\\\\lesssim -3$ , most MP stars are CEMP stars and generally do not show clear enhancements in heavy elements (CEMP-no stars, e.g. Yong et al. 2013; Norris et al. 2013; Bonifacio et al. 2015; Yoon et al. 2016). In addition to carbon, most CEMP-no stars have supersolar $\\\\mathrm{[N / Fe]}$ , $\\\\mathrm{[O / Fe]}$ , $\\\\mathrm{[Na / Fe]}$ , $\\\\mathrm{[Mg / Fe]}$ , and $\\\\mathrm{[Al / Fe]}$ ratios. The most discussed scenarios to explain these nearly pristine objects that are enriched in light elements rely on massive stellar models experiencing significant mixing at the time of the supernova and possibly strong fallback (e.g. Umeda & Nomoto 2003; Limongi et al. 2003; Nomoto et al. 2003; Iwamoto et al. 2005; Heger & Woosley 2010; Tominaga et al. 2007b, 2014; Ishigaki et al. 2018) and models experiencing mid to fast rotation during their lives (e.g. Meynet et al. 2006, 2010; Hirschi 2007; Joggerst et al. 2010; Maeder et al. 2015; Takahashi et al. 2014; Choplin et al. 2017a, 2019). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,835,939,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"At $[\\\\mathrm{Fe / H}]\\\\gtrsim -3$ , many CEMP stars with clear enhancement of heavy elements were found. This includes CEMP stars with clear $s$ -process signatures (CEMP- $s$ stars, e.g. Burris et al. 2000; Simmerer et al. 2004; Sivarani et al. 2004; Placco et al. 2013) and $r$ -process signatures (CEMP- $r$ stars, e.g. Sneden et al. 2003; Ji et al. 2016; Hansen et al. 2018; Sakari et al. 2018). The origin of the CEMP- $r$ stars is tightly linked to the $r$ -process site (cf. first \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,67,371,105]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A&A 639, A126 (2020) \\nhttps://doi.org/10.1051/0004-6361/202037966 \\n© ESO 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[754,71,937,118]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Astronomy & Astrophysics \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[389,941,606,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Article published by EDP Sciences \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[826,941,939,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A126, page 1 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[55,93,492,445]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"paragraph). Most of the CEMP- $s$ stars are found in binary systems (Hansen et al. 2016) and are thought to have acquired their $s$ -processed material, from a now extinct AGB companion, during a (wind) mass transfer episode (e.g. Stancliffe & Glebbeek 2008; Bisterzo et al. 2010; Masseron et al. 2010; Lugaro et al. 2012; Hollek et al. 2015; Abate et al. 2015). An efficient $s$ -process is also expected in rotating massive stars (cf. Sect. 2) and therefore these objects could explain at least a part of the CEMP- $s$ sample (Choplin et al. 2017b; Banerjee et al. 2019). In addition to CEMP- $s$ and CEMP- $r$ stars, one also finds $r + s$ CEMP stars, which are likely made of a combination of $s$ - and $r$ -process patterns (Gull et al. 2018), and CEMP- $r/s$ stars (also named CEMP- $i$ stars, e.g. Roederer et al. 2016). This last class shows intermediate abundance patterns for which neither an $s$ -process nor an $r$ -process pattern, and likely nor a combination of both, can reasonably reproduce the abundances (Jonsell et al. 2006; Lugaro et al. 2012; Bisterzo et al. 2012; Abate et al. 2016). An intermediate neutron capture process, that is, an $i$ -process operating at neutron densities in between the $s$ - and $r$ -process (first named by Cowan & Rose 1977), may be a solution to explain these stars<sup>1</sup> (Dardelet et al. 2014; Roederer et al. 2016; Hampel et al. 2016, 2019). The $i$ -process may operate in AGB or super-AGB stars (Herwig et al. 2011; Jones et al. 2017) in rapidly accreting white dwarfs (Denissenkov et al. 2017, 2019) or in the helium shell of very low (or zero) metallicity massive stars experiencing proton ingestion events during late evolutionary stages (Banerjee et al. 2018; Clarkson et al. 2018). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,445,490,563]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In addition to the $s$ -, $r$ -, and $i$ -processes, one finds the $n$ -process. It consists in a short neutron burst in the helium shell of massive stars when the supernova shock wave passes through it (Blake & Schramm 1976; Truran et al. 1978; Thielemann et al. 1979; Blake et al. 1981; Hillebrandt et al. 1981; Rauscher et al. 2002; Meyer et al. 2004). Most of the neutron are provided by the ${}^{22}\\\\mathrm{Ne}(\\\\alpha,\\\\mathrm{n})$ reaction. It has been shown that the $n$ -process could explain some anomalous isotopic signatures in meteorites (Meyer et al. 2000; Pignatari et al. 2015, 2018). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,564,492,708]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Here, we propose a new scenario providing abundance patterns midway between the $s$ - and $r$ -process and which can possibly explain the metal-poor stars having these types of intermediate abundance patterns. This scenario relies on two successive neutron capture processes in the same source: an efficient $s$ -process followed by a strong $n$ -process. The basic working of it is explained in Sect. 2. The codes used and methods are presented in Sect. 3, the results and comparisons with the metal-poor star C29528-028 are presented in Sects. 4 and 5, respectively, followed by discussions in Sect. 6. A summary and the main conclusions are given in Sect. 7. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,727,485,759]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. The helium shell of a rotating massive star hit by a jet \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,764,492,896]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This section describes the basic working of the scenario discussed throughout this paper. By progressively transporting chemical elements from a burning region to another rotational mixing impacts the nucleosynthesis during stellar evolution (e.g. Meynet & Maeder 2000; Heger et al. 2000; Brott et al. 2011; Chieffi & Limongi 2013; Choplin et al. 2016). Especially, rotation has been found to increase the production of $^{13}\\\\mathrm{C}$ and $^{22}\\\\mathrm{Ne}$ , which release neutrons by $(\\\\alpha, n)$ reactions. It boosts the efficiency of the $s$ -process in massive stars, mainly during the core helium burning stage (Pignatari et al. 2008; Frischknecht \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,93,937,120]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"et al. 2012, 2016; Limongi & Chieffi 2018; Choplin et al. 2018; Banerjee et al. 2019, see also Sect. 4.1). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,120,937,288]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As mentioned in Sect. 1, at the time of the supernova, the shock wave passing through the helium shell can trigger the $n$ -process. Its efficiency very much depends on the pre-supernova amount of ${}^{22}\\\\mathrm{Ne}$ and the ability of the explosion to burn it during the shock passage. In case of a rotating progenitor, the $n$ -process can be particularly efficient. On the one hand, rotation produces more ${}^{22}\\\\mathrm{Ne}$ during the evolution and allows for a higher amount of unburnt ${}^{22}\\\\mathrm{Ne}$ in the helium shell at the pre-supernova stage. On the other hand, rotation may trigger energetic jet-like explosions (e.g. Woosley 1993; MacFadyen & Woosley 1999; Woosley & Heger 2006), thus leading to high temperatures in the helium shell and therefore an efficient activation of the ${}^{22}\\\\mathrm{Ne}(\\\\alpha, n)$ reaction. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,288,939,341]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The combined effect of fast rotation and jet-like explosion can induce an efficient $s$ -process during evolution and an efficient $n$ -process during explosion. In this paper we examine the combination of these two effects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,359,601,373]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. Methods \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,380,937,524]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We modelled the evolution and explosion of a $40M_{\\\\odot}$ star by combining a one-dimensional stellar evolution code with a two-dimensional explosion code. The Geneva stellar evolution code (Eggenberger et al. 2008) was used to compute a pre-supernova $40M_{\\\\odot}$ model at a metallicity of $Z = 10^{-3}$ with an initial rotation rate on the zero-age main sequence of $\\\\upsilon_{\\\\mathrm{ini}} / \\\\upsilon_{\\\\mathrm{crit}} = 0.8^2$ . This corresponds to an initial equatorial velocity of $704\\\\mathrm{km s^{-1}}$ . The nuclear network was coupled to the evolution and used throughout the entire process. It comprises 737 isotopes from hydrogen to polonium. We refer to Choplin & Hirschi (2020) for more details on the initial set up of the model. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,524,939,760]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The jet-like explosion was modelled with a two-dimensional relativistic hydrodynamical code (Tominaga et al. 2007a; Tominaga 2009). At $t = 0$ , a jet was launched at the mass coordinate $1.93M_{\\\\odot}$ , lasting for 10 seconds with a constant energy deposition rate of $10^{51}\\\\mathrm{erg s^{-1}}$ . The total energy deposited is then $10^{52}\\\\mathrm{erg}$ which corresponds to the typical energy of a hypernova (e.g. Nomoto et al. 2004, 2006). The opening angle is 5 degrees and the Lorentz factor is $\\\\Gamma = 100$ . The hydrodynamics is followed for $5\\\\times 10^{5}\\\\mathrm{s}$ . The thermodynamic histories are recorded by $2.5\\\\times 10^{4}$ mass particles representing Lagrangian mass elements of the stellar mantle. The initial grid is linear with a resolution of 100 along the $\\\\theta$ -direction and logarithmic with a resolution of 250 in the $r$ -direction. The nucleosynthesis of mass particles initially located in the helium shell was calculated in post-processing with a neutron-rich nuclear network of 1812 isotopes. Nucleosynthesis tests with different network sizes were carried out in order to reduce the network size as much as possible without missing isotopes. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,776,591,789]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. Results \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,797,937,865]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"During its life, this rotating $40M_{\\\\odot}$ model loses $16M_{\\\\odot}$ through stellar winds: $8\\\\%$ of the mass is lost during the main sequence, $82\\\\%$ during core helium burning, and $10\\\\%$ after core helium burning. The final mass of the model is then $M_{\\\\mathrm{fin}} = 24M_{\\\\odot}$ with a hydrogen envelope that is mainly composed of helium \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[423,65,574,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A&A 639,A126 (2020) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[502,872,937,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 The initial equatorial velocity is $\\\\upsilon_{\\\\mathrm{ini}}$ and $\\\\upsilon_{\\\\mathrm{crit}}$ is the initial equatorial velocity at which the gravitational acceleration is balanced by the centrifugal force. It is defined as $\\\\upsilon_{\\\\mathrm{crit}} = \\\\sqrt{\\\\frac{2GM}{3R_{\\\\mathrm{pb}}}}$ , where $R_{\\\\mathrm{pb}}$ is the polar radius at the break-up velocity (see Maeder & Meynet 2000). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[57,904,492,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"<sup>1</sup> Such a process has also been proposed to explain the isotopic signature of presolar grains (Jadhav et al. 2013; Liu et al. 2014). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[57,940,171,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A126, page 2 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[72,97,475,311]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 1. Pre-supernova abundance profile of the rotating $40M_{\\\\\\\\odot}$ progenitor model. The outer layers are shown. The shaded areas show the convective zones. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0985/cfaa0eb3f8daf78e98f664f80adeaeb0852240d77ac4a55180eb65f55e686044.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[55,376,490,468]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"(71% in mass). The final surface hydrogen mass fraction is 0.3 (Fig. 1) and the total hydrogen mass left in the star is $1.4M_{\\\\odot}$ . For comparison purposes, the same model without rotation loses $6.42M_{\\\\odot}$ , has a final hydrogen envelope of $18.29M_{\\\\odot}$ (composed of $\\\\sim 45\\\\%$ hydrogen and $\\\\sim 55\\\\%$ helium), has a final surface hydrogen mass fraction of 0.73, and the total hydrogen mass that is left in the star is $8.2M_{\\\\odot}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,483,428,510]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.1. Rotation-induced nucleosynthesis during stellar evolution \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,517,490,714]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We recall below how rotation boosts the $s$ -process during the evolution of massive stars (cf. discussions in Pignatari et al. 2008; Frischknecht et al. 2016; Limongi & Chieffi 2018; Choplin et al. 2018; Banerjee et al. 2019). During the core helium burning phase, ${}^{12}\\\\mathrm{C}$ and ${}^{16}\\\\mathrm{O}$ are transported by rotation-induced mixing from the helium core to the hydrogen shell, which boosts the CNO cycle in the hydrogen shell and synthesises primary ${}^{13}\\\\mathrm{C}$ and ${}^{14}\\\\mathrm{N}$ . Due to the growth of the convective helium core combined with the backward diffusion of hydrogen burning products, the extra ${}^{13}\\\\mathrm{C}$ and ${}^{14}\\\\mathrm{N}$ are engulfed in the helium core The ${}^{14}\\\\mathrm{N}$ is quickly transformed into ${}^{22}\\\\mathrm{Ne}$ through ${}^{14}\\\\mathrm{N}(\\\\alpha ,\\\\gamma)^{18}\\\\mathrm{F}(\\\\beta^{+})^{18}\\\\mathrm{O}(\\\\alpha ,\\\\gamma)^{22}\\\\mathrm{Ne}$ . Neutrons, which are mainly released by ${}^{13}\\\\mathrm{C}(\\\\alpha ,n)$ and ${}^{22}\\\\mathrm{Ne}(\\\\alpha ,n)$ , trigger the $s$ -process provided any heavy seed (e.g. ${}^{56}\\\\mathrm{Fe}$ ) is present in the helium burning core. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,713,490,806]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the present model, this effect boosts the $s$ -process by a factor of $\\\\sim 10 - 1000$ for elements with $35 < Z < 82$ (Fig. 2). The same model without rotation only experiences a modest enhancement of elements with $Z < 45$ (Fig. 2, black line). At the pre-supernova stage, the mass fraction of $^{22}\\\\mathrm{Ne}$ that is left (unburnt) in the helium shell is $2.2 \\\\times 10^{-2}$ (Fig. 1), which is $\\\\sim 20$ times higher than for the same model but without rotation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,820,406,834]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.2. Jet-induced nucleosynthesis: Light elements \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,841,490,895]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The jet penetrates into the helium shell after $2\\\\mathrm{s}$ . The mass particles located at the bottom of the helium shell have pre-jet temperatures of $0.3 - 0.4\\\\mathrm{GK}$ . Those with $\\\\theta_{\\\\mathrm{ini}} \\\\leq 10^{\\\\circ}$ reach $1 < T < 1.5\\\\mathrm{GK}$ during the passage of the jet (Fig. 3). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[517,96,924,311]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 2. Integrated mass fractions of the material above the bottom of the helium shell (after beta decays) at the pre-supernova stage. The red (black) solid line shows a low metallicity $40M_{\\\\\\\\odot}$ model computed with (without) rotation. The black dashed line shows the initial chemical composition of the models. The vertical dotted lines show the location of Sr, Ba, and Pb. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0139/85910a95400dd22877d30f3461cc5d5ac9f54d3f28457ddc440d4425f6da30ce.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[502,417,939,601]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Close to the jet axis, the high temperature activates $^{22}\\\\mathrm{Ne}(\\\\alpha ,n)$ , but also $^{13}\\\\mathrm{C}(\\\\alpha ,n)$ and $^{17}\\\\mathrm{O}(\\\\alpha ,n)$ , the isotopes $^{13}\\\\mathrm{C}$ and $^{17}\\\\mathrm{O}$ being produced by $^{12}\\\\mathrm{C}(n,\\\\gamma)$ and $^{16}\\\\mathrm{O}(n,\\\\gamma)$ (Fig. 4). Even closer to the jet axis and deeper in the helium shell, the higher temperature efficiently produces $^{24}\\\\mathrm{Mg}$ , $^{28}\\\\mathrm{Si}$ , and $^{32}\\\\mathrm{S}$ (Fig. 5) through $(\\\\alpha ,\\\\gamma)$ reactions. Some $(\\\\alpha ,p)$ reactions, such as $^{24}\\\\mathrm{Mg}(\\\\alpha ,p)^{27}\\\\mathrm{Al}$ and $^{27}\\\\mathrm{Mg}(\\\\alpha ,p)^{30}\\\\mathrm{Si}$ , also become strong and, therefore, they release protons, which activate some $(p,\\\\gamma)$ reactions. For instance, $^{31}\\\\mathrm{P}$ is enhanced (Fig. 5) through $^{30}\\\\mathrm{Si}(p,\\\\gamma)^{31}\\\\mathrm{P}$ . The high $^{35}\\\\mathrm{Cl}$ abundance comes from the chain $^{24}\\\\mathrm{Mg}(\\\\alpha ,p)^{27}\\\\mathrm{Al}(\\\\alpha ,p)^{30}\\\\mathrm{Si}(\\\\alpha ,\\\\gamma)^{34}\\\\mathrm{S}(p,\\\\gamma)^{35}\\\\mathrm{Cl}$ . The high $^{36}\\\\mathrm{Ar}$ and $^{39}\\\\mathrm{K}$ mainly come from $^{34}\\\\mathrm{S}(p,\\\\gamma)^{35}\\\\mathrm{Cl}(p,\\\\gamma)^{36}\\\\mathrm{Ar}$ and $^{34}\\\\mathrm{S}(\\\\alpha ,\\\\gamma)^{38}\\\\mathrm{Ar}(p,\\\\gamma)^{39}\\\\mathrm{K}$ , respectively. Some Ti is also formed thanks to $^{44}\\\\mathrm{Ca}(p,\\\\gamma)^{45}\\\\mathrm{Sc}(p,\\\\gamma)^{46}\\\\mathrm{Ti}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,615,865,630]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.3. Jet-induced nucleosynthesis: Heavy elements \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,637,937,871]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"During the jet explosion, the $(\\\\alpha ,n)$ reactions lead to a burst of neutrons. For mass particles that are initially along the jet axis $(\\\\theta_{\\\\mathrm{ini}}\\\\lesssim 5^{\\\\circ})$ and with initial mass coordinates of $M_{\\\\mathrm{r,in i}}\\\\sim$ $15.5 - 18M_{\\\\odot}$ , the neutron density reaches $n_{\\\\mathrm{n}} > 10^{19}\\\\mathrm{cm}^{-3}$ during $\\\\sim 0.1\\\\mathrm{s}$ (Fig. 7, left panel). The neutron exposure4 of these mass particles goes up to $1.35\\\\mathrm{mbarn^{-1}}$ (Fig. 7). Despite $n_{\\\\mathrm{n}}$ values being close to $r$ -process values, the abundant light elements in the helium shell (especially $^{12}\\\\mathrm{C}$ and $^{16}\\\\mathrm{O}$ ) act as strong neutron poisons. This reduces the amount of available neutron for heavy seeds and does not lead to $r$ -process nucleosynthesis. Nevertheless, during the burst, isotopes that are far from the valley of stability are produced (Fig. 8, bottom panel). The pre-jet abundance pattern is therefore shifted towards higher mass numbers compared to the initial pattern (Fig. 9). In particular, the first $(A\\\\sim 80 - 90)$ and second $(A\\\\sim 130 - 140)$ s-process peaks that were built during stellar evolution are shifted to higher atomic masses (see also Fig. 6). Details on the nucleosynthesis are given below. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[270,65,724,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A. Choplin et al.: A strong neutron burst in jet-like supernovae of spinstars \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[55,904,489,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 Produced from the initial hydrogen and helium content of the star, but not from the initial metals. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[502,892,937,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 The neutron exposure was computed as $\\\\tau = \\\\int n_{\\\\mathrm{n}}\\\\sqrt{2k_{\\\\mathrm{B}}T / m_{\\\\mathrm{n}}}\\\\mathrm{d}t$ with $n_{\\\\mathrm{n}}$ the neutron density, $k_{\\\\mathrm{B}}$ the Boltzmann constant, $T$ the temperature, and $m_{\\\\mathrm{n}}$ the neutron mass. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[826,941,937,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A126, page 3 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,96,480,337]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0109/e4502ea7b9c9cd8ef6bdcab6c8340bf5d599ecf15bf6c4fb7eec02d70cb86176.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[517,96,917,336]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 3. Location of the mass particles after $2.8\\\\\\\\mathrm{s}$ (left panel) and $5.4\\\\\\\\mathrm{s}$ (right panel). The colour shows the temperature of the mass particles. The inner grey circle shows the central remnant. The black circle with a radius of $\\\\\\\\sim 0.7\\\\\\\\times 10^{10}\\\\\\\\mathrm{cm}$ shows the location of the bottom of the helium shell. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0337/5364749ec6329a225efe98b4ec4e4e49941984900b245d018730ef8f92c28dd7.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[72,392,478,598]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 4. Flowchart of a mass particle with $M_{\\\\\\\\mathrm{r,ini}} = 16.53M_{\\\\\\\\odot}$ (i.e. originally in the helium shell, cf. Fig. 1) and $\\\\\\\\theta_{\\\\\\\\mathrm{ini}} = 3.15^{\\\\\\\\circ}$ at its temperature peak. Mass fractions of isotopes are shown by the red colourmap. Black squares denote stable isotopes. Net reaction rates, considering forward and reverse reactions, are shown by arrows. Arrows are coloured as a function of the reaction type: yellow for $(\\\\\\\\alpha, \\\\\\\\gamma)$ , cyan for $(n, \\\\\\\\gamma)$ , green for $(\\\\\\\\alpha, n)$ , and blue for $(\\\\\\\\gamma, \\\\\\\\alpha)$ and $(n, \\\\\\\\alpha)$ . Rates below $7\\\\\\\\times 10^{22}\\\\\\\\mathrm{cm s^{-1}}$ are not shown. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0654/50ccb3ad5ed8152e83c626c866d2bcc041eb33fd2d16487a383eff6857043922.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[55,720,492,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"During the jet explosion, $^{56,57,58,60}\\\\mathrm{Fe}$ are mostly transformed into $^{60-64}\\\\mathrm{Fe}$ by neutron captures. After the explosion, $^{60-64}\\\\mathrm{Fe}$ eventually decay to the stable $^{60,61,62,64}\\\\mathrm{Ni}$ and $^{63}\\\\mathrm{Cu}$ isotopes. This has the overall effect of destroying Fe and somewhat increasing Ni and Cu (Figs. 6 and 10). The $^{59}\\\\mathrm{Co}$ isotope, which is the only stable isotope of Co, is mainly transformed into $^{62-69}\\\\mathrm{Co}$ isotopes which decay to Ni, Cu, Zn, and $^{69}\\\\mathrm{Ga}$ . The production of $^{59}\\\\mathrm{Fe}$ , $^{59}\\\\mathrm{Mn}$ , and $^{59}\\\\mathrm{Cr}$ , which will decay to $^{59}\\\\mathrm{Co}$ , is too small to replenish $^{59}\\\\mathrm{Co}$ and therefore the final Co abundance stays low (Fig. 10). The higher final Zn abundance is mainly due to the decay of $^{66,67,68}\\\\mathrm{Ni}$ to $^{66,67,68}\\\\mathrm{Zn}$ isotopes. The final Mo is also enhanced, mainly thanks to the decay of neutron-rich $\\\\mathrm{Zr}^{(96-100)\\\\mathrm{Zr}}$ isotopes to stable Mo isotopes. The final Ru is enhanced thanks to the decay of the neutron-rich $\\\\mathrm{Zr}^{(101,102,104)\\\\mathrm{Zr}}$ , Nb, and Mo isotopes to stable Ru isotopes. We note that $^{103}\\\\mathrm{Rh}$ , which is the only stable isotope of Rh, is largely \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[519,392,926,545]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 5. Effect of the jet on C-Ti elements for a mass particle with $M_{\\\\\\\\mathrm{r,ini}} = 15.78M_{\\\\\\\\odot}$ and $\\\\\\\\theta_{\\\\\\\\mathrm{ini}} = 0.45^{\\\\\\\\circ}$ . We note that $X_{\\\\\\\\mathrm{jet}}$ are the post-jet mass fractions and $X_{\\\\\\\\mathrm{nojet}}$ are the mass fractions of the same mass particle that would not have experienced a jet explosion. In both cases, elements are beta decayed. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0143/5f4be77868e8e22aea142ab895bfaeb45fac5fef900342184b3f14ecea538902.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[514,627,934,785]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 6. Same as Fig. 5, but for Fe-Ho elements and for a mass particle with $M_{\\\\\\\\mathrm{r,ini}} = 16.53M_{\\\\\\\\odot}$ and $\\\\\\\\theta_{\\\\\\\\mathrm{ini}} = 3.15^{\\\\\\\\circ}$ (same mass particle as in Fig. 4). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0515/b559dcb295d99bcd7b524de7268252ec994067b1a29f08612dc2bf082e628ed2.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[502,837,939,932]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"enhanced by the decay of $^{103}\\\\mathrm{Zr}$ , $^{103}\\\\mathrm{Nb}$ , and $^{103}\\\\mathrm{Mo}$ . It is similar for Nd, Sm, Eu, Gd, Tb, and Dy ( $Z = 60 - 66$ ) elements whose final abundances are raised (Figs. 6 and 10) because of the decays of the neutron-rich isotopes of Cs, Ba, La, Ce, and Pr ( $Z = 55 - 59$ ). The final Tm, Lu, and Ta abundances are lower because they experience efficient neutron captures until the neutron magic number 126 (Fig. 8), and they are not \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[423,65,574,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A&A 639,A126 (2020) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[58,941,171,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A126, page 4 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[87,98,467,297]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0356/c6fbef3dd3b9aa207ce157387a86e0b27ca6b7c4483b414effa39a15612d45f5.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[97,309,465,511]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 7. Maximum neutron density (top) and neutron exposure (bottom) during the jet explosion as a function of the initial mass coordinate. Coloured lines show different initial angles. Each point represents a mass particle with initial coordinates $\\\\\\\\theta_{\\\\\\\\mathrm{ini}}$ and $M_{\\\\\\\\mathrm{r,ini}}$ . The two dashed lines show the initial location of the bottom of helium and hydrogen shells. The shaded areas show the convective zone at the pre-jet stage (see also Fig. 1). \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0885/dd8297e1d384dfd4ffe85a0c8e104793e5a843c3898ac0e1213b3f02666478da.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[55,619,492,789]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"efficiently replenished by neutron-rich isotopes for elements with a lower atomic mass. For instance, most of the initial $^{169-173}\\\\mathrm{Tm}$ are transformed into $^{195}\\\\mathrm{Tm}$ , which eventually decay to $^{195}\\\\mathrm{Pt}$ , and $\\\\mathrm{Tm}$ is only slightly replenished by the decay of $^{169}\\\\mathrm{Sm}$ , $^{169}\\\\mathrm{Eu}$ , and $^{169}\\\\mathrm{Gd}$ , whose post-jet mass fractions are small (about $10^{-11}$ ). The abundance of $^{209}\\\\mathrm{Bi}$ also increases (Fig. 10) because of the decay of the unstable $^{209}\\\\mathrm{Tl}$ and $^{209}\\\\mathrm{Pb}$ isotopes, which are produced during the jet explosion. Furthermore, $\\\\mathrm{Pb}$ is not affected by the jet explosion because of a closed loop of beta and alpha decays leading back to $\\\\mathrm{Pb}$ (or possibly $^{209}\\\\mathrm{Bi}$ ). For instance, any unstable $^{210}\\\\mathrm{Pb}$ produced during the explosion experiences double beta decay to $^{210}\\\\mathrm{Po}$ , and then alpha decay to the stable $^{206}\\\\mathrm{Pb}$ isotope. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,789,492,869]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The stable isotopes, which are shielded by isotopes with the same mass and a lower atomic number, are not replenished by beta decays and are therefore completely destroyed by the jet. This is the case for $^{136}\\\\mathrm{Ba}$ or $^{148}\\\\mathrm{Sm}$ (Fig. 6) whose final mass fractions are nearly zero because they are shielded by the stable $^{136}\\\\mathrm{Xe}$ and $^{148}\\\\mathrm{Nd}$ isotopes, respectively. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,883,304,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4.4. Case of a spherical explosion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,903,490,932]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As a test, we ran two spherical explosions: one with the same total energy ( $E_{\\\\mathrm{TOT}} = 10^{52}$ erg) and one with $E_{\\\\mathrm{TOT}} = 10^{53}$ erg. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,97,934,271]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0058/8e11e6f024e6e277a4e23158f126179397eabfe59bf699adb3b35694bbbf51de.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[507,273,934,448]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 8. Pre-jet mass fractions (top panel) and post-jet mass fractions (before beta decays, bottom panel) for a mass particle at $M_{\\\\\\\\mathrm{r,inii}} = 16.53M_{\\\\\\\\odot}$ and $\\\\\\\\theta_{\\\\\\\\mathrm{ini}} = 3.15^{\\\\\\\\circ}$ (same mass particle as in Fig. 4). Black squares denote stable isotopes. The light blue line shows a typical $r$ -process flow for comparison purposes (taken from Arnould & Goriely 2020, their Fig. 5). The grey line shows the neutron drip line. Thin dotted lines show the location of the magic numbers. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0260/40274f8b541638baee974a0b4639b098160560550162ed4dfc52e8eb25308e15.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[502,561,939,799]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For the $10^{52}$ erg spherical explosion, the bottom of the helium shell is heated up to $\\\\sim 0.6$ GK. In this case, the $(\\\\alpha, n)$ reactions are weaker and the neutron density goes up to $\\\\sim 10^{15} \\\\mathrm{~cm}^{-3}$ . It leads to a much smaller neutron exposure that slightly affects the distribution of heavy elements. For a $10^{53}$ erg spherical explosion, the bottom of the helium shell is heated up to $\\\\sim 1$ GK, which leads to a maximal neutron density of about $\\\\sim 10^{19-20} \\\\mathrm{~cm}^{-3}$ , that is, similar to the jet-explosion discussed throughout this paper. In this case, the abundances of heavy elements are significantly affected in the same way as in Figs. 9 and 10. This means that $\\\\gtrsim 10$ times more energetic spherical explosions could lead to a similar nucleosynthesis as the $10^{52}$ erg jet-like explosion considered in this work. We note that a $10^{53}$ erg explosion corresponds to an extreme case which may not be realistic. Consequently, the nucleosynthetic signature of a boosted $n$ -process (as discussed throughout this paper) very likely points towards jet-like, or at least aspherical, explosions. We plan to explore the effect of various opening angles and explosion energies in a future work. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,820,907,835]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5. Signature in the metal-poor star CS29528-028 \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,841,939,895]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The chemical signature of jet-like explosions from rotating stars may be seen at the surface of observed metal-poor stars that have formed with the material ejected by previous sources. Here, we focus on CS29528-028 which has $\\\\mathrm{[Fe / H] - 2.12}$ $T_{\\\\mathrm{eff}} = 7100\\\\mathrm{K}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[270,65,724,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A. Choplin et al.: A strong neutron burst in jet-like supernovae of spinstars \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[502,904,937,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"5 The strongest explosions detected have $10^{52} < E < 10^{53}$ erg (see e.g. Fig. 2 in Nomoto et al. 2013). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_footnote\"\n },\n {\n \"bbox\": \"[826,941,937,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A126, page 5 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[67,96,480,249]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 9. Pre-jet and post-jet mass fractions for the mass particle at $M_{\\\\\\\\mathrm{r,ini}} = 16.53M_{\\\\\\\\odot}$ and $\\\\\\\\theta_{\\\\\\\\mathrm{ini}} = 3.15^{\\\\\\\\circ}$ (the same mass particle as in Figs. 1, 4, and 8). The vertical dotted lines show the location of $^{88}\\\\\\\\mathrm{Sr}$ , $^{138}\\\\\\\\mathrm{Ba}$ , and $^{208}\\\\\\\\mathrm{Pb}$ . \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0440/b88a7d8fb98afa0690863773bd7f6b8e9b52ec31a1ceb14eb911a43b05bdafe1.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[70,309,478,463]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 10. Effect of the jet on heavy elements for the mass particle at $M_{\\\\\\\\mathrm{r,ini}} = 16.53M_{\\\\\\\\odot}$ and $\\\\\\\\theta_{\\\\\\\\mathrm{ini}} = 3.15^{\\\\\\\\circ}$ (the same mass particle as in Figs. 1, 4, 8, and 9). The solid red line shows the composition after the jet explosion and after beta decays. The solid black line shows the composition if no jet explosion occurred (still after beta decays). Dashed lines show the patterns before beta decays. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0825/511444d483db14ffcbd532aaf45380416e4f083d0082902ebb9ea9ca08886501.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[55,564,490,669]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"and $\\\\log g = 4.27$ (Allen et al. 2012). It was classified as a carbon-enhanced metal-poor star with heavy abundances midway between the $s$ - and $r$ -process (CEMP- $r/s$ Beers & Christlieb 2005) because of its high $[\\\\mathrm{C / Fe}] = 2.76$ , enrichment in trans-Fe elements, and intermediate $[\\\\mathrm{Ba / Eu}] = 0.33$ (Aoki et al. 2007; Allen et al. 2012). Aoki et al. (2007) reported a $[\\\\mathrm{Na / Fe}]$ ratio of 2.68, but with a suggested NLTE correction of $-0.7$ , thus giving $[\\\\mathrm{Na / Fe}]_{\\\\mathrm{NLTE}} = 1.98$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,670,492,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We compared the abundances of CS29528-028 with four models. The first and second ones are $40M_{\\\\odot}$ non-rotating and rotating models, respectively, which did not experience jet-induced nucleosynthesis (orange and black lines in Fig. 11). The mass cut was set at a mass coordinate of $1.93M_{\\\\odot}$ (just as the jet model, cf. Sect. 3). The ejecta of the non-rotating (rotating) model was mixed with 150 $(400)M_{\\\\odot}$ of ISM material to produce the fits shown in Fig. 11. The third model (rot+jet_A, blue pattern) shows the integrated chemical composition of all ejected mass particles after the jet. For the fourth model, we searched for the best fit by considering the dependence of the yields in the final angle $\\\\theta_{\\\\mathrm{fin}}$ and final velocity $v_{\\\\mathrm{fin}}$ of the ejected material. Indeed, a neighbouring halo hosting a future star may not be enriched by the full ejecta, but only by a part of it, having a certain angle range. Also, the higher velocity material is more likely to reach and enrich a neighbouring halo. The rot+jet_B model (red pattern in Fig. 11) shows the best fit when the final angle range and the velocity threshold $v_{\\\\mathrm{th}}$ are left as free parameters; it is important to specify that only the mass particles with $v_{\\\\mathrm{fin}} > v_{\\\\mathrm{th}}$ were considered in this case. This model corresponds to \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[514,96,929,227]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0348/13cfe466b2d2fa5c9aaa4bf2a0fba76f10e2982942acb61e22c35367b7a9197d.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[512,229,929,282]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 11. Best fits (top panel) and their residuals (bottom panel) for the metal-poor star CS29528-028. The squares are the abundances from Aoki et al. (2007), and the circles are from Allen et al. (2012). Only an upper limit was derived for nitrogen. When two measurements were available for one element, the most recent one (Allen et al. 2012) was selected to calculate $\\\\\\\\chi^2$ and used to plot the residuals. The four patterns show the best fits and their $\\\\\\\\chi^2$ value for four models (cf. text for details). All models were considered after beta decay. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0669/3457e2d9bde6380891b18f536a9e5e056d47a6ba87d37f9a4411950c95de27c9.jpg\",\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[502,413,937,478]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"the integration of the mass particles with $7 < \\\\theta_{\\\\mathrm{fin}} < 17^{\\\\circ}$ and with $v_{\\\\mathrm{fin}} > 0.04\\\\mathrm{c}$ . The mass particles in this angle range are located in between the two dashed lines shown in Fig. 12. The mass particles with $v_{\\\\mathrm{fin}} > 0.04\\\\mathrm{c}$ are enclosed by the outermost contour shown in Fig. 12. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,479,937,621]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Without rotation, the enrichment in elements with $Z > 40$ cannot be reproduced. Rotation provides elements from the second $s$ -process peak but lacks Nd and Eu. Jet-induced nucleosynthesis boosts the production of the elements beyond the first and second $s$ -process peaks (cf. Sect. 4.3) and, therefore, can provide the required Nd and Eu (rot+jet_B model). However, if the ejecta is fully mixed (rot+jet_A model), Nd and Eu are underproduced. This is because in this case the material processed by the jet is diluted with a large amount of unprocessed (or slightly processed) material, which blurs the nucleosynthesis signature of the jet. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,621,937,674]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The rot+jet_B model requires that the fastest ejecta in a given angle range reaches a nearby halo hosting the future CS29528-028 star. The requirements of this scenario are stringent, meaning that it may be a rare event. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,705,623,719]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6. Discussion \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,726,759,741]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6.1. The efficiency of the $n$ -process \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,747,937,931]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"First, the strength of the $n$ -process very much depends on the amount of ${}^{22}\\\\mathrm{Ne}$ in the helium-shell at the pre-SN stage. In a non-rotating model, this amount is directly linked to the initial amount of CNO elements: During the main-sequence, the CNO cycle transforms most of the initial CNO into ${}^{14}\\\\mathrm{N}$ and the ${}^{14}\\\\mathrm{N}$ is converted into ${}^{22}\\\\mathrm{Ne}$ during helium burning by the chain ${}^{14}\\\\mathrm{N}(\\\\alpha,\\\\gamma)^{18}\\\\mathrm{F}(\\\\beta^{+})^{18}\\\\mathrm{O}(\\\\alpha,\\\\gamma)^{22}\\\\mathrm{Ne}$ . Therefore, higher metallicity stars, which contain more CNO at birth, are more likely to experience a more efficient $n$ -process. At solar metallicity, the initial sum of CNO elements in a mass fraction is about $10^{-2}$ , which leads to a ${}^{22}\\\\mathrm{Ne}$ mass fraction at the pre-SN stage of about $10^{-2}$ at maximum. This is similar to the case discussed here (Fig. 1), meaning that an energetic explosion at solar metallicity should also lead to an efficient $n$ -process. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[423,65,574,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A&A 639,A126 (2020) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[58,941,171,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A126, page 6 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[80,98,467,464]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig. 12. Location of the mass particles at $t = 5 \\\\\\\\times 10^{5}$ s. The coloured particles represent the particles originally in the helium shell. The colourmap shows the initial angles of these particles. The two dashed lines show $\\\\\\\\theta = 7$ and $17^{\\\\\\\\circ}$ . Iso-velocity contours are shown for particles that have the highest velocities $(v_{\\\\\\\\mathrm{fin}} > 0.04c)$ . Lighter contours correspond to higher velocities. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0771/1eea3ce9c2acc2cb0464bd865d9d7d85c348f16d46550a16de15a95a41bf7726.jpg\",\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[55,565,489,669]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Rotation-induced mixing syntheses additional primary $^{22}\\\\mathrm{Ne}$ during the core-helium burning phase (cf. Sect. 4.1). Some of it is burnt during the evolution, thus boosting the $s$ -process, and some of it is left at the pre-SN stage. If the leftover $^{22}\\\\mathrm{Ne}$ is burnt during the explosion, that boosts the $n$ -process. Rotation can therefore provide a significant amount of $^{22}\\\\mathrm{Ne}$ at the pre-SN stage, even at low metallicity, and thus leads to a boosted $n$ -process at low metallicity. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,670,492,760]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Nevertheless, the $n$ -process scales with the abundances of existing heavy seeds (e.g. Fe, Sr, Ba) in the helium shell at the pre-SN stage. This process merely redistributes the abundances of heavy elements in the helium shell. If the abundances of the heavy seed are very small in the shell at the pre-SN stage, the $n$ -process continues to operate but the absolute abundances of heavy elements stay very small. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,760,490,851]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Finally, the strength of the $n$ -process is highly dependent on the peak temperature reached in the helium-shell during the explosion. It the peak temperature is too low, the ${}^{22}\\\\mathrm{Ne}(\\\\alpha ,n)$ reaction is not efficiently activated and the $n$ -process stays weak, regardless of the pre-SN ${}^{22}\\\\mathrm{Ne}$ abundance. For a given energy, an aspherical explosion allows for a higher peak temperature to be reached in the helium shell (cf. Sect. 4.4). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,851,490,932]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"For instance, Rauscher et al. (2002) reported that for non-rotating solar metallicity $\\\\sim 20M_{\\\\odot}$ stars exploding as spherical type II SNe with $10^{51} \\\\lesssim E \\\\lesssim 2 \\\\times 10^{51}$ erg, the $n$ -process only slightly redistributes the heavy elements at the bottom of the helium shell (cf. their section 5.4). These models contain $^{22}\\\\mathrm{Ne}$ , but it is likely not significantly burnt during the explosion. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,93,717,108]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6.2. The $n$ - and the $i$ -process \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,114,939,311]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the nuclear chart, the boosted $n$ -process that is studied here populates a region midway between the $s$ -process and $r$ -process regions (Fig. 8). However, this process differs from the $i$ -process. The latter is associated with hydrogen ingestion in a convective helium burning region, which triggers the chain ${}^{12}\\\\mathrm{C}(p,\\\\gamma)^{13}\\\\mathrm{N}(\\\\beta^{+})^{13}\\\\mathrm{C}(\\\\alpha ,n)$ and leads to neutron densities in between the $s-$ and $r$ -process (typically $n_{n}\\\\sim 10^{13}\\\\mathrm{cm}^{-3}-$ $10^{15}\\\\mathrm{cm}^{-3}$ , Cowan & Rose 1977; Malaney 1986; Dardelet et al. 2014; Clarkson et al. 2018; Denissenkov et al. 2019; Hampel et al. 2019). Typical neutron exposures are $1\\\\lesssim \\\\tau \\\\lesssim 20\\\\mathrm{mbarn}^{-1}$ and the timescale involved is $\\\\gtrsim 1$ day. By contrast, in the case of the $n$ -process, the neutrons are mainly provided by the ${}^{22}\\\\mathrm{Ne}(\\\\alpha ,n)$ reaction; the timescale is shorter ( $\\\\sim 1$ s) because of the explosive nature of the event. Also, the neutron density is higher and the neutron exposure is similar or lower (Fig. 7). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,330,828,344]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"6.3. On the production of Pb in massive stars \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,350,939,414]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The abundance of $\\\\mathrm{Pb}$ is challenging to determine in metal-poor stars because it generally relies on a single line, which may be blended by a CH line. Although $\\\\mathrm{Pb}$ is not detected in CS29528-028, some CEMP- $r/s$ stars have a high $\\\\mathrm{Pb}$ abundance (e.g. Placco et al. 2013). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,416,937,651]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We recall that any Pb that is synthesised during the massive star evolution in the helium shell should not be affected by the passage of the jet (cf. Sect. 4.3). Thus, if any Pb is synthesised in massive stars, it should occur during stellar evolution. The rotating massive stellar models of Limongi & Chieffi (2018) and Banerjee et al. (2019) produce a significant amount of Pb during their lives, while only small or modest amounts are synthesised in similar models from Frischknecht et al. (2012, 2016), Choplin et al. (2018), Choplin & Hirschchi (2020), and from this work (cf. Fig 2). Among the important parameters impacting the production of Pb is the treatment of rotation in the stellar interior, which varies from code to code. An efficient internal rotational mixing during stellar evolution favours the production of Pb: It provides more $^{22}\\\\mathrm{Ne}$ and $^{13}\\\\mathrm{C}$ (cf. Sect. 2) and thus increases the neutron source ( $^{13}\\\\mathrm{C},$ $^{22}\\\\mathrm{Ne}$ ) over seed (e.g. $^{56}\\\\mathrm{Fe}$ ) ratio, thus boosting the production of heavier $s$ -elements, such as Pb. Unfortunately, the physics of rotation still suffers from important uncertainties and therefore a firm answer cannot be given now. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,674,752,688]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"7. Summary and conclusions \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,695,937,903]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We inspected the combined effect of fast rotation and jet-like explosion on the helium shell nucleosynthesis of a low metallicity $40M_{\\\\odot}$ star. As has already been found, rotation boosts the $s$ -process during the evolution and leaves a high amount of unprocessed ${}^{22}\\\\mathrm{Ne}$ in the helium shell at the pre-supernova stage. An energetic jet-like explosion heats the helium shell up to $\\\\sim 1.5\\\\mathrm{GK}$ . It efficiently activates $(\\\\alpha ,n)$ reactions (especially ${}^{22}\\\\mathrm{Ne}(\\\\alpha ,n)$ ) and leads to neutron densities of $10^{19} - 10^{20}\\\\mathrm{cm}^{-3}$ for $\\\\sim 0.1$ s. This neutron burst shifts the $s$ -process pattern towards heavier elements. In particular, the production of Mo, Ru, and Rh (right after the first $s$ -process peak) and Nd, Sm, Eu, and Gb (right after the second $s$ -process peaks) is significantly boosted. A spherical explosion, with the energy equally distributed to all angles, does not heat the helium shell sufficiently enough to produce these types of high neutron densities unless the explosion energies is extremely high, about $10^{53}$ erg. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[502,904,937,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Overall we have shown that the helium shell of a rotating massive star experiences two successive efficient neutron \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[270,65,724,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A. Choplin et al.: A strong neutron burst in jet-like supernovae of spinstars \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[826,941,937,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"6\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A126, page 7 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[55,93,490,198]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"capture processes: an efficient $s$ -process during the evolution and an efficient $n$ -process during a jet-like explosion. It gives a material whose chemical composition is midway between the $s$ - and $r$ -process. Such a scenario may explain the metal-poor stars showing these types of intermediate abundance patterns. In particular, the abundances of the CEMP- $r/s$ star CS29528-028 are compatible with the yields of our jet model, provided a non-homogeneous mixing of the ejecta. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,199,490,288]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"We also note that the $r$ -process may occur in the jet or accretion disc of jet-like explosions (e.g. Winteler et al. 2012; Nishimura et al. 2015; Siegel et al. 2019). Depending on the degree of mixing between the jet, disc, and stellar mantle material, combinations of $s-$ , $n-$ , and $r$ -process patterns may result and produce a variety of chemical signatures in the interstellar medium. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[55,313,490,357]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Acknowledgements. The authors thank an anonymous referee for constructive comments that improved the manuscript. A.C. acknowledges funding from the Swiss National Science Foundation under grant P2GEP2_184492. B.S.M. acknowledges funding from NASA Grant NNX17AE32G. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,382,154,397]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"References \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[57,404,490,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Abate, C., Pols, O. R., Izzard, R. G., & Karakas, A. I. 2015, A&A, 581, A22 \\\",\\\"Abate, C., Stancliffe, R. J., & Liu, Z.-W. 2016, A&A, 587, A50 \\\",\\\"Allen, D. M., Ryan, S. G., Rossi, S., Beers, T. C., & Tsangarides, S. 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M., et al. 2016, ApJ, 833, 20 \\\"]\",\n \"page_idx\": \"7\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[423,65,574,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A&A 639,A126 (2020) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[57,941,171,954]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"7\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A126, page 8 of 8 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.1051/0004-6361/202037966"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Astronomy and Space Sciences"},"sha256":{"kind":"string","value":"28b0efd48358373fe94c2433a669b5af5737cf8189ec9bd8b22bec5191eb909e"},"title":{"kind":"string","value":"A strong neutron burst in jet-like supernovae of spinstars"}}},{"rowIdx":274,"cells":{"abstract":{"kind":"string","value":"Yabani mantarlardan zehirlenme riski korkusu insanları kültüre alınabilen mantar türleri üretimini artırmaktadır. Bu mantar türleri içerisinde yer alan istiridye mantarı üretimindeki bazı avantajlar nedeniyle son yıllarda tercih edilir olmuştur. Mantar üretiminin artmasında üretim ortamlarında bölgesel çeşitliliğin sağlanması çok önemlidir. Bu çalışmada Van ve çevresine mantar üretimini yaygınlaştırmak ve bölge üreticilerinin kolay temin edebilecekleri saman ve atıl durumda olan demlenmiş çay atıklarında üretimin etkinliğini araştırmak amaçlanmıştır. Buğday samanı, demleme çay atığı ve hazır mantar üretim kitleriyle kurulan çalışma tesadüf parselleri deneme desenine göre dört tekerrürlü olarak tasarlanmıştır. Elde edilen mantarlarda, ilk hasat, karpofor ağırlığı, toplam verim, karpofor ölçüleri, makro ve mikro elementler parametrelerine bakılmıştır. Yapılan çalışmada çay ortamında üretilen mantar verilerinin, mantar üretimi yapan firmalardan alınan hazır kitlerden alınan mantar verilerine daha yakın sonuç alındığı görülmüştür."},"author":{"kind":"string","value":"Murat Çetin|Turgay Kabay|Suat Şensoy"},"content_list":{"kind":"list like","value":[{"bbox":"[94,199,835,237]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The Effect of Different Production Environments on Yield and Quality in Mushroom (Pleurotus Ostreatus) Production# ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[94,250,440,265]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Murat Çetin $^{1,a}$ , Turgay Kabay $^{2,b}$ , Suat Şensoy $^{2,c}$ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,265,640,275]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"<sup>1</sup>Graduate School of Natural and Applied Sciences, Van Yüizunciu Yl University, Van, Türkiye ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,275,640,288]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$^{2}$ Department of Horticulture, Faculty of Agriculture, Van Yüzünçü Yil University, Van Türkiye ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,288,233,300]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"*Corresponding author ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,302,238,317]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ARTICLE INFO ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[94,324,277,347]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This study was produced from Murat Çetin's master's thesis. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,359,196,370]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Research Article ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,382,231,393]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Received: 23/03/2022 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,394,231,405]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Accepted:17/11/2022 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,439,161,451]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Keywords: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,451,121,462]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Tea ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,464,208,474]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Oyster Mushrooms ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,475,132,485]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Straw ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,487,161,497]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Production ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,498,144,508]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Türkiye ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[287,305,393,317]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ABSTRACT ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[285,324,899,472]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Fear of the risk of poisoning from wild mushrooms increases the production of cultivated mushroom species. Oyster mushrooms, which are among these mushroom species, have been preferred in recent years due to some advantages in production. It is very important to ensure regional diversity in production environments in increasing mushroom production. In this study, it is aimed to expand mushroom production in Van and its surroundings and to investigate the efficiency of production in straw and inactive tea wastes that can be easily obtained by the producers of the region. The study, which was established with wheat straw, tea waste and ready-made mushroom production kits, was designed in a randomized plot design with four replications. The parameters of the first harvest, carpophore weight, total yield, carpophore measurements, macro and micro elements were examined in the mushrooms obtained. In the study, it was seen that the mushroom data produced in the tea media were closer to the mushroom data obtained from the ready-made kits obtained from the companies producing mushrooms. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[315,537,678,550]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Türk Tarim-Gida Bilim ve Teknoloji Dergisi, 11(1): 29-34, 2023 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[94,552,899,590]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Farkl Üretim Ortamlarin İstiridye Mantarı (Pleurotus Ostreatus) Üretiminde Verim ve Kalite Üzerine Etkisi ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[94,596,267,615]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"MAKALE BILGISI ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[94,634,215,646]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Araşirma Makalesi ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,670,231,681]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Gelis : 23/03/2022 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,682,231,693]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Kabul : 17/11/2022 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,719,211,730]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Anahtar Kelimeler: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,731,122,741]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Cay ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,743,196,753]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Istiridye Mantari ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,755,137,764]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Saman ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,766,141,776]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Uretim ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[95,777,144,788]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Türkiye ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[287,602,315,615]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"OZ ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[285,623,900,760]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Yabani mantarlardan zehirlenme riski korkusu insanlar kulture alnabilen mantar turleri uretimini artirmaktadir. Bu mantar turleri icerisinde yer alan istiridye mantari uretimindeki bazı avantajlar nedeniyle son yllarda terih edilir olmustur. Mantar uretiminin artmasinda uretim ortamlarinda bolgesel ceşitligin saglanması;cok onemlidir. Bu calismada Van ve cevesine mantar uretimini yayginlastirmak ve bolge ureticilerinin kolay temin edebilecekleri saman ve atil durumda對於 demlenmisçay atiklarnda uretimin etkinligini araistirmak amaclamnistir. Bugday samani, demleme cay atigi ve hazir mantar uretim kitleriyle kurulan calisma tesaduf parselleri deneme desinen gore dört tekerrülü olarak tasarlanmistr. Elde edilen mantarlarda, ilk hasat, karpofor aigriligi, toplam verim, karpofor olçuleri, makro ve mikro elementler parametrelerine bakilmistr. Yapilan calismada cay ortaminda uretilen mantar verilerinin, mantar uretimi yanapan firlalardan alinan hazir kitlerden alinan mantar verilerine daha)yakin sonuc alindigi gürümstür. 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Food Science and Technology, 11(1): 29-34, 2023 \nDOI: https://doi.org/10.24925/turjaf.v11i1.29-34.5181 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[110,97,206,162]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"TURJAF ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[245,121,880,142]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Turkish Journal of Agriculture - Food Science and Technology ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[206,167,892,179]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Available online, ISSN: 2148-127X | www.agrifoodscience.com | Turkish Science and Technology Publishing (TURSTEP) ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[236,910,287,925]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CC 1 S BY NC ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[305,913,766,923]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This work is licensed under Creative Commons Attribution 4.0 International License ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[885,929,904,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"29 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[90,66,132,80]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Giris ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[92,87,485,426]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Ülkemizde gerek yabani formu gerekse kulturyetişiriciliginde onemli bir yere sahip olan istiridye mantarı (Pleurotus ostreatus), beyaz Şapkali mantar (Agaricus bisporus) turunden sonra en Yaygün yetişirilenmantar turdur. Istiridye mantarı meş, kayın, gürgen gibi açaç kütükleri ile lignin ve selülozca zengin her turltarımsal bitki artiklar kullanılarak kolayıklayetişirilebilmektedir. Istiridye mantarı yetişiriligi sonunda ortayaçkan bitkisel atiklar hayvan beslenmesi ve tarımsal uretimde farkı amaçlar icin kullanılabilmektedir. Buğday samanı (WS), mırı sapı (CS), kavak talası (PS) ve Ferula communis bitki atigi (FPW) tek basına kullanınan ve bu substratlara %20 buğday kepeşi (WB) ve pirinci kepeşi (RB) eklenerek mantar üretim kompostlarinin denendişi calismada, Doğu Anadolu Bolgesınde kolaycabulun bilan FPW'nin, P. eryngii mantar yetişiriligi hem tek basına hem de WB veya RB ile karişirilaram kullanılabilir oldugu belirtilmektedir (Kibar 2016). Kompost hazirlamak icin hammadde olarak kullanılan 1 kg balya, pirinç kepeşi, mercimek artikları ve 50, 100 ve 150g dozlarsında ayç;cigi samanı katkı maddesi olarak kullanın calismada, en kisa surende pirinç kepeşinde misel sarimi elde edildigi, en yükbsek miktardaki toplam verim, 100 gram dozdaki mercimek atiklarında elde edildigi belirtilmektedir (Yildiz, 1998). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,428,487,495]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Odun talasları vefindik kabukları ile hazirlanan kompostlara asilanan shiitake mantar miseli tohumluğu calismasinda, en yüksek verimlilik ve biyolojik etkinlik degerleri meşte talasik kompostundan elde edildigi belirtilmektedir (Yalçın ve ark., 2020). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,497,487,577]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Orta Karadeniz Bölgesinden toplanan Lactarius pyragalus, L. controversus ve L. semisanguifluus türlerine ait mantar örneklerinden, L. pyragalus mantar türün kuru madde, kul, protein, N, Fe, Mg, Mn ve K içeriği bakimindan daha zengin oldugu belirtilmışı (Pekşen ve ark., 2007). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,579,487,715]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Bolu ilinin farkllokasyonlarindan elde edilen 4 farklizolatin (PO-141, PO-142, PO-143 ve PO-144) saman, talas ve kepek karisimindan $(\\% 45$ saman $^+$ $45$ talas $^+$ $10$ kepek) olusan ortamda, misel gelisim suresi, ilk hasat suresi, mantar aigriligi, verim, sapka uzunlugu, sapka eni, sap uzunlugu, sap capi, mantarin renk ozellikleri, pH, kul, kuru madde, SCKM (suda czünebilir kuru madde) ve protein iceriklerinin bakildigi calismada en yuksek verimin PO-143 izolatindan elde edildigi belirtilmistir (Kibar, 2019). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,715,487,784]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Atik cay yaprakları, bugday kepeşi, tavuk gübresi ve Güvercin gübresi gibi aktivator malzemelerin karıminin incelendişi calismada atik cay ile bugday kepeşi karıminda en iyi mantar veriminin/elde edildigi belirtilm,stir (Yigitbası ve ark., 2007). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,784,487,852]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Baobab meyvesi, bugday samani, misir kocani ve talas ortamilarinin istiridye mantarinin verimi ve biyolojik etkinligine bakildigi calismada en iyi sonuc bugday samani ve en duşuk sonuc ise baobab meyve kabugundan elde edildigi belirtilmistir (Tavarwisa ve ark., 2021). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,852,487,921]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Farkl P. ostreatus ceşitlerinin buyümesini ve verimini degerlendirmek amacíyla, Çeltik samani, buğday samani, talas ve bunlarin kombinasyonları ortamilarnda üretilen mantarlarda en iyi verim buğday samanindan elde edildigi belirtilmektedir (Abid ve ark., 2020). Pleurotus mantar ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,87,904,141]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"türünun bugday, celtik, arpa, misiR, cay yapragi vb. ve samanları ortamlarında yapilan üretim calismasında en iyi sonucun bugday ve celtik samanlarında elde edildigi belirtilmistir (Garg ve ark., 2017). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,141,904,223]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Istiridye mantarin (P. ostreatus) üretim imkânlarını araşirildigi calismada, tekstin atişi ve zeytin posasi ortamlarina %75, %50 ve %25 oranlarinda meşte talası karşirilarak hazirlanan ortamları, misel gelisiimi, hasat süresi, verim ve biyolojik etkinlik (BE) üzerine olumlu etki attigi belirtilmektedir (Sözbir 2021). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,224,904,347]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dūnyada en fazla üretimi yapilan Pleurotus spp., Pleurotus major-caju ve Pleurotus ostreatus türlerinin bugday samani, bugday kepeşi, Çeltik kavuzu (pirinç kavuzu) ve parçalanmş misir koçani materyalleri ve bunlarin degişik oranlarda hazırlanan karişimlarda, en yüksek mantar verimi ve biyolojik etkinlik orani, %60 bugday samani + %40 misir koçani ve %95 bugday samani + %5 bugday kepeşi uygulamalarindan elde edildigi belirtilmektedir (Aksu ve Uygur 2005). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,347,905,659]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dört istiridye mantari türün, Pleurotus ostreatus (gri), P. ostreatus (beyaz), P. cornucopiae var. citrinopileatus (parlak sari) ve P. Salmonoestramineus (pembe) %100 bugday samani, %70 bugday samani, %20 beyaz talas ve %10 hurma lifi, %50 bugday samani, %50 beyaz talas olmak üzere üç ortamda, karpoflorarin C, N, Co, Pb, Fe, Ni, Cu, Zn, Cd ve Mn iceriginin etkilerinin incelendişi calismada, üç ortamda da mineral elementler acisindan istatistiksel olarak fark olmadigi belirtilmektedir (Owaid ve ark., 2015). Kultur mantarlarinin besin iceriklerinin araşirildigi calismada; N, P, K, Ca, Mg, Fe, Cu, Zn ve Mn iceriklerinin istatistiksel olarak buyük farklihlkar gosterdiigi ve bu farkliliŋin farkli ticari isletmelerden alinmasi ve farkl i kymasal bileşmlere sahip olmasindan kaynaklandigi belirtilmistir (Sönmez ve ark., 2016). Ganoderma lucidum mantarlarinin verim ve morfolojik özellikleri uzerine etkilerini belirlendişi calismada, meşehizar tozu (ince tala) ve odun yongasi (kaba talas) ile %10, 15, 20 ve 25 oraninda Cay atigi (CA) karissimarindan hazirlanan yetistirme ortamlari kullanımsi sonucunda en yüksek verim meşene odun yongasinda elde edildigi belirtilmektedir (Yakupoğlu ve Pekşen, 2011). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,675,660,689]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Materyal ve Yontem ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[504,701,904,810]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Istiridye mantarinin (Pleurotus ostreatus (gri))yetistricilik ortamlarinda performanslarinin belirlenmesi amacyla yapilan bu calisma, 2 litrelik misel asili hazir kitler (%90 meş talaşi + %10 bugday kepeşi), Denizli ilinde bulunan Agroma sirketinden temin edilm,stir. Yetistirme ortam olarak, bugday samani veçay artigi kullanlm,stir. Deneme tesaduf parselleri deneme desanine gore üc tekerrurlu olarak dizayn edilm,stir. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[504,810,904,921]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Ev veçay ocaklarinda demlenmis ve atik durumdakiçay artiklari ile bugday samanlari $100^{\\circ}\\mathrm{C}$ de 1 saat kaynatildiktan sonra temiz bir ortü uzerinde sogumayabirakilmistir. Soguyan saman veçay atiklari 2 litrelik plastik torbalara bir sira yaklaşik 5-6 cm kalinliginda %100 bugday samani ve 1 sira ise tohumluk misel homojen bir dagilmla posetlerin dinisa dokru asilama yapilmis ve her bir 2 litrelik turbada 25 g tohumluk misel kullanilmistir. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,40,774,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Çetin et al. / Turkish Journal of Agriculture - Food Science and Technology, 11(1): 29-34, 2023 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[885,929,905,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"30 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[89,66,487,148]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Miseller aşlandık tan sonra misel geleşimi icin 20-25°C sıçaklık, %90 nem ve %100 karanlık oluzturmak amacıyla 8 günk iklim odasinın isikları acılmamıştir. Nem oluzturmak icin iklim odasa su dolu kaplar konulmugs ve zemin hergün sulanmıştir. Sıçaklık ile elektriklı istificantar ile saglanmıştir. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[115,162,312,175]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Yaplan Ölçüm ve Analizler ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,175,487,231]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Calismada farkli ortamlarda istiridye mantari uretim calismasinda, ilk hasat, karpofor, toplam verim, mantar olculeri, makro ve mikro element analizleriGPCklestirilmistir. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,244,184,256]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Irk Hasat ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,256,487,299]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Ilk hasat missellerin asilandig tarihten itibaren ilk urun alindigi tarih arasindaki gezcen surenin gun olarak belirlenmesiyle bulunmustur. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,313,240,326]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Karpofor Aigrilgi ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,326,487,354]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Karpoforagrlhig,hasat edilen mantar orneklerinin hassas terazide tartulmasiyla gram olarak hesaplanmistir. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,367,220,380]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Toplam Verim ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,380,487,435]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Her bir mantar kitinden elde edilen urunlerin, ilk hasattan son hasada kadar hassas terazide tartimlarinin yapilmasi ve bunlarin toplanmasi ile gram cinsinden belirlenmistir. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,449,302,463]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sap Uzunluğu ve Kalınkı ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,463,487,489]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Istiridye mantarlarinin nap kalinligi ve uzunlugu djital kumpas ile mm cinsinden olçumlustür. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,504,226,517]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"KarpoforAlani ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,517,487,545]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Istiridye mantar ornekleri kagida qizilip, planimetre ile $\\mathrm{cm}^2$ cinsinden olçulup hesaplanmistr. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[114,558,310,571]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mineral Element Analizleri ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,571,487,708]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Her mantar ortamindaki kitlerden alinan istiridye mantar ornekleri once açıkta daha sonra $65^{\\circ}\\mathrm{C}^\\prime$ de 48 saat etüvde kurutulduktan sonra $550^{\\circ}\\mathrm{C}$ kül firqinnda kül olusuncaya kadar yakilm生物质. Elde edilen kül, $\\% 3,3^{\\prime}$ luk HCl' de gezündürulm ve mavi bantl滤tre kagensinda suzuldukten sonra makro ve mikro besin elementi okumaları Yüzuncu Yl Universitesi Bilimsel Araştrima ve Uygulama Merkezinde atomik absorbsiyon cihazinda yapilm生物质 (Kabay 2019; Kacar ve ark., 2006; Kuşvuran, 2010). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[531,66,727,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Verilerin Degerlendirilmesi ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[505,80,905,231]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Istiridye mantar turu uretim ortamlarindaki kitlerden elde edilen ilk hasat, karpofor aigriligi, mantar olçuleri, makro ve mikro besin elementi iceriklerininarasindaki farkliliigi belirlemek icin tek yönlu varyans analizi uygulanmiistr (Yeşilova ve Denizhan, 2016). Varyans analizi sonucunda uretim ortamindaki parametreler arasi fark istatistiksel olarak onemli bulundugunda, hangi parametrelerin birbirinden farkl oldugunu saptamak icin Duncan Coklu Karılaşirma Testi kullanilmistr (Duncan, 1955). Verilerin analizi SAS 9.1.4. istatistik yazilim programinda yapilmistr (SAS, 2018). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,244,665,258]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Bulgular ve Tartışma ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[505,271,905,338]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Van ve cevre illerde istiridye mantar uretiminin efektif bir sekildegerekelestirilebilecegini gostermek amaciyla, bolgede kolay temin cay artig ve buğday samani ortamlarinda istiridye mantar uretimi, ticari olarak uretim yapan sirketlerin hazirladig ortamlarla kiyasanmistir. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,340,905,449]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Yapilan calismada, istiridye mantarinin saman ve cay ortamlarinda yetişirilmesinde ilk hasatgün sayilari, istatistiksel olarak aynı grupta yer almistir. Saman ortamnda tohumluk misel ekiminden 38,25跑去 sonra ilk hasat yapilrken, cay ortamnda 37,0跑去 ilk hasatGPCklesmiistir. Hazir kit olarak adlandirilan, firmadan temin edilen ve meşete talas+bugday kepeşi ortamnda ekildigi durumunda isel ilk hasat 33,25跑去 yapilmstir (Cizelge 1). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,449,904,531]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Karpofor aigrigi verilerinde istatistiksel olarak fark görtelmemistir. Yani ticari anlamda üretim yapan sirket ortamyla ayni aigriga sahip mantarlar elde edilmistir. Saman ortaminda karpofor aigrigi 22,01 g, Cay ortamnda $23,35\\mathrm{g}$ ve hazir kit ortamnda ise 22,13 g olmustur (Cizelge 1). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,531,905,599]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Ilk hasattan son hasada kadar her uretim ortamindaki toplam verim bakimindan istatistiksel olarak ortamlararasindaki fark gorulmemistir. Saman ortaminda toplam verim 1249,16 g, cay ortaminda toplam verim 1293,35 g ve hazir kit ortaminda ise 1356,09 g urun alinmistr. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,599,905,709]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Bugday samani (WS), misi r sapi (CS), kavak talaşi (PS) ve Ferula communis bitki atigi (FPW) tek basina kullananan ve bu substratlara%20 bugday kepegi (WB) ve pirinç kepegi (RB) eklenerek mantar üretim kompostlarinin denendişi calismada, Doğu Anadolu Bölgesi nde bol miktarda ve kolayca bulunabilen FPW'nin, P. eryngii mantar yetistiriciligiinde hem tek basina hem de WB veya RB ile karişürilarak kullanilabilir oldugu beirtilmistir (Kibar 2016) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,749,904,808]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0644/79d42dc8c2888b0587e97febfe3aaa7745da72bdf6499aeee65f8524f564f220.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":"<table><tr><td>Tür</td><td>Ortam</td><td>İlk hasat(gün)</td><td>Karpofor ağırkıngı(g)</td><td>Toplam verim (g)</td></tr><tr><td rowspan=\"3\">İstiridye mantarı</td><td>Saman</td><td>38,25a</td><td>22,01a</td><td>1249,16a</td></tr><tr><td>Çay</td><td>37,0a</td><td>23,35a</td><td>1293,35a</td></tr><tr><td>Hazır kit</td><td>33,25b</td><td>22,13a</td><td>1356,09a</td></tr></table>","table_caption":"[\"Cizelge 1. Üretim ortamlarindaki mantar ilk hasadı (gün), karpofor ağırkı (g) ve toplam verim (g) Table 1. Mushroom first harvest (days), carpophore weight (g) and total yield (g) in production media \"]","table_footnote":"[\"P<0,05 \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[92,858,904,917]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0874/1062fa9ecc6fd8d292d7b14feaf9e9795f9e69d702e53a28ba1468ce51bf8fea.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":"<table><tr><td>Çeşit</td><td>Ortam</td><td>Karpofor uzunluk (mm)</td><td>Karpofor kalınlık(mm)</td><td>Karpofor alanı (cm2)</td></tr><tr><td rowspan=\"3\">İstridye mantarı</td><td>Saman</td><td>3,53a</td><td>2,42a</td><td>61,09a</td></tr><tr><td>Çay</td><td>3,58a</td><td>2,45a</td><td>60,25a</td></tr><tr><td>Hazır kit</td><td>3,61a</td><td>2,39a</td><td>62,96a</td></tr></table>","table_caption":"[\"Cizelge 2. Üretim ortamlarindaki karpofor ölcüleri ve karpofor alanı (cm²) \\nTable 2. Carpophore dimensions and carpophore area in production media (cm²) \"]","table_footnote":"[\"P<0.05 \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[220,40,774,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Çetin et al. / Turkish Journal of Agriculture - Food Science and Technology, 11(1): 29-34, 2023 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[885,929,902,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"31 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[92,93,905,152]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0177/48851929a9cb28fada395043eb4b6ddd7efbe15653870a87cf9c63f88c786717.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":"<table><tr><td>Çeşit</td><td>Ortam</td><td>K (%)</td><td>Ca (%)</td><td>Mg (%)</td></tr><tr><td rowspan=\"3\">İstridye Mantari</td><td>Saman</td><td>0,46b</td><td>0,05b</td><td>0,14b</td></tr><tr><td>Çay</td><td>0,63a</td><td>0,06ab</td><td>0,15ab</td></tr><tr><td>Hazır kit</td><td>0,67a</td><td>0,07a</td><td>0,17a</td></tr></table>","table_caption":"[\"Cizelge 3. Farkl üretim ortamlarindan elde edilen mantarlarin K, Ca ve Mg icerikleri (%) \",\"Table 3. K, Ca and Mg contents of mushrooms obtained from different production media (%) \"]","table_footnote":"[\"$\\\\mathrm{P < 0.05}$ \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[92,203,905,263]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":"images/0690/e6762e34a39bd58f25a55a46d8cf17ff34bba60352f9758bec9da93df892e829.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":"<table><tr><td>Çeşit</td><td>Ortam</td><td>Fe (ppm)</td><td>Zn (ppm)</td><td>Mn (ppm)</td><td>Cu (ppm)</td></tr><tr><td rowspan=\"3\">Istridye mantari</td><td>Saman</td><td>66.97a</td><td>146.26b</td><td>4.06b</td><td>74.36a</td></tr><tr><td>Çay</td><td>66.44a</td><td>151.18ab</td><td>4.17ab</td><td>74.29a</td></tr><tr><td>Hazır kit</td><td>69.22a</td><td>153.91a</td><td>4.60a</td><td>76.85a</td></tr></table>","table_caption":"[\"Cizelge 4. Farkl üretim ortamlarindan elde edilen mantarlarin Fe, Zn, Mn ve Cu icerikleri (ppm) \",\"Table 4. Fe, Zn, Mn and Cu contents (ppm) of mushrooms obtained from different production media \"]","table_footnote":"[\"P<0.05 \"]","text":null,"text_format":null,"text_level":null,"type":"table"},{"bbox":"[92,287,485,423]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Kompost hazirlamak icin hammadde olarak kullanlan $1\\mathrm{kg}$ balya, pirinç kepeghi, mercimek artikları ve 50, 100 ve $150\\mathrm{g}$ dozlarnda ayciçehi samani katkı maddesi olarak kullanlan calismada, en kisa surede pirinç kepeşinde sarim saglandı, en yüksek toplam verim, $100\\mathrm{g}$ mercimek atigianda elde edildigi belirtilmektedir (Yildüz, 1998). Mantar uretiminde turbalarin mantar uretim substratina onemli bir girdi ve kompost malzemelerine $\\% 60$ ve $\\% 36$ katkı bulundugu belirtilmektedir (Robinson ve ark., 2019). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,424,485,558]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Odn talasları ve finden kabuklari ile hazirlanan kompostlara asilanan shiitake mantar miseli calismasindo, %100 finden kabugu ile üretilen mantarların, meş ve kayın talasına,göre verim bakimindan daha Dennis degerler verdişi tespit edilirken, en yuksek verimlilik ve biyolojik etkinlik degerleri meş talasik kompostundan elde edilmis, kimiyasal icerik sonuclarina,göre, finden kabugu ve karsımları toplam azot ve protein bakimindan en yuksek degerlere sahip oldugu belirtilmektedir (Yalçın ve ark., 2020). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,561,485,627]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Yapilan calismada mantar sap uzunluklarinin ortamlararasindaki fark istoristikselormalk onemsiz cikmistr. Saman ortamindaki mantar sap uzunlugu $3,53\\mathrm{mm}$ ,cay ortaminda 3,58 ve hazir kit ortamnda ise $3,61~\\mathrm{mm}$ olarak olculmustur. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,629,485,711]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Istiridye mantarlarinin üretim ortamilarndaki mantar sap kalinligıarasinda istatistiksel olarak fark görtulmemişir. Sasan ortamindaki sap kalinligı 2,41 mm,çay ortamindaki sap kalinligı 2,45 mm ve hazir kit ortaminda ise sap kalinligı 2,39 mm olarak olçülm,stür (Cizelge 2). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,711,485,806]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mantar üretim ortamlarindaki karpofor alanlariyla ilgili veriler sekil Çizelge 2 de verilmistir. Çizelge incelendigiinde ortamlardaki karpofor alanlariarasinda istatistiksel olarak fark güruml memistir. Saman ortamnda mantar karpofor alanı $61,09~\\mathrm{cm}^2$ ,çay ortamnda 60,25 ve hazir katte ise karpofor alanı $62,96~\\mathrm{cm}^2$ olarak olçumlustir (Çizelge 2). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,807,485,916]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Ganoderma lucidum mantarinda farkl ortamarin verim ve morfolojik özellikleri üzerine etkilerini belirlendigi calismada, meşehizar tozu (ince talaş) ve odun yongası (kaba talaş) ile %10, 15, 20 ve 25 oranindaçay atişi (CA) karişimilarindan hazirlanan yetistirme ortamlari kullanimasi sonucunda en yüksek verim meşehodun yongasında 73,07 g/kg ortam ile 90:10 CA ortamindan, meşehizar tozu ile hazirlanan karişmlarda ise 21,21 g/kg ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,287,902,313]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ortam ile 75:25 CA ortamindan elde edildigi belirtilmektedir (Yakupoğlu ve Pekşen, 2011). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,315,902,382]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Pleurotus mantar türünun bugday, celtik, arpa, misir vb.çay yaprakları ve samanlari ortamlarinda yapilan üretim calismasinda en iyi sonucun bugday ve celtik samanlarinda elde edildigi belirtilmistir (Garg ve ark., 2017). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,382,902,464]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Istiridye mantarin (P. ostreatus) üretim imkânlarinin araşirildigi calismada, tekstil atigi ve zeytin posasi ortamlarina %75, %50 ve %25 oranlarinda meştaşa karişirilarak hazirlanan ortamlarda, misel gelisimi, hasat suresi, toplam zaman, verim ve biyolojik etkinlik üzerine olumlu etki attigi belirtilmektedir (Sözbir 2021). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,464,902,574]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Pleurotus sajor-caju ve Pleurotus ostreatus türlerinin, buğday samani, buğday kepeşi, Çeltik kavuzu (pirinç kavuzu) ve parçalanmş mır koşani materyalleri ve bunlarin degişik oranlarda hazirlanan karişimlarda, en yüksek mantar verimi ve biyolojik etkinlik orani, %60 buğday samani + %40 mır koşani ve %95 buğday samani + %5 buğday kepeşi uygulamalarindan elde edildigi belirtilmşir (Aksu ve Uygur 2005). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,574,902,642]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Bu denemede degerlendirilen yetistricticilik ortamlarinda yapilan uretim ile hazir yetistricticilik ortamlarinda elde edilen mantarlin karpofor olculeri ve alanıarasinda istatistiksel olarak fark g Ruralmemis olup diger calismalarla benzer sonuclar elde edilmestiţir. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[509,643,904,901]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Mantar üretim ortamlarindan elde edilen istiridye mantarlarinin K (potasyum) iceriigi istatistiksel olarak onemli bulunmustur. Çizelge 3'de deGORuldugu gibi, saman ortamlarinda üretilen istiridye mantarinin potasyum iceriigi %0,46,çay ortaminda %0,63 ve hazir kit (%90 meşete talas + %10 buğday kepeşi karişimi) ortaminda %0,67 olarak tespit edilmşir (Çizelge 3). Kalsiyum (Ca) icerikleri incelendigiinde ortamlararasinda fark istatistiksel olarak onemli bulunmustur. Sasan ortamlarinda üretilen istiridye mantarinin kalsiyum (Ca) iceriigi %0,052,çay ortaminda kalsiyum (Ca) %0,061 ve hazir kit (%90 meşete talas + %10 buğday kepeşi karişimi) ortaminda %0,068 olarak belirlenmustir (Çizelge 3). Magnezyum (Mg) icerikleri incelendigiinde, ortamlararasinda fark istatistiksel olarak onemli bulunmustur. Sasan ortamlarinda üretilen istiridye mantarinin magnezyum (Mg) iceriigi %0,052,çay ortaminda %0,061 ve hazir kit (%90 meşete talas + %10 buğday kepeşi karişimi) %0,068 olarak tespit edilmşir (Çizelge 3). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[510,902,902,929]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Uretilen istiridye mantarlarinin mikro besin elementlerden demir (Fe) icerigi istatistiksel olarak onemli ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[220,40,774,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Çetin et al. / Turkish Journal of Agriculture - Food Science and Technology, 11(1): 29-34, 2023 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[885,931,904,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"32 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[92,66,485,380]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"bununmustur. Cizelge 4'de de güruldügün gibi samsam ortamlarinda üretilen istiridye mantarınim demir (Fe) icerişi 66,44 ppm,çay ortaminda 66,98 ppm ve hazir kit (%90 meşte talası+%10 buğday kepeşi karişi) ortaminda 69,22 ppm olarak tespit edilmşir (Cizelge 4). Cinko (Zn) icerikleri incelendigiinde ortamlararasinda fark istatistiksel olarak onemli bununmustur. Saman ortaminda üretilen istiridye mantarınin Cinko (Zn) icerişi 146,26 ppm,çay ortaminda 151,18 ppm ve hazir kit (%90 mese talası+%10 buğday kepeşi karişi) ortamnda 153,91 ppm olarak tespit edilmşir (Cizelge 4). Mangan (Mn) icerikleri incelendigiinde, ortamlararasindaki fark istatistiksel olarak onemli bununmustur. Saman ortaminda üretilen istiridye mantarınin Mangan (Mn) icerişi 4,058 ppm,çay ortamnda 4,17 ppm ve hazir kit (%90 mese talası+%10 buğday kepeşi karişi) ortamnda 4,61 ppm Çiqmşir (Cizelge 4). Bakır (Cu) icerikleri sekil ve Cizelge incelendigiinde ortamlararasinda fark istatistiksel olarak onemli bunmamşir. Saman ortaminda üretilen istiridye mantarınin bakir (Cu) icerişi 74,36 ppm,çay ortamnda 74,29 ppm ve hazir kit (%90 meşte talası+%10 buğday kepeşi karişi) ortamnda 76,85 ppm olarak tespit edilmşir (Cizelge 4) ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[92,382,485,749]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Dört istiridye mantari türände, P. ostreatus (gri), P. ostreatus (beyaz), P. cornucopiae var. citrinopileatus (parlak sari) ve P. salmonoestramineus (pembe), %100 buğday samani, %70 buğday samani, %20 beyaz talas ve %10 Irak hurma lifi, %50 buğday samani, %50 beyaz talas olmak üzere üç ortamda, karpoforlarin C, N, Co, Pb, Fe, Ni, Cu, Zn, Cd ve Mn icerikleri incelenmistir, üç ortamda da mineral elementler açisündan istatistiksel olarak fak gozemlenmis ve genel olarak, Fe, Ni ve Cd hazirlanan üretim ortamlarindan elde edilen mantarlarda ve karpofor verimlerinde artş oldugu belirtilmektedir (Owaid ve ark., 2015). Dogal yetişen mantar örneklerinde yapilan calismada, Besleyici oldugu ayrica Ca, K ve fe iceriklerinin yüksek oldugu belirtilmektedir (Aksoy ve ark., 2020; Selem ve ark., 2021). Samsun ve Ordu illerin bazı ilç ve köylerinden toplanan ve halk tarafindan tüketilen Lactarius pyragalus, L. controversus ve L. semisanguifluus türleri icinde, L. pyragalus mantar türün kuru madde, kul, protein, N, Fe, Mg, Mn ve K icerişi bakimindan.da zengin oldugu belirtilmistir (Peksen ve ark., 2007). Antalya'nin Korkuteli ilçesinde yetistirilen kultur mantarlarinin besin iceriklerinin arastrildigi calismada; N, P, K, Ca, Mg, Fe, Cu, Zn ve Mn iceriklerinin istatistiksel olarak buyuk farklıklar gösterligi ve bu farklıgün üretim ortamlarin farkli ticari isletmelerden alınması ve farklı kymasal bileşilmere sahip olmasindan kaynaklandigi belirtilmistir (Sonmez ve ark., 2016). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[89,750,487,818]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Bu calismada degerlendirilen yeti stiricilik ortamlarinda yapilan uretim ile hazir yeti stiricilik ortamlarinda elde edilen mantarlarda yaplan, olcum, gozlem ve analiz sonuclarinin diger arastirmacilarin yaptigi calismalarla benzer sonuclar oldugu tespit edilmistir. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[90,832,139,845]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Sonuc ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[89,858,489,928]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Van ve cevre illerde istiridye mantarinin üretimi cok azdir. Bu nedenle, bu calismada Van ve cevre illerde istiridye mantarinin üretiminin yayginlastrupimamacylya kolay temin edilen ortam sedan bugday samani ve atik olarak gürulen demlenmis Cay ortamlarinda üretilen ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,66,904,216]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"istiridye mantari orneklerinde ilk hasat, karpofor aigriligi, toplam verim, karpofor olçuleri ve karpofor alanı, makro ve mikro elementler iceriklerine bakilmışı. Mantar üretiminde kullananan %100 bugday samanı ve %100 çay ortamlarındaki ilk hasat, karpofor aigriligi, toplam verim, karpofor olçuleri ve karpofor alanı, makro ve mikro elementler icerik değerleri, Denizl’ de bulunan ticari mantar üretim sirketi Agroma firmasından temin edilen %90 meş talaşi ve + 10 bugday kepeşi seksmişindan olşan hazır kitlerden alınan mantar ornekleriyile benzer ve)yakın sonuclara varilmışı. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[505,217,904,258]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Bu calisma sonucunun özellikle Van ve cevresindeki mantar üreticileriISTA olmak üzere, tum arastirmacı ve üreticilere fayda saglayacağinancindayiz. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[507,271,589,285]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Kaynaklar ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[505,294,905,922]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Abid AH, Hamid A, Naz RMM, Shah SZA, Anjum S, Khan MT, Ilyas M. 2020. 74. Farkli lignoseluloz substratlartinin istiridye mantarinin (Pleurotus ostreatus) buyümesi ve verimi üzerindeki etkisi. Saf ve Uygulamali Biyoloji (PAB), 9(1): 768-775. \",\"Aksoy C, Aksoy H, Tirasoglu E, Üçler AÖ. 2020. Ordu (Mesudiye ve Kabadüz) Köy ve Yaylalarminda Yetişen Bazı Tübbi ve Aromatik Bitki ve Mantar Örneklerinde Ca, K ve Fe Element Analizi. Türk Tarım-Gida Bilim ve Teknologi dergisi, 8(3): 694-697. \",\"Aksu S, Uygur AM. 2005. Bazı kayınmantarı (Pleurotus spp.) türlerinin organik olarak üretimi üzerinde araşirmalar. Anadolu Ege Tarımsal Araşirma Enstitü Sü Dergisi, 15(2): 1-26. \",\"Cat A, Comak T, Catal M. 2018. Istiridye mantarinin (Pleurotus ostreatus) tohumluk misel uretimi uzerine bir on calisma. Mediterranean Agricultural Sciences, 31(1): 21-25. \",\"Duncan DB. 1955. Multiple range and multiple F test. Biometrics, 11: 1-42. \",\"Fukushima M, Shimada KI, Ohashi T, Saitoh H, Sonoyama K, Sekikawa M, Nakano M. 2001. Investigation of gene expressions related to cholesterol metabolism in rats fed diets enriched in n-6 or n-3 fatty acid with a cholesterol after long-term feeding using quantitative-competitive RT-PCR analysis. Journal of nutritional science and vitaminology, 47(3): 228-235. \",\"Garg P, Saxena G, Kanodia S, Gupta S. 2017. Conversion of Urban Waste into Highly Nutritious Food by Pleurotus Cultivation. \",\"Hanger 2021. https://www.hayger.com/istiridye-mantar-yetistiriciligi.html \",\"Kabay T. 2019. Effects of different potassium doses on development of high temperature-sensitive bean plants. Fresenius Environmental Bulletin, 28(1): 320-325. \",\"Kacar B, Katkat B, Öztürk Ş. 2006. Bitki Fizyolojisı. 2. Baskı. Nobel Yayın Dağıtmı, Ankara. 563. \",\"Kibar B. 2016. Farklı Yetişirme Ortamlarinin Pleurotus eryngii Mantarinin Gelifimi ve Verimi Üzerine Etkileri. Uluslararasi Tarim ve Yaban Hayati Bilimleri Dergisi, 2(1): 1-9. \",\"Kibar B. 2019. Farkl Pleurotus ostreatus (Istiridye Mantari) Izolatlarin Verim ve Baz Kalite Özelliklerinin Belirlenmesi. Uluslararası Tarim ve Yaban Hayat Bilimleri Dergisi, 5(2): 223-230. \",\"Kurt R, Can A, Sivrikaya H. 2018. \\\"The current status with the problems and some suggestions of mushroom cultivation in Bartin province.\\\"Bartin Orman Fakultesi Dergisi 20.2: 176-183. \",\"Kusvuran S. 2010. Kavunlarda Kuraklik ve Tuzluluğa Toleransi Fizyolojik Mekanizmaları Arasindaki Baglantilar (Doktora tezi, basilmamı). Ükurova Üniversitesi, Fen Bilimleri Enstitusi, Adana. \"]","page_idx":"4","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[220,40,774,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Çetin et al. / Turkish Journal of Agriculture - Food Science and Technology, 11(1): 29-34, 2023 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[885,929,904,942]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"33 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[90,65,487,385]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Ma Y, Li X, Fu Z, Zhang L. 2019. Structural design and thermal performance simulation of shade roof of double-slope greenhouse for mushroom-vegetable cultivation. International Journal of Agricultural and Biological Engineering, 12(3): 126-133. \",\"SAS, 2018. SAS/Stat Software Hangen and Enhanced. SAS Institute Incorporation, Cary, NC. \",\"Owaid MN, Al-Saeedi SSS, Abed IA. 2015. Beyaz, gri, sarı ve pembe istiridye mantarlarınin (yüksek mantarlar) mineral madde icerişi. Gida, 40(6): 319-326. \",\"Peksen A, Kibar B, Yakupoglu G. 2007. Yenilebilir bazı lactarius türlerinin morfolojik Özelliklerinin, protein ve mineral iceriklerinin belirlenmesi. Anadolu Tarim Bilimleri Dergisi, 22(3): 301-305. \",\"Robinson B, Winans K, Kendall A, Dlott J, Dlott F. 2019. A life cycle assessment of Agaricus bisporus mushroom production in the USA. The International Journal of Life Cycle Assessment, 24(3): 456-467. \",\"Sönmez S, Üras DS, Demir E, Nil ÖZEN, Kılıç E. 2016. Antalya-Korkuteli Yöresinde Üretilen Kultur Mantarların (Agaricus bisporus) Beslenme Durumlarin Belirlenmesi. Cukurova Tarım ve Gida Bilimleri Dergisi, 31(3): 215-219. \",\"Sözbir GD. 2021. istiridye mantarin (Pleurotus ostreatus) yetistirilmesinde bazı endüstriyel atikları kullanım olanakların bilirlenmesi. Turkish Journal of Forest Science, 5(1): 187-197. \"]","page_idx":"5","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[509,65,905,424]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"Selem E, Alp Y, Sensoy S, Uzun Y, Cavusoglu S, Karatas N, Ercisli S, Yilmaz N, Ekiert H, Hosam OE, Szopa A. 2021. Biochemical and Morphological Characteristics of Some Macrofungi Grown Naturally. Journal of Fungi, 7(10): 851. \",\"Tavarwisa DM, Govera C, Mutetwa M, Ngezimana W. 2021. Baobab meyve kabuklarin n istiridye mantar (Pleurotus ostreatus) yetistirmek icin substrat olarak uygunluğunun degerlendirilmesi. Uluslararasi Tarim Bilimleri Dergisi. \",\"Yakupoglu G, Peksen A. 2011.çay atıgindan hazirlanan farkl kompost ve partikul��kılığün Ganoderma lucidum mantarinin verimi ve bazimorfolojik özellikleri üzerine etkisi. Ekoloji, 20(78): 41-47. \",\"Yalçın M, Akçay C, Sözbir GD. 2020. Meş, Kayın Odunu ve Fündüz Kabugu Atıklardan Lentinus edodes (Şitaki) Mantari Üretimi. Düzce Universitesi Bilim ve Teknoloji Dergisi, 8(3): 2051-2061. \",\"Yesilova A, Denizhan E. 2016. Modelling mite counts using poisson and negative binomial. Fresen. Environ. Bull. 25,5062-5066. \",\"Yildiz A. 1998. Effects of Various Proportions of Different Additive Substances on the Miselle Growth of Pleurotus florida Fovose, on Druation of Formation and Development of Basidiocarps and on the Yield. Turkish Journal of Biology, 22(1): 127-142 \",\"Yigitbasi ON, Baysal E, Colak M, Toker H, Simsek H, Yilmaz, F. 2007. Cultivation of Agaricus bisporus on some compost formulas and locally available casing materials. Part II: Waste tea leaves-based compost formulas and locally available casing materials. African Journal of Biotechnology, 6(2). \"]","page_idx":"5","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[220,40,774,53]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Çetin et al. / Turkish Journal of Agriculture - Food Science and Technology, 11(1): 29-34, 2023 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[885,929,904,941]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"34 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[94,199,835,237]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The Effect of Different Production Environments on Yield and Quality in Mushroom (Pleurotus Ostreatus) Production# \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,250,440,265]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Murat Çetin $^{1,a}$ , Turgay Kabay $^{2,b}$ , Suat Şensoy $^{2,c}$ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,265,640,275]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"<sup>1</sup>Graduate School of Natural and Applied Sciences, Van Yüizunciu Yl University, Van, Türkiye \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,275,640,288]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$^{2}$ Department of Horticulture, Faculty of Agriculture, Van Yüzünçü Yil University, Van Türkiye \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,288,233,300]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"*Corresponding author \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,302,238,317]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ARTICLE INFO \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,324,277,347]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This study was produced from Murat Çetin's master's thesis. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,359,196,370]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Research Article \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,382,231,393]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Received: 23/03/2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,394,231,405]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Accepted:17/11/2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,439,161,451]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Keywords: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,451,121,462]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Tea \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,464,208,474]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Oyster Mushrooms \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,475,132,485]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Straw \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,487,161,497]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Production \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,498,144,508]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Türkiye \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[287,305,393,317]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ABSTRACT \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[285,324,899,472]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Fear of the risk of poisoning from wild mushrooms increases the production of cultivated mushroom species. Oyster mushrooms, which are among these mushroom species, have been preferred in recent years due to some advantages in production. It is very important to ensure regional diversity in production environments in increasing mushroom production. In this study, it is aimed to expand mushroom production in Van and its surroundings and to investigate the efficiency of production in straw and inactive tea wastes that can be easily obtained by the producers of the region. The study, which was established with wheat straw, tea waste and ready-made mushroom production kits, was designed in a randomized plot design with four replications. The parameters of the first harvest, carpophore weight, total yield, carpophore measurements, macro and micro elements were examined in the mushrooms obtained. In the study, it was seen that the mushroom data produced in the tea media were closer to the mushroom data obtained from the ready-made kits obtained from the companies producing mushrooms. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[315,537,678,550]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Türk Tarim-Gida Bilim ve Teknoloji Dergisi, 11(1): 29-34, 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,552,899,590]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Farkl Üretim Ortamlarin İstiridye Mantarı (Pleurotus Ostreatus) Üretiminde Verim ve Kalite Üzerine Etkisi \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,596,267,615]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"MAKALE BILGISI \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[94,634,215,646]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Araşirma Makalesi \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,670,231,681]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Gelis : 23/03/2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,682,231,693]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Kabul : 17/11/2022 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,719,211,730]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Anahtar Kelimeler: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,731,122,741]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Cay \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,743,196,753]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Istiridye Mantari \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,755,137,764]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Saman \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,766,141,776]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Uretim \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[95,777,144,788]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Türkiye \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[287,602,315,615]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"OZ \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[285,623,900,760]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Yabani mantarlardan zehirlenme riski korkusu insanlar kulture alnabilen mantar turleri uretimini artirmaktadir. Bu mantar turleri icerisinde yer alan istiridye mantari uretimindeki bazı avantajlar nedeniyle son yllarda terih edilir olmustur. Mantar uretiminin artmasinda uretim ortamlarinda bolgesel ceşitligin saglanması;cok onemlidir. Bu calismada Van ve cevesine mantar uretimini yayginlastirmak ve bolge ureticilerinin kolay temin edebilecekleri saman ve atil durumda對於 demlenmisçay atiklarnda uretimin etkinligini araistirmak amaclamnistir. Bugday samani, demleme cay atigi ve hazir mantar uretim kitleriyle kurulan calisma tesaduf parselleri deneme desinen gore dört tekerrülü olarak tasarlanmistr. Elde edilen mantarlarda, ilk hasat, karpofor aigriligi, toplam verim, karpofor olçuleri, makro ve mikro elementler parametrelerine bakilmistr. Yapilan calismada cay ortaminda uretilen mantar verilerinin, mantar uretimi yanapan firlalardan alinan hazir kitlerden alinan mantar verilerine daha)yakin sonuc alindigi gürümstür. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,833,252,845]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"a muratcetin1993@gmail.com \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,846,228,857]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"e suatsensoy@gmail.com \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[268,834,477,846]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://orcid.org/0000-0003-4975-6370 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[268,847,475,856]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ID https://orcid.org/0000-0001-7129-6185 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,834,653,846]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"b turgaykabay@gmail.com \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[668,834,875,845]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"https://orcid.org/0000-0002-3239-0037 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[258,65,737,90]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Turkish Journal of Agriculture - Food Science and Technology, 11(1): 29-34, 2023 \\nDOI: https://doi.org/10.24925/turjaf.v11i1.29-34.5181 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[110,97,206,162]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"TURJAF \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[245,121,880,142]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Turkish Journal of Agriculture - Food Science and Technology \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[206,167,892,179]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Available online, ISSN: 2148-127X | www.agrifoodscience.com | Turkish Science and Technology Publishing (TURSTEP) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[236,910,287,925]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CC 1 S BY NC \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[305,913,766,923]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This work is licensed under Creative Commons Attribution 4.0 International License \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[885,929,904,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"29 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[90,66,132,80]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Giris \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,87,485,426]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Ülkemizde gerek yabani formu gerekse kulturyetişiriciliginde onemli bir yere sahip olan istiridye mantarı (Pleurotus ostreatus), beyaz Şapkali mantar (Agaricus bisporus) turunden sonra en Yaygün yetişirilenmantar turdur. Istiridye mantarı meş, kayın, gürgen gibi açaç kütükleri ile lignin ve selülozca zengin her turltarımsal bitki artiklar kullanılarak kolayıklayetişirilebilmektedir. Istiridye mantarı yetişiriligi sonunda ortayaçkan bitkisel atiklar hayvan beslenmesi ve tarımsal uretimde farkı amaçlar icin kullanılabilmektedir. Buğday samanı (WS), mırı sapı (CS), kavak talası (PS) ve Ferula communis bitki atigi (FPW) tek basına kullanınan ve bu substratlara %20 buğday kepeşi (WB) ve pirinci kepeşi (RB) eklenerek mantar üretim kompostlarinin denendişi calismada, Doğu Anadolu Bolgesınde kolaycabulun bilan FPW'nin, P. eryngii mantar yetişiriligi hem tek basına hem de WB veya RB ile karişirilaram kullanılabilir oldugu belirtilmektedir (Kibar 2016). Kompost hazirlamak icin hammadde olarak kullanılan 1 kg balya, pirinç kepeşi, mercimek artikları ve 50, 100 ve 150g dozlarsında ayç;cigi samanı katkı maddesi olarak kullanın calismada, en kisa surende pirinç kepeşinde misel sarimi elde edildigi, en yükbsek miktardaki toplam verim, 100 gram dozdaki mercimek atiklarında elde edildigi belirtilmektedir (Yildiz, 1998). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,428,487,495]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Odun talasları vefindik kabukları ile hazirlanan kompostlara asilanan shiitake mantar miseli tohumluğu calismasinda, en yüksek verimlilik ve biyolojik etkinlik degerleri meşte talasik kompostundan elde edildigi belirtilmektedir (Yalçın ve ark., 2020). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,497,487,577]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Orta Karadeniz Bölgesinden toplanan Lactarius pyragalus, L. controversus ve L. semisanguifluus türlerine ait mantar örneklerinden, L. pyragalus mantar türün kuru madde, kul, protein, N, Fe, Mg, Mn ve K içeriği bakimindan daha zengin oldugu belirtilmışı (Pekşen ve ark., 2007). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,579,487,715]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Bolu ilinin farkllokasyonlarindan elde edilen 4 farklizolatin (PO-141, PO-142, PO-143 ve PO-144) saman, talas ve kepek karisimindan $(\\\\% 45$ saman $^+$ $45$ talas $^+$ $10$ kepek) olusan ortamda, misel gelisim suresi, ilk hasat suresi, mantar aigriligi, verim, sapka uzunlugu, sapka eni, sap uzunlugu, sap capi, mantarin renk ozellikleri, pH, kul, kuru madde, SCKM (suda czünebilir kuru madde) ve protein iceriklerinin bakildigi calismada en yuksek verimin PO-143 izolatindan elde edildigi belirtilmistir (Kibar, 2019). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,715,487,784]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Atik cay yaprakları, bugday kepeşi, tavuk gübresi ve Güvercin gübresi gibi aktivator malzemelerin karıminin incelendişi calismada atik cay ile bugday kepeşi karıminda en iyi mantar veriminin/elde edildigi belirtilm,stir (Yigitbası ve ark., 2007). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,784,487,852]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Baobab meyvesi, bugday samani, misir kocani ve talas ortamilarinin istiridye mantarinin verimi ve biyolojik etkinligine bakildigi calismada en iyi sonuc bugday samani ve en duşuk sonuc ise baobab meyve kabugundan elde edildigi belirtilmistir (Tavarwisa ve ark., 2021). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,852,487,921]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Farkl P. ostreatus ceşitlerinin buyümesini ve verimini degerlendirmek amacíyla, Çeltik samani, buğday samani, talas ve bunlarin kombinasyonları ortamilarnda üretilen mantarlarda en iyi verim buğday samanindan elde edildigi belirtilmektedir (Abid ve ark., 2020). Pleurotus mantar \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,87,904,141]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"türünun bugday, celtik, arpa, misiR, cay yapragi vb. ve samanları ortamlarında yapilan üretim calismasında en iyi sonucun bugday ve celtik samanlarında elde edildigi belirtilmistir (Garg ve ark., 2017). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,141,904,223]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Istiridye mantarin (P. ostreatus) üretim imkânlarını araşirildigi calismada, tekstin atişi ve zeytin posasi ortamlarina %75, %50 ve %25 oranlarinda meşte talası karşirilarak hazirlanan ortamları, misel gelisiimi, hasat süresi, verim ve biyolojik etkinlik (BE) üzerine olumlu etki attigi belirtilmektedir (Sözbir 2021). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,224,904,347]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dūnyada en fazla üretimi yapilan Pleurotus spp., Pleurotus major-caju ve Pleurotus ostreatus türlerinin bugday samani, bugday kepeşi, Çeltik kavuzu (pirinç kavuzu) ve parçalanmş misir koçani materyalleri ve bunlarin degişik oranlarda hazırlanan karişimlarda, en yüksek mantar verimi ve biyolojik etkinlik orani, %60 bugday samani + %40 misir koçani ve %95 bugday samani + %5 bugday kepeşi uygulamalarindan elde edildigi belirtilmektedir (Aksu ve Uygur 2005). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,347,905,659]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dört istiridye mantari türün, Pleurotus ostreatus (gri), P. ostreatus (beyaz), P. cornucopiae var. citrinopileatus (parlak sari) ve P. Salmonoestramineus (pembe) %100 bugday samani, %70 bugday samani, %20 beyaz talas ve %10 hurma lifi, %50 bugday samani, %50 beyaz talas olmak üzere üç ortamda, karpoflorarin C, N, Co, Pb, Fe, Ni, Cu, Zn, Cd ve Mn iceriginin etkilerinin incelendişi calismada, üç ortamda da mineral elementler acisindan istatistiksel olarak fark olmadigi belirtilmektedir (Owaid ve ark., 2015). Kultur mantarlarinin besin iceriklerinin araşirildigi calismada; N, P, K, Ca, Mg, Fe, Cu, Zn ve Mn iceriklerinin istatistiksel olarak buyük farklihlkar gosterdiigi ve bu farkliliŋin farkli ticari isletmelerden alinmasi ve farkl i kymasal bileşmlere sahip olmasindan kaynaklandigi belirtilmistir (Sönmez ve ark., 2016). Ganoderma lucidum mantarlarinin verim ve morfolojik özellikleri uzerine etkilerini belirlendişi calismada, meşehizar tozu (ince tala) ve odun yongasi (kaba talas) ile %10, 15, 20 ve 25 oraninda Cay atigi (CA) karissimarindan hazirlanan yetistirme ortamlari kullanımsi sonucunda en yüksek verim meşene odun yongasinda elde edildigi belirtilmektedir (Yakupoğlu ve Pekşen, 2011). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,675,660,689]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Materyal ve Yontem \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,701,904,810]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Istiridye mantarinin (Pleurotus ostreatus (gri))yetistricilik ortamlarinda performanslarinin belirlenmesi amacyla yapilan bu calisma, 2 litrelik misel asili hazir kitler (%90 meş talaşi + %10 bugday kepeşi), Denizli ilinde bulunan Agroma sirketinden temin edilm,stir. Yetistirme ortam olarak, bugday samani veçay artigi kullanlm,stir. Deneme tesaduf parselleri deneme desanine gore üc tekerrurlu olarak dizayn edilm,stir. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[504,810,904,921]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Ev veçay ocaklarinda demlenmis ve atik durumdakiçay artiklari ile bugday samanlari $100^{\\\\circ}\\\\mathrm{C}$ de 1 saat kaynatildiktan sonra temiz bir ortü uzerinde sogumayabirakilmistir. Soguyan saman veçay atiklari 2 litrelik plastik torbalara bir sira yaklaşik 5-6 cm kalinliginda %100 bugday samani ve 1 sira ise tohumluk misel homojen bir dagilmla posetlerin dinisa dokru asilama yapilmis ve her bir 2 litrelik turbada 25 g tohumluk misel kullanilmistir. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,40,774,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Çetin et al. / Turkish Journal of Agriculture - Food Science and Technology, 11(1): 29-34, 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[885,929,905,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"30 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[89,66,487,148]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Miseller aşlandık tan sonra misel geleşimi icin 20-25°C sıçaklık, %90 nem ve %100 karanlık oluzturmak amacıyla 8 günk iklim odasinın isikları acılmamıştir. Nem oluzturmak icin iklim odasa su dolu kaplar konulmugs ve zemin hergün sulanmıştir. Sıçaklık ile elektriklı istificantar ile saglanmıştir. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[115,162,312,175]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Yaplan Ölçüm ve Analizler \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,175,487,231]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Calismada farkli ortamlarda istiridye mantari uretim calismasinda, ilk hasat, karpofor, toplam verim, mantar olculeri, makro ve mikro element analizleriGPCklestirilmistir. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,244,184,256]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Irk Hasat \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,256,487,299]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Ilk hasat missellerin asilandig tarihten itibaren ilk urun alindigi tarih arasindaki gezcen surenin gun olarak belirlenmesiyle bulunmustur. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,313,240,326]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Karpofor Aigrilgi \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,326,487,354]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Karpoforagrlhig,hasat edilen mantar orneklerinin hassas terazide tartulmasiyla gram olarak hesaplanmistir. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,367,220,380]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Toplam Verim \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,380,487,435]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Her bir mantar kitinden elde edilen urunlerin, ilk hasattan son hasada kadar hassas terazide tartimlarinin yapilmasi ve bunlarin toplanmasi ile gram cinsinden belirlenmistir. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,449,302,463]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sap Uzunluğu ve Kalınkı \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,463,487,489]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Istiridye mantarlarinin nap kalinligi ve uzunlugu djital kumpas ile mm cinsinden olçumlustür. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,504,226,517]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"KarpoforAlani \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,517,487,545]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Istiridye mantar ornekleri kagida qizilip, planimetre ile $\\\\mathrm{cm}^2$ cinsinden olçulup hesaplanmistr. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[114,558,310,571]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mineral Element Analizleri \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,571,487,708]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Her mantar ortamindaki kitlerden alinan istiridye mantar ornekleri once açıkta daha sonra $65^{\\\\circ}\\\\mathrm{C}^\\\\prime$ de 48 saat etüvde kurutulduktan sonra $550^{\\\\circ}\\\\mathrm{C}$ kül firqinnda kül olusuncaya kadar yakilm生物质. Elde edilen kül, $\\\\% 3,3^{\\\\prime}$ luk HCl' de gezündürulm ve mavi bantl滤tre kagensinda suzuldukten sonra makro ve mikro besin elementi okumaları Yüzuncu Yl Universitesi Bilimsel Araştrima ve Uygulama Merkezinde atomik absorbsiyon cihazinda yapilm生物质 (Kabay 2019; Kacar ve ark., 2006; Kuşvuran, 2010). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[531,66,727,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Verilerin Degerlendirilmesi \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,80,905,231]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Istiridye mantar turu uretim ortamlarindaki kitlerden elde edilen ilk hasat, karpofor aigriligi, mantar olçuleri, makro ve mikro besin elementi iceriklerininarasindaki farkliliigi belirlemek icin tek yönlu varyans analizi uygulanmiistr (Yeşilova ve Denizhan, 2016). Varyans analizi sonucunda uretim ortamindaki parametreler arasi fark istatistiksel olarak onemli bulundugunda, hangi parametrelerin birbirinden farkl oldugunu saptamak icin Duncan Coklu Karılaşirma Testi kullanilmistr (Duncan, 1955). Verilerin analizi SAS 9.1.4. istatistik yazilim programinda yapilmistr (SAS, 2018). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,244,665,258]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Bulgular ve Tartışma \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,271,905,338]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Van ve cevre illerde istiridye mantar uretiminin efektif bir sekildegerekelestirilebilecegini gostermek amaciyla, bolgede kolay temin cay artig ve buğday samani ortamlarinda istiridye mantar uretimi, ticari olarak uretim yapan sirketlerin hazirladig ortamlarla kiyasanmistir. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,340,905,449]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Yapilan calismada, istiridye mantarinin saman ve cay ortamlarinda yetişirilmesinde ilk hasatgün sayilari, istatistiksel olarak aynı grupta yer almistir. Saman ortamnda tohumluk misel ekiminden 38,25跑去 sonra ilk hasat yapilrken, cay ortamnda 37,0跑去 ilk hasatGPCklesmiistir. Hazir kit olarak adlandirilan, firmadan temin edilen ve meşete talas+bugday kepeşi ortamnda ekildigi durumunda isel ilk hasat 33,25跑去 yapilmstir (Cizelge 1). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,449,904,531]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Karpofor aigrigi verilerinde istatistiksel olarak fark görtelmemistir. Yani ticari anlamda üretim yapan sirket ortamyla ayni aigriga sahip mantarlar elde edilmistir. Saman ortaminda karpofor aigrigi 22,01 g, Cay ortamnda $23,35\\\\mathrm{g}$ ve hazir kit ortamnda ise 22,13 g olmustur (Cizelge 1). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,531,905,599]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Ilk hasattan son hasada kadar her uretim ortamindaki toplam verim bakimindan istatistiksel olarak ortamlararasindaki fark gorulmemistir. Saman ortaminda toplam verim 1249,16 g, cay ortaminda toplam verim 1293,35 g ve hazir kit ortaminda ise 1356,09 g urun alinmistr. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,599,905,709]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Bugday samani (WS), misi r sapi (CS), kavak talaşi (PS) ve Ferula communis bitki atigi (FPW) tek basina kullananan ve bu substratlara%20 bugday kepegi (WB) ve pirinç kepegi (RB) eklenerek mantar üretim kompostlarinin denendişi calismada, Doğu Anadolu Bölgesi nde bol miktarda ve kolayca bulunabilen FPW'nin, P. eryngii mantar yetistiriciligiinde hem tek basina hem de WB veya RB ile karişürilarak kullanilabilir oldugu beirtilmistir (Kibar 2016) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,749,904,808]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0644/79d42dc8c2888b0587e97febfe3aaa7745da72bdf6499aeee65f8524f564f220.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Tür</td><td>Ortam</td><td>İlk hasat(gün)</td><td>Karpofor ağırkıngı(g)</td><td>Toplam verim (g)</td></tr><tr><td rowspan=\\\"3\\\">İstiridye mantarı</td><td>Saman</td><td>38,25a</td><td>22,01a</td><td>1249,16a</td></tr><tr><td>Çay</td><td>37,0a</td><td>23,35a</td><td>1293,35a</td></tr><tr><td>Hazır kit</td><td>33,25b</td><td>22,13a</td><td>1356,09a</td></tr></table>\",\n \"table_caption\": \"[\\\"Cizelge 1. Üretim ortamlarindaki mantar ilk hasadı (gün), karpofor ağırkı (g) ve toplam verim (g) Table 1. Mushroom first harvest (days), carpophore weight (g) and total yield (g) in production media \\\"]\",\n \"table_footnote\": \"[\\\"P<0,05 \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[92,858,904,917]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0874/1062fa9ecc6fd8d292d7b14feaf9e9795f9e69d702e53a28ba1468ce51bf8fea.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Çeşit</td><td>Ortam</td><td>Karpofor uzunluk (mm)</td><td>Karpofor kalınlık(mm)</td><td>Karpofor alanı (cm2)</td></tr><tr><td rowspan=\\\"3\\\">İstridye mantarı</td><td>Saman</td><td>3,53a</td><td>2,42a</td><td>61,09a</td></tr><tr><td>Çay</td><td>3,58a</td><td>2,45a</td><td>60,25a</td></tr><tr><td>Hazır kit</td><td>3,61a</td><td>2,39a</td><td>62,96a</td></tr></table>\",\n \"table_caption\": \"[\\\"Cizelge 2. Üretim ortamlarindaki karpofor ölcüleri ve karpofor alanı (cm²) \\\\nTable 2. Carpophore dimensions and carpophore area in production media (cm²) \\\"]\",\n \"table_footnote\": \"[\\\"P<0.05 \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[220,40,774,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Çetin et al. / Turkish Journal of Agriculture - Food Science and Technology, 11(1): 29-34, 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[885,929,902,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"31 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[92,93,905,152]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0177/48851929a9cb28fada395043eb4b6ddd7efbe15653870a87cf9c63f88c786717.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Çeşit</td><td>Ortam</td><td>K (%)</td><td>Ca (%)</td><td>Mg (%)</td></tr><tr><td rowspan=\\\"3\\\">İstridye Mantari</td><td>Saman</td><td>0,46b</td><td>0,05b</td><td>0,14b</td></tr><tr><td>Çay</td><td>0,63a</td><td>0,06ab</td><td>0,15ab</td></tr><tr><td>Hazır kit</td><td>0,67a</td><td>0,07a</td><td>0,17a</td></tr></table>\",\n \"table_caption\": \"[\\\"Cizelge 3. Farkl üretim ortamlarindan elde edilen mantarlarin K, Ca ve Mg icerikleri (%) \\\",\\\"Table 3. K, Ca and Mg contents of mushrooms obtained from different production media (%) \\\"]\",\n \"table_footnote\": \"[\\\"$\\\\\\\\mathrm{P < 0.05}$ \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[92,203,905,263]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": \"images/0690/e6762e34a39bd58f25a55a46d8cf17ff34bba60352f9758bec9da93df892e829.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": \"<table><tr><td>Çeşit</td><td>Ortam</td><td>Fe (ppm)</td><td>Zn (ppm)</td><td>Mn (ppm)</td><td>Cu (ppm)</td></tr><tr><td rowspan=\\\"3\\\">Istridye mantari</td><td>Saman</td><td>66.97a</td><td>146.26b</td><td>4.06b</td><td>74.36a</td></tr><tr><td>Çay</td><td>66.44a</td><td>151.18ab</td><td>4.17ab</td><td>74.29a</td></tr><tr><td>Hazır kit</td><td>69.22a</td><td>153.91a</td><td>4.60a</td><td>76.85a</td></tr></table>\",\n \"table_caption\": \"[\\\"Cizelge 4. Farkl üretim ortamlarindan elde edilen mantarlarin Fe, Zn, Mn ve Cu icerikleri (ppm) \\\",\\\"Table 4. Fe, Zn, Mn and Cu contents (ppm) of mushrooms obtained from different production media \\\"]\",\n \"table_footnote\": \"[\\\"P<0.05 \\\"]\",\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"table\"\n },\n {\n \"bbox\": \"[92,287,485,423]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Kompost hazirlamak icin hammadde olarak kullanlan $1\\\\mathrm{kg}$ balya, pirinç kepeghi, mercimek artikları ve 50, 100 ve $150\\\\mathrm{g}$ dozlarnda ayciçehi samani katkı maddesi olarak kullanlan calismada, en kisa surede pirinç kepeşinde sarim saglandı, en yüksek toplam verim, $100\\\\mathrm{g}$ mercimek atigianda elde edildigi belirtilmektedir (Yildüz, 1998). Mantar uretiminde turbalarin mantar uretim substratina onemli bir girdi ve kompost malzemelerine $\\\\% 60$ ve $\\\\% 36$ katkı bulundugu belirtilmektedir (Robinson ve ark., 2019). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,424,485,558]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Odn talasları ve finden kabuklari ile hazirlanan kompostlara asilanan shiitake mantar miseli calismasindo, %100 finden kabugu ile üretilen mantarların, meş ve kayın talasına,göre verim bakimindan daha Dennis degerler verdişi tespit edilirken, en yuksek verimlilik ve biyolojik etkinlik degerleri meş talasik kompostundan elde edilmis, kimiyasal icerik sonuclarina,göre, finden kabugu ve karsımları toplam azot ve protein bakimindan en yuksek degerlere sahip oldugu belirtilmektedir (Yalçın ve ark., 2020). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,561,485,627]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Yapilan calismada mantar sap uzunluklarinin ortamlararasindaki fark istoristikselormalk onemsiz cikmistr. Saman ortamindaki mantar sap uzunlugu $3,53\\\\mathrm{mm}$ ,cay ortaminda 3,58 ve hazir kit ortamnda ise $3,61~\\\\mathrm{mm}$ olarak olculmustur. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,629,485,711]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Istiridye mantarlarinin üretim ortamilarndaki mantar sap kalinligıarasinda istatistiksel olarak fark görtulmemişir. Sasan ortamindaki sap kalinligı 2,41 mm,çay ortamindaki sap kalinligı 2,45 mm ve hazir kit ortaminda ise sap kalinligı 2,39 mm olarak olçülm,stür (Cizelge 2). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,711,485,806]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mantar üretim ortamlarindaki karpofor alanlariyla ilgili veriler sekil Çizelge 2 de verilmistir. Çizelge incelendigiinde ortamlardaki karpofor alanlariarasinda istatistiksel olarak fark güruml memistir. Saman ortamnda mantar karpofor alanı $61,09~\\\\mathrm{cm}^2$ ,çay ortamnda 60,25 ve hazir katte ise karpofor alanı $62,96~\\\\mathrm{cm}^2$ olarak olçumlustir (Çizelge 2). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,807,485,916]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Ganoderma lucidum mantarinda farkl ortamarin verim ve morfolojik özellikleri üzerine etkilerini belirlendigi calismada, meşehizar tozu (ince talaş) ve odun yongası (kaba talaş) ile %10, 15, 20 ve 25 oranindaçay atişi (CA) karişimilarindan hazirlanan yetistirme ortamlari kullanimasi sonucunda en yüksek verim meşehodun yongasında 73,07 g/kg ortam ile 90:10 CA ortamindan, meşehizar tozu ile hazirlanan karişmlarda ise 21,21 g/kg \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,287,902,313]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ortam ile 75:25 CA ortamindan elde edildigi belirtilmektedir (Yakupoğlu ve Pekşen, 2011). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,315,902,382]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Pleurotus mantar türünun bugday, celtik, arpa, misir vb.çay yaprakları ve samanlari ortamlarinda yapilan üretim calismasinda en iyi sonucun bugday ve celtik samanlarinda elde edildigi belirtilmistir (Garg ve ark., 2017). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,382,902,464]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Istiridye mantarin (P. ostreatus) üretim imkânlarinin araşirildigi calismada, tekstil atigi ve zeytin posasi ortamlarina %75, %50 ve %25 oranlarinda meştaşa karişirilarak hazirlanan ortamlarda, misel gelisimi, hasat suresi, toplam zaman, verim ve biyolojik etkinlik üzerine olumlu etki attigi belirtilmektedir (Sözbir 2021). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,464,902,574]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Pleurotus sajor-caju ve Pleurotus ostreatus türlerinin, buğday samani, buğday kepeşi, Çeltik kavuzu (pirinç kavuzu) ve parçalanmş mır koşani materyalleri ve bunlarin degişik oranlarda hazirlanan karişimlarda, en yüksek mantar verimi ve biyolojik etkinlik orani, %60 buğday samani + %40 mır koşani ve %95 buğday samani + %5 buğday kepeşi uygulamalarindan elde edildigi belirtilmşir (Aksu ve Uygur 2005). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,574,902,642]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Bu denemede degerlendirilen yetistricticilik ortamlarinda yapilan uretim ile hazir yetistricticilik ortamlarinda elde edilen mantarlin karpofor olculeri ve alanıarasinda istatistiksel olarak fark g Ruralmemis olup diger calismalarla benzer sonuclar elde edilmestiţir. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[509,643,904,901]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Mantar üretim ortamlarindan elde edilen istiridye mantarlarinin K (potasyum) iceriigi istatistiksel olarak onemli bulunmustur. Çizelge 3'de deGORuldugu gibi, saman ortamlarinda üretilen istiridye mantarinin potasyum iceriigi %0,46,çay ortaminda %0,63 ve hazir kit (%90 meşete talas + %10 buğday kepeşi karişimi) ortaminda %0,67 olarak tespit edilmşir (Çizelge 3). Kalsiyum (Ca) icerikleri incelendigiinde ortamlararasinda fark istatistiksel olarak onemli bulunmustur. Sasan ortamlarinda üretilen istiridye mantarinin kalsiyum (Ca) iceriigi %0,052,çay ortaminda kalsiyum (Ca) %0,061 ve hazir kit (%90 meşete talas + %10 buğday kepeşi karişimi) ortaminda %0,068 olarak belirlenmustir (Çizelge 3). Magnezyum (Mg) icerikleri incelendigiinde, ortamlararasinda fark istatistiksel olarak onemli bulunmustur. Sasan ortamlarinda üretilen istiridye mantarinin magnezyum (Mg) iceriigi %0,052,çay ortaminda %0,061 ve hazir kit (%90 meşete talas + %10 buğday kepeşi karişimi) %0,068 olarak tespit edilmşir (Çizelge 3). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[510,902,902,929]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Uretilen istiridye mantarlarinin mikro besin elementlerden demir (Fe) icerigi istatistiksel olarak onemli \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[220,40,774,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Çetin et al. / Turkish Journal of Agriculture - Food Science and Technology, 11(1): 29-34, 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[885,931,904,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"32 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[92,66,485,380]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"bununmustur. Cizelge 4'de de güruldügün gibi samsam ortamlarinda üretilen istiridye mantarınim demir (Fe) icerişi 66,44 ppm,çay ortaminda 66,98 ppm ve hazir kit (%90 meşte talası+%10 buğday kepeşi karişi) ortaminda 69,22 ppm olarak tespit edilmşir (Cizelge 4). Cinko (Zn) icerikleri incelendigiinde ortamlararasinda fark istatistiksel olarak onemli bununmustur. Saman ortaminda üretilen istiridye mantarınin Cinko (Zn) icerişi 146,26 ppm,çay ortaminda 151,18 ppm ve hazir kit (%90 mese talası+%10 buğday kepeşi karişi) ortamnda 153,91 ppm olarak tespit edilmşir (Cizelge 4). Mangan (Mn) icerikleri incelendigiinde, ortamlararasindaki fark istatistiksel olarak onemli bununmustur. Saman ortaminda üretilen istiridye mantarınin Mangan (Mn) icerişi 4,058 ppm,çay ortamnda 4,17 ppm ve hazir kit (%90 mese talası+%10 buğday kepeşi karişi) ortamnda 4,61 ppm Çiqmşir (Cizelge 4). Bakır (Cu) icerikleri sekil ve Cizelge incelendigiinde ortamlararasinda fark istatistiksel olarak onemli bunmamşir. Saman ortaminda üretilen istiridye mantarınin bakir (Cu) icerişi 74,36 ppm,çay ortamnda 74,29 ppm ve hazir kit (%90 meşte talası+%10 buğday kepeşi karişi) ortamnda 76,85 ppm olarak tespit edilmşir (Cizelge 4) \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[92,382,485,749]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Dört istiridye mantari türände, P. ostreatus (gri), P. ostreatus (beyaz), P. cornucopiae var. citrinopileatus (parlak sari) ve P. salmonoestramineus (pembe), %100 buğday samani, %70 buğday samani, %20 beyaz talas ve %10 Irak hurma lifi, %50 buğday samani, %50 beyaz talas olmak üzere üç ortamda, karpoforlarin C, N, Co, Pb, Fe, Ni, Cu, Zn, Cd ve Mn icerikleri incelenmistir, üç ortamda da mineral elementler açisündan istatistiksel olarak fak gozemlenmis ve genel olarak, Fe, Ni ve Cd hazirlanan üretim ortamlarindan elde edilen mantarlarda ve karpofor verimlerinde artş oldugu belirtilmektedir (Owaid ve ark., 2015). Dogal yetişen mantar örneklerinde yapilan calismada, Besleyici oldugu ayrica Ca, K ve fe iceriklerinin yüksek oldugu belirtilmektedir (Aksoy ve ark., 2020; Selem ve ark., 2021). Samsun ve Ordu illerin bazı ilç ve köylerinden toplanan ve halk tarafindan tüketilen Lactarius pyragalus, L. controversus ve L. semisanguifluus türleri icinde, L. pyragalus mantar türün kuru madde, kul, protein, N, Fe, Mg, Mn ve K icerişi bakimindan.da zengin oldugu belirtilmistir (Peksen ve ark., 2007). Antalya'nin Korkuteli ilçesinde yetistirilen kultur mantarlarinin besin iceriklerinin arastrildigi calismada; N, P, K, Ca, Mg, Fe, Cu, Zn ve Mn iceriklerinin istatistiksel olarak buyuk farklıklar gösterligi ve bu farklıgün üretim ortamlarin farkli ticari isletmelerden alınması ve farklı kymasal bileşilmere sahip olmasindan kaynaklandigi belirtilmistir (Sonmez ve ark., 2016). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,750,487,818]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Bu calismada degerlendirilen yeti stiricilik ortamlarinda yapilan uretim ile hazir yeti stiricilik ortamlarinda elde edilen mantarlarda yaplan, olcum, gozlem ve analiz sonuclarinin diger arastirmacilarin yaptigi calismalarla benzer sonuclar oldugu tespit edilmistir. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[90,832,139,845]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Sonuc \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[89,858,489,928]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Van ve cevre illerde istiridye mantarinin üretimi cok azdir. Bu nedenle, bu calismada Van ve cevre illerde istiridye mantarinin üretiminin yayginlastrupimamacylya kolay temin edilen ortam sedan bugday samani ve atik olarak gürulen demlenmis Cay ortamlarinda üretilen \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,66,904,216]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"istiridye mantari orneklerinde ilk hasat, karpofor aigriligi, toplam verim, karpofor olçuleri ve karpofor alanı, makro ve mikro elementler iceriklerine bakilmışı. Mantar üretiminde kullananan %100 bugday samanı ve %100 çay ortamlarındaki ilk hasat, karpofor aigriligi, toplam verim, karpofor olçuleri ve karpofor alanı, makro ve mikro elementler icerik değerleri, Denizl’ de bulunan ticari mantar üretim sirketi Agroma firmasından temin edilen %90 meş talaşi ve + 10 bugday kepeşi seksmişindan olşan hazır kitlerden alınan mantar ornekleriyile benzer ve)yakın sonuclara varilmışı. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,217,904,258]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Bu calisma sonucunun özellikle Van ve cevresindeki mantar üreticileriISTA olmak üzere, tum arastirmacı ve üreticilere fayda saglayacağinancindayiz. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[507,271,589,285]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Kaynaklar \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[505,294,905,922]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Abid AH, Hamid A, Naz RMM, Shah SZA, Anjum S, Khan MT, Ilyas M. 2020. 74. Farkli lignoseluloz substratlartinin istiridye mantarinin (Pleurotus ostreatus) buyümesi ve verimi üzerindeki etkisi. Saf ve Uygulamali Biyoloji (PAB), 9(1): 768-775. \\\",\\\"Aksoy C, Aksoy H, Tirasoglu E, Üçler AÖ. 2020. Ordu (Mesudiye ve Kabadüz) Köy ve Yaylalarminda Yetişen Bazı Tübbi ve Aromatik Bitki ve Mantar Örneklerinde Ca, K ve Fe Element Analizi. Türk Tarım-Gida Bilim ve Teknologi dergisi, 8(3): 694-697. \\\",\\\"Aksu S, Uygur AM. 2005. Bazı kayınmantarı (Pleurotus spp.) türlerinin organik olarak üretimi üzerinde araşirmalar. Anadolu Ege Tarımsal Araşirma Enstitü Sü Dergisi, 15(2): 1-26. \\\",\\\"Cat A, Comak T, Catal M. 2018. Istiridye mantarinin (Pleurotus ostreatus) tohumluk misel uretimi uzerine bir on calisma. Mediterranean Agricultural Sciences, 31(1): 21-25. \\\",\\\"Duncan DB. 1955. Multiple range and multiple F test. Biometrics, 11: 1-42. \\\",\\\"Fukushima M, Shimada KI, Ohashi T, Saitoh H, Sonoyama K, Sekikawa M, Nakano M. 2001. Investigation of gene expressions related to cholesterol metabolism in rats fed diets enriched in n-6 or n-3 fatty acid with a cholesterol after long-term feeding using quantitative-competitive RT-PCR analysis. Journal of nutritional science and vitaminology, 47(3): 228-235. \\\",\\\"Garg P, Saxena G, Kanodia S, Gupta S. 2017. Conversion of Urban Waste into Highly Nutritious Food by Pleurotus Cultivation. \\\",\\\"Hanger 2021. https://www.hayger.com/istiridye-mantar-yetistiriciligi.html \\\",\\\"Kabay T. 2019. Effects of different potassium doses on development of high temperature-sensitive bean plants. Fresenius Environmental Bulletin, 28(1): 320-325. \\\",\\\"Kacar B, Katkat B, Öztürk Ş. 2006. Bitki Fizyolojisı. 2. Baskı. Nobel Yayın Dağıtmı, Ankara. 563. \\\",\\\"Kibar B. 2016. Farklı Yetişirme Ortamlarinin Pleurotus eryngii Mantarinin Gelifimi ve Verimi Üzerine Etkileri. Uluslararasi Tarim ve Yaban Hayati Bilimleri Dergisi, 2(1): 1-9. \\\",\\\"Kibar B. 2019. Farkl Pleurotus ostreatus (Istiridye Mantari) Izolatlarin Verim ve Baz Kalite Özelliklerinin Belirlenmesi. Uluslararası Tarim ve Yaban Hayat Bilimleri Dergisi, 5(2): 223-230. \\\",\\\"Kurt R, Can A, Sivrikaya H. 2018. \\\\\\\"The current status with the problems and some suggestions of mushroom cultivation in Bartin province.\\\\\\\"Bartin Orman Fakultesi Dergisi 20.2: 176-183. \\\",\\\"Kusvuran S. 2010. Kavunlarda Kuraklik ve Tuzluluğa Toleransi Fizyolojik Mekanizmaları Arasindaki Baglantilar (Doktora tezi, basilmamı). Ükurova Üniversitesi, Fen Bilimleri Enstitusi, Adana. \\\"]\",\n \"page_idx\": \"4\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[220,40,774,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Çetin et al. / Turkish Journal of Agriculture - Food Science and Technology, 11(1): 29-34, 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[885,929,904,942]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"33 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[90,65,487,385]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Ma Y, Li X, Fu Z, Zhang L. 2019. Structural design and thermal performance simulation of shade roof of double-slope greenhouse for mushroom-vegetable cultivation. International Journal of Agricultural and Biological Engineering, 12(3): 126-133. \\\",\\\"SAS, 2018. SAS/Stat Software Hangen and Enhanced. SAS Institute Incorporation, Cary, NC. \\\",\\\"Owaid MN, Al-Saeedi SSS, Abed IA. 2015. Beyaz, gri, sarı ve pembe istiridye mantarlarınin (yüksek mantarlar) mineral madde icerişi. Gida, 40(6): 319-326. \\\",\\\"Peksen A, Kibar B, Yakupoglu G. 2007. Yenilebilir bazı lactarius türlerinin morfolojik Özelliklerinin, protein ve mineral iceriklerinin belirlenmesi. Anadolu Tarim Bilimleri Dergisi, 22(3): 301-305. \\\",\\\"Robinson B, Winans K, Kendall A, Dlott J, Dlott F. 2019. A life cycle assessment of Agaricus bisporus mushroom production in the USA. The International Journal of Life Cycle Assessment, 24(3): 456-467. \\\",\\\"Sönmez S, Üras DS, Demir E, Nil ÖZEN, Kılıç E. 2016. Antalya-Korkuteli Yöresinde Üretilen Kultur Mantarların (Agaricus bisporus) Beslenme Durumlarin Belirlenmesi. Cukurova Tarım ve Gida Bilimleri Dergisi, 31(3): 215-219. \\\",\\\"Sözbir GD. 2021. istiridye mantarin (Pleurotus ostreatus) yetistirilmesinde bazı endüstriyel atikları kullanım olanakların bilirlenmesi. Turkish Journal of Forest Science, 5(1): 187-197. \\\"]\",\n \"page_idx\": \"5\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[509,65,905,424]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": \"[\\\"Selem E, Alp Y, Sensoy S, Uzun Y, Cavusoglu S, Karatas N, Ercisli S, Yilmaz N, Ekiert H, Hosam OE, Szopa A. 2021. Biochemical and Morphological Characteristics of Some Macrofungi Grown Naturally. Journal of Fungi, 7(10): 851. \\\",\\\"Tavarwisa DM, Govera C, Mutetwa M, Ngezimana W. 2021. Baobab meyve kabuklarin n istiridye mantar (Pleurotus ostreatus) yetistirmek icin substrat olarak uygunluğunun degerlendirilmesi. Uluslararasi Tarim Bilimleri Dergisi. \\\",\\\"Yakupoglu G, Peksen A. 2011.çay atıgindan hazirlanan farkl kompost ve partikul��kılığün Ganoderma lucidum mantarinin verimi ve bazimorfolojik özellikleri üzerine etkisi. Ekoloji, 20(78): 41-47. \\\",\\\"Yalçın M, Akçay C, Sözbir GD. 2020. Meş, Kayın Odunu ve Fündüz Kabugu Atıklardan Lentinus edodes (Şitaki) Mantari Üretimi. Düzce Universitesi Bilim ve Teknoloji Dergisi, 8(3): 2051-2061. \\\",\\\"Yesilova A, Denizhan E. 2016. Modelling mite counts using poisson and negative binomial. Fresen. Environ. Bull. 25,5062-5066. \\\",\\\"Yildiz A. 1998. Effects of Various Proportions of Different Additive Substances on the Miselle Growth of Pleurotus florida Fovose, on Druation of Formation and Development of Basidiocarps and on the Yield. Turkish Journal of Biology, 22(1): 127-142 \\\",\\\"Yigitbasi ON, Baysal E, Colak M, Toker H, Simsek H, Yilmaz, F. 2007. Cultivation of Agaricus bisporus on some compost formulas and locally available casing materials. Part II: Waste tea leaves-based compost formulas and locally available casing materials. African Journal of Biotechnology, 6(2). \\\"]\",\n \"page_idx\": \"5\",\n \"sub_type\": \"ref_text\",\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"list\"\n },\n {\n \"bbox\": \"[220,40,774,53]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Çetin et al. / Turkish Journal of Agriculture - Food Science and Technology, 11(1): 29-34, 2023 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[885,929,904,941]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"34 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n }\n]","isConversational":false},"doi":{"kind":"string","value":"10.24925/turjaf.v11i1.29-34.5181"},"is_oa":{"kind":"bool","value":true,"string":"true"},"language":{"kind":"string","value":"en"},"sci_category":{"kind":"string","value":"Medicine and Health Sciences"},"sha256":{"kind":"string","value":"cbaa1c99410bebd4aafb5ac24f7b129d82fabd419825e7f532c14b38e4fe22d8"},"title":{"kind":"string","value":"Farklı Üretim Ortamlarının İstiridye Mantarı (Pleurotus Ostreatus) Üretiminde Verim ve Kalite Üzerine Etkisi"}}},{"rowIdx":275,"cells":{"abstract":{"kind":"string","value":""},"author":{"kind":"string","value":"Oleg E. Sidoryuk|Peter Y. Lobanov|Pavel I. Abramov|Leonid A. Skvortsov|Eugene V. Kuznetsov"},"content_list":{"kind":"list like","value":[{"bbox":"[60,131,243,144]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"PAPER • OPEN ACCESS ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,157,919,201]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Pulse laser thermography as a non-destructive method of latent surface defects of materials ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[60,219,611,232]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"To cite this article: Pavel I. Abramov et al 2020 IOP Conf. Ser.: Mater. Sci. Eng. 904 012001 ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,273,389,286]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"View the article online for updates and enhancements. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[60,42,596,60]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conference Series: Materials Science and Engineering ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[245,938,751,950]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"0","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"This content was downloaded from IP address 61.6.233.111 on 04/11/2020 at 18:44 ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[115,229,818,272]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Pulse laser thermography as a non-destructive method of latent surface defects of materials ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[235,307,848,337]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Pavel I. Abramov, Eugene V. Kuznetsov, Peter Y. Lobanov, Oleg E. Sidoryuk and Leonid A. Skvortsov<sup>a</sup> ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[235,344,721,360]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"JSC Polyus Research Institute of M.F.Stelmakh, Moscow, Russia ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[235,388,416,406]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"aIskvortsov@gmail.com ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[233,419,880,514]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Abstract. The time dependences of the surface temperature increment of painted metal objects were studied depending on the thickness of the layer subjected to corrosion, as well as putty, restoring erosion defects on it. Hidden under a layer of paint, they cannot be detected remotely during normal visual observation. At the same time they are well detected by pulsed laser thermography. The experimental data in the work are compared with the results of mathematical modeling. Particular attention is paid to eliminating possible distortions caused by external contamination of the tested objects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[115,542,250,556]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1. Introduction ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[115,557,882,722]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Remote detection of latent defects on the surface of materials based on active photothermal radiometry (thermography) is a very attractive technology, the beginning of which was laid in the late 70s - early 80s of the last century [1 - 4]. Over the years, this technology has undergone significant development. In the broad sense of the word, one can speak of flash thermography [5, 6] and modulation (lock-in) IR thermography [7, 8]. In this case pulsed, or non-stationary, thermography is the most common form of non-destructive assessment of the object of study using the thermographic method (NDE, nondestructive evaluation) [9 - 13]. This is due to the possibility of studying significant areas on the surface of the object in the presence of a high-speed IR camera with a large field of view, which is of fundamental importance for increasing the productivity of non-destructive testing of materials. Therefore, the main attention in the future will be given to the possibilities and development of this particular type of material research. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[115,722,880,903]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The physical principle underlying the use of flash thermography for non-destructive testing is to measure the time dependence of surface temperature changes, while lock-in thermography allows you to study the phase of the photothermal signal. In both cases, the difference in thermal diffusion in different places of the sample due to the presence of defects and inhomogeneities in it affects the measurement result. In other words, subsurface defects change the rate of thermal diffusion, thereby manifesting itself in a change in the parameters of the recorded photothermal signal in the places where defects exist relative to areas where they are absent. Any inhomogeneities, such as inclusions, subsurface defects, or porous formations distort the propagation of thermal waves and modify the temperature response on the surface of the sample in comparison with the defect-free region. Due to the direct relationship between the thermal and mechanical properties, the detection of the distribution of the thermal signal allows mapping of the physical properties of the material under study during its scanning. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,64,208,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ICMSC 2020 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,64,880,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Publishing ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,80,880,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conf. Series: Materials Science and Engineering 904 (2020) 012001 doi:10.1088/1757-899X/904/1/012001 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,913,198,934]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"CC BY ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[200,913,880,936]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[112,938,369,950]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Published under licence by IOP Publishing Ltd ","text_format":null,"text_level":null,"type":"footer"},{"bbox":"[497,940,507,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"1","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"1 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[110,134,882,223]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The development of flash thermography and lock-in thermography methods is pulse phase thermography based on the application of the Fourier transform to the function of temperature change over time [14, 15]. Pulse phase thermography maximally implements the idea of taking into account the fundamental differences in temperature evolution in defective and defect-free (reference) areas of the test object. However, its implementation in practice requires considerable time, since one has to deal with sequences consisting of several hundred and even thousands of images. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[110,224,884,313]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the classic active pulsed thermographic technique (flash thermography), the studied surface of the object is heated under the influence of radiation from one or several flash lamps, after which its cooling is recorded using an IR camera. This method has long been used for non-destructive and noncontact investigation of interfaces between the surface layer (coating) and the base material (substrate), for example, to detect adhesion defects (delaminations), local corrosion foci, surface cracks that change the one-dimensional heat flux from the surface [13]. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[110,315,880,404]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"However, a significant divergence of radiation from flash lamps and its low spectral brightness significantly limit the scope of flash thermography, in particular, when testing objects located at a considerable distance from the heating source. At the same time, just such a task is currently gaining more urgency and attention of researchers, since it is related to remote monitoring of structures, for example, in the form of bridges, tanks for transporting and storing petroleum products, liquefied gas, car bodies, building walls and etc. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,405,882,464]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The aim of this work is to demonstrate a new approach for remote monitoring of the surface condition of various structures located at considerable distances from the heating source using pulsed laser thermography, which excludes the influence of external factors (for example, contamination of the object's surface) on the detection of \"camouflaged\" subsurface defects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,464,882,510]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The solution to this problem became possible in connection with the creation of powerful and at the same time compact semiconductor lasers emitting at different wavelengths of the electromagnetic spectrum (from UV to far IR). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,524,304,539]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2. Experimental setup ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[112,569,882,600]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The studied sample (1) is affected by laser radiation pulses (2) formed by an electromechanical chopper (3). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[191,605,495,825]","code_body":null,"code_caption":null,"image_caption":"[\"Fig.1 shows an experimental setup for remote analysis of the surface of materials by means of pulsed laser thermography. \"]","image_footnote":"[]","img_path":"images/0385/b9ef0ef8dbd9647c0ce70bca10a2fdc49f5c3e2a98df43b71557601b1eac5b41.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[611,596,842,825]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 1. a) Scheme of non-destructive testing of hidden subsurface defects using laser pulse thermography; b) Photo of the experimental setup. \"]","image_footnote":"[\"1 — sample, 2 — laser, 3 — radiation chopper, 4 — infrared camera, 5 — control panel, 6 — monitor, 7 — computer, 8 — hidden subsurface defect, 9 — protective coating (paint) \"]","img_path":"images/0458/014d42eb997d60025970a27acb9764bd60d2583d2e41d5684146ab42af2dd9dc.jpg","list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[112,65,208,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ICMSC 2020 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,65,880,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Publishing ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[110,80,880,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conf. Series: Materials Science and Engineering 904 (2020) 012001 doi:10.1088/1757-899X/904/1/012001 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[497,939,507,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"2","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"2 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[110,134,882,223]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The source of laser radiation in the work was the assembly of semiconductor laser diodes (average radiation power $90\\mathrm{W}$ ) with a generation wavelength of $915\\mathrm{nm}$ , having a common optical fiber output. The duration of laser exposure was set by a timer from the control panel (5), which was connected electrically with a laser chopper. An IR camera (4) was used to register a map of local temperature increments on the surface of the test sample. Thermographic images were presented on a monitor screen (6) and could be adjusted using a special computer program (7). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,224,880,253]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The laser exposure area and the corresponding power of laser radiation density could be changed using a tunable lens. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,254,880,313]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Samples in the form of bars of structural steel of the St3 grade with surface defects (8) under a dark protective coating layer (9) were used as a target. At the same time, the areas exposed to corrosion on the surface of the test areas did not appear in any way when remotely observing samples using a visible range CCD camera or a thermal imaging camera in the absence of laser radiation. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,313,880,344]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"As an infrared camera, FLIR Tau2 with a resolution of $336 \\times 256$ with a pixel size of $17\\mu \\mathrm{m}$ and a sensitivity of $0.05\\mathrm{mK}$ was used. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,359,331,373]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3. Thermographic results ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[110,374,882,492]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"When a sample is irradiated with laser radiation, latent defects in the form of rust-affected areas are clearly visible when observed using an infrared camera located at a distance of $10\\mathrm{m}$ associated with a laser system (Fig. 2). The same figure shows the result of visualization of a hidden defect under similar conditions in the form of cross-shaped surface cracks $2\\mathrm{mm}$ deep, obtained by means of spark erosion, coated with polyester putty, followed by polishing and painting the surface with alkyd enamel. Such masking of surface cracks also made it impossible to visualize them in the visible range of the spectrum even at high magnification, as well as when observed with a thermal imager. However hidden defects of this kind can be visualized using pulsed laser thermography (Fig. 2b). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[169,493,458,667]","code_body":null,"code_caption":null,"image_caption":"[\"(a) \"]","image_footnote":"[]","img_path":"images/0117/fbe35f695339308024c9090150c8b4b2ea8c9816bbbafb20d5ebbf2d365303c0.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[551,493,826,667]","code_body":null,"code_caption":null,"image_caption":"[\"(b) \",\"Figure 2. Thermographic images observed after laser irradiation of a metal plate with local defects under a layer of paint: (a) iron corrosion centers, (b) cross-shaped surface cracks \"]","image_footnote":"[]","img_path":"images/0969/c7280138a9d12a7b890cbfeaab47328619e409520c811de33b5d68a71611564c.jpg","list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[112,749,880,794]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In the above figures a thermal footprint is clearly visible due to a violation of the heat sink in the defective area of the test sample, hidden by a protective coating. In this case, the paint coating absorbed at least $80\\%$ of the radiation energy, the emissivity in the region of $7.5 - 13~{\\mu\\mathrm{m}}$ was 0.9. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,794,880,839]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Fig.3 shows the time dependences of the increment in the surface temperature of the sample depending on the thickness of the layer subjected to corrosion (Fig. 3a) and the thickness of the protective layer hiding cross-shaped traces of erosion (Fig. 3b). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,839,880,868]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"These dependencies can be used as the basis for quantitative estimates of the parameters of latent surface defects in materials. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,869,880,900]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Under real conditions, the detection of hidden near-surface defects by pulsed laser thermography can distort the presence of a number of factors. In particular, external surface contamination can give ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,65,208,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ICMSC 2020 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,65,880,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Publishing ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[110,80,880,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conf. Series: Materials Science and Engineering 904 (2020) 012001 doi:10.1088/1757-899X/904/1/012001 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[497,939,507,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"3","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"3 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[110,133,882,223]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"an ambiguous interpretation in the infrared region. The presence on the surface of areas with increased absorption of laser radiation leads to their overheating in comparison with the rest of the sample. On the other hand, the presence of stains of a foreign substance can be accompanied by a local change in the emissivity of the surface. In both cases, testing the object by means of laser thermography gives a picture of heterogeneity, which can hide the presence of defects under the surface or distort their nature. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[124,247,460,426]","code_body":null,"code_caption":null,"image_caption":"[\"(a) \"]","image_footnote":"[]","img_path":"images/0434/247ba059505f7a588c3e46e0bcd75846a3f9fcfabd43bff0b4fea7f8dfbe05ad.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[500,252,836,426]","code_body":null,"code_caption":null,"image_caption":"[\"(b) \",\"Figure 3. Time dependences of changes in the surface temperature of plates made of St3 steel when exposed to laser radiation with a power density of $0.4\\\\mathrm{W/cm}^2$ for 33 seconds and subsequent cooling for different thicknesses $h$ of the surface layers of (a) corrosion products of hydrated iron oxide: $1 - h = 0,25\\\\mathrm{mm}$ , $2 - h = 0,5\\\\mathrm{mm}$ , $3 - h = 0,8\\\\mathrm{mm}$ , $4 - h = 1,1\\\\mathrm{mm}$ , $5 - h = 2,3\\\\mathrm{mm}$ ; (b) polyester putty: $1 - h = 0,25\\\\mathrm{mm}$ , $2 - h = 0,5\\\\mathrm{mm}$ , $3 - h = 1,6\\\\mathrm{mm}$ , $4 - h = 2,5\\\\mathrm{mm}$ \"]","image_footnote":"[]","img_path":"images/0947/98326dc6aedba47204e26a3de5356af734666fa231b099fa4b8b2834fff07fae.jpg","list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[110,536,882,626]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"It is possible to eliminate false responses by comparing the images of the thermal imager with the corresponding images of the visible range camera, on which obvious surface contamination is usually clearly observed. And only when a homogeneous picture is recorded in the latter case, we can talk about the possibility of detecting latent defects using laser thermography. Unfortunately, it is not always possible to clean the surface from contamination, especially for remote objects located in hard-to-reach places. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[110,627,880,687]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"In addition, the above experimental results do not allow us to unequivocally state that there is a corrosion defect at the interface. At the same time, another approach is possible to solve the problem associated with filtering false test results. In this case it can be assumed that the shape of these thermal radiation pulses is a determining factor in the procedure for detecting and recognizing latent defects. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[110,687,880,731]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A computer program for analyzing thermographic images made it possible to correct external contaminants, taking into account the analysis technique for cooling the irradiated surface described in the next section. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,747,484,760]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4. Computer simulation of thermal processes ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[110,760,882,866]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The simulation of the results of laser irradiation was carried out on samples of a simplified composition: with a massive base of heat-conducting material (metal) and a surface layer with low heat conductivity (polymer) of various thicknesses, which imitated a surface defect. It is believed that all objects are covered with a thin film of the same protective paint to ensure equal absorption coefficients of laser radiation and emissivity in the spectral range of the recorded thermal signal. As model objects, samples from steel bars with a thickness of $H = 60 \\mathrm{~mm}$ with plastic layers of various thicknesses $h$ were considered. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,866,882,897]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Laser heating is modeled by the one-dimensional equation of heat conduction along the $x$ axis written for two contacting materials with thicknesses $h$ , $H$ and thermal diffusivity coefficients ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,65,208,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ICMSC 2020 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,65,880,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Publishing ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,80,880,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conf. Series: Materials Science and Engineering 904 (2020) 012001 doi:10.1088/1757-899X/904/1/012001 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[497,939,507,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"4","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"4 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[112,131,552,149]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$\\alpha_{1} = 1.5 \\times 10^{-7} \\mathrm{~m}^{2} / \\mathrm{s}$ and $\\alpha_{2} = 1.3 \\times 10^{-5} \\mathrm{~m}^{2} / \\mathrm{s}$ , respectively. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,149,882,179]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"At the initial time, the temperature of the sample is uniform and equal to $T_{0}$ . The condition at the interface: $T_{1}(h) = T_{2}(h)$ , on the surface: $T(h + H) = T_{0}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,179,611,193]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The problem described by the system of equations must be solved: ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[391,196,880,271]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"$$\n\\left\\{ \\begin{array}{l} \\frac {\\partial T}{\\partial t} = \\alpha_ {1} \\frac {\\partial^ {2} T}{\\partial x ^ {2}}, \\quad 0 < x < h \\\\ \\frac {\\partial T}{\\partial t} = \\alpha_ {2} \\frac {\\partial^ {2} T}{\\partial x ^ {2}}, \\quad h < x < h + H \\end{array} \\right. \\tag {1}\n$$","text_format":"latex","text_level":null,"type":"equation"},{"bbox":"[112,274,882,319]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Numerical simulation of the problem was carried out using finite-difference analysis. Fig. 4a shows the graphs of the obtained time dependence of the surface temperature $T_{norm}$ of a number of samples on the dimensionless parameter $k = t / \\tau$ ( $\\tau$ is the duration of the pulse exposure) in a normalized form. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[161,330,487,488]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0748/b6173aafd1e6565dd2e39f4d69a7d9a1c2d190431633f4c65413723b7f1b0dbc.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[497,330,816,489]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 4a. The calculated time dependences of the relative surface temperatures of the layered structure for different values of $h$ . The data are presented in dimensionless coordinates $k = t / \\\\tau$ for a laser pulse duration of $\\\\tau = 20$ sec. $1 - h = 0$ ; $2 - h = 0.2$ mm; $3 - h = 0.5$ mm; $4 - h = 1,1$ mm. \",\"Figure 4b. Dependences of the integrals of normalized temperatures on the thickness $h$ of the surface layer of polymer: 1 - integral from $k = 0$ to $k = 1$ (heating during a laser pulse), 2 - integral from $k = 1$ to $k = 5$ (cooling) \"]","image_footnote":"[]","img_path":"images/0007/dffe6a47fd6c67f6dac9b3c6830e04c06c21e4bf1b421e5a1b02dc2fea5e6092.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[112,598,882,673]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"Figure 4b shows the dependences of the normalized temperature integrals on the thickness $h$ of the surface layer for the heating process (curve 1) and cooling (curve 2). It can be seen that the dependence of the quantity under consideration on $h$ is weak and ambiguous in the region of action of the laser pulse. But when the object cools down, analysis of the integral of the thermal signal can give an unambiguous answer about the value of $h$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,673,880,702]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An example showing the advantage of the described approach is illustrated by the images shown in Fig. 5. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[154,702,374,856]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0124/4d14c26cf6d258fad75f5bfd4fdd9b415e1cb293fdb394ccff477f0ec5522f96.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[376,702,613,856]","code_body":null,"code_caption":null,"image_caption":"[]","image_footnote":"[]","img_path":"images/0417/f282e015f9bc9389b688a519e6fa451ffa1c344dd92fb243944d6ba0c9b2b969.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[615,702,855,856]","code_body":null,"code_caption":null,"image_caption":"[\"Figure 5. a - surface image in visible light (there is a dark spot on the paint); b - spatial distribution of the thermal signal recorded in pulsed laser thermography of the same sample; c - the result of the analysis of subsurface defects using the described technique \"]","image_footnote":"[]","img_path":"images/0089/0d145c717d7f21ae30db6af8a3863fc58fdfa3851044ca86a5d84636c537cc4d.jpg","list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"image"},{"bbox":"[112,65,208,77]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ICMSC 2020 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,65,880,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Publishing ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[110,80,880,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conf. Series: Materials Science and Engineering 904 (2020) 012001 doi:10.1088/1757-899X/904/1/012001 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[497,939,507,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"5","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5 ","text_format":null,"text_level":null,"type":"page_number"},{"bbox":"[110,151,882,287]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"The general view of the sample in visible light is reflected in Fig. 5a. On the surface of the paint coating there is a stain of contamination, which leads to an increase in local absorption of laser radiation. The corresponding zone of increased heating is manifested in the results of pulsed thermography, based only on a comparative analysis of the amplitude characteristics of the heat signal from various parts of the surface of the investigated object (Fig. 5b). This distorts the expected results of a study of subsurface material defects. At the same time, the use of computer processing of a series of consecutive IR images of a sample after exposure to laser heating in accordance with the method of mathematical modeling described above allows identifying precisely surface defects hidden by polymer putty under a common paint layer (Fig. 5c). ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,287,880,317]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"With appropriate calibration it is possible not only to detect but also to identify the nature of latent defects in the surface layer of the material. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[112,331,226,346]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"5. Summary ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[110,346,882,420]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"A new approach to visualization of a hidden defect has been developed by \"extracting\" it from a digital image of a distorted thermal field caused by heating of surface contamination. This approach is carried out using pulsed laser thermography by analyzing and processing the attenuation curve of the photothermal signal. It is shown that it is possible to detect corrosion products of hydrated iron oxide with a thickness of 100 microns or less at a distance of $10\\mathrm{m}$ . ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[110,420,882,467]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"An experimental technique for detecting hidden surface defects in materials can satisfy the needs of remote monitoring of metal structures in the form of bridges, ships, tanks for transporting and storing petroleum products, etc. ","text_format":null,"text_level":null,"type":"text"},{"bbox":"[115,481,205,493]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"References ","text_format":null,"text_level":"1","type":"text"},{"bbox":"[115,495,885,782]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":"[\"[1] P.E. Nordal and S.O. Kanstad: Physica Scripta Vol. 20 (1979), p. 659 \",\"[2] G.M. Zverev and L.A. Skvortsov: Izv. Akad. Nauk, USSR, Ser. Fiz. Vol. 45 (1981), p. 644 \",\"[3] P.E. Nordal and S.O. Kanstad: Infrared Physics Vol. 25 (1985), p. 295 \",\"[4] V.M. Kirillov and L.A. Skvortsov: Quantum Electronics 36 (2006), p. 797 \",\"[5] W.J. Parker, R.J. Jenkins, C.P. Butler and G.L. Abbott: Journal of Applied Physics Vol. 32 (1961), p. 1679 \",\"[6] S.M. Shepard, in: Thermosense XXIII, Int. Soc. for Opt. and Photonics Vol. 4360 (2001), p. 511 \",\"[7] V.N. Lopatkin, O.E. Sidoryuk, L.A. Skvortsov: Sov J Quantum Electron Vol. 15 (1985), p. 216 \",\"[8] O. Breitenstein and M. Langenkamp, in: Basics and Use for Functional Diagnostics of Electronics Components (Springer-Verlag Berlin Heidelberg 2003) \",\"[9] X.P. Maldague: Materials Evaluation Vol. 60 (2002), p.1060 \",\"[10] J.M. Milne and W.N. Reynolds, in: 1984 Cambridge Symposium, Int. Soc. for Opt. and Photonics (1985), p. 119 \",\"[11] S.K. Lau, D.P. Almond and J.M. Milne: NDT & E International Vol. 24 (1991), p. 195 \",\"[12] S.M. Shepard, J.R. Lhota and T. Ahmed: Nondestructive Testing and Evaluation Vol. 22 (2007), p. 113 \",\"[13] M. Hain, J. Bartl and V. Jacko, in Proc. of the 7th Int. Conf. on Measurement, Bratislava, Inst. of Measurement Science SAS (2009), p. 339 \",\"[14] X. Maldague, F. Galmiche and A. Ziadi: Infrared physics & technology Vol. 43 (2002), p. 175 \"]","page_idx":"6","sub_type":"ref_text","table_body":null,"table_caption":null,"table_footnote":null,"text":null,"text_format":null,"text_level":null,"type":"list"},{"bbox":"[112,65,208,78]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"ICMSC 2020 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[774,65,880,79]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Publishing ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[112,80,880,96]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"IOP Conf. Series: Materials Science and Engineering 904 (2020) 012001 doi:10.1088/1757-899X/904/1/012001 ","text_format":null,"text_level":null,"type":"header"},{"bbox":"[497,940,507,948]","code_body":null,"code_caption":null,"image_caption":null,"image_footnote":null,"img_path":null,"list_items":null,"page_idx":"6","sub_type":null,"table_body":null,"table_caption":null,"table_footnote":null,"text":"6 ","text_format":null,"text_level":null,"type":"page_number"}],"string":"[\n {\n \"bbox\": \"[60,131,243,144]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"PAPER • OPEN ACCESS \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,157,919,201]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Pulse laser thermography as a non-destructive method of latent surface defects of materials \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,219,611,232]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"To cite this article: Pavel I. Abramov et al 2020 IOP Conf. Ser.: Mater. Sci. Eng. 904 012001 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,273,389,286]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"View the article online for updates and enhancements. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[60,42,596,60]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Conference Series: Materials Science and Engineering \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[245,938,751,950]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"0\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"This content was downloaded from IP address 61.6.233.111 on 04/11/2020 at 18:44 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[115,229,818,272]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Pulse laser thermography as a non-destructive method of latent surface defects of materials \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[235,307,848,337]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Pavel I. Abramov, Eugene V. Kuznetsov, Peter Y. Lobanov, Oleg E. Sidoryuk and Leonid A. Skvortsov<sup>a</sup> \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[235,344,721,360]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"JSC Polyus Research Institute of M.F.Stelmakh, Moscow, Russia \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[235,388,416,406]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"aIskvortsov@gmail.com \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[233,419,880,514]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Abstract. The time dependences of the surface temperature increment of painted metal objects were studied depending on the thickness of the layer subjected to corrosion, as well as putty, restoring erosion defects on it. Hidden under a layer of paint, they cannot be detected remotely during normal visual observation. At the same time they are well detected by pulsed laser thermography. The experimental data in the work are compared with the results of mathematical modeling. Particular attention is paid to eliminating possible distortions caused by external contamination of the tested objects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[115,542,250,556]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1. Introduction \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[115,557,882,722]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Remote detection of latent defects on the surface of materials based on active photothermal radiometry (thermography) is a very attractive technology, the beginning of which was laid in the late 70s - early 80s of the last century [1 - 4]. Over the years, this technology has undergone significant development. In the broad sense of the word, one can speak of flash thermography [5, 6] and modulation (lock-in) IR thermography [7, 8]. In this case pulsed, or non-stationary, thermography is the most common form of non-destructive assessment of the object of study using the thermographic method (NDE, nondestructive evaluation) [9 - 13]. This is due to the possibility of studying significant areas on the surface of the object in the presence of a high-speed IR camera with a large field of view, which is of fundamental importance for increasing the productivity of non-destructive testing of materials. Therefore, the main attention in the future will be given to the possibilities and development of this particular type of material research. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[115,722,880,903]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The physical principle underlying the use of flash thermography for non-destructive testing is to measure the time dependence of surface temperature changes, while lock-in thermography allows you to study the phase of the photothermal signal. In both cases, the difference in thermal diffusion in different places of the sample due to the presence of defects and inhomogeneities in it affects the measurement result. In other words, subsurface defects change the rate of thermal diffusion, thereby manifesting itself in a change in the parameters of the recorded photothermal signal in the places where defects exist relative to areas where they are absent. Any inhomogeneities, such as inclusions, subsurface defects, or porous formations distort the propagation of thermal waves and modify the temperature response on the surface of the sample in comparison with the defect-free region. Due to the direct relationship between the thermal and mechanical properties, the detection of the distribution of the thermal signal allows mapping of the physical properties of the material under study during its scanning. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,64,208,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ICMSC 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,64,880,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Publishing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,80,880,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Conf. Series: Materials Science and Engineering 904 (2020) 012001 doi:10.1088/1757-899X/904/1/012001 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,913,198,934]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"CC BY \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[200,913,880,936]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[112,938,369,950]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Published under licence by IOP Publishing Ltd \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"footer\"\n },\n {\n \"bbox\": \"[497,940,507,948]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"1\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"1 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[110,134,882,223]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The development of flash thermography and lock-in thermography methods is pulse phase thermography based on the application of the Fourier transform to the function of temperature change over time [14, 15]. Pulse phase thermography maximally implements the idea of taking into account the fundamental differences in temperature evolution in defective and defect-free (reference) areas of the test object. However, its implementation in practice requires considerable time, since one has to deal with sequences consisting of several hundred and even thousands of images. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,224,884,313]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the classic active pulsed thermographic technique (flash thermography), the studied surface of the object is heated under the influence of radiation from one or several flash lamps, after which its cooling is recorded using an IR camera. This method has long been used for non-destructive and noncontact investigation of interfaces between the surface layer (coating) and the base material (substrate), for example, to detect adhesion defects (delaminations), local corrosion foci, surface cracks that change the one-dimensional heat flux from the surface [13]. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,315,880,404]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"However, a significant divergence of radiation from flash lamps and its low spectral brightness significantly limit the scope of flash thermography, in particular, when testing objects located at a considerable distance from the heating source. At the same time, just such a task is currently gaining more urgency and attention of researchers, since it is related to remote monitoring of structures, for example, in the form of bridges, tanks for transporting and storing petroleum products, liquefied gas, car bodies, building walls and etc. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,405,882,464]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The aim of this work is to demonstrate a new approach for remote monitoring of the surface condition of various structures located at considerable distances from the heating source using pulsed laser thermography, which excludes the influence of external factors (for example, contamination of the object's surface) on the detection of \\\"camouflaged\\\" subsurface defects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,464,882,510]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The solution to this problem became possible in connection with the creation of powerful and at the same time compact semiconductor lasers emitting at different wavelengths of the electromagnetic spectrum (from UV to far IR). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,524,304,539]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2. Experimental setup \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,569,882,600]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The studied sample (1) is affected by laser radiation pulses (2) formed by an electromechanical chopper (3). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[191,605,495,825]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Fig.1 shows an experimental setup for remote analysis of the surface of materials by means of pulsed laser thermography. \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0385/b9ef0ef8dbd9647c0ce70bca10a2fdc49f5c3e2a98df43b71557601b1eac5b41.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[611,596,842,825]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"Figure 1. a) Scheme of non-destructive testing of hidden subsurface defects using laser pulse thermography; b) Photo of the experimental setup. \\\"]\",\n \"image_footnote\": \"[\\\"1 — sample, 2 — laser, 3 — radiation chopper, 4 — infrared camera, 5 — control panel, 6 — monitor, 7 — computer, 8 — hidden subsurface defect, 9 — protective coating (paint) \\\"]\",\n \"img_path\": \"images/0458/014d42eb997d60025970a27acb9764bd60d2583d2e41d5684146ab42af2dd9dc.jpg\",\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[112,65,208,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ICMSC 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,65,880,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Publishing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[110,80,880,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Conf. Series: Materials Science and Engineering 904 (2020) 012001 doi:10.1088/1757-899X/904/1/012001 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[497,939,507,948]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"2\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"2 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[110,134,882,223]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The source of laser radiation in the work was the assembly of semiconductor laser diodes (average radiation power $90\\\\mathrm{W}$ ) with a generation wavelength of $915\\\\mathrm{nm}$ , having a common optical fiber output. The duration of laser exposure was set by a timer from the control panel (5), which was connected electrically with a laser chopper. An IR camera (4) was used to register a map of local temperature increments on the surface of the test sample. Thermographic images were presented on a monitor screen (6) and could be adjusted using a special computer program (7). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,224,880,253]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The laser exposure area and the corresponding power of laser radiation density could be changed using a tunable lens. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,254,880,313]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Samples in the form of bars of structural steel of the St3 grade with surface defects (8) under a dark protective coating layer (9) were used as a target. At the same time, the areas exposed to corrosion on the surface of the test areas did not appear in any way when remotely observing samples using a visible range CCD camera or a thermal imaging camera in the absence of laser radiation. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,313,880,344]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"As an infrared camera, FLIR Tau2 with a resolution of $336 \\\\times 256$ with a pixel size of $17\\\\mu \\\\mathrm{m}$ and a sensitivity of $0.05\\\\mathrm{mK}$ was used. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,359,331,373]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3. Thermographic results \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,374,882,492]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"When a sample is irradiated with laser radiation, latent defects in the form of rust-affected areas are clearly visible when observed using an infrared camera located at a distance of $10\\\\mathrm{m}$ associated with a laser system (Fig. 2). The same figure shows the result of visualization of a hidden defect under similar conditions in the form of cross-shaped surface cracks $2\\\\mathrm{mm}$ deep, obtained by means of spark erosion, coated with polyester putty, followed by polishing and painting the surface with alkyd enamel. Such masking of surface cracks also made it impossible to visualize them in the visible range of the spectrum even at high magnification, as well as when observed with a thermal imager. However hidden defects of this kind can be visualized using pulsed laser thermography (Fig. 2b). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[169,493,458,667]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(a) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0117/fbe35f695339308024c9090150c8b4b2ea8c9816bbbafb20d5ebbf2d365303c0.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[551,493,826,667]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(b) \\\",\\\"Figure 2. Thermographic images observed after laser irradiation of a metal plate with local defects under a layer of paint: (a) iron corrosion centers, (b) cross-shaped surface cracks \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0969/c7280138a9d12a7b890cbfeaab47328619e409520c811de33b5d68a71611564c.jpg\",\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[112,749,880,794]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In the above figures a thermal footprint is clearly visible due to a violation of the heat sink in the defective area of the test sample, hidden by a protective coating. In this case, the paint coating absorbed at least $80\\\\%$ of the radiation energy, the emissivity in the region of $7.5 - 13~{\\\\mu\\\\mathrm{m}}$ was 0.9. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,794,880,839]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Fig.3 shows the time dependences of the increment in the surface temperature of the sample depending on the thickness of the layer subjected to corrosion (Fig. 3a) and the thickness of the protective layer hiding cross-shaped traces of erosion (Fig. 3b). \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,839,880,868]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"These dependencies can be used as the basis for quantitative estimates of the parameters of latent surface defects in materials. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,869,880,900]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Under real conditions, the detection of hidden near-surface defects by pulsed laser thermography can distort the presence of a number of factors. In particular, external surface contamination can give \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,65,208,77]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ICMSC 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,65,880,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Publishing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[110,80,880,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Conf. Series: Materials Science and Engineering 904 (2020) 012001 doi:10.1088/1757-899X/904/1/012001 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[497,939,507,948]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"3\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"3 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[110,133,882,223]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"an ambiguous interpretation in the infrared region. The presence on the surface of areas with increased absorption of laser radiation leads to their overheating in comparison with the rest of the sample. On the other hand, the presence of stains of a foreign substance can be accompanied by a local change in the emissivity of the surface. In both cases, testing the object by means of laser thermography gives a picture of heterogeneity, which can hide the presence of defects under the surface or distort their nature. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[124,247,460,426]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(a) \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0434/247ba059505f7a588c3e46e0bcd75846a3f9fcfabd43bff0b4fea7f8dfbe05ad.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[500,252,836,426]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": \"[\\\"(b) \\\",\\\"Figure 3. Time dependences of changes in the surface temperature of plates made of St3 steel when exposed to laser radiation with a power density of $0.4\\\\\\\\mathrm{W/cm}^2$ for 33 seconds and subsequent cooling for different thicknesses $h$ of the surface layers of (a) corrosion products of hydrated iron oxide: $1 - h = 0,25\\\\\\\\mathrm{mm}$ , $2 - h = 0,5\\\\\\\\mathrm{mm}$ , $3 - h = 0,8\\\\\\\\mathrm{mm}$ , $4 - h = 1,1\\\\\\\\mathrm{mm}$ , $5 - h = 2,3\\\\\\\\mathrm{mm}$ ; (b) polyester putty: $1 - h = 0,25\\\\\\\\mathrm{mm}$ , $2 - h = 0,5\\\\\\\\mathrm{mm}$ , $3 - h = 1,6\\\\\\\\mathrm{mm}$ , $4 - h = 2,5\\\\\\\\mathrm{mm}$ \\\"]\",\n \"image_footnote\": \"[]\",\n \"img_path\": \"images/0947/98326dc6aedba47204e26a3de5356af734666fa231b099fa4b8b2834fff07fae.jpg\",\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": null,\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"image\"\n },\n {\n \"bbox\": \"[110,536,882,626]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"It is possible to eliminate false responses by comparing the images of the thermal imager with the corresponding images of the visible range camera, on which obvious surface contamination is usually clearly observed. And only when a homogeneous picture is recorded in the latter case, we can talk about the possibility of detecting latent defects using laser thermography. Unfortunately, it is not always possible to clean the surface from contamination, especially for remote objects located in hard-to-reach places. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,627,880,687]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"In addition, the above experimental results do not allow us to unequivocally state that there is a corrosion defect at the interface. At the same time, another approach is possible to solve the problem associated with filtering false test results. In this case it can be assumed that the shape of these thermal radiation pulses is a determining factor in the procedure for detecting and recognizing latent defects. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,687,880,731]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"A computer program for analyzing thermographic images made it possible to correct external contaminants, taking into account the analysis technique for cooling the irradiated surface described in the next section. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,747,484,760]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4. Computer simulation of thermal processes \",\n \"text_format\": null,\n \"text_level\": \"1\",\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[110,760,882,866]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The simulation of the results of laser irradiation was carried out on samples of a simplified composition: with a massive base of heat-conducting material (metal) and a surface layer with low heat conductivity (polymer) of various thicknesses, which imitated a surface defect. It is believed that all objects are covered with a thin film of the same protective paint to ensure equal absorption coefficients of laser radiation and emissivity in the spectral range of the recorded thermal signal. As model objects, samples from steel bars with a thickness of $H = 60 \\\\mathrm{~mm}$ with plastic layers of various thicknesses $h$ were considered. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,866,882,897]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"Laser heating is modeled by the one-dimensional equation of heat conduction along the $x$ axis written for two contacting materials with thicknesses $h$ , $H$ and thermal diffusivity coefficients \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,65,208,78]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"ICMSC 2020 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[774,65,880,79]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Publishing \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[112,80,880,96]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"IOP Conf. Series: Materials Science and Engineering 904 (2020) 012001 doi:10.1088/1757-899X/904/1/012001 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"header\"\n },\n {\n \"bbox\": \"[497,939,507,948]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"4\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"4 \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"page_number\"\n },\n {\n \"bbox\": \"[112,131,552,149]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$\\\\alpha_{1} = 1.5 \\\\times 10^{-7} \\\\mathrm{~m}^{2} / \\\\mathrm{s}$ and $\\\\alpha_{2} = 1.3 \\\\times 10^{-5} \\\\mathrm{~m}^{2} / \\\\mathrm{s}$ , respectively. \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,149,882,179]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"At the initial time, the temperature of the sample is uniform and equal to $T_{0}$ . The condition at the interface: $T_{1}(h) = T_{2}(h)$ , on the surface: $T(h + H) = T_{0}$ . \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[112,179,611,193]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"The problem described by the system of equations must be solved: \",\n \"text_format\": null,\n \"text_level\": null,\n \"type\": \"text\"\n },\n {\n \"bbox\": \"[391,196,880,271]\",\n \"code_body\": null,\n \"code_caption\": null,\n \"image_caption\": null,\n \"image_footnote\": null,\n \"img_path\": null,\n \"list_items\": null,\n \"page_idx\": \"5\",\n \"sub_type\": null,\n \"table_body\": null,\n \"table_caption\": null,\n \"table_footnote\": null,\n \"text\": \"$$\\n\\\\left\\\\{ \\\\begin{array}{l} \\\\frac {\\\\partial T}{\\\\partial t} = \\\\alpha_ {1} \\\\frac {\\\\partial^ {2} T}{\\\\partial x ^ {2}}, \\\\quad 0 < x <